Subject: Re: CH Question >mtx014@linux.services.coventry.ac.uk (Robert Low) >>What sets A and B do we know of for which A has less cardinality than >>B but B is not a function of the powerset of A? >> (What does it mean for B to be a function of the power set of A >> anyway?) >e.g. P(P(A)) or P(A)u{0} Not that you¹ve answered the question, but in any case I refer you to my previous answer. A={1} B={a,b} B has greater cardinality that A and is not a function of the power set of A. (Whatever you might mean by Œfunction of the power set¹.) -- Rob. http://www.mis.coventry.ac.uk/~mtx014/ === Subject: Re: CH Question >mtx014@linux.services.coventry.ac.uk (Robert Low) >>What sets A and B do we know of for which A has less cardinality than >>B but B is not a function of the powerset of A? >> >> (What does it mean for B to be a function of the power set of A >> anyway?) >e.g. P(P(A)) or P(A)u{0} > Not that you¹ve answered the question, but in any case I refer > you to my previous answer. > A={1} > B={a,b} > B has greater cardinality that A and is not a function of > the power set of A. (Whatever you might mean by Œfunction > of the power set¹.) Besides B=P(P(A)) e.g. You know I was referring to inÞnite sets, right? In any case, I am. C-B === Subject: Re: CH Question Originator: mtx014@linux.services.coventry.ac.uk (Robert Low) >What sets A and B do we know of for which A has less cardinality than >B but B is not a function of the powerset of A? OK, then. A is the integers, and B is the set of continuous functions from the reals to the reals. A has cardinality aleph_0, and B has cardinality 2^aleph_0, though B is not (in any obvious sense) a function of the power set of A (except the trivial sense that there exists a bijection between the two). Or are you *really* asking whether there are any cardinalities in between aleph_0 and 2^aleph_0, or 2^aleph_0 and 2^(2^aleph_0), etc? (In which case surely you already know the answer to you question.) -- Rob. http://www.mis.coventry.ac.uk/~mtx014/ === Subject: Re: CH Question >What sets A and B do we know of for which A has less cardinality than >B but B is not a function of the powerset of A? > OK, then. A is the integers, and B is the set of continuous > functions from the reals to the reals. A has cardinality > aleph_0, and B has cardinality 2^aleph_0, though B is > not (in any obvious sense) a function of the power set of > A (except the trivial sense that there exists a bijection > between the two). > Or are you *really* asking whether there are any cardinalities > in between aleph_0 and 2^aleph_0, or 2^aleph_0 and 2^(2^aleph_0), > etc? (In which case surely you already know the answer to > you question.) Actually, I was pondering the equation Ngenerally functions of P(N) such as P(N)u{0}. Then I wondered if >anyone knew of any other way of deÞning (c.f. proving) a set A that >satisÞes Nfunction of P(A). tay? Alas, the more you explain, the less I understand what you¹re trying to get at. So, is the example I gave (and you didn¹t mention) an example of what you asked for or not? I repeat it here: A = N B = continuous functions from R to R. Or am I currently thrashing about on deck with a hook in the corner of my mouth? -- Rob. http://www.mis.coventry.ac.uk/~mtx014/ === Subject: Re: CH Question >mtx014@linux.services.coventry.ac.uk (Robert Low) >>>What sets A and B do we know of for which A has less cardinality than >>>B but B is not a function of the powerset of A? >>(What does it mean for B to be a function of the power set of A >>anyway?) >e.g. P(P(A)) or P(A)u{0} >>Not that you¹ve answered the question, but in any case I refer >>you to my previous answer. >>A={1} >>B={a,b} >>B has greater cardinality that A and is not a function of >>the power set of A. (Whatever you might mean by Œfunction >>of the power set¹.) > Besides B=P(P(A)) e.g. > You know I was referring to inÞnite sets, right? In any case, I am. So Charlie-Boo¹s question doesn¹t make any large amount of sense on any literal-minded reading--or at least he has not yet conveyed that sense to us. But my eldritch mental abilities are telling me that what he *really* wants to know is whether the existence of distinct inÞnite cardinalities can be deduced by an argument that doesn¹t invoke powersets. The answer to that question is in some sense no -- probably the most available precise sense in fact, though not clearly the most correct one. To be precise, if we let ZFC- be the collection of axioms of ZFC with Powerset omitted, then ZFC- is consistent with the statement all sets are countable. A model is HC, the collection of hereditarily countable sets. === Subject: C. Lorentz Coord. Xforms vs SR-cult Fraud and Corruption The Maxwell-Lorentz-Einstein Fraud -------------------------------------------------------- Preamble -------------- Could you trust the Ku Klux Klan to conduct an honest investigation of the NAACP? No matter how sincere the investigators might be, their biases and learned distortions and misrepresentation of the NAACP and blacks in general would make honesty impossible. Just so, less than insightful opinion and later True Believer blindness has resulted in a number of fraudulent claims by Relativity cultists against aspects of Newtonian-Galilean physics. True Believer cultists have proved time and again that their treatment of the Œdiscredited¹ Newtonian-Galilean physics is based on misrepresentation and bogus logic. And in all cases in these newsgrouos the True Believers respond with viciousness and irrelevancy. Except when they deign to actually try a relevant respone and prove themselves Brain Dead. Hopefully, this version of this post of the series will be contain at least one example. Whether or not any of modern physical fact Þts Newton is not material to the question of these bogus claims of the cult. We are here to do anything and everything that requires or encourages systematic examination of premises and logic, of Special Relativity. No premises are more basic than those involved in the three frauds named herein, and discussed in this series. Among the frauds are the twin original claims that Special Relativity is necessary: (a) the Newtonian-Galilean coordinate transformations do not work invariantly on Maxwell¹s electrodynamics equations and (b) the famous Michelson-Morley experiment does not Þt the classical Newtonian-Galilean model and only Þts Special Relativity. Another, very serious fraud is (c) the implied claim that the Lorentz-Einstein coordinate transformations of Special Relativity actually are applied to Maxwell, completing the fraudulent claims against the Newton-consistent Galilean transformations. There are many more rotten fruit from the SR-tree to be buried before you know the nature of their whole orchard. Look for other posts in this series. By the way, look up the word Œcorrupt¹ in your dictionary if you think it only describes policemen and politicians who take bribes. ............................................................. ............... .............. ............................................................. ............... .............. The Maxwell-Lorentz-Einstein Fraud -------------------------------------------------------- The SR-cult claim that Maxwell¹s Equations are invariant under the Lorentz-Einstein (coordinate) transformations is fraudulent, as shall be shown here. But what if the claim were true? Every such equation is in x,y,z,t - with x,y,z representing lengths of the projections of some length onto of this series to be invariant under the Newtonian-Galilean transformations. Let the second dashed line below represent the distance some x represents from a critical point - a source - that is setup contiguous with the x-origin. x¹ @--------------------------@x0¹ @---------------------------------------------------@xO x The dashes of the top line represent - in either the L-E or N-G transforms - the distance the x¹ corresponding to x represents. A completely different distance regardless of the units of measurement and coordinate system involved. Obviously, any invariance of such equations must be as valid as ENRON, Haliburton, and Harken accounting. Indeed, completely nonsensical equations may be found to be Œinvariant¹ when the actual usage of the L-R transforms is applied. However, the Œwhat if¹ is not necessary. The SRian claim is fraudulent. We can let virtually any actual, physical electromagnetic equation in x,y,z,t stand-in for Maxwell¹s differential forms because the SRian claim is that Newtonian-Galilean transforms of such equations do not series). Let us start by considering some basic EM equations. For the sake of convenience let us deÞne the constant a=1/(4*Pi*e0), where e0 is a constant, the Œpermittivity¹ of free space. Instead of using vector equations per se we¹ll isolate each spatial dimension. F=force. q and Q are point sources of electrical charge. One charge is at the origin, the other at X=(x y z). The distance X repesents (Q from q) is |X|=sqrt(x^2 + y^2 + z^2 ). Fx = (aqQx) / ( |X|^3 ) = aqQx/( x^2 + y^2 + z^2 )^1.5. Fy = (aqQy) / ( |X|^3 ) = aqQy/( x^2 + y^2 + z^2 )^1.5. Fz = (aqQz) / ( |X|^3 ) = aqQz/( x^2 + y^2 + z^2 )^1.5. The spurious invariance under the Lorentz-Einstein transformations depends on the use of a time term, so we can¹t get invariance for this basic EM (vector) equation under those L-ET. Time is of absolutely no relevance in these equations. Yet, to claim invariance you would have to throw in a time coordinate transform, But, without a nonsensical time term, letting there be no movement in the y or z directions: Fx¹ = (aqQg(x-ut)) / ( (gx-gut)^2 + y^2 + z^2 )^1.5, with no change in Fy and Fz and where g = 1/sqrt(1-(v^2/c^2)). Do we really need to sum either Fx¹, Fy¹, Fz¹ or their squares , or do whatever, to see if there is invariance there? Even in proper form (with difference expressions like (x1-x0) ) there can be no invariance of such equations under the LET. But this whole episode with F is irrelevant to what SRian cultists call transforming with the Lorentz-Einstein Transformations. Why? Because they don¹t transform the x,y,z,t coordinates, the transforms of which are, with no motion along the y and z axes: x¹ = g(x-ut) y¹ = y z¹ = z t¹ = g(t-vx/c^2). g is always in the numerator where x and t are placed, and the same would be true for the y¹ and z¹ expressions if there were movement along those axes. So, what do the SR-cultists transform? Well, let¹s take Melvin Schwartz¹ page 129 of Principles of Electrodynamics to see what he is transforming. He deÞnes and transforms a four-dimensional F matrix ... four dimensional? Does that mean he will transform time also? Of course not. Here are his transformations. ... through a Lorentz transformation. Bx, By, Bz are magnetic Þeld forces parallel to the three coordinate axes. Ex, Ey, Ez are electrical Þeld forces parallel to the three coordinate axes. The direction of relative movement he chose to illustrate is parallel to the x-axis, no movement along the other axes. Bx¹ = Bx By¹ = g(By + vEz/c) Bz¹ = g(Bz - vEy/c) Ex¹ = Ex Ey¹ = g(Ey - vBz/c) Ez¹ = g(Ez + vBy/c) ŒClearly¹ the x,y,z,t coordinates are not transformed. Simple sample expressions of E and B or their components with distance components make this clear, as do some expressions that include no distance component at all. Why distance? Because that is what x,y,z coordinates represent. Why no distance component? Because the equation is about a (limited in practice) uniform Þeld where there is no change by distance within the limits. Using a, q, etc, from above, and other values we need not deÞne: E=aq/r^2, which would be E=aq/x^2 if the distance in question is parallel to the x-axis. E=2an/R, where R is the distance from the center of a cylinder, which would be E=2an/x if the distance is along the x-axis. V=ap(cos(theta))/r^2, where r is a distance, which would be V=ap(cos(theta))/x^2 is the distance is along the x-axis (V is used in some expressions for V.) E=ke0q/A where A is an area, E=ke0q/xy if the area(s) are perpendicular to the z-axis. The list could be much longer and we could do the same thing for expressions for B. The key point is that every one of these expressions have the distance (x,y) components in the denominator. Yet in all of the B and E transforms given g is applied to the numerator of the transformed quantity. If the coordinates were being transformed g would have to be in the numerator, as would the subtractive (or additive) terms in the transformations. We do have examples available where a distance term also - ALSO - appears in the numerator, but in those examples distance terms show up in even greater Œforce¹ in the denominators. We started with such an example: Fx = (aqQx) / ( |X|^3 ) = aqQx/( x^2 + y^2 + z^2 )^1.5. Fy = (aqQy) / ( |X|^3 ) = aqQy/( x^2 + y^2 + z^2 )^1.5. Fz = (aqQz) / ( |X|^3 ) = aqQz/( x^2 + y^2 + z^2 )^1.5. The claim that any physical (physics) equation in x,y,z is invariant under the Lorentz-Einstein COORDINATE Transformations is an absolute fraud. The fraud is especially despicable... well, corrupt, because of the companion corruption in the strawman argument that there is any equation in x,y,z - properly expressed in difference terms - that is this series. The SR-cult does manage a further corruption (well, two) that enables the delusion that equations are invariant under the Lorentz-Einstein Coordinate Transforms. Any corrupt bookkeeper or clerk knows how to do it. If you overspend the limit the boss imposed you must cook the books but keep the balance correct: transform the actual expense to something under the limit and phoney up another entry to exactly compensate. True Believer SR-cult responses ------------------------------------------------------------- ---- Focus well on negative Œresponses¹. Are they vicious ranting? If not, are the replies actually responsive? How dare you say my soups suck! exclaimed the angry chef, my peach pies are perfect Do they rant about gravity, or how Relativity is proved correct a million times each day, or some other Œwe are proved right¹ rave that doesn¹t deal in details about the debunking done here? It is typically General Relativity or items about the energy and mass of moving objects that are being waved at you, and such items are completely irrelevant to coordinate transformations and invariance.. Just ask them for a list of all the observations that have been made of the shortening (contraction) of moving objects that Special Relativity says always occurs. Rarely, there is actually a response that has some relevance to the material posted, and those are proofs of their Brain Death. eleaticus === Subject: Re: C. Lorentz Coord. Xforms vs SR-cult Fraud and Corruption > The Maxwell-Lorentz-Einstein Fraud > -------------------------------------------------------- > Preamble > -------------- > Could you trust the Ku Klux Klan to conduct an honest investigation of > the NAACP? No matter how sincere the investigators might be, their > biases and learned distortions and misrepresentation of the NAACP and > blacks in general would make honesty impossible. > Just so, less than insightful opinion and later True Believer > blindness has resulted in a number of fraudulent claims by Relativity > cultists against aspects of Newtonian-Galilean physics. > True Believer cultists have proved time and again that their treatment > of the Œdiscredited¹ Newtonian-Galilean physics is based on > misrepresentation and bogus logic. > And in all cases in these newsgrouos the True Believers respond with > viciousness and irrelevancy. Except when they deign to actually try a > relevant respone and prove themselves Brain Dead. Hopefully, this > version of this post of the series will be contain at least one > example. > Whether or not any of modern physical fact Þts Newton is not material > to the question of these bogus claims of the cult. We are here to do > anything and everything that requires or encourages systematic > examination of premises and logic, of Special Relativity. No premises > are more basic than those involved in the three frauds named herein, > and discussed in this series. > Among the frauds are the twin original claims that Special Relativity > is necessary: (a) the Newtonian-Galilean coordinate transformations do > not work invariantly on Maxwell¹s electrodynamics equations and (b) > the famous Michelson-Morley experiment does not Þt the classical > Newtonian-Galilean model and only Þts Special Relativity. > Another, very serious fraud is (c) the implied claim that the > Lorentz-Einstein coordinate transformations of Special Relativity > actually are applied to Maxwell, completing the fraudulent claims > against the Newton-consistent Galilean transformations. Nobody ever claimed that Newtonian physics is inconsistent. It is perfectly constistent in all events that move at the fanastic speed of evolution. Which is also isomorphically equal to the speed of grass growing, which is also identically equally to the speed of Greece, and the speed of pi, the speed of boring, and the speed of Plato, and the speed of mathematics, and the speed of Duh. And nobody ever claimed that Maxwell¹s equations do not work in electrodynamics. They do not work in atoms, because they are WRONG by at least an electron, but no more than a proton. Since they fail to predict anything about the DC circuits, the fanstically ignorant UN astrologers from the French Eco-Police and the US Air Force call Thermonuclear bombs. > There are many more rotten fruit from the SR-tree to be buried before > you know the nature of their whole orchard. Look for other posts in > this series. Since SR is already known to be a simple physical observational fact from taking an elevator ride to the top of the Sears Tower in Chicago, SR is wrong iff IBM built the Sears Tower. Built since IBM are already known to be recursive Goedelian dips, it is not wrong. > By the way, look up the word Œcorrupt¹ in your dictionary if you think > it only describes policemen and politicians who take bribes. We have. That¹s why we bribed the FBI to bribe the Dictionary to bribe the Police. That why we are completely innocent of money laundering. The worst the Marines can convict us of is being Navy people. === Subject: Well, ZZBunker? Re: C. Lorentz Coord. Xforms vs SR-cult Fraud and Corruption > We have. That¹s why we bribed the FBI to bribe > the Dictionary to bribe the Police. > That why we are completely innocent of money laundering. > The worst the Marines can convict us of is > being Navy people. Congratulations! You have proved yourself capable of being at least a jerk, if not an ass, and of not having sufÞcient honesty to actually respond to the details of logic/etc. So, can you now prove yourself capable of relenting in your desire to prove irrelevant to any actual discussion, and do something helpful? Maxwell and invariance are an important combination of topics and as many expressions as I know of for E, H, B, etc, I do not know just what exemplars of them would be best for demonstrating particulars of their transformation by Newton-theoretic coordinate tranformations. The Œproblem¹ is different than in the case of the Lorentz transforms of Maxwell because in the Newton case it actually is the coordinates x,y,z that are transformed, rather than - essentially - the inverse of the coordinates. So, please provide a set of expressions - appropriate for full exposition of Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate expressions. Obviously (ha!) the result would be that Þnally I come headsup (as we poker players say) with my tremendous error in thinking that transforming Maxwell Newton-wise without the three strawmen corruptions will prove invariant. eleaticus === Subject: Re: Well, ZZBunker? Re: C. Lorentz Coord. Xforms vs SR-cult Fraud and Corruption > We have. That¹s why we bribed the FBI to bribe > the Dictionary to bribe the Police. > That why we are completely innocent of money laundering. > The worst the Marines can convict us of is > being Navy people. > Congratulations! > You have proved yourself capable of being at least a jerk, if not an ass, > and of not having sufÞcient honesty to actually respond to the details of > logic/etc. > So, can you now prove yourself capable of relenting in your desire to prove > irrelevant to any actual discussion, and do something helpful? > Maxwell and invariance are an important combination of topics and as many > expressions as I know of for E, H, B, etc, I do not know just what exemplars > of them would be best for demonstrating particulars of their transformation > by Newton-theoretic coordinate tranformations. If Maxwell or his equations had somehing to do with logical invariance, we would actually call you Von Neumann, or some honary title like that. Rather than a simple recurive Goedel-wannabee retard. With a Greek nom-de-plume that even Goedel, and probably even French and Italian philosophers, like Galileo, would spit on. And most likely, even Plato, would fart on. Do you even know why there is a H Þeld, independent of the B Þeld idiot. I¹ll give you a hint. It has the null set to do with Newton, Maxwell, or Hamiton. And has everything to do with Gauss. === Subject: Re: Well, ZZBunker? Re: C. Lorentz Coord. Xforms vs SR-cult Fraud and Corruption [snip crap] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: C. Lorentz Coord. Xforms vs SR-cult Fraud and Corruption > The Maxwell-Lorentz-Einstein Fraud > -------------------------------------------------------- [snip 300 lines of trolled garbage] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: C. Lorentz Coord. Xforms vs SR-cult Fraud and Corruption posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB I don¹t visit sci.physics anymore because of this kind of stuff. I guess one has to sort thru it, the price of access to everyone. Van === Subject: Re: C. Lorentz Coord. Xforms vs SR-cult Fraud and Corruption format=þowed; charset=iso-8859-1; reply-type=original > I don¹t visit sci.physics anymore because of this kind of stuff. > I guess one has to sort thru it, the price of access to everyone. Just keep track of the Operation Troll Shouldrer posts.. they list this troll and other trolls like it.. Seeya === Subject: Well, Van Jacques? > I don¹t visit sci.physics anymore because of this kind of stuff. > I guess one has to sort thru it, the price of access to everyone. > Van Congratulations! You have proved yourself capable of being at least a jerk, if not an ass, and of not having sufÞcient honesty to actually respond to the details of logic/etc. So, can you now prove yourself capable of relenting in your desire to prove irrelevant to any actual discussion, and do something helpful? Maxwell and invariance are an important combination of topics and as many expressions as I know of for E, H, B, etc, I do not know just what exemplars of them would be best for demonstrating particulars of their transformation by Newton-theoretic coordinate tranformations. The Œproblem¹ is different than in the case of the Lorentz transforms of Maxwell because in the Newton case it actually is the coordinates x,y,z that are transformed, rather than - essentially - the inverse of the coordinates. So, please provide a set of expressions - appropriate for full exposition of Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate expressions. Obviously (ha!) the result would be that Þnally I come headsup (as we poker players say) with my tremendous error in thinking that transforming Maxwell Newton-wise without the three strawmen corruptions will prove invariant. eleaticus === Subject: Re: Well, Van Jacques? [snip crap] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: (Not quite) Cantor¹s diagonal proof > >- I could never > > show that the number created by the diagonal was repeating. I posted it in > > hopes that someone could show me why I kept running into the same problem > > over and over without the circular argument of It fails because the > > rational are countable and could instead point out where exactly Cantor¹s > > Method fails on rational numbers. > > > > I don¹t understand your last point. If you replace real with > > rational in Cantor¹s theorem and his proof. The proof would be > > incorrect because the diagonal number produced need not be rational. > Why? > That¹s a question for you to answer. If you purported that the > diagonal proof also applied to the rationals then you would have to > prove that the diagonal number created for an arbitrary list of > rationals is itself rational. If not then there would be a gap in > your proof. So forget I said the diagonal number produced need not > be rational (which is true). Instead I would like to say prove that > the diagonal number is rational. so you cannot justify your statement that If you replace real with rational in Cantor¹s theorem and his proof the proof would be incorrect > > So, you wouldn¹t have a proof that the set of rationals is > > uncountable. There is nothing surprising there. > > > > I just don¹t see the point in raising objections to a proof without > > pointing out what the error is. Which line of the proof is wrong? > > That¹s what I would ask an objector. > The concept of unique number is wrong. > Ok. Then you are objecting to something prior to the proof. So why > bother discussing Cantor¹s proof at all? he¹s the one who claims anti-diag is unique. Here¹s an infnite list of reals 0.0xxxxxx.. 0.1xxxxxx.. 0.2xxxxxx.. 0.0xxxxxxx.. 0.3xxxxxx.. 0.5xxxxxx.. 0.8xxxxxx.. 0.1xxxxxxx.. 0.2xxxxxxxx.. 0.0xxxxxxx.. 0.1xxxxxxxx.. As you can see, 0.0xxxx.. appears repeatedly, so 0.0 is covered inÞnitely many times 0.1xxxxx.. appears an inÞnite number of times. It doesn¹t matter what the digits the are, they are all present. 0.abcxxx.. is present for EVERY a, b and c. 0.abcdefghijklmnopqrstuvwxyz...... is ON THE LIST for ALL values of a, b, c, d, e, ... z by extension every digit combination is present. You claim there is ONE digit that is different, but that digit CANNOT appear at digit position 1. 0.1xxxx 0.2xxxx 0.3xxxx these are all on the list of computable reals. 0.11xxxx.. 0.12xxxx.. 0.13xxsxx.. these are all on the list of computable reals. The contradictory digit on your list must be after the 2nd decimal place mustn¹t it? Your contradiction dissapears altogether because it cannot occur at a Þnite decimal. The digits 1, 2, 3, 4, 5 .. 9, 0 are virtually identical and interchangable, they merely adjust the region on the numberline but have *no semantic difference*, to make a formula claiming this number (which is always only a variable) is DIFFERENT to this number is nonsense, they are just DIGITS Countable inÞnity is bigger than you can conceive or mathematically manipulate.. Herc is mustn¹t a word? > The whole reason we *introduced digits* for > numbers was exactly to distinguish numbers. > I thought it was to make arithmetic and notation easier. > 0.xyz... is different to 0.ayz... because x =/= a > You can¹t come along and say, now we will use a different digit here, here, here ,here... > Why not? > that is merely the *deÞnition* of a unique cardinal. > That doesn¹t make sense. > We laugh at your hyperinÞnities, > I don¹t have any hyperinÞnities. > Halt is a deÞned function, > What does that have to do with my post? > anti diag is an illusion. > Show me the single contradictory digit from your proof. What digit position? > That doesn¹t make sense. > -Leonard Blackburn > Herc === Subject: Re: (Not quite) Cantor¹s diagonal proof >> >> >- I could never >> > show that the number created by the diagonal was repeating. I posted it in >> > hopes that someone could show me why I kept running into the same problem >> > over and over without the circular argument of It fails because the >> > rational are countable and could instead point out where exactly Cantor¹s >> > Method fails on rational numbers. >> > >> > I don¹t understand your last point. If you replace real with >> > rational in Cantor¹s theorem and his proof. The proof would be >> > incorrect because the diagonal number produced need not be rational. >> >> Why? >> That¹s a question for you to answer. If you purported that the >> diagonal proof also applied to the rationals then you would have to >> prove that the diagonal number created for an arbitrary list of >> rationals is itself rational. If not then there would be a gap in >> your proof. So forget I said the diagonal number produced need not >> be rational (which is true). Instead I would like to say prove that >> the diagonal number is rational. > so you cannot justify your statement that > If you replace real with rational in Cantor¹s theorem and his proof the proof would be incorrect The diagonal argument depends on the least upper bound property of the real numbers. The diagonal argument produces a decimal digit string, which is associated with a certain inÞnite series. The partial sums of that series form a set of real numbers that is nonempty and bounded above. The least upper bound of that set is the required number. The same argument does not work when applied to the rationals, since the rationals do not satisfy the LUB property. And, by the way, there is nothing circular about the argument that if the original list contains all of the rational numbers, then the number produced by the diagonal argument, which is necessarily different from any number in the list, must therefore be irrational. -- Dave Seaman Judge Yohn¹s mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Automorphisms of small non-Albelian groups posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB I¹m starting a new thread on this in the hope that someone will reply. I Þnd this interesting, but hard to Þnd material on (for me at least, a physicist, depending on the net). > [...] > But I know that A(S_3) = S_3, but not how to show it. > The identity is Þxed, and there are 2 elements with |x| = 3, > and 3 with |x| = 2. Interchange of x and x^2 if |x| = 3 gives one > auto. Wait, I think I have it. > Let g = x^i y^j ; |x| = 2 ; i in Z_2 ; |y| = 3 ; j in Z_3. > f(x^i y^j) = x^i y^(2j) is an auto of order 2 (f^2 = 1). > h(x^i y^j) = x^i y^(j+1) is an auto of order 3, so Right. My error. > A(G) = S_3. Right? > Well... You¹ve shown that Aut(S_3) has automorphisms of orders 2 > and 3, but you already knew that since S_3 has trivial center, > so S_3 =~ Inn(S_3) and Inn(G) is known to be a normal subgroup > of Aut(G). What you need to show is that S_3 has no *outer* > automorphisms. > Hint: Find a presentation and count how many ways its generators > can be mapped to elements of the group. > -- > Jim Heckman By a presentation you mean a presentation of S_3, like x^3 = y^2 = 1, yxy^(-1) = x^2 ; right? Generators x,y. 1) (x,y) --> f(x,y) = (x^2,y) ; |f| = 2, i.e., f(f(x,y) = 1 for f in A = A(S_3), 2) (x,y) --> g(x,y) = (x,xy) |g| = 3 for g in A(S_3), if fgf = g^2 then A =~ S_3. We Þnd that g(g(x,y)) = (x,x^2y) ; f(g(f(x,y))) = f(x^2,x^2y) = (x,x^2y). QED Is this what you meant? I repost my other questions following this post. If anyone has any comments I would be grateful. Van === Subject: Re: Automorphisms of small non-Albelian groups posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB Also, I want to show that A(S_4) = S_4. I know that A(N) = S_3, where N =~ Z_2 x Z_2 is the normal subgp, and I think I recall reading that all autos are inner here, but I don¹t see how to proceed. While I am at it, a repost of a previous post; Autos of Q = quaternions = A(Q); Q = +/- (1,e_i) , i = 1,2,3. center Z(Q) = Z_2 ; Q/Z = Z_2 x Z_2 =~ Inn(Q) < A(Q) (actually Inn(Q) is a normal subgp of A(Q)). A(Q)/Inn(Q) =~ S_3 ; since each permutation of (1,2,3) permutes the 3 e_i of Q. I think the idea is here, but not well presented If anyone has a better way or comments, they are welcome. Auto of Z_n are discussed in detail in elem texts, but I haven¹t seen much on autos of non-abelian grps in the notes I have read. Anyone have suggestions of online notes that deal with this? Other texts? === Subject: Re: Automorphisms of small non-Albelian groups posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB Another repost (I usually don¹t repost--forgive me) > Auto of Q = quaternions = A(Q); Q = +/- (1,e_i) , i = 1,2,3. > center Z(Q) = Z_2 ; Q/Z = Z_2 x Z_2 =~ Inn(Q) < A(Q) > (actually Inn(Q) is a normal subgp of A(Q)). > A(Q)/Inn(Q) =~ S_3 ; since each permutation of (1,2,3) > permutes the 3 e_i of Q. > I think the idea is here, but not well presented > If anyone has a better way or comments, they are welcome. > Take a cube. Write the six elements of order 4 of Q on the six > faces i opposite -i etc. Each rotation of the cube induces > an automorphism of Q. Aut(Q) is the symmetry group of the cube. > -- > Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html > Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9 > Francis Wheen, _How Mumbo-Jumbo Conquered the World_ That is good. I like it and its clear. Not A_4, the rot syms, but S_4, all the syms of the cube. And you don¹t have to worry about inner vs outer autos. I got this prob. from Milne¹s notes. He is the one who who gave the above, A(Q)/Inn(Q) =~ S_3. I don¹t see how to proceed from this though. Same for S_4 with its normal subgp N and S_4/N =~ S_3. So I have the autos of N = S_3 = autos of S_4/N, but again, I don¹t see how to proceed. It is true that all the autos of S_4 are inner, isn¹t it? If so, since Z is trivial, Milne says that this means that S_4 is complete, whatever that means. Van === Subject: Re: Automorphisms of small non-Albelian groups > It is true that all the autos of S_4 are inner, isn¹t it? Yes: S_4 has 4 subgroups of order 6. No automorphism save the trivial one takes each of these to itself. -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9 Francis Wheen, _How Mumbo-Jumbo Conquered the World_ === Subject: Re: Automorphisms of small non-Albelian groups posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB First a note to Jim Heckman; I do know what a presentation is. My mind just went blank for some reason when I read that word. S_3 = where x^3 = 1 ; y^2 = 1, yxy(-1) = x^2 is a presentation of S_3, right? ------------ I will have to think about Robin Chapman¹s post. --------------- I think I have made some progress on A(S_4) = S_4, though it doesn not involve S_4/N =~ S_3. The map C: S_4 --> A(S_4) ; g --> C_g ; and C_g acts by conjugation is into and thus onto since S_4 is Þnite. Thus if I can show that all autos of S_4 are inner, S_4 = A(S_4). I don¹t know how to proceed here though. I would also like to look at S_6. I will post what Milne says about it later. Van === Subject: Re: Automorphisms of small non-Albelian groups posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB G is complete if C: G --> A(G) = Inn(G) is an isomorphism. C_g in A(G) = Inn(G) is conjugation. We must have 1) Center Z is trivial 2) The above map C is onto, every auto is inner. commutative; Aut(S6)/Inn(S6) = ~ C_2, and hence S_6 has outer autos. See Rotman 1995, Theorems 7.5, 7.10. ------ I would like to proceed a little with this, but have never done anything with S_6. I guess that would be a place to start. I did a little with A_5 and the dodecahedron once. Any comments are welcome. Van === Subject: Re: Automorphisms of small non-Albelian groups posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB Robin Chapman; >> It is true that all the autos of S_4 are inner, isn¹t it? >Yes: S_4 has 4 subgroups of order 6. No automorphism save the trivial one >takes each of these to itself. Yes, the 4 subgps iso to S_3, the perms with i Þxed, i = 1,2,3,4. Its easy to show the inner autos can¹t leave any 3 numbers Þxed, since an interchange (ij) involves 2 numbers, and any element can be written as a product of interchanges. How about this; For any auto f: S_4 --> S_4, suppose that f is restricted to the subgroup H_i = ~S_3 that leaves i Þxed, for i = 1,2,3,4. so f(H_i) subset H_i. To show; if f(H_i) subset H_i, then f = 1. Damn, I thought I made some progress, but I see I just have stated the problem as you did. I¹ll have to work on this further. I don¹t know how to proceed yet. Even though theree is nothing in this post, I will post it to ask for more help. Any more hints/suggestions would be welcome. Van === Subject: Re: Automorphisms of small non-Albelian groups > Robin Chapman; > It is true that all the autos of S_4 are inner, isn¹t it? >>Yes: S_4 has 4 subgroups of order 6. No automorphism save the trivial > one >>takes each of these to itself. > Yes, the 4 subgps iso to S_3, the perms with i Þxed, i = 1,2,3,4. > Its easy to show the inner autos can¹t leave any 3 numbers Þxed, > since an interchange (ij) involves 2 numbers, and any element > can be written as a product of interchanges. > How about this; For any auto f: S_4 --> S_4, suppose that > f is restricted to the subgroup H_i = ~S_3 that leaves i Þxed, > for i = 1,2,3,4. > so f(H_i) subset H_i. > To show; if f(H_i) subset H_i, then f = 1. > Damn, I thought I made some progress, but I see I just have stated > the problem as you did. > I¹ll have to work on this further. I don¹t know how to proceed yet. > Even though theree is nothing in this post, I will post it > to ask for more help. What does an automorphism Þxing each H_i do to the permutation (3 4)? -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9 Francis Wheen, _How Mumbo-Jumbo Conquered the World_ === Subject: Re: Automorphisms of small non-Albelian groups >> Robin Chapman; >> It is true that all the autos of S_4 are inner, isn¹t it? > Yes: S_4 has 4 subgroups of order 6. No automorphism save the trivial >> one > takes each of these to itself. >> Yes, the 4 subgps iso to S_3, the perms with i Þxed, i = 1,2,3,4. >> Its easy to show the inner autos can¹t leave any 3 numbers Þxed, >> since an interchange (ij) involves 2 numbers, and any element >> can be written as a product of interchanges. >> How about this; For any auto f: S_4 --> S_4, suppose that >> f is restricted to the subgroup H_i = ~S_3 that leaves i Þxed, >> for i = 1,2,3,4. >> so f(H_i) subset H_i. >> To show; if f(H_i) subset H_i, then f = 1. >> Damn, I thought I made some progress, but I see I just have stated >> the problem as you did. >> I¹ll have to work on this further. I don¹t know how to proceed yet. >> Even though theree is nothing in this post, I will post it >> to ask for more help. > What does an automorphism Þxing each H_i do to the permutation (3 4)? I see. Of course. If f Þxes H_i, it Þxes i for each i, so it must be the identity. I don¹t know what the matter with my mind was this morning. The inner autos permute the H_i, and so can be thought of as permuting the i, so every inner auto is a permutation of the H_i = a permutation of (1,2,3,4), is an element of S_4. If f is a non identity auto which is outer, it must leave the H_i (and thus the i) Þxed, but we have just shown that such an f must be the identity, so we have a contradiction, and all autos must be inner. I hesitate to post this as my thinking has been so muddy lately, but I been making a fool of myself so often, what does it matter? Van it is not a permuation of the H_i, thus it leave -- What should such fellows as I do, crawling between earth and heaven? We are arrant knaves all; believe none of us. === Subject: Re: Automorphisms of small non-Albelian groups > Robin Chapman; >>> It is true that all the autos of S_4 are inner, isn¹t it? >> Yes: S_4 has 4 subgroups of order 6. No automorphism save the trivial > one >> takes each of these to itself. > > Yes, the 4 subgps iso to S_3, the perms with i Þxed, i = 1,2,3,4. > Its easy to show the inner autos can¹t leave any 3 numbers Þxed, > since an interchange (ij) involves 2 numbers, and any element > can be written as a product of interchanges. > > How about this; For any auto f: S_4 --> S_4, suppose that > f is restricted to the subgroup H_i = ~S_3 that leaves i Þxed, > for i = 1,2,3,4. > so f(H_i) subset H_i. > > To show; if f(H_i) subset H_i, then f = 1. > > Damn, I thought I made some progress, but I see I just have stated > the problem as you did. > I¹ll have to work on this further. I don¹t know how to proceed yet. > Even though theree is nothing in this post, I will post it > to ask for more help. >> What does an automorphism Þxing each H_i do to the permutation (3 4)? > I see. Of course. If f Þxes H_i, it Þxes i for each i, so it > must be the identity. I don¹t know what the matter with my mind was this > morning. > The inner autos permute the H_i, and so can be thought of as permuting > the i, so every inner auto is a permutation of the H_i = a permutation > of (1,2,3,4), is an element of S_4. If f is a non identity auto which > is outer, it must leave the H_i (and thus the i) Þxed, but we have > just shown that such an f must be the identity, so we have a contradiction, > and all autos must be inner. > I hesitate to post this as my thinking has been so muddy lately, > but I been making a fool of myself so often, what does it matter? > Van How about this. If f is any auto, f in A(G), and C_x is an inner auto, C_x(y) = xyx^(-1), then f(C_x(y)) = f(xyx^(-1)) = f(x) f(y) [f(x)]^(-1) = C_f(x)(f(y)) ; or f C_x f^(-1) = C_f(x) ; so the inner autos indeed form a normal subgp of all autos A(G). But we already know this, and it doesn¹t use the above about auto permuting the H_i. I think one has to say that an auto that permutes the H_i permutes (1,2,3,4), so every auto is in S_4. Since the image of the map C: S_4 --> A(S_4) is S_4, where C is conjugation, and C is into, every auto is inner, and A(S_4) = S_4. I guess that¹s what I said above. Does this arguement seem OK? After this, on to S_5 and S_6. It looks like S_6 may have some interesting properties. |S_6| = 720, but 6 = 3.2 probably makes things a bit easier to handle. I don¹t know. Van -- The horror, the horror--Joseph Conrad, Heart of Darness === Subject: Re: Cute little next-to-nothing. >This is doubtless well-known to all graph theorists and many others, >but I just noticed it recently and thought it was rather cute. >The fully transitive 3x3 lattice, naturally embedded in a torus... > d e f > : : : > | | | >a ...---*------*------*---... a > | | | > | | | > | | | >b ...---*------*------*---... b > | | | > | | | > | | | >c ...---*------*------*---... c > | | | > : : : > d e f ...is SELF-COMPLEMENTARY! > Are you saying that if you redraw the graph with all the connections > þipped, it¹s the same graph? > . . . . > / / / > * * * > / / / > X X > / / / > * * * > / / / > X X > / / / > * * * > / / / > . . . . > I see how they¹re isomorphic, but why worry about the torus? The > complementary edges cross each other where the originals don¹t. That¹s only because you drew it with edges crossing. It¹s always possible to avoid crossing edges if the graph is embeddable, and in this case it¹s quite easy: g h.j k m.n p r.q a /¹ / /¹ / /¹ a .* / .* / .* / b¹/ / .¹/ / .¹/ / b / /.¹ / /.¹ / /.¹ c /¹ / /¹ / /¹ c .* / .* / .* / d¹/ / .¹/ / .¹/ / d / /.¹ / /.¹ / /.¹ e /¹ / /¹ / /¹ e .* / .* / .* / f¹/ / .¹/ / .¹/ / f g h j k m n p r q Dan Hoey Hoey@AIC.NRL.Navy.Mil === Subject: Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev A) > Galilean/Newtonian Invariance > -------------------------------------------------- > Linear equations > ------------------------------- > Inverse-square equations > -------------------------------------------- > A Brain Dead True Believer Response > ------------------------------------------------------------ > A Corrupt True Believer ŒResponse¹ > ------------------------------------------------------- [snip 340 lines of trolled garbage] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Originally trolled across sci.physics sci.physics.relativity alt.physics sci.math sci.answers alt.answers news.answers Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: B. Newtonian Micheslon-Morley vs SR-cult fraud and corruption (Rev A) > Michelson-Morley Experiment versus Newtonian-Galilean Physics > ------------------------------------------------------------- ---------------- ------------------------- > The ŒIntrinsic¹ Energy Model of Light > -------------------------------------------------------- > Absolute Motion? > --------------------------- >[snip 200 lines of trolled garbage] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! ing imbecile Oren Webster, Phys. Rev. Lett. 88(1) 010401 (2002) Phys. Rev. Lett. 42(9) 549 (1979) Phys. Bull. 21 255 (1970) Europhysics Lett. 56(2) 170 (2001) Gen. Rel. Grav. 34(9) 1371 (2002) Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: B. Newtonian Micheslon-Morley vs SR-cult fraud and corruption (Rev A) black hole evaporation has a ring to it (it must be consistent with real-number arithemetic e.g.). Michelson and Morley found anomalies in the speed of light that were quite regular, though slight, and DCMiller improved the accuracy of this measuerment. unfortunately, herr doktor-professor Einstein, on one of his few trips to Caltech, said that Miller must have been mistaken, QED. > Minkowski geometry is equiconsistent with the theory of real numbers > and with arithmetic. > His refusal to accept that t¹ must be introduced as a separate > variable springs from a massive emprical stupidity re space and time > are described as a four-dimensional manifold, with four coordinates > instead of a time evolution of a three-dimensional manifold, and that > the change of coordinate system should be a change of four > coordinates, and not a time-dependent change of three coordinates. > Black hole evaporation > > http://arXiv.org/abs/gr-qc/0301024 > Nordtvedt Effect --A HYDROGEN (sic; cracked methane) ECONOMY?... The Three Phases of Exploitation of the Protocols of the Elders of Kyoto (sik): BORE/GUSH/NADIR @ http://www.tarpley.net. Http://www.tarpley.net/bushb.htm (partial contents, below): 17 -- THE ATTEMPTED COUP D¹ETAT, 3/30/81 (87K) 18 -- IRAN-CONTRA (140K) 19 -- THE LEVERAGED BUYOUT MOB (67K) 20 -- THE PHONY WAR ON DRUGS (26K) 21 -- OMAHA (25K) 22 -- GEORGE #9 TAKES THE PRESIDENCY (112K) 23 -- THE END OF HISTORY (168K) 24 -- THE NEW WORLD ORDER (255K) 25 -- THYROID STORM (139K) http://quincy4board.homestead.com/Þles/curriculum/Cosmo === Subject: Re: B. Newtonian Micheslon-Morley vs SR-cult fraud and corruption (Rev A) >>Michelson-Morley Experiment versus Newtonian-Galilean Physics >>----------------------------------------------------------- --------------- ---------------------------- >>The ŒIntrinsic¹ Energy Model of Light >>-------------------------------------------------------- >>Absolute Motion? >>--------------------------- >>[snip 200 lines of trolled garbage] > eleaticus, Oren Webster, is a despised and stooopid troll, no you can¹t babysit my kids === Subject: Re: HELP - Galois group of a polynomial The Þrst 2 problems can be solved by Þnding the resolvent cubic; that way easy, I Þgured that out. And #3 was easy too: we observe that it is irreducible by Eisentien, and since it had exactly 2 non-real roots, the Galois group is isomorphic to S_5. Myerson, that simply because someone can¹t solve a problem, it automatically means it is a homework assignment. In fact it was not in my case. sci.math is not a research group: it is a place where mathematicians and students (including high schools students reading advanced mathematics) meet to discuss problems--homework or not. What you Þnd trivial may be insurmoutable for someone else. Perhaps he is studying the material on his own; or perhaps his instuctor is less helpful. Whatever the case, you have no business judging him or his reason for posting a problem on sci.math When you offer help, do so without sneering. NC > At the risk of doing OP¹s homework, there¹s another approach === Subject: Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > Galilean/Newtonian Invariance > -------------------------------------------------- > Linear equations > ------------------------------- > Inverse-square equations > -------------------------------------------- > A Brain Dead True Believer Response > ------------------------------------------------------------ > A Corrupt True Believer ŒResponse¹ > ------------------------------------------------------- > Preamble > -------------- > Could you trust the Ku Klux Klan to conduct an honest investigation of > the NAACP? No matter how sincere the investigators might be, their > biases and learned distortions and misrepresentation of the NAACP and > blacks in general would make honesty impossible. Can you trust a crank like Eleaticus to stop spamming the same rot? Obviously not. Rest of junk mercifully snipped. > Rarely, there is actually a response that has some relevance to the > material posted, and those are proofs of their Brain Death. Time and time again his material has been refuted eg my challenge how he can explain the non Galilean invariance of the EM wave equation derived from Maxwell¹s equations has never been refuted - it predicts the speed of EM radiation is the same in all inertial frames in violation of the Galilean transformations. He simply continues to claim it has - a typical crank tactic. Bill === Subject: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > Time and time again his material has been refuted eg my challenge how he can > explain the non Galilean invariance of the EM wave equation derived from > Maxwell¹s equations has never been refuted - it predicts the speed of EM > radiation is the same in all inertial frames in violation of the Galilean > transformations. He simply continues to claim it has - a typical crank > tactic. Congratulations! You have proved yourself capable of being at least a jerk, if not an ass, and of not having sufÞcient honesty to actually respond to the details of logic/etc. So, can you now prove yourself capable of relenting in your desire to prove irrelevant to any actual discussion, and do something helpful? Maxwell and invariance are an important combination of topics and as many expressions as I know of for E, H, B, etc, I do not know just what exemplars of them would be best for demonstrating particulars of their transformation by Newton-theoretic coordinate tranformations. The Œproblem¹ is different than in the case of the Lorentz transforms of Maxwell because in the Newton case it actually is the coordinates x,y,z that are transformed, rather than - essentially - the inverse of the coordinates. So, please provide a set of expressions - appropriate for full exposition of Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate expressions. Obviously (ha!) the result would be that Þnally I come headsup (as we poker players say) with my tremendous error in thinking that transforming Maxwell Newton-wise without the three strawmen corruptions will prove invariant. eleaticus > Bill === Subject: Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) [snip crap] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > Time and time again his material has been refuted eg my challenge how he > can > explain the non Galilean invariance of the EM wave equation derived from > Maxwell¹s equations has never been refuted - it predicts the speed of EM > radiation is the same in all inertial frames in violation of the Galilean > transformations. He simply continues to claim it has - a typical crank > tactic. > Congratulations! > You have proved yourself capable of being at least a jerk, if not an ass, > and of not having sufÞcient honesty to actually respond to the details of > logic/etc. > So, can you now prove yourself capable of relenting in your desire to prove > irrelevant to any actual discussion, and do something helpful? > Maxwell and invariance are an important combination of topics and as many > expressions as I know of for E, H, B, etc, I do not know just what exemplars > of them would be best for demonstrating particulars of their transformation > by Newton-theoretic coordinate tranformations. > The Œproblem¹ is different than in the case of the Lorentz transforms of > Maxwell because in the Newton case it actually is the coordinates x,y,z that > are transformed, rather than - essentially - the inverse of the coordinates. > So, please provide a set of expressions - appropriate for full exposition of > Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate > expressions. I have chosen not to go down the path of an explicit proof but of showing a logical consequence of the theory shows Maxwell¹s equations are not Galilean invariant. The reason is you are so confused about what invariance is it would be futile. I have given you this link before http://hyperphysics.phy-astr.gsu.edu/hbase/waves/emwv.html#c1 . This represents a wave traveling at velocity c as explained here http://hyperphysics.phy-astr.gsu.edu/hbase/waves/waveq.html# c1. Now if Maxwell¹s equations were Galilean invariant then in a frame traveling at velocity v relative to another frame the waves would be seen to be traveling at speed c-v. But the wave equation demands they travel at speed c - thus Maxwell¹s equations are not Galilean invariant. Please detail the error in logic or admit Maxwell¹s equations are not Galilean invariant. The explicit detail is: 1. The link above derives the EM wave equation form Maxwell¹s equations. 2. The other link shows such an equation represents waves traveling at velocity c. 3. If Maxwell¹s equations are true in an inertial frame then EM waves will travel at velocity c in any inertial frame. 4. All initial frames move at content velocity relative to each other and any frame moving at constant velocity to an inertial frame is also inertial - see the deÞnition of inertial frame http://plato.stanford.edu/entries/spacetime-iframes/. 5. If Maxwell¹s equations are Galilean invariant then a frame traveling at velocity v to another inertial frame will see c as c-v. 6. This however is logically incompatible with the fact the speed must be c in any inertial frame - hence Maxwell¹s equations must not be Galilean invariant. Bill > Obviously (ha!) the result would be that Þnally I come headsup (as we poker > players say) with my tremendous error in thinking that transforming Maxwell > Newton-wise without the three strawmen corruptions will prove invariant. > eleaticus > Bill === Subject: Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > > Time and time again his material has been refuted eg my challenge how he > can > > explain the non Galilean invariance of the EM wave equation derived from > > Maxwell¹s equations has never been refuted - it predicts the speed of EM > > radiation is the same in all inertial frames in violation of the > Galilean > > transformations. He simply continues to claim it has - a typical crank > > tactic. > Congratulations! > You have proved yourself capable of being at least a jerk, if not an ass, > and of not having sufÞcient honesty to actually respond to the details of > logic/etc. > So, can you now prove yourself capable of relenting in your desire to > prove > irrelevant to any actual discussion, and do something helpful? > Maxwell and invariance are an important combination of topics and as many > expressions as I know of for E, H, B, etc, I do not know just what > exemplars > of them would be best for demonstrating particulars of their > transformation > by Newton-theoretic coordinate tranformations. > The Œproblem¹ is different than in the case of the Lorentz transforms of > Maxwell because in the Newton case it actually is the coordinates x,y,z > that > are transformed, rather than - essentially - the inverse of the > coordinates. > So, please provide a set of expressions - appropriate for full exposition > of > Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate > expressions. > I have chosen not to go down the path of an explicit proof but of showing a > logical consequence of the theory shows Maxwell¹s equations are not Galilean > invariant. The reason is you are so confused about what invariance is it > would be futile. > I have given you this link before > http://hyperphysics.phy-astr.gsu.edu/hbase/waves/emwv.html#c1 . This > represents a wave traveling at velocity c as explained here > http://hyperphysics.phy-astr.gsu.edu/hbase/waves/waveq.html# c1. Now if > Maxwell¹s equations were Galilean invariant then in a frame traveling at > velocity v relative to another frame the waves would be seen to be traveling > at speed c-v. But the wave equation demands they travel at speed c - thus > Maxwell¹s equations are not Galilean invariant. > Please detail the error in logic or admit Maxwell¹s equations are not > Galilean invariant. The explicit detail is: > 1. The link above derives the EM wave equation form Maxwell¹s equations. > 2. The other link shows such an equation represents waves traveling at > velocity c. > 3. If Maxwell¹s equations are true in an inertial frame then EM waves will > travel at velocity c in any inertial frame. > 4. All initial frames move at content velocity relative to each other and > any frame moving at constant velocity to an inertial frame is also > inertial - see the deÞnition of inertial frame > http://plato.stanford.edu/entries/spacetime-iframes/. > 5. If Maxwell¹s equations are Galilean invariant then a frame traveling at > velocity v to another inertial frame will see c as c-v. > 6. This however is logically incompatible with the fact the speed must be c > in any inertial frame - hence Maxwell¹s equations must not be Galilean > invariant. > Bill Your conclusion that Maxwell¹s equations must not be galilean invariant rests on the premise that c is constant in all inertial frames. The deduction is valid but it can be sound or unsound depending on the truth of your premise. Listen poor Hobba: Validity and truth of infrerences are independent concepts. A valid deduction does not guaranty soundness. Whe you and your likes are going to understand that? Fundamental theory of Logic: Truth and Validity are independent. Furthermore, Any false formula implies a truth formula. Poor impeciles, read Aristotle. Mike === Subject: Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > > > > > > Time and time again his material has been refuted eg my challenge how he > can > > explain the non Galilean invariance of the EM wave equation derived from > > Maxwell¹s equations has never been refuted - it predicts the speed of EM > > radiation is the same in all inertial frames in violation of the > Galilean > > transformations. He simply continues to claim it has - a typical crank > > tactic. > > > > Congratulations! > > > > You have proved yourself capable of being at least a jerk, if not an ass, > > and of not having sufÞcient honesty to actually respond to the details of > > logic/etc. > > > > So, can you now prove yourself capable of relenting in your desire to > prove > > irrelevant to any actual discussion, and do something helpful? > > > > Maxwell and invariance are an important combination of topics and as many > > expressions as I know of for E, H, B, etc, I do not know just what > exemplars > > of them would be best for demonstrating particulars of their > transformation > > by Newton-theoretic coordinate tranformations. > > > > The Œproblem¹ is different than in the case of the Lorentz transforms of > > Maxwell because in the Newton case it actually is the coordinates x,y,z > that > > are transformed, rather than - essentially - the inverse of the > coordinates. > > > > So, please provide a set of expressions - appropriate for full exposition > of > > Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate > > expressions. > I have chosen not to go down the path of an explicit proof but of showing a > logical consequence of the theory shows Maxwell¹s equations are not Galilean > invariant. The reason is you are so confused about what invariance is it > would be futile. > I have given you this link before > http://hyperphysics.phy-astr.gsu.edu/hbase/waves/emwv.html#c1 . This > represents a wave traveling at velocity c as explained here > http://hyperphysics.phy-astr.gsu.edu/hbase/waves/waveq.html# c1. Now if > Maxwell¹s equations were Galilean invariant then in a frame traveling at > velocity v relative to another frame the waves would be seen to be traveling > at speed c-v. But the wave equation demands they travel at speed c - thus > Maxwell¹s equations are not Galilean invariant. > Please detail the error in logic or admit Maxwell¹s equations are not > Galilean invariant. The explicit detail is: > 1. The link above derives the EM wave equation form Maxwell¹s equations. > 2. The other link shows such an equation represents waves traveling at > velocity c. > 3. If Maxwell¹s equations are true in an inertial frame then EM waves will > travel at velocity c in any inertial frame. > 4. All initial frames move at content velocity relative to each other and > any frame moving at constant velocity to an inertial frame is also > inertial - see the deÞnition of inertial frame > http://plato.stanford.edu/entries/spacetime-iframes/. > 5. If Maxwell¹s equations are Galilean invariant then a frame traveling at > velocity v to another inertial frame will see c as c-v. > 6. This however is logically incompatible with the fact the speed must be c > in any inertial frame - hence Maxwell¹s equations must not be Galilean > invariant. > Bill > Your conclusion that Maxwell¹s equations must not be galilean > invariant rests on the premise that c is constant in all inertial > frames. Please read point 3 - If Maxwell¹s equations are true in an inertial frame then EM waves will travel at velocity c in any inertial frame - the wave equation was deriveed from Maxwells eqations so the the ocncusion follows from the premise. > The deduction is valid but it can be sound or unsound depending on the > truth of your premise. Certainly. Which is what I was showing - namely if Maxwell¹s equations are true in inertial frames (premise) then they can not be Galilean invariant (conclusion). > Listen poor Hobba: Validity and truth of infrerences are independent > concepts. A valid deduction does not guaranty soundness. Whe you and > your likes are going to understand that? > Fundamental theory of Logic: Truth and Validity are independent. > Furthermore, > Any false formula implies a truth formula. Poor impeciles, read > Aristotle. Learn some logic and stop ******* yourself or you will go blinder than you already obviously are. Bill > Mike === Subject: Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > So, please provide a set of expressions - appropriate for full exposition > of > Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate > expressions. > I have chosen not to go down the path of an explicit proof but of showing a > logical consequence of the theory shows Maxwell¹s equations are not Galilean > invariant. The reason is you are so confused about what invariance is it > would be futile. As you quoted, you weren¹t asked for any kind of proof. You were asked for a set of expressions appropriate for demonstrating invariance or the lack of en re Maxwell and Newton-theoretic coordinate transforms. The links you Œprovide¹ did not do that. eleaticus === Subject: Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) [snip crap] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > > So, please provide a set of expressions - appropriate for full > exposition > of > > Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate > > expressions. > I have chosen not to go down the path of an explicit proof but of showing > logical consequence of the theory shows Maxwell¹s equations are not > Galilean > invariant. The reason is you are so confused about what invariance is it > would be futile. > As you quoted, you weren¹t asked for any kind of proof. You were asked for a > set of expressions appropriate for demonstrating invariance or the lack of > en re Maxwell and Newton-theoretic coordinate transforms. > The links you Œprovide¹ did not do that. Yes they did - and a gave a very detailed logical analysis showing so. Bill > eleaticus === Subject: Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > I have chosen not to go down the path of an explicit proof but of showing a > logical consequence of the theory shows Maxwell¹s equations are not Galilean > invariant. The reason is you are so confused about what invariance is it > would be futile. I agree that SR-cultism has reached some rather ridiculous ideas en re invariance, derived from non-physical math stuff that is not relevant for physics, I reckon. But the idea of invariance has only one relevance to physics: a mathematical statement of a universal law can be valid only if it is the same for all observers/users for the same situation, in the sense of being the same statement - but using local measurements - and in providing the same numerical results. Anything else is pure crap. You agree or not? eleaticus === Subject: Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) >[snip crap] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > I have chosen not to go down the path of an explicit proof but of showing > logical consequence of the theory shows Maxwell¹s equations are not > Galilean > invariant. The reason is you are so confused about what invariance is it > would be futile. > I agree that SR-cultism has reached some rather ridiculous ideas en re > invariance, derived from non-physical math stuff that is not relevant for > physics, I reckon. Based on what - your writing that have been shown to be rubbish? As to what I think of SR I must refer to an ancient post of Tom Roberts that expresses my view quite well: > But the idea of invariance has only one relevance to physics: a mathematical > statement of a universal law can be valid only if it is the same for all > observers/users for the same situation, in the sense of being the same > statement - but using local measurements - and in providing the same > numerical results. > Anything else is pure crap. > You agree or not? No I do not agree. The POR applies only to inertial frames and only to laws of nature; where one must ensure one understands what meant by law of nature. GR is based on the principle of general invariance - not on the principle that all the laws of nature are the same in all coordinate accelerated frame - however the laws of nature should be put in a form that does not depend on coordinate systems. The principle of invariance says that when that is done the terms can be divided into absolute and dynamical. That is the key to GR - see Chapter 7 Ohanian and RufÞni - Gravitation and Space-time. The real key is symmetry - for SR the symmetry implied by the POR, for GR the symmetry implied by the principle of general invariance. Bill > eleaticus === Subject: Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > No I do not agree. The POR applies only to inertial frames and only to laws > of nature; where one must ensure one understands what meant by law of > nature. GR is based on the principle of general invariance - not on the > principle that all the laws of nature are the same in all coordinate > accelerated frame - however the laws of nature should be put in a form that > does not depend on coordinate systems. The principle of invariance says > that when that is done the terms can be divided into absolute and dynamical. > That is the key to GR - see Chapter 7 Ohanian and RufÞni - Gravitation and > Space-time. > The real key is symmetry - for SR the symmetry implied by the POR, for GR > the symmetry implied by the principle of general invariance. > Bill Analogously, I seek in vain for a real something in classical mechanics (or in the special theory of relativity) to which I can attribute the different behaviour of bodies considered with respect to the reference systems K and K1.1) Newton saw this objection and attempted to invalidate it, but without success. But E. Mach recognsed it most clearly of all, and because of this objection he claimed that mechanics must be placed on a new basis. It can only be got rid of by means of a physics which is conformable to the general principle of relativity, since the equations of such a theory hold for every body of reference, whatever may be its state of motion. A. Einstein. Ref: http://www.beyondweird.com/einstein/contents/ch21.htm Look at the mirror Bill Hobba and ask yourself: Am I a lier? If am not, what am I? A stupid man? Then make your choice. You will be forgiven for your ignorance. Along with your Ohanian and RufÞni friends. Observable phenomena cannot and do not single out ANY state of motion. GR is a failure as far as it being a theory of Relativistic dynamics. It is just another absolutism like Newton¹s, as you admitted. Actually GR is a poor heuristic in the same way that Christianity is a mediocre religion. Both were invented from people in the same state of mind. People that arrived at a bad mix of observational consequences and deductive logic. Mike === Subject: Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > No I do not agree. The POR applies only to inertial frames and only to laws > of nature; where one must ensure one understands what meant by law of > nature. GR is based on the principle of general invariance - not on the > principle that all the laws of nature are the same in all coordinate > accelerated frame - however the laws of nature should be put in a form that > does not depend on coordinate systems. The principle of invariance says > that when that is done the terms can be divided into absolute and dynamical. > That is the key to GR - see Chapter 7 Ohanian and RufÞni - Gravitation and > Space-time. > The real key is symmetry - for SR the symmetry implied by the POR, for GR > the symmetry implied by the principle of general invariance. > Bill > Analogously, I seek in vain for a real something in classical > mechanics (or in the special theory of relativity) to which I can > attribute the different behaviour of bodies considered with respect to > the reference systems K and K1.1) Newton saw this objection and > attempted to invalidate it, but without success. But E. Mach recognsed > it most clearly of all, and because of this objection he claimed that > mechanics must be placed on a new basis. It can only be got rid of by > means of a physics which is conformable to the general principle of > relativity, since the equations of such a theory hold for every body > of reference, whatever may be its state of motion. A. Einstein. > Ref: http://www.beyondweird.com/einstein/contents/ch21.htm > Look at the mirror Bill Hobba and ask yourself: Am I a lier? If am > not, what am I? A stupid man? Einstein is not the last word on relativity. Kretchmann took him to task and Einstein admitted he was wrong. This is discussed in full detail in the reference given ie the standard text Ohanian and RufÞni. > Then make your choice. You will be forgiven for your ignorance. Along > with your Ohanian and RufÞni friends. What choice - Einstein was wrong - it is now well known he made contradictory statements eg - see http://www.bun.kyoto-u.ac.jp/~suchii/Einstein/ generalcovar.html. Notice: ŒThis section is quite important, in order to understand the meaning and signiÞcance of Einstein¹s general principle of relativity. In section 18, Einstein formulated it thus: (1) All bodies of reference K, K¹, etc., are equivalent for the description of natural phenomena (formulations of the general laws of nature), whatever may be their state of motion. But now Einstein says that this actually does not hold. Instead, he says that the following should replace it: (2) All Gaussian co-ordinate systems are essentially equivalent for the formulation of the general laws of nature.¹ Understandinhg what is going on in GR has moved on since Eisnteins time (it even was worked out in Einteins time and I have no doubt Einsten agreed just like he eventually agreed with Kretchmann). See also http://modeling.la.asu.edu/R&E/SecretsGenius.pdf - ŒIt is of interest to note that all this is related to a complex of misleading statements by Einstein concerning (1) the equivalence of gravitational forces with accelerated systems, (2) the origin of centrifugal forces (or Mach¹s principle), and (3) the role of covariance in distinguishing special and general relativity. On the last point Einstein was called to task by Kretchmann (1917). Each of these points have been the subject of much discussion and debate in the physics community. The issues involved in the Þrst and third points are now well understood by the experts, thought they continue to cause problems for novices. The second point involves fundamental physical issues that have not yet been resolved. Einstein¹s statement on these points suggests that he may have harbored some misconceptions of his own about relativity. Even so, he insisted that these ideas played indispensable heuristic roles in the development of general relativity.¹ > Observable phenomena cannot and do not single out ANY state of motion. Based on what - your say so? > GR is a failure as far as it being a theory of Relativistic dynamics. GR is a theory fully in accord with experiment - which is all that can be asked. Mumbo jumbo proffered by philosophy wankers not withstanding. > It is just another absolutism like Newton¹s, as you admitted. That depends on your deÞnition of absolutism. That the principle of general invariance demands the laws of nature take the same covariant form in all coordinate systems is generally not looked upon as Œabsolutism¹. > Actually GR is a poor heuristic in the same way that Christianity is a > mediocre religion. Both were invented from people in the same state of > mind. People that arrived at a bad mix of observational consequences > and deductive logic. The experimental evidence against GR is? Bill > Mike === Subject: Equivalence my ass! Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > No I do not agree. The POR applies only to inertial frames and only to laws > of nature; where one must ensure one understands what meant by law of > nature. GR is based on the principle of general invariance - not on the > principle that all the laws of nature are the same in all coordinate > accelerated frame - however the laws of nature should be put in a form that > does not depend on coordinate systems. The principle of invariance says > that when that is done the terms can be divided into absolute and dynamical. > That is the key to GR - see Chapter 7 Ohanian and RufÞni - Gravitation and > Space-time. Actually, I have demonstrated on these newsgroups that in Newtonian terms objects moving inertially in the view of an inertial observer also move in straight lines and with equal distances per time unit in the view of accelerating systems. I shall be doing so again in my new series, which was going to be on the lines of X. GR-cult idiocies. I¹ll give you a clue which would make it quickly obvious to honest people of competence. Let there be three beacons A,B,C in a straight line and with the distance from A to B equal to the distance from B to C. Let an inertial object pass A at t=0 and proceed past B to C. The transit time from A to B will equal that from B to C. In the accelerating system note the coordinates at all three times of A, B, C, transform the 3-coordinates and note that at all times A,B,C are in a straight line (as evidenced by B¹-A¹ = C¹-B¹). Hence, the inertial object did move in a straight line and the object made each sub-transit in equal times. Quod erat the pearl cast before you. eleaticus === Subject: Re: Equivalence my ass! Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) [snip crap] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: Equivalence my ass! Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) eleaticus says... >Actually, I have demonstrated on these newsgroups that in Newtonian terms >objects moving inertially in the view of an inertial observer also move in >straight lines and with equal distances per time unit in the view of >accelerating systems. When you demonstrate something that you can easily show to be false, that¹s an indication that maybe you made a mistake. You know it¹s false because you can try it out yourself and see. Hop in a car, and look out the window at some stationary object, say, a tree. The tree is moving inertially (at constant speed 0) in the rest frame of the ground. In the view of your car, the tree is also point of view of your car, the tree will start moving *backwards*. Try it! So the speed of the tree is *not* constant from the point of view of your accelerating car. So the conclusion of your demonstration is observably false. -- Daryl McCullough Ithaca, NY === Subject: Re: Equivalence my ass! Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > eleaticus says... >Actually, I have demonstrated on these newsgroups that in Newtonian terms >objects moving inertially in the view of an inertial observer also move in >straight lines and with equal distances per time unit in the view of >accelerating systems. > When you demonstrate something that you can easily show to be false, > that¹s an indication that maybe you made a mistake. You know it¹s > false because you can try it out yourself and see. > Hop in a car, and look out the window at some stationary object, say, > a tree. The tree is moving inertially (at constant speed 0) in the > rest frame of the ground. In the view of your car, the tree is also > point of view of your car, the tree will start moving *backwards*. > Try it! So the speed of the tree is *not* constant from the point > of view of your accelerating car. > So the conclusion of your demonstration is observably false. There¹s another demonstration that shows this beautifully. You and a buddy go to the playground with a basketball and get on one of those rotatable turntables that the kids spin on until they get nauseous. Once you¹ve gotten up to speed, you and your buddy stand at opposite points on the perimeter of the turntable and toss the ball to each other. The path of a thrown ball in this rotating frame is something that has to be seen to be believed! With practice, you can throw the ball directly across the turntable and catch it yourself! PD === Subject: Yes, Paul?Re: Equivalence my ass! Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > So the conclusion of your demonstration is observably false. > There¹s another demonstration that shows this beautifully. You and a > buddy go to the playground with a basketball and get on one of those > rotatable turntables that the kids spin on until they get nauseous. > Once you¹ve gotten up to speed, you and your buddy stand at opposite > points on the perimeter of the turntable and toss the ball to each > other. The path of a thrown ball in this rotating frame is something > that has to be seen to be believed! With practice, you can throw the > ball directly across the turntable and catch it yourself! I told y¹all how to do it, how to show that the relative velocity wrt to an accelerating system has nothing to do with the question of whether the inertial obect actually travels a straight line as deÞned by the continual comparison of Œmilestone¹ coordinates: B¹-A¹ = C¹-B¹. Either Œyou¹ have the intellectual honesty necessary to check it out, or you don¹t. Which is it in your case, Paul? eleaticus > PD === Subject: Re: Equivalence my ass! Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > eleaticus says... >Actually, I have demonstrated on these newsgroups that in Newtonian terms >objects moving inertially in the view of an inertial observer also move in >straight lines and with equal distances per time unit in the view of >accelerating systems. > When you demonstrate something that you can easily show to be false, > that¹s an indication that maybe you made a mistake. You know it¹s > false because you can try it out yourself and see. > Hop in a car, and look out the window at some stationary object, say, > a tree. The tree is moving inertially (at constant speed 0) in the > rest frame of the ground. In the view of your car, the tree is also > point of view of your car, the tree will start moving *backwards*. > Try it! So the speed of the tree is *not* constant from the point > of view of your accelerating car. > So the conclusion of your demonstration is observably false. Daryl - could not have expressed it better myself. Saves me the trouble. Bill > -- > Daryl McCullough > Ithaca, NY === Subject: Re: Equivalence my ass! Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > Hop in a car, and look out the window at some stationary object, say, > a tree. The tree is moving inertially (at constant speed 0) in the > rest frame of the ground. In the view of your car, the tree is also > point of view of your car, the tree will start moving *backwards*. > Try it! So the speed of the tree is *not* constant from the point > of view of your accelerating car. So, you don¹t know how to transform simple location vectors to an accelerating coordinate system. Hardly a sound basis for your viewpoint. eleaticus === Subject: Re: Equivalence my ass! Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) eleaticus says... >So, you don¹t know how to transform simple location vectors to an >accelerating coordinate system. I don¹t know what *you* mean by that, no. You are using these terms in a completely nonstandard way. So please demonstrate what in the world you are talking about. In the frame of the ground, the positions of car and tree are given by: x_tree(t) = 0 x_car(t) = 1/2 a t^2 where a = the acceleration of the car as measured from the ground, and t = the time since the car passed the tree. I would say that in the frame of the *car*, the positions are given by x¹_tree(t) = -1/2 a t^2 x¹_car(t) = 0 What equations do *you* use for the position of the tree relative to the car? -- Daryl McCullough Ithaca, NY === Subject: Re: Equivalence my ass! Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) [snip trolled garbage] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Were there to be internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) they would automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: Equivalence my ass! Re: Well, Hobba? Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) : eleaticus says... : : >Actually, I have demonstrated on these newsgroups that in Newtonian terms : >objects moving inertially in the view of an inertial observer also move in : >straight lines and with equal distances per time unit in the view of : >accelerating systems. : : When you demonstrate something that you can easily show to be false, : that¹s an indication that maybe you made a mistake. You know it¹s : false because you can try it out yourself and see. : : Hop in a car, and look out the window at some stationary object, say, : a tree. The tree is moving inertially (at constant speed 0) in the : rest frame of the ground. In the view of your car, the tree is also : point of view of your car, the tree will start moving *backwards*. : Try it! So the speed of the tree is *not* constant from the point : of view of your accelerating car. : : So the conclusion of your demonstration is observably false. : : -- : Daryl McCullough : Ithaca, NY As you reach the top of a hill, travelling with constant velocity v, your headlights illuminate the previously hidden tree and your eyes detect its existence. Are you at the top of the hill when you see the tree, or beyond it? Einstein thinks you are still at the top. Androcles. === Subject: Re: A. Newtonian Invariance vs SR-cult fraud and corruption (Rev B) > Galilean/Newtonian Invariance > -------------------------------------------------- > Linear equations > ------------------------------- > Inverse-square equations > -------------------------------------------- > A Brain Dead True Believer Response > ------------------------------------------------------------ > A Corrupt True Believer ŒResponse¹ > ------------------------------------------------------- [snip 340 lines of trolled garbage] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Originally trolled across sci.physics sci.physics.relativity alt.physics sci.math sci.answers alt.answers news.answers Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: Physics upgrade. >>>>>Axiom 1 >>>>>No two objects in the physical universe can be identical. Two fotons of the same frequency are identical. Geert-Jan Uytdewilligen === Subject: New countable inÞniity logic As all the programmers here know, the inÞnite list of all computable numbers UTM(n) neN produces all numbers with every combination of digits. You cannot defeat inÞnity. Say you have an *inÞnite* list of computable real numbers. Then Cantor comes along and shows an anti-diagonal. Of course he can¹t write down an inÞnitely long number so he has to abbreviate his anti-diag witness to uncountability of reals. Anti diag = 0.456456456456123456.. Given this list of numbers, UTM(n) neN Will there be numbers matching 0.456456456456123456xxxxxxxx Certainly. Regardless of what anti-diag number is presented it will appear on the list of computable numbers. All 10 long digit sequences are present on the list of computable numbers All 100 long digit sequences are present on the list of computable numbers All 1000 long digit sequences are present on the list of computable numbers All 1000000 long digit sequences are present on the list of computable numbers All 100000000000000 long digit sequences are present on the list of computable numbers All 10^100000000000000 long digit sequences are present on the list of computable numbers Not only that, every given number will appear on the list of computable numbers AN INFINITE NUMBER OF TIMES. So why do people claim they have magic numbers that don¹t occur in UTM(n) neN, this is an inÞnite set of all computer programs, what could it miss? Cantors diagonal procedure relies on an inÞnite process that examines every number in the list. What possible numbers can this result in? As cantors algorithm is processing, it goes further and further down the list of countable reals. When it has examined in the order of 10^n numbers, every combination of n digits has already appeared. Examined 100 numbers. 10^2 0.01.. 0.02.. 0.03.. 0.04.. 0.05.. 0.10.. 0.11.. 0.12.. .. 0.99 You only need several hundred outputs from UTM(n) neN and its probable you have covered every 2 digit combination. That means anti-diag only has a contradictory digit after 3 or more digits. What happens when you¹ve examined in the order of 10^10 numbers? The difference in Cantors number to all numbers on the list must be after the 10th decimal place. So how many numbers are we examining altogether? what is log(oo)? Now if Cantors-antt-diag =/= any number on the list, that means there exists SOME DIFFERENT DIGIT. But the constraint that Cantors proof overlooks, is that unique digit (given all preceding digits are matched) MUST APPEAR AT SOME **FINITE** DIGIT POSITION. But it doesn¹t, by induction 1 ALL preÞxes of anti-diag are computable. 2 INFINITE preÞxes of anti-diag are computable 3 INFINITE digits of anti-diag are present on the list of computable numbers. So what are people doing when they run their Þnger down the diagonal a few pixels and claim its a new number? Lets rearrange the list into a tree. Start at the parent node with 10 branches 0.0xxxxxxx 0.0xxxxxxx 0.0xxxxxxx 0.1xxxxxxx 0.1xxxxxxx 0.1xxxxxxx 0.2xxxxxxx 0.2xxxxxxx 0.2xxxxxxx ... 0.9xxxxxxx 0.9xxxxxxx 0.9xxxxxxx Each of the 10 branches contains every computable number with the same preÞx. x0 = UTM(n) neN | 0.0 < x < 0.1 x1 = UTM(n) neN | 0.1 < x < 0.2 .. x9 = UTM(n) neN | 0.9 < x < 1 Then we further subdivide those 10 sections. x0 - x01 - x02 - x03 x1 - x11 - x12 - x13 x2 - x21 - x22 - x23 .. x9 - x91 - x98 - x99 We repeat this process indeÞnately and we have inÞnitely many branches, each 10 wide, similar to a chess search search space, computers handle them up to about 20 levels deep. Now we have some exponential steps to see what is happening as we construct Cantors number. The 1st digit of anti-diag does not equal the 1st digit of the 1st computable numbers. Say it was 0.3.... That means anti diag could still be on the list of computable numbers, because x0, x1, x2, x4, x5, x6, x7, x8, x9 could contain anti-diag, all we know is it doesn¹t start with 3. Next digit, the second digit of the second computable number is 2, 0.32, we know anti-diag doesn¹t have a 2 next. That leaves us with x00, x01, x03, x04.. x09 x10, x01, x03, x04.. x09 x20, x21, x23, x24.. x29 .. x90, x91, x93, x94, x99 as long as 2 does not appear in the second position. Every iteration of Cantors function, it places further and further restrictions on the countable real. With inÞnite restrictions does it make a new number? Get real! Herc > > pointing out what the error is. Which line of the proof is wrong? > > That¹s what I would ask an objector. > The concept of unique number is wrong. > Ok. Then you are objecting to something prior to the proof. So why > bother discussing Cantor¹s proof at all? he¹s the one who claims anti-diag is unique. Here¹s an infnite list of reals 0.0xxxxxx.. 0.1xxxxxx.. 0.2xxxxxx.. 0.0xxxxxxx.. 0.3xxxxxx.. 0.5xxxxxx.. 0.8xxxxxx.. 0.1xxxxxxx.. 0.2xxxxxxxx.. 0.0xxxxxxx.. 0.1xxxxxxxx.. As you can see, 0.0xxxx.. appears repeatedly, so 0.0 is covered inÞnitely many times 0.1xxxxx.. appears an inÞnite number of times. It doesn¹t matter what the digits the are, they are all present. 0.abcxxx.. is present for EVERY a, b and c. 0.abcdefghijklmnopqrstuvwxyz...... is ON THE LIST for ALL values of a, b, c, d, e, ... z by extension every digit combination is present. You claim there is ONE digit that is different, but that digit CANNOT appear at digit position 1. 0.1xxxx 0.2xxxx 0.3xxxx these are all on the list of computable reals. 0.11xxxx.. 0.12xxxx.. 0.13xxsxx.. these are all on the list of computable reals. The contradictory digit on your list must be after the 2nd decimal place mustn¹t it? Your contradiction dissapears altogether because it cannot occur at a Þnite decimal. The digits 1, 2, 3, 4, 5 .. 9, 0 are virtually identical and interchangable, they merely adjust the region on the numberline but have *no semantic difference*, -- http://www.winternet.com/~mikelr/þame76.html === Subject: Re: New countable inÞniity logic > As all the programmers here know, the inÞnite list of all computable numbers UTM(n) neN > produces all numbers with every combination of digits. You cannot defeat inÞnity. Careful. This (countable) list of computable numbers contains all numbers with every FINITE combination (sequence of digits in the deminal expansion) of digits, and all numers with every REPEATING inÞnite decimal expansion, but only SOME numbers with a non-repeating inÞnite decimal expansion. > Say you have an *inÞnite* list of computable real numbers. I assume by an inÞnite list you mean an enumeration with cardinality Aleph_0. But you don¹t make clear whether or not you¹re considering a COMPLETE enumeration of ALL of the computable numbers. This is important. > Then Cantor comes along and shows an anti-diagonal. If the enumeration is not complete, then there is no contradiction that the diagonal is missing from the enumeration AND computable. The enumeration never claimed that it was complete. If the enumeration is complete, then the diagonal is, indeed, uncomputable. To see this, try to COMPUTE a COMPLETE enumeration of the computable numbers. Let¹s be sure we know what we mean by this. Ignoring digits to the left of the decimal point, such a computation would, for given i,j>=0, return the ith digit of the decimal expansion of the jth number in the list. A second program could then be written which called the above program with increasing k, with i=j=k, to get the kth digit of the kth computable number, and then alter it a la Cantor, to give the kth digit of a new number. And if all of this were possible, then, yes, it would look as if we had a new computable number not in the original enumeration, which would be a contradiction. But it isn¹t possible to perform this computation, because of the halting problem. We can¹t build a TM (or program a UTM) which enumerates ALL of the computable numbers, because we can only enumerate what¹s computable by enumerating TMs. But some TMs don¹t halt, and furthermore we can¹t write a general program to determine if an arbitrary TM will halt or not. Sooner or later, as we enumerate the TMs in order to enumerate ALL computable numbers, we will come to a TM which does not halt, and which our program cannot establish is non-halting. Thus our program will stall at this TM, and run forever trying in vain to calculate the kth digit of the computable number we¹re hoping it embodies. Now, if you can come up with a TM which computes a list of ALL computable numbers WITHOUT needing to enumerate TMS, then we will all have to think again. :) === Subject: Re: New countable inÞniity logic > I assume by an inÞnite list you mean an enumeration with cardinality > Aleph_0. An enumeration is a function, and so doesn¹t really have cardinality. What I meant to say is that the list itself has cardinality Aleph_0. > We can¹t build a TM (or program a UTM) which enumerates ALL of the > computable numbers, because we can only enumerate what¹s computable by > enumerating TMs. But some TMs don¹t halt, and furthermore we can¹t write a > general program to determine if an arbitrary TM will halt or not. Sooner or > later, as we enumerate the TMs in order to enumerate ALL computable numbers, > we will come to a TM which does not halt, and which our program cannot > establish is non-halting. Thus our program will stall at this TM, and run > forever trying in vain to calculate the kth digit of the computable number > we¹re hoping it embodies. This isn¹t to say that there isn¹t an enumeration of computable numbers, nor that there isn¹t a diagonalization of that enumeration! We can well-deÞne such things easliy, provided we can use expressions like the mth TM which halts in our deÞnition. Once we well-deÞne our enumeration of computable numbers, and well-deÞne our diagonalization, we have without doubt precisely described a particular, deÞnite, real number. But it is not computable! Because we cannot compute the enumeration. This sounds strange, but is no stranger really than deÞning sqrt(2) and then discovering it isn¹t the ratio of two integers. === Subject: Re: New countable inÞniity logic > Once we well-deÞne our enumeration of computable numbers, and well-deÞne > our diagonalization, we have without doubt precisely described a particular, > deÞnite, real number. But it is not computable! Because we cannot compute > the enumeration. One more thing to make this even clearer. We could design our enumeration so that the Þrst 1,000,000 computable numbers in the enumeration are generated by TMs known to halt, and only at the 1,000,001th start a systematic enumeration of TMs. According to this scheme, we could get the Þrst 1,000,000 digits of our uncomputable diagonal. Looks like progress! In fact, we could come up with all sorts of ways to delay the real search for a COMPLETE list. For any N, you can come up with a scheme which gives the Þrst N digits of the uncomptable diagonal *according to that scheme*. But to satisfy the judges, a certain single scheme (program) has to be completely deÞned beforehand which computes the nth digit no matter how large n is, AND is guaranteed to include ALL the computable numbers. Sooner or later, your program is going to have to start enumerating TMs, and then the halting problem will strike. === Subject: Re: New countable inÞniity logic > Once we well-deÞne our enumeration of computable numbers, and well-deÞne > our diagonalization, we have without doubt precisely described a > particular, > deÞnite, real number. But it is not computable! Because we cannot > compute > the enumeration. > One more thing to make this even clearer. > We could design our enumeration so that the Þrst 1,000,000 computable > numbers in the enumeration are generated by TMs known to halt, and only at > the 1,000,001th start a systematic enumeration of TMs. According to this > scheme, we could get the Þrst 1,000,000 digits of our uncomputable > diagonal. Looks like progress! > In fact, we could come up with all sorts of ways to delay the real search > for a COMPLETE list. For any N, you can come up with a scheme which gives > the Þrst N digits of the uncomptable diagonal *according to that scheme*. > But to satisfy the judges, a certain single scheme (program) has to be > completely deÞned beforehand which computes the nth digit no matter how > large n is, AND is guaranteed to include ALL the computable numbers. Sooner > or later, your program is going to have to start enumerating TMs, and then > the halting problem will strike. I call these doorman arguments, they stop computability even being an issue with regard to numbers. Some programs don¹t halt, we don¹t know which ones, does not detract from the fact UTM(n, 0) neN *contains* the full set of computable numbers. A different paradigm UTM(n, d) n,deN can even halt on a digit by digit basis, for each given digit d. This is just a Œhardware¹ issue, getting the desired subset out from the machine. I get this one all the time, all FINITE preÞxes, isn¹t that the same as ALL Þnite preÞxes, which is ALL preÞxes, which is every digit. The combinations are covered for inÞnitely long digit sequences, for unlimited length. Herc¹s theorem : An inÞnite set of digit sequences that has no bound to the length of the preÞxes containing every digit sequence combination contains every combination of inÞnite length. Herc === Subject: Re: New countable inÞniity logic [...] >>diagonal. Looks like progress! [...] >>Sooner >>or later, your program is going to have to start enumerating TMs, and then >>the halting problem will strike. (and then thunder? :) ) > I call these doorman arguments, they stop computability even being an issue with regard to numbers. > Some programs don¹t halt, we don¹t know which ones, does not detract from the fact UTM(n, 0) neN > *contains* the full set of computable numbers. A different paradigm UTM(n, d) n,deN can even halt > on a digit by digit basis, for each given digit d. This is just a Œhardware¹ issue, getting the desired subset out > from the machine. > I get this one all the time, all FINITE preÞxes, isn¹t that the same as ALL Þnite preÞxes, which is ALL preÞxes, > which is every digit. The combinations are covered for inÞnitely long digit sequences, for unlimited length. > Herc¹s theorem : > An inÞnite set of digit sequences that has no bound to the length of the preÞxes containing every digit sequence combination > contains every combination of inÞnite length. This is how Champernowne¹s irrational number begins in base 10: 0.123456789101112131415161718192021222324252627282930313233343 53637383940414 2434 44546474849505152535455565758596061626364656667686970717273747 57677787980818 28 38485868788899091929394959697989910010110210310410510610710810 91101111121131 14 11511611711811912012112212312412512612712812913013113213313413 51361371381391 40 14114214314414514614714814915015115215315415515615715815916016 11621631641651 66... /* credit due to Simon Plouffe, see: http://www.worldwideschool.org/library/books/sci/math/ MiscellaneousMathemati calConstants/toc.html */ In the list of digit sequences: 0.000000000000.. 0.1000000000.... 0.20000000. ... 0.90000000... 0.010000000... 0.02000000.. ... 0.99000000.... 0.0010000000... ... 0.999000000000... .... which I think contains all Þnite preÞxes, Champernowne¹s number won¹t appear. David Bernier === Subject: Re: New countable inÞniity logic > [...] >>diagonal. Looks like progress! >> > [...] >>Sooner >>or later, your program is going to have to start enumerating TMs, and then >>the halting problem will strike. >> > (and then thunder? :) ) > I call these doorman arguments, they stop computability even being an issue with regard to numbers. > Some programs don¹t halt, we don¹t know which ones, does not detract from the fact UTM(n, 0) neN > *contains* the full set of computable numbers. A different paradigm UTM(n, d) n,deN can even halt > on a digit by digit basis, for each given digit d. This is just a Œhardware¹ issue, getting the desired subset out > from the machine. > I get this one all the time, all FINITE preÞxes, isn¹t that the same as ALL Þnite preÞxes, which is ALL preÞxes, > which is every digit. The combinations are covered for inÞnitely long digit sequences, for unlimited length. > Herc¹s theorem : > An inÞnite set of digit sequences that has no bound to the length of the preÞxes containing every digit sequence combination > contains every combination of inÞnite length. > This is how Champernowne¹s irrational number begins in base 10: > 0.123456789101112131415161718192021222324252627282930313233343 536373839404142 434 > 44546474849505152535455565758596061626364656667686970717273747 576777879808182 8 > 38485868788899091929394959697989910010110210310410510610710810 911011111211311 4 > 11511611711811912012112212312412512612712812913013113213313413 513613713813914 0 > 14114214314414514614714814915015115215315415515615715815916016 116216316416516 6... > /* credit due to Simon Plouffe, see: > http://www.worldwideschool.org/library/books/sci/math/ MiscellaneousMathematic alConstants/toc.html > */ > In the list of digit sequences: > 0.000000000000.. > 0.1000000000.... > 0.20000000. > ... > 0.90000000... > 0.010000000... > 0.02000000.. > ... > 0.99000000.... > 0.0010000000... > ... > 0.999000000000... > .... > which I think contains all Þnite preÞxes, > Champernowne¹s number won¹t appear. right! lucky I posted this a few minutes before being corrected! any chance of retracting that one? {0.1 0.2... 0.11, 0.12..} is a counter example Herc === Subject: Re: New countable inÞniity logic > Herc¹s theorem : > An inÞnite set of digit sequences that has no bound to the length of the preÞxes containing every digit sequence combination > contains every combination of inÞnite length. any chance of retracting that one? {0.1 0.2... 0.11, 0.12..} is a counter example Herc === Subject: Re: New countable inÞniity logic Originator: joshp@bayes.joshpurinton.com (Josh Purinton) >Lets rearrange the list into a tree. Roughly speaking, Cantor proved (you might say, tried to prove) that no list can contain all the reals. But since its impossible to make a list of all the branches of your tree, your tree is not a counterexample to Cantor¹s conclusion. The reason for this has to do with the deÞnition of a list. Again, roughly speaking, each element of a list has a natural number index giving its position in the list. Do the lists of which you speak have this property? -- Josh Purinton === Subject: Re: New countable inÞniity logic >Lets rearrange the list into a tree. > Roughly speaking, Cantor proved (you might say, tried to prove) that > no list can contain all the reals. But since its impossible to make a > list of all the branches of your tree, your tree is not a counterexample > to Cantor¹s conclusion. > The reason for this has to do with the deÞnition of a list. > Again, roughly speaking, each element of a list has a natural number > index giving its position in the list. Do the lists of which you speak > have this property? Function for generating what I believe to be |-|erc¹s computable list: Convert the natural number directly to its natural decimalic expansion by placing a decimal point in front of the number; unless it has already been used, in which case a decimal point and the least number of zeroes will be added as a place holder in front of the number to form an unused number. Applying this method at the Þrst stage gives 1: 0.100... 2: 0.200... : 8: 0.800... 9: 0.900... At the second stage, 10^1 (10) thru 99, the same procedure is followed except that all inputs that would otherwise cause a replica output (10, 20, ..., 90 giving 0.1, 0.2, ..., 0.9) generate using the second part of the method; namely, place a zero placeholder in front of the otherwise repeated number to obtain (0.01, 0.02, ..., 0.09) or (1 to 9)/100. This method at the second stage produces 10: 0.01000... 11: 0.11000... 12: 0.12000... : 20: 0.02000... 21: 0.21000... : 99: 0.99000... At the third stage, 10^2 (100) thru 999, the same procedure is followed and in this case all inputs that would otherwise cause a repeating output (100, 110, 120, ..., 200, 210, ..., 990) generate using the second part of the method namely placing either one or two zero placeholders in front of the usual numbers (0.001, 0.011, 0.012, ..., 0.002, 0.021, ..., 0.099) or (1 to 99)/1000 This method of generating the list is equivalent to a method of rewriting and reordering the list at every power of ten to produce |-|erc¹s more orderly list (same set). (1 thru 9 ): divide each number by10: Stage1: 0.1, 0.2, 0.3 ... 0.9 (1 thru 99): divide each number by 100: Stage 2: 0.01, 0.02, 0.03, ..., 0.99 (1 thru 999): divide each number by 1000 Stage 3: 0.001, 0.002, 0.003, ..., 0.999 At each stage (power of ten), these sets have the same members as the set enumerated above by the speciÞed algorithm and are thus equivalent sets. OR EXPRESSED Stage 1 Stage 2 Stage 3 n N n N n N 10^1 10^ 2 10^3 __ _____ __ _____ __ _____ 1: 0.01000... 1: 0.001000... 2: 0.002000... : 2: 0.02000... 20: 0.02000... : : 9: 0.09000... 90: 0.090000... : : 99: 0.099000... 1: 0.1000... 10: 0.10000... 100: 0.100000... 11: 0.11000... : : 9: 0.9000... 90: 0.90000... 900: 0.900000... : : 99: 0.99000... 990: 0.990000... : 999: 0.999000... |-|erc¹s point that the Cantor diagonal method is not generating a new Þnite number for this list seems correct. Further to the extent that one allows n to approach inÞnity as the naturals are agreed to do, any iniÞnite decimalic number in the range 0 - 1 (corresponding to any Cantoresk named diagonal) will also be approached and can be found on the list to the same number of digits as the *namer* can explicitly specify (truncate) that number in decimalic form. In other words there is no Þrst digit which a Cantoresk diagonal namer can Þrst name that is not found on the list. These diagonal arguments seem faulty. As n approaches inÞnity, the new lowest number in the list approaches the number zero with the smallest inÞntesimal (1-0.999... = 0.00...001) and the largest number in the list approaches the the number one with the same smallest inÞntesimal (difference) from one (1 - 0.999...=0?). All numbers in between these two extremes are either listed reals (those that truncate and end in zeroes) or are reals that are being approached inÞntesimally as n approaches inÞnity. Since the counting numbers are inÞnite in theoretical range (not practice), the common sense notion that as n gets larger and larger, that it is in fact without bound, all of the real numbers not speciÞcally listed are approached *simulatneously* as n approaches inÞnity. Under such circumstances, to deny that the reals are countable would seem to be tantamount to arguing that the counting numbers (natural numbers that are inÞnite in extent) themselves are not countable. After all if you accept that by counting high enough and using the one to one correspondence above, the N may approach arbtrarily close to any particular one of the continuing (eg repeating or irrational) decimalically expanded reals (e.g. 1/3,1/7, or 3^0.5 / 6) so as to render the difference (delta = Nr-N) between the N=f(n) and the speciÞc real (Nr) smaller than any speciÞable diifference. If there can be no speciÞable difference between N=f(n) and the arbitary real Nr, what rationale is used to practically distinguish such nonspeciÞable differences? How can one further proceed to claim that 0.9999... = 1? Don Whitehurst whitat@umndot.edu === Subject: Re: New countable inÞniity logic >Lets rearrange the list into a tree. > Roughly speaking, Cantor proved (you might say, tried to prove) that > no list can contain all the reals. But since its impossible to make a > list of all the branches of your tree, your tree is not a counterexample > to Cantor¹s conclusion. > The reason for this has to do with the deÞnition of a list. > Again, roughly speaking, each element of a list has a natural number > index giving its position in the list. Do the lists of which you speak > have this property? if you can¹t iterate through a tree data structure you never studied programming Herc === Subject: Re: Alternative sci.math archive Discussion, linux) > However, I did Þnally Þnd the message where he commented on my > location through the Math Forum. Then I went and checked: they are > impression the comments preceded the mongrel post. They were actually > made a few months later. Mea culpa grandissima. Though, the apparent root of that thread is mysteriously missing. Man, them historians will curse James for this. Like drop-kicking old Chinese vases for sport or something. -- Run mathematicians, RUN!!! I¹m coming for you. It may take a few months, but I¹ll get [computer veriÞcation of my proof] and then your lives will be ended as you previously knew it. -- JSH meets PVS === Subject: multi-base converter programs Are there any custom multi-base-n converter programs that handle n-decimals? So if base-12 is chosen, 1/9 would show 0.14 - http://mysite.verizon.net/vze8adrh/news.html (proÞle) --Tim923 My email is valid. === Subject: Re: multi-base converter programs > Are there any custom multi-base-n converter programs that handle > n-decimals? > So if base-12 is chosen, 1/9 would show 0.14 The unix calculator Œbc¹ does this. A Windows version is included in the ports of common GNU utilities to native Win32 found at Although for some reason this happens: H:>bc bc 1.05 Copyright 1991, 1992, 1993, 1994, 1997, 1998 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty¹. scale=10 obase=12 1/9 .13BBBBBBBB -- Larry Lard Replies to group please === Subject: Re: multi-base converter programs posting-account=UtgH7gwAAACpBhTelVPOXNP7RAfbtQrK > Are there any custom multi-base-n converter programs that handle > n-decimals? > So if base-12 is chosen, 1/9 would show 0.14 > http://mysite.verizon.net/vze8adrh/news.html (proÞle) --Tim923 My email is valid. Python and the GMPY module can do bases 2-32. > import gmpy > f = þoat(1)/9 > for base in range(2,33): print Base:,base,gmpy.fdigits(f,base,8,0,0,1) Base: 2 mpf(Œ1.11001e-4¹) Base: 3 mpf(Œ1.e-2¹) Base: 4 mpf(Œ1.3013013e-2¹) Base: 5 mpf(Œ2.3421024e-2¹) Base: 6 mpf(Œ4.e-2¹) Base: 7 mpf(Œ5.3053053e-2¹) Base: 8 mpf(Œ7.0707071e-2¹) Base: 9 mpf(Œ0.1¹) Base: 10 mpf(Œ0.11111111¹) Base: 11 mpf(Œ0.12498612¹) Base: 12 mpf(Œ0.14¹) Base: 13 mpf(Œ0.15a15a16¹) Base: 14 mpf(Œ0.17ac6318¹) Base: 15 mpf(Œ0.1a¹) Base: 16 mpf(Œ0.1c71c71c¹) Base: 17 mpf(Œ0.1f1f1f1f¹) Base: 18 mpf(Œ0.2¹) Base: 19 mpf(Œ0.22222222¹) Base: 20 mpf(Œ0.248hfb24¹) Base: 21 mpf(Œ0.27¹) Base: 22 mpf(Œ0.29h29h2a¹) Base: 23 mpf(Œ0.2chka52d¹) Base: 24 mpf(Œ0.2g¹) Base: 25 mpf(Œ0.2jb2jb2j¹) Base: 26 mpf(Œ0.2n2n2n2n¹) Base: 27 mpf(Œ0.3¹) Base: 28 mpf(Œ0.33333333¹) Base: 29 mpf(Œ0.36cpmg36¹) Base: 30 mpf(Œ0.3a¹) Base: 31 mpf(Œ0.3do3do3e¹) Base: 32 mpf(Œ0.3hose73i¹) === Subject: Re: multi-base converter programs The ones I¹ve seen seem too frightened to consider n-decimals in other bases. - http://mysite.verizon.net/vze8adrh/news.html (proÞle) --Tim923 My email is valid. === Subject: Re: Jordan theorem ^OX9W/.#XpUmm`>TD2zNE-t}emfPkFR.Z5`þY:3QYT$>dUwN^sm;MBV: F7aL9x*q!` ln!l}>Y6_45$%R|P7DSrBkEph@1-;P*s~F_28vO@e4p/¹>}Pc?@rl8cz] d9RXOt Is there somewhere on the Web (or in one of the classical books, by Rudin > for instance) a proof of the general version (simple C^0 closed curve C => > 2 connected components in R^2- C, and C common boundary of those > components)? The classical book, Rolfsen¹s _Knots and Links_, has a proof in the very Þrst chapter. === Subject: Re: Improving Archimedes >> All we know that Archimedes calculated Pi by doubling the >> sides of an inscrit exagon and of a circumscrit exagon. >> The limit of the perimeter of both is the circumference. >> That limit divided by the diameter is Pi. In modern algebra: >> Ao = 3*sqr(3)/2 ; Bo = Ao/2 >> A(n+1) = 2*An*Bn/(An + Bn) B(n+1) = sqr[A(n+1)*Bn] >> Iterating, the values of A(n+1) and B(n+1) aproximate to Pi >> Perhaps Archimedes noted that the mean don¹t improve to much >> the result. Perhaps he noted that Pi~[A(n+1) + 2*B(n+1)]/3 was >> much better. But as a good mathematician he did not publish >> that formula because he could not to demonstrate it. >> Without the improvement [A(4)+ B(4)]/2 = 3.1393 >> With the improvement Pi(4) = 3.141592... > Here is a comparison of the two results: > Mean of (An + Bn)/2 (An + 2*Bn)/3 > 1.- 3.23205080 3.1547005 > 2.- 3.16060942 3.14234911 > 3.- 3.14614427 3.14163905 > 4.- 3.14271820 3.14159554 > 5.- 3.14187327 3.14159228 > 6.- 3.14166276 3.14159266 > 7.- 3.14161017 3.14159265 (Correct to the 9th digit) > It is possible to Þnd an explanation of the efectiveness of > this improvement? > Sin(x) ~ x - x^3/6; tan(x) ~ x + x^3/3. 2*sin(x) + tan(x) ~ 3x ; sin(x) is 1/2 side of polygon inscrit. tan(x) is 1/2 side of polygon circumscrit. That¹s why Archimedes, if he knew the improvement, was not capable of furnish a demonstration. === Subject: Re: Talk about Attacking the Conclusions > JSH constantly whines that everyone is attacking his conclusions and > that this is a fallacy because his suppositions and logic are intact. > Aside from the fact that this isn¹t true (people have been attacking > his logic and pointing out gaping holes) it¹s funny to point out that > he does the same thing. All he¹ll do is attack the conclusions posters > have drawn based on his inacuracies. He won¹t actually directly attack > or even acknowledge the points they make. In essence he¹s attacking > their conclusions. > JSH constantly whines that everyone is attacking his conclusions and > that this is a fallacy because his suppositions and logic are intact. > Aside from the fact that this isn¹t true (people have been attacking > his logic and pointing out gaping holes) it¹s funny to point out that > he does the same thing. All he¹ll do is attack the conclusions posters > have drawn based on his inacuracies. He won¹t actually directly attack > or even acknowledge the points they make. In essence he¹s attacking > their conclusions. JSH constantly whines that everyone is attacking his conclusions and that this is a fallacy because his suppositions and logic are intact. Aside from the fact that this isn¹t true (people have been attacking his logic and pointing out gaping holes) it¹s funny to point out that he does the same thing. All he¹ll do is attack the conclusions posters have drawn based on his inacuracies. He won¹t actually directly attack or even acknowledge the points they make. In essence he¹s attacking their conclusions. === Subject: Re: Have you tried MIT¹s openCourseware? > Looking MIT¹s opencourseware (OCW) for Analysis I (Fall 2002), it doesn¹t > seem very helpful. There is only a listing of chapers you should cover in > some time frame. Assingments are also listed. Where exactly are the > explanations besides the book? I could buy the book and learn on my own. > What is the advantage of using MIT OCW? > Brett You may Þnd the Fall 2000 Web site interesting. It is at http://www-math.mit.edu/~rbm/18.101.html David Ames === Subject: Re: JSH: The object ring does not exist. > Simpler: (2(v+w)+1)(14(v-w)-3) = 28vv+8v+1 - 4(7ww+5w+1) = 0 > So -1/2 = v+w or v-w = 3/14 is in Z[v,w] < J > Simpler: deduce 1/2 in J via v = i/2, w = (1+i)/2, > namely (2(v+w)-1)(2(v-w)+1) = 4vv+1 - 2(2ww-2w+1) = 0 Better: (2(v+w)-1)(5(v-w)-2) = 10vv-9v+1 -10ww+w+1 = 0 Hence -1/2 = v+w or v-w = 2/5 is in Z[v,w] < J with v root of 10vv-9v+1, w root of -10ww+w+1 This avoids the triviality of the above examples where 1/2 is already in Z[v], which is clear from the minimal polys: 28vv+8v+1, 4vv+1; e.g -1 = 28vv+8v = 2(14vv+4v). I presume Dik desires a _nontrivial_ example, i.e. one satisfying Z[v,w]/Q > Z but Z[v]/Q = Z[w]/Q = Z. Below I show the better example here satisÞes this. In passing I prove some useful results characterizing just what types of non-integral extensions introduce proper fractions, a topic which has been lurking in the background of many threads here on related topics. First, as remarked above, either 1/2 or 2/5 is in Z[v,w] so, indeed, Z[v,w]/Q > Z introduces fractions. But the intermediate extensions don¹t introduce fractions, i.e. CLAIM R/Q = Z for R = Z[v] (similarly for R = Z[w]) PROOF By the Corollary to the Theorem below, because f-f(0) is primitive, it follows that every ideal in Z survives when it is extended to R = Z[v] = Z[x]/(f(x)) i.e. (n) < 1 in Z => (n) < 1 in R, which implies that R contains no proper fraction m/n, (m,n) = 1, else Z Bezout => j m + n k = 1 for some j,k in Z => j m/n + k = 1/n in R => (n) = 1 in R QED THEOREM Let P be a prime ideal in the domain D. P extends to 1 in R = D[x]/(f(x)), i.e. PR = R, <=> (P,f) = (P,f0) = 1, where f0 := f(0) i.e. iff constant coef f0 of f is coprime to P and all other coefs of f are equal zero (mod P). PROOF P = 1 in R <=> (P,f)=1 in D[x] <=> (f)=1 in D/P[x] <=> f = f0 = unit in D/P (since D/P domain via P prime) <=> (P,f) = (P,f0) = 1. QED COROLLARY With same notation, if f-f(0) is primitive, i.e. if ideal generated by all coefs of f except its constant coef is equal to 1, then every prime ideal P in D has its extension in R unequal to 1, i.e. P survives in R; hence every ideal I of D survives in R (via I

0 therefore f != f(0) (mod P). This is one of the fundamental properties of integral extensions versus non-integral extensions: integral extension are always survival extensions but, as we learned from the above Theorem not all non-integral extensions need be survival extensions. For further discussion see my prior posts [1]. --Bill Dubuque === Subject: Re: JSH: The object ring does not exist. > Better: (2(v+w)-1)(5(v-w)-2) = 10vv-9v+1 -10ww+w+1 = 0 > Hence -1/2 = v+w or v-w = 2/5 is in Z[v,w] < J Should be 1/2 = v+w ... --Bill Dubuque === Subject: Re: JSH: Now a change >> This all, again, boils down to the requirement that the intersection of >> that ring and Q is Z. There is not a single largest such ring. There >> are many such rings so that if you add a single number the intersection >> will include numbers from Q not in Z. For instance, start with the >> algebraic integers. Now go two ways: >> 1. Start adding a single root of 7x^2 + 5x + 1; continue adding numbers >> until you can not add any number anymore without violating the >> requirement. >> 2. Start adding a single root of 28x^2 + 8x + 1 and continue in a similar >> way. > If r is a root of f(x) = 28x^2 + 8x + 1 then 1/(2r) is a root of x^2+4x+7, > and so an algebraic integer. That puts 1/2 into the extended ring. It is much simpler: that 2|1 in any ring containing r is clear from its min.poly: 1 = -2 (14 r^2 + 4r) To avoid this ensure min.poly f has gcd of nonconstant coefs = 1. In other words, choose f(x) so that f(x)-f(0) is primitive. See my prior post [1] for much more about this. > Why not just use the other root of 7x^2 + 5x + 1? Because the current deÞnition of the object ring J speciÞes that it contains at least one root of reverse-monic polynomials; it needn¹t contain both roots. So Dik sought a simple example where adjoining one such root from either polynomial does not introduce proper fractions but adjoining both roots does, i.e. Z[v]/Q = Z[w]/Q = Z but Z[v,w]/Q > Z. In [1] I gave a correct example of such behavior, namely: (2(v+w)-1)(5(v-w)-2) = 10vv-9v+1 -10ww+w+1 = 0 Hence -1/2 = v+w or v-w = 2/5 is in Z[v,w] < J with v root of 10vv-9v+1, w root of -10ww+w+1 See [1] for much further detail. --Bill Dubuque === Subject: Well, Kolker? Re: Uncle assAl: (SR) Lorentz t¹, x¹ = Intervals > Apparently you do not know the difference between empirical > falsiÞability and mathematical inconsistency. Your other postings on > the invariance of Maxswell¹s equations under Galilean transform is > indicative you do not know dickey-doo about mathematics. We know that > Maxwell¹s equations are not microscopically true, but they are > consistent and they are NOT galilean invariant. Congratulations! You have proved yourself capable of being at least a jerk, if not an ass, and of not having sufÞcient honesty to actually respond to the details of logic/etc. So, can you now prove yourself capable of relenting in your desire to prove irrelevant to any actual discussion, and do something helpful? Maxwell and invariance are an important combination of topics and as many expressions as I know of for E, H, B, etc, I do not know just what exemplars of them would be best for demonstrating particulars of their transformation by Newton-theoretic coordinate tranformations. The Œproblem¹ is different than in the case of the Lorentz transforms of Maxwell because in the Newton case it actually is the coordinates x,y,z that are transformed, rather than - essentially - the inverse of the coordinates. So, please provide a set of expressions - appropriate for full exposition of Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate expressions. Obviously (ha!) the result would be that Þnally I come headsup (as we poker players say) with my tremendous error in thinking that transforming Maxwell Newton-wise without the three strawmen corruptions will prove invariant. eleaticus > Bob Kolker === Subject: Re: Well, Kolker? Re: Uncle assAl: (SR) Lorentz t¹, x¹ = Intervals [snip crap] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Well, Gisse? Re: Uncle assAl: (SR) Lorentz t¹, x¹ = Intervals > Let me guess, you are going to spawn *yet another* thread about how I > am a liar or something else? Congratulations! You have proved yourself capable of being at least a jerk, if not an ass, and of not having sufÞcient honesty to actually respond to the details of logic/etc. So, can you now prove yourself capable of relenting in your desire to prove irrelevant to any actual discussion, and do something helpful? Maxwell and invariance are an important combination of topics and as many expressions as I know of for E, H, B, etc, I do not know just what exemplars of them would be best for demonstrating particulars of their transformation by Newton-theoretic coordinate tranformations. The Œproblem¹ is different than in the case of the Lorentz transforms of Maxwell because in the Newton case it actually is the coordinates x,y,z that are transformed, rather than - essentially - the inverse of the coordinates. So, please provide a set of expressions - appropriate for full exposition of Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate expressions. Obviously (ha!) the result would be that Þnally I come headsup (as we poker players say) with my tremendous error in thinking that transforming Maxwell Newton-wise without the three strawmen corruptions will prove invariant. eleaticus > Oh noes! === Subject: Re: Well, Gisse? Re: Uncle assAl: (SR) Lorentz t¹, x¹ = Intervals [snip crap] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Well, Mori-Max Re: Uncle assAl: (SR) Lorentz t¹, x¹ = Intervals > Let me guess, you are going to spawn *yet another* thread about how I > am a liar or something else? > Well Eric, he *is* on the troll shoulder list... grin.. you elucidate at your > peril.. Congratulations! You have proved yourself capable of being at least a jerk, if not an ass, and of not having sufÞcient honesty to actually respond to the details of logic/etc. So, can you now prove yourself capable of relenting in your desire to prove irrelevant to any actual discussion, and do something helpful? Maxwell and invariance are an important combination of topics and as many expressions as I know of for E, H, B, etc, I do not know just what exemplars of them would be best for demonstrating particulars of their transformation by Newton-theoretic coordinate tranformations. The Œproblem¹ is different than in the case of the Lorentz transforms of Maxwell because in the Newton case it actually is the coordinates x,y,z that are transformed, rather than - essentially - the inverse of the coordinates. So, please provide a set of expressions - appropriate for full exposition of Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate expressions. Obviously (ha!) the result would be that Þnally I come headsup (as we poker players say) with my tremendous error in thinking that transforming Maxwell Newton-wise without the three strawmen corruptions will prove invariant. eleaticus === Subject: Re: Well, Mori-Max Re: Uncle assAl: (SR) Lorentz t¹, x¹ = Intervals [snip crap] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Well, Uncle assAl? Re: Invariant Galilean Transformations (FAQ) On All Laws > With your permission, I will also ram your exposition down his > stooopid face every time he trolls his crap. Congratulations! You have proved yourself capable of being at least a jerk, if not an ass, and of not having sufÞcient honesty to actually respond to the details of logic/etc. So, can you now prove yourself capable of relenting in your desire to prove irrelevant to any actual discussion, and do something helpful? Maxwell and invariance are an important combination of topics and as many expressions as I know of for E, H, B, etc, I do not know just what exemplars of them would be best for demonstrating particulars of their transformation by Newton-theoretic coordinate tranformations. The Œproblem¹ is different than in the case of the Lorentz transforms of Maxwell because in the Newton case it actually is the coordinates x,y,z that are transformed, rather than - essentially - the inverse of the coordinates. So, please provide a set of expressions - appropriate for full exposition of Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate expressions. Obviously (ha!) the result would be that Þnally I come headsup (as we poker players say) with my tremendous error in thinking that transforming Maxwell Newton-wise without the three strawmen corruptions will prove invariant. eleaticus > -- > Uncle Al > http://www.mazepath.com/uncleal/ > (Toxic URL! Unsafe for children and most mammals) > http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: Well, Uncle assAl? Re: Invariant Galilean Transformations (FAQ) On All Laws [snip crap] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Well, McAnal? Re: Invariant Galilean Transformations (FAQ) On All Laws > Certainly. It is irritating when an individual such as Eleaticus, who has > never learnt multivariable calculus, and who obviously knows nothing about > it, presumes to lecture people who actually do know about the subject. Congratulations! You have proved yourself capable of being at least a jerk, if not an ass, and of not having sufÞcient honesty to actually respond to the details of logic/etc. So, can you now prove yourself capable of relenting in your desire to prove irrelevant to any actual discussion, and do something helpful? Maxwell and invariance are an important combination of topics and as many expressions as I know of for E, H, B, etc, I do not know just what exemplars of them would be best for demonstrating particulars of their transformation by Newton-theoretic coordinate tranformations. The Œproblem¹ is different than in the case of the Lorentz transforms of Maxwell because in the Newton case it actually is the coordinates x,y,z that are transformed, rather than - essentially - the inverse of the coordinates. So, please provide a set of expressions - appropriate for full exposition of Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate expressions. Obviously (ha!) the result would be that Þnally I come headsup (as we poker players say) with my tremendous error in thinking that transforming Maxwell Newton-wise without the three strawmen corruptions will prove invariant. eleaticus > David > ----- === Subject: Re: Well, McAnal? Re: Invariant Galilean Transformations (FAQ) On All Laws [snip crap] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Well, Paul? Re: A SR-cult fraud and corruption (Rev A) Congratulations! You have proved yourself capable of being at least a jerk, if not an ass, and of not having sufÞcient honesty to actually respond to the details of logic/etc. So, can you now prove yourself capable of relenting in your desire to prove irrelevant to any actual discussion, and do something helpful? Maxwell and invariance are an important combination of topics and as many expressions as I know of for E, H, B, etc, I do not know just what exemplars of them would be best for demonstrating particulars of their transformation by Newton-theoretic coordinate tranformations. The Œproblem¹ is different than in the case of the Lorentz transforms of Maxwell because in the Newton case it actually is the coordinates x,y,z that are transformed, rather than - essentially - the inverse of the coordinates. So, please provide a set of expressions - appropriate for full exposition of Maxwell¹s - for Ex, Ey. Ez, etc, complete with explicit coordinate expressions. Obviously (ha!) the result would be that Þnally I come headsup (as we poker players say) with my tremendous error in thinking that transforming Maxwell Newton-wise without the three strawmen corruptions will prove invariant. eleaticus > Paul === Subject: Re: Well, Paul? Re: A SR-cult fraud and corruption (Rev A) [snip crap] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Psychotic ineducable boring troll Eleaticus, Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t¹ = t, x¹ = x - vt, y¹ = y, z¹ = z. His refusal to accept that t¹ must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to Þelds over space and time (electric and magnetic Þelds for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt¹ = d/dt + v d/dx, d/dx¹ = d/dx, d/dy¹ = d/dy, d/dz¹ = d/dz. This shows the necessity of introducing a new variable t¹, since partial differentiation with respect to t¹ (constant x¹, y¹, z¹) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt¹ = dt/dt¹ d/dt + dx/dt¹ d/dx + dy/dt¹ d/dy + dz/dt¹ d/dz, d/dx¹ = dt/dx¹ d/dt + dx/dx¹ d/dx + dy/dx¹ d/dy + dz/dx¹ d/dz, d/dy¹ = dt/dy¹ d/dt + dx/dy¹ d/dx + dy/dy¹ d/dy + dz/dy¹ d/dz, d/dz¹ = dt/dz¹ d/dt + dx/dz¹ d/dx + dy/dz¹ d/dy + dz/dz¹ d/dz. The presence of the term involving d/dx in the expression for d/dt¹ is indicative of the fact that x depends on t¹ (x¹, y¹, z¹, being held constant), as can be seen from the fact that the coefÞcient of d/dx in the expression for d/dt¹ is dx/dt¹. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt¹ is indicative of t¹ depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation. The Þrst advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell¹s Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y - v B_z, E_z¹ = E_z + v B_y, B_x¹ = B_x, B_y¹ = B_y, B_z¹ = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x¹ = E_x, E_y¹ = E_y, E_z¹ = E_z, B_x¹ = B_x, B_y¹ = B_y + v/c^2 E_z, B_z¹ = B_z - v/c^2 E_y, rho¹ = rho, J_x¹ = J_x - v rho, J_y¹ = J_y, J_z¹ = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell¹s Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM Þeld for the two cases are inconsistent with each other. The transformation law for the EM Þeld which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM Þeld which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell¹s equations are invariant under the Lorentz Transformation, with transformation laws: E_x¹ = E_x, E_y¹ = gamma (E_y - v B_z), E_z¹ = gamma (E_z + v B_y), B_x¹ = B_x, B_y¹ = gamma (B_y + v/c^2 E_z), B_z¹ = gamma (B_z - v/c^2 E_y), rho¹ = gamma (rho - v/c^2 J_x), J_x¹ = gamma (J_x - v rho), J_y¹ = J_y, J_z¹ = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity. http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf http://users.powernet.co.uk/bearsoft/Paper6.pdf http://users.powernet.co.uk/bearsoft/LPHrel.html Longitudinal and transverse mass http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Quadratic Matrix Equation Consider the matrix equation: lambda^2*I_n - lambda*D - H = 0, where lambda is a scalar, I_n the n x n identity, D a diagonal n x n matrix and H an n x n matrix whose eigenvalues are known. Is it possible to solve for the 2*n possible values for lambda? Note that the problem simpliÞes if the diagonal entries of D are all the same, but I¹m interested in the general solution. Any ideas?! Josh === Subject: Re: Quadratic Matrix Equation X-RFC2646: Format=Flowed; Original > Consider the matrix equation: > lambda^2*I_n - lambda*D - H = 0, > where lambda is a scalar, I_n the n x n identity, D a diagonal n x n > matrix and H an n x n matrix whose eigenvalues are known. > Is it possible to solve for the 2*n possible values for lambda? Note > that the problem simpliÞes if the diagonal entries of D are all the > same, but I¹m interested in the general solution. Any ideas?! > Josh If the eigenvalues are distinct, then you can write H = P D¹/P so, use multiply both sides of your equation by P and /P, and you get something like this: L^2*I - L M - D¹ = 0 Which implies that M and H are similar(well, they both are diagonalizable, so ofcourse) subtracting the two equations give L(M - D) + (H - D¹) = 0 or LB - C = 0 then if B is similar to a diagonal so that B = SD¹¹/S you get LD¹¹ - E = 0 now, the crucial step where L^2 was removed didn¹t actually depend on H being diagonalizable, you can actually use any two matricies P and D¹ such that H = PD¹/P and you can get rid of L^2.... though, you will have to check that L works cause maybe its possible to pick up extraneous solutions( haven¹t really checked this method out, since I just came up with it... and so I could be missing the point...). === Subject: Re: Quadratic Matrix Equation >Consider the matrix equation: > lambda^2*I_n - lambda*D - H = 0, >where lambda is a scalar, I_n the n x n identity, D a diagonal n x n >matrix and H an n x n matrix whose eigenvalues are known. >Is it possible to solve for the 2*n possible values for lambda? Note >that the problem simpliÞes if the diagonal entries of D are all the >same, but I¹m interested in the general solution. Any ideas?! I suspect you don¹t mean that equation: it implies H is a linear combination of I and D (and in particular must be diagonal), and there will be at most one possible value for lambda if the diagonal entries of D are not all the same. Do you mean (lambda^2 I - lambda D - H) v = 0 where v is a nonzero vector? This is equivalent to the ordinary 2n x 2n eigenvector equation M x = lambda x [ use Þxed-width font] [ 0 I ] [ v ] where in block-matrix form M = [ H D ] and x = [ w ], for then M x = lambda x becomes w = lambda v H v + D w = lambda w i.e. H v + lambda D v = lambda^2 v. However, you can also get the lambda values directly as the roots of the polynomial det(lambda^2 I - lambda D - H). Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Quadratic Matrix Equation Of course, you are correct. My original post was in error, but you have anticipated what my real question was. Let me reformulate the question. Let D = diag(d_i), where the d_i are possibly different. Let H be Hurwitz (i.e., its eigs in the open left-half complex plane). For what values of d_i is M (as you have written below) Hurwitz? If the d_i¹s are all the same (say d_i = d), then I believe d < 0 solves the problem. But what about the general case? I¹m puzzled, as it seems this should be relatively simple. Josh > I suspect you don¹t mean that equation: it implies H is a linear > combination of I and D (and in particular must be diagonal), and there > will be at most one possible value for lambda if the diagonal entries > of D are not all the same. Do you mean > (lambda^2 I - lambda D - H) v = 0 > where v is a nonzero vector? This is equivalent to the ordinary > 2n x 2n eigenvector equation M x = lambda x > [ use Þxed-width font] > [ 0 I ] [ v ] > where in block-matrix form M = [ H D ] and x = [ w ], for then > M x = lambda x becomes > w = lambda v > H v + D w = lambda w > i.e. H v + lambda D v = lambda^2 v. > However, you can also get the lambda values directly as the roots of the > polynomial det(lambda^2 I - lambda D - H). === Subject: Re: Quadratic Matrix Equation >Let D = diag(d_i), where the d_i are possibly different. Let H be >Hurwitz (i.e., its eigs in the open left-half complex plane). For >what values of d_i is M (as you have written below) Hurwitz? If the >d_i¹s are all the same (say d_i = d), then I believe d < 0 solves the >problem. But what about the general case? I¹m puzzled, as it seems >this should be relatively simple. In other words, if all roots of f(lambda) = det(lambda I - H) are in the left half plane, when are all roots of g(lambda) = det(lambda^2 I - lambda D - H) in the left half plane? In the case all d_i = d, g(lambda) = f(lambda^2 - d lambda). Since all you know about f is that its roots are in the open left half plane, what you need is that the function z -> z^2 - d z should map the closed right half plane into itself. Unfortunately, that never happens: the image of the closed right half plane under this transformation will always be either the whole plane (if Re(d) >= 0) or the region to the right of a parabola opening to the left. In the case where the d_i are not all equal, there¹s apparently no nice relation between g and f; in any case I would be very surprised if you could ever conclude that the roots of g are all in the left half plane given that the roots of f are there. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: phase of symmetrical rectangular fn hello I am reading a book on DSP and a diagram shows the DFT(Discrete fourier transform) of a rectangluar fn centered abt 0 the real part of the DFT is the sinc fn the imaginary part is zero throughout the phase as shown in the diagram is a wave alternating pi or in the -ve time axis and -pi and 0 in the positive axis I cant understand how the phase can be pi or -pi it should always be = zero accdng to me because the imaginary part of the DFT is always zero. and phase = tan_inverse ( Imaginary part / real part ) so if Imaginary part is zero throughout...how could phase ever be -pi or +pi pls advise what im missing? === Subject: Re: phase of symmetrical rectangular fn You should tell us what book you are referring to: Title, author, publisher. Eckard Blumschein === Subject: Generate all combinations in a lotto game I would like to generate all 324632 combiations in the 5/35 lotto game and eventually all combinations in any n/N lotto game. What kind of mathematics do I need to employ and is there a site where it is available? Stig Holmquist === Subject: Re: Generate all combinations in a lotto game === >Subject: Generate all combinations in a lotto game >Message-id: >I would like to generate all 324632 combiations in the 5/35 lotto game >and eventually all combinations in any n/N lotto game. What kind of >mathematics do I need to employ Algebra. But what you really want is a programming language and an algorithm. Not sure why you want to generate all the combinations. Most people want to create practical subsets such as wheels or boxes. What kind of resources do you have? WIndows? Linux? Excel? For reasonable sized combinations, you can even generate them in Access (or any other SQL database). >and is there a site where it is available? I doubt you¹ll Þnd one that will generate all the combinations. Most sites are geared towards the practical subsets. >Stig Holmquist -- Mensanator Ace of Clubs === Subject: Re: Generate all combinations in a lotto game === >>Subject: Generate all combinations in a lotto game >>Message-id: >>I would like to generate all 324632 combiations in the 5/35 lotto game >>and eventually all combinations in any n/N lotto game. What kind of >>mathematics do I need to employ >Algebra. But what you really want is a programming language and >an algorithm. Not sure why you want to generate all the combinations. >Most people want to create practical subsets such as wheels or boxes. >What kind of resources do you have? WIndows? Linux? Excel? >For reasonable sized combinations, you can even generate them in >Access (or any other SQL database). >>and is there a site where it is available? >I doubt you¹ll Þnd one that will generate all the combinations. Most sites >are geared towards the practical subsets. >>Stig Holmquist Mensanator responded as above. I¹ve a speciÞc reason for wanting to generate all combinations in any lotto game, n/N. Each set of numbers must have a variance. So far nobody has offered a formula for predicting it. I¹ve an idea of how to do it and need complete sets of combinations to test it. So far I¹ve tested a few hundred actual draws, and their mean differ by only a few percent from my predictions. If I simulated a drawing and test as many samples as there are combinations I would be missing about 38% because of dupications. I suspect the formula will show some relationship to the n/N ratio. In most lottto games the ratio is less than less than 1/5 and can be as low as 1/10. Experts have told me there is no formula, but I would like to see how far off I might be for any given lotto. Stig Holmquist === Subject: Re: Generate all combinations in a lotto game === >Subject: Re: Generate all combinations in a lotto game >Message-id: <01vhn01v4n5j1u0fj3tq09v1jph7g21t6n@4ax.com> === >Subject: Generate all combinations in a lotto game >Message-id: >I would like to generate all 324632 combiations in the 5/35 lotto game >and eventually all combinations in any n/N lotto game. What kind of >mathematics do I need to employ >>Algebra. But what you really want is a programming language and >>an algorithm. Not sure why you want to generate all the combinations. >>Most people want to create practical subsets such as wheels or boxes. >>What kind of resources do you have? WIndows? Linux? Excel? >>For reasonable sized combinations, you can even generate them in >>Access (or any other SQL database). >and is there a site where it is available? >>I doubt you¹ll Þnd one that will generate all the combinations. Most sites >>are geared towards the practical subsets. >Stig Holmquist >Mensanator responded as above. >I¹ve a speciÞc reason for wanting to generate all >combinations in any lotto game, n/N. >Each set of numbers must have a variance. So far nobody >has offered a formula for predicting it. I¹ve an idea of how to >do it and need complete sets of combinations to test it. >So far I¹ve tested a few hundred actual draws, and their mean >differ by only a few percent from my predictions. >If I simulated a drawing and test as many samples as there are >combinations I would be missing about 38% because of dupications. >I suspect the formula will show some relationship to the n/N ratio. >In most lottto games the ratio is less than less than 1/5 and can be >as low as 1/10. Experts have told me there is no formula, but I >would like to see how far off I might be for any given lotto. >Stig Holmquist Here¹s the general idea. The Þrst ball counts from 1 to N-(n-1). The second ball counts from the current value of the Þrst ball+1 to N-(n-2). . . . The nth ball counts from the current value of the (n-1)th ball+1 to N. count = 0 n = 35 for a in range(1,n-3): for b in range(a+1,n-2): for c in range(b+1,n-1): for d in range(c+1,n): for e in range(d+1,n+1): print a,b,c,d,e count += 1 print count -- Mensanator Ace of Clubs === Subject: Re: Generate all combinations in a lotto game === >Subject: Re: Generate all combinations in a lotto game >Message-id: <01vhn01v4n5j1u0fj3tq09v1jph7g21t6n@4ax.com> === >Subject: Generate all combinations in a lotto game >Message-id: > >I would like to generate all 324632 combiations in the 5/35 lotto game >and eventually all combinations in any n/N lotto game. What kind of >mathematics do I need to employ >> >>Algebra. But what you really want is a programming language and >>an algorithm. Not sure why you want to generate all the combinations. >>Most people want to create practical subsets such as wheels or boxes. >>What kind of resources do you have? WIndows? Linux? Excel? >>For reasonable sized combinations, you can even generate them in >>Access (or any other SQL database). >> >and is there a site where it is available? >> >>I doubt you¹ll Þnd one that will generate all the combinations. Most sites >>are geared towards the practical subsets. >> > >Stig Holmquist >Mensanator responded as above. >I¹ve a speciÞc reason for wanting to generate all >combinations in any lotto game, n/N. >Each set of numbers must have a variance. So far nobody >has offered a formula for predicting it. I¹ve an idea of how to >do it and need complete sets of combinations to test it. >So far I¹ve tested a few hundred actual draws, and their mean >differ by only a few percent from my predictions. >If I simulated a drawing and test as many samples as there are >combinations I would be missing about 38% because of dupications. >I suspect the formula will show some relationship to the n/N ratio. >In most lottto games the ratio is less than less than 1/5 and can be >as low as 1/10. Experts have told me there is no formula, but I >would like to see how far off I might be for any given lotto. >Stig Holmquist > Here¹s the general idea. > The Þrst ball counts from 1 to N-(n-1). > The second ball counts from the current value of the Þrst ball+1 to > N-(n-2). > The nth ball counts from the current value of the (n-1)th ball+1 to N. > count = 0 > n = 35 > for a in range(1,n-3): > for b in range(a+1,n-2): > for c in range(b+1,n-1): > for d in range(c+1,n): > for e in range(d+1,n+1): > print a,b,c,d,e > count += 1 > print count Sticking with Python: def itercomb(n, k, start=None): if k > n: raise StopIteration if start is None: current = range(k) else: current = list(start) while current[0] != n - k: yield current for index in range(-1, -k - 1, -1): if current[index] != n + index: current[index] += 1 for other_index in range(index + 1, 0): current[other_index] = current[index] + other_index - index break yield current ------------------------------------------------------ > import iter > for comb in iter.itercomb(6, 3): print comb [0, 1, 2] [0, 1, 3] . . . [2, 4, 5] [3, 4, 5] or increase the Þrst parameter by 1 and use a start value as the balls are numbered from 1. > for comb in iter.itercomb(7, 3, [1,2,3]): print comb [1, 2, 3] [1, 2, 4] . . . [3, 5, 6] [4, 5, 6] Duncan === Subject: Re: Generate all combinations in a lotto game !3KEIp?*w`|bL5qr,H)LFO6Q=qx~iH4DN;i;/yuIsqbLLCh/!U#X[S~( 5eZ41to5f%E@¹ELIi $t^ VcLWP@J5p^rst0+(Œ>Er0=^1{]M9!p?&:z]|;&=NP3AhB!B_bi^]Pfkw >> . >> The nth ball counts from the current value of the (n-1)th ball+1 to N. >> count = 0 >> n = 35 >> for a in range(1,n-3): >> for b in range(a+1,n-2): >> for c in range(b+1,n-1): >> for d in range(c+1,n): >> for e in range(d+1,n+1): >> print a,b,c,d,e >> count += 1 >> print count > Sticking with Python: > def itercomb(n, k, start=None): > if k > n: > raise StopIteration > if start is None: > current = range(k) > else: > current = list(start) > while current[0] != n - k: > yield current > for index in range(-1, -k - 1, -1): > if current[index] != n + index: > current[index] += 1 > for other_index in range(index + 1, 0): > current[other_index] = current[index] + other_index - > index > break > yield current > ------------------------------------------------------ >> import iter >> for comb in iter.itercomb(6, 3): > print comb guile> ((lambda (r n N) (r r n N (list N) 1 Œ())) (lambda (r n N cur cl all) (cond ((< (car cur) 1) (if (= cl 1) all (r r n N (cons (- (cadr cur) 1) (cddr cur)) (- cl 1) all))) ((= cl n) (r r n N (cons (- (car cur) 1) (cdr cur)) cl (cons cur all))) ((r r n N (cons (- (car cur) 1) cur) (+ cl 1) all)))) 3 6) ((1 2 3) (1 2 4) (1 3 4) (2 3 4) (1 2 5) (1 3 5) (2 3 5) (1 4 5) (2 4 5) (3 4 5) (1 2 6) (1 3 6) (2 3 6) (1 4 6) (2 4 6) (3 4 6) (1 5 6) (2 5 6) (3 5 6) (4 5 6)) Ok, perhaps it is a bit exaggerated to do the recursion without the side effect of a function deÞnition, but apart from that... -- David Kastrup, Kriemhildstr. 15, 44793 Bochum === Subject: EFFICIENCY: PRIME TEST vs PRIME GENERATOR by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i9M279r22583; Here¹s a math question that may have been answered in the literature, but I haven¹t seen it anywhere. Maybe one of you professionals can help. Let¹s suppose we have an algorithm (function?) that will take a positive integer x as input and output the xth prime. Say it takes some time to compute this prime, but unlike the sieve of Erastothenes it does it without looking at composites. In other words, the sieve has to strike out every multiple of 2,3,5... but this algorithm directly produces the xth prime without testing or dealing in any way (except intrinsically) with non-primes. We¹ll call this algorithm f(x), though it¹s doubtful that a single function would Þt the description. Now, let e(n) be a measure of the efÞciency of any primality test for declaring a number of size n to be either prime or composite, given in hours. Let E(n) be the time it takes to Þnd a prime, given in hours. For example, the USUAL test runs on odd numbers, checking for primality. The time it takes to prove one such number is either composite or prime is e(n), given size n. Then E(n) is e(n) TIMES the number of composites tested before Þnding a prime. Now, f(x) as described above doesn¹t waste time checking composites, so e(n)=E(n) for it. Therefore, my question is, given a target range of size n, how fast would f(x) need to be in order to be as efÞcient as our fastest primality test now used, in terms of E(x), to Þnd several consecutive primes in the target range? I don¹t have an example of a system that spits out the nth prime on command, but I have something close. As an example, look at the absolute value of 15 plus or minus 2^x, for outputs less than 7^2=49. No such output can have a factor of 2,3, or 5. This is one of a sequence of equations which gets all primes less than 49. I write this as abs( 15 +/- 2^x ) = q(x), where q(x)<49. Actually, if you want the entire theory in a nutshell, look at abs( 3^y * 5^z +/- 2^x ) = q1(x,y,z) where q1(x,y,z)<49, then look at q2(x,y,z)= abs( 2^x*3^y +/- 5^z ) and q3(x,y,z) = abs( 2^x*5^z +/- 3^y), where qi<49. You can see that I¹ve partitioned the set {2,3,5} into two disjoint sets, one on each side of the +/-. If you work this out using all three functions, you will get every prime less than 49, depending on the integer exponents >0 that you input. When q1 gets tired, move to q2, etc. For the next step in the algorithm, partition the set {2,3,...43}, which you found in the last step, into two disjoint subsets, one on each side of the +/-, with each prime independently exponentiated with positive integers, and the output will be prime when it is less than 47^2=2209. To get all primes in that range, repartition the sets as necessary. I haven¹t actually gotten that high so far, but I have found every single prime less than 37^2=1369 using this method. Now, my question wasn¹t exactly about this algorithm, since the primes it Þnds come in no linear order and my algorithm does have repeated outputs i.e. it might produce 29 six times (though I expect the repeats to dwindle at high prime values). Also notice that, like the sieve, you can get a set enriched with primes simply by ignoring the less-than test, for example, 15 +/- 2^x will eliminate all composites with 2,3, or 5 as factors, even if we look at outputs higher than 49. My question was about an ideal program that produces the 85th prime when we input the number 85, though the answer may be pertenant to my algorithm to a large extent. Here¹s a simpliÞcation (example) of what my question is about: Let¹s pick a range, say all x between 10^60 and 10^61. Now, let e=the efÞciency of standard programs in proving x is either prime or composite, in terms of the time it takes. Let E=the time it takes to Þnd (and prove the primality of) a prime number Then E = e * (the number of integers you tested before Þnding the prime) So, if you can prove a number is prime in 100 hours, and it takes my program 1000 hours to generate a prime, then e=100 for you and 1000 for me, yours is ten times more efÞcient than mine at PROVING PRIMALITY. However, if you examined 100 integers before Þnding the prime, then it took you 10000 hours to Þnd the prime, so E=10000 for you and still only 1000 for me, and mine is ten times more efÞcient than yours for FINDING A PRIME. Now, I think my question is more clear, i.e. how efÞcient must a program of the second type be, in order to be as fast as the Þrst type, using the measure E? Incidently, very soon in the process, the addition becomes too large and only subtraction can be used (this happens when one side or the other of the +/- must contain enough factors to make it greater than the next prime squared). Even so, all primes (so far) can be found with subtraction alone. The size of the exponents needed seems to grow very, very slowly. Maybe if you DON¹T use every partition, you might require very large exponents. I believe, based only on the experience of having solved so many of these, that it WILL be possible to put upper bounds on the exponents that depend only on the size of the prime. Let me illustrate what seems to be a natural phenomenon when doing these computations. abs(15+/-2^x) 13,11,7,1,17,49stop subtracting 17,19,23,31,47,79stop adding Now increment exponent on 3: abs(45+/-2^x) and keep going, incrementing exponents on the 3 and 5 as needed. At some point, you will increment an exponent on 3 or 5 to get the next larger size on the left, and you will get NO OUTPUTS less than 49, particularly with subtraction. I call this the beginning of a desert, where no outputs are to be found. At that point, you could stubbornly try higher exponents on the left, until you Þnd a power of 2 on the right that produces more solutions within 49. It might be possible to Þnd all primes in this fashion, BUT... The interesting thing that I¹ve discovered is that, so far, this isn¹t necessary. At the point you reach this desert, simply repartition the set and continue: abs(10+/-3^x) and abs(6+/-5^x) incrementing powers on the left as needed. So far, this has been sufÞcient to Þnd all primes in the given range. There are a staggering number of variables to consider when looking for large primes. The fact that I haven¹t found an exception (a skipped prime) so far is encouraging, particularly when you consider how unlikely it seems that I would get any sufÞciently small solutions at all for some of the larger primes. The highest I¹ve gone so far included partitioning and exponentiating primes from the set {2,3,5,7,11,13,17,19,23,29, and 31} and I found every prime from 37 to 37^2=1369, without going beyond the natural desert that I mentioned. One way I¹ve thought about proving no primes are skipped is the following: 29, 30, 31, 32, 33, 34, 35, ...... ,58, 59, 60, 61, 62 0, 1, 2, 3, 4, 5, 6, ........,29, 30, 31, 32, 33 subtract a bottom number from the corresponding top number to get 29. Now, to Þt my abs( +/- ) scheme, every top/bottom pair must have a 2, a 3, and a 5 in it, along with no other primes. Now, 2 is in every pair. 3 is in two-thirds of the pairs, and 5 is in two-Þfths of the pairs. So to Þnd a pair that has 2,3, and 5 in it, we only need to look at 2/3 * 2/5 = 4/15 so out of 15 such pairs, four of them will have 2,3, and 5 as factors of one number or the other. It get¹s trickier when we try to eliminate higher primes from the pairs, but notice that Þve-sevenths of them will NOT have a seven as a factor, nine-elevenths will NOT have 11, eleven-thirteenths will NOT have 13, Þfteen-seventeenths will NOT have 17, etc. So multiply all of these by the 4/15 that we found above. Where do we cut it off? I¹m still working out the details, but it looks like if our fraction is greater than 1/n, and we¹ve considered less than n pairs so far, we can say there exists a representation o! f the prime that Þts the form given. Or something like that, like I said I¹m still looking at it. To all interested, I suggest working out all of the primes less than 121 this way, doing the process may answer questions more efÞciently than I can, and if you still don¹t have faith in this process after trying it out, I¹ll be very, very surprised. To start out, look at f(x)=abs(105+/-2^x), it is a fascinating exponential expression, with reþection where it becomes negative, and every prime that it puts out occurs on integer values of x. Graphing some of these things in three dimensions is interesting, also, though adjustments are needed because the exponents are all positive, and the plus gets graphed separate from the minus, etc. If you all have a spare minute, please try a couple, you¹ll be surprised at how easy it is to Þll the whole range from 11 to 121. Remember, I did all primes to 1369 in my head, Þrst checking odds by division to see if they were prime, and then Þnding a form that Þts the procedure given. You will also get a single output that isn¹t usually considered prime, the number 1. 1=3-2=10-9=15-14 etc. all come from the correct form. I believe it wouldn¹t be too hard to prove that you can always get the number 1. Also, I note the similarity with the theorem that says you can get every multiple of the gcd of two numbers by using linear combinations of them. I wonder if you can get all RELATIVELY PRIME multiples of the gcd of the left and right sides, i.e. all multiples of 1 that are relatively prime to the left and right, using linear combinations of the left and right with the coefÞcients restricted to factors already present in that side. Ex: Left->15, Right->2 now use a coefÞcient having only 1,3,5 as factors, to multiply by the left, and a coefÞcient having only 1,2 as factors to multiply by the right, then subtract the two results. Can we Þnd all multiples of 1, relatively prime to 15 and 2, with this restricted linear combination? Good question, I think the a! nswer is yes, at least if we use the other two partitions in the same way. Given, there is no perfect formula to Þnd the xth prime by inputting x. However, my algorithm does satisfy the one requirement that it Þnds primes without any undue checking of composite numbers. All else being the same, if a test Þnds primes without hours being wasted on numbers that are not prime, it will be more efÞcient. Say your favorite testing algorithm is testing a number that will prove to be prime, it may be a little faster than mine, BUT if you are testing one hundred numbers, of which only one is prime, mine will Þnd several primes before yours Þnds that one. Aaron === Subject: Re: EFFICIENCY: PRIME TEST vs PRIME GENERATOR X-RFC2646: Format=Flowed; Original > Here¹s a math question that may have been answered in the literature, but > I haven¹t seen it anywhere. Maybe one of you professionals can help. > The following was taken from a few entries I¹ve made elsewhere. > Anticipating that some of the same questions may come up, I have put some > advance for your patience. > Let¹s suppose we have an algorithm (function?) that will take a positive > integer x as input and output the xth prime. Say it takes some time to > compute this prime, but unlike the sieve of Erastothenes it does it > without looking at composites. In other words, the sieve has to strike out > every multiple of 2,3,5... but this algorithm directly produces the xth > prime without testing or dealing in any way (except intrinsically) with > non-primes. We¹ll call this algorithm f(x), though it¹s doubtful that a > single function would Þt the description. > Now, let e(n) be a measure of the efÞciency of any primality test for > declaring a number of size n to be either prime or composite, given in > hours. > Let E(n) be the time it takes to Þnd a prime, given in hours. > For example, the USUAL test runs on odd numbers, checking for primality. > The time it takes to prove one such number is either composite or prime is > e(n), given size n. Then E(n) is e(n) TIMES the number of composites > tested before Þnding a prime. > Now, f(x) as described above doesn¹t waste time checking composites, so > e(n)=E(n) for it. > Therefore, my question is, given a target range of size n, how fast would > f(x) need to be in order to be as efÞcient as our fastest primality test > now used, in terms of E(x), to Þnd several consecutive primes in the > target range? > check 33 and 35 before Þnding 37 to be prime, while f(x) just goes > straight to the next prime, 37, thus saving time. How slow could f(x) be > to still be just as efÞcient? Thought this might be an interesting > question. > I don¹t have an example of a system that spits out the nth prime on > command, but I have something close. As an example, look at the absolute > value of 15 plus or minus 2^x, for outputs less than 7^2=49. No such > output can have a factor of 2,3, or 5. This is one of a sequence of > equations which gets all primes less than 49. I write this as abs( 15 +/- > 2^x ) = q(x), where q(x)<49. Actually, if you want the entire theory in a > nutshell, look at > abs( 3^y * 5^z +/- 2^x ) = q1(x,y,z) where q1(x,y,z)<49, > then look at q2(x,y,z)= abs( 2^x*3^y +/- 5^z ) and > q3(x,y,z) = abs( 2^x*5^z +/- 3^y), where qi<49. You can see that I¹ve > partitioned the set {2,3,5} into two disjoint sets, one on each side of > the +/-. If you work this out using all three functions, you will get > every prime less than 49, depending on the integer exponents >0 that you > input. When q1 gets tired, move to q2, etc. For the next step in the > algorithm, partition the set {2,3,...43}, which you found in the last > step, into two disjoint subsets, one on each side of the +/-, with each > prime independently exponentiated with positive integers, and the output > will be prime when it is less than 47^2=2209. To get all primes in that > range, repartition the sets as necessary. I haven¹t actually gotten that > high so far, but I have found every single prime less than 37^2=1369 using > this method. > Now, my question wasn¹t exactly about this algorithm, since the primes it > Þnds come in no linear order and my algorithm does have repeated outputs > i.e. it might produce 29 six times (though I expect the repeats to dwindle > at high prime values). Also notice that, like the sieve, you can get a set > enriched with primes simply by ignoring the less-than test, for example, > 15 +/- 2^x will eliminate all composites with 2,3, or 5 as factors, even > if we look at outputs higher than 49. My question was about an ideal > program that produces the 85th prime when we input the number 85, though > the answer may be pertenant to my algorithm to a large extent. > Here¹s a simpliÞcation (example) of what my question is about: > Let¹s pick a range, say all x between 10^60 and 10^61. > Now, let e=the efÞciency of standard programs in proving x is either > prime or composite, in terms of the time it takes. > Let E=the time it takes to Þnd (and prove the primality of) a prime > number > Then E = e * (the number of integers you tested before Þnding the prime) > So, if you can prove a number is prime in 100 hours, and it takes my > program 1000 hours to generate a prime, then e=100 for you and 1000 for > me, yours is ten times more efÞcient than mine at PROVING PRIMALITY. > However, if you examined 100 integers before Þnding the prime, then it > took you 10000 hours to Þnd the prime, so E=10000 for you and still only > 1000 for me, and mine is ten times more efÞcient than yours for FINDING A > PRIME. > Now, I think my question is more clear, i.e. how efÞcient must a program > of the second type be, in order to be as fast as the Þrst type, using the > measure E? > I welcome all coments, both positive and negative criticism. I¹ve already > stated my algorithm has a setback or two, such at duplicate prime outputs. > I just want to know, in theory, if we had an oracle program of this > type, how fast would it have to be, in terms of the size of the primes, to > clarify a question that I think is worth studying. > Incidently, very soon in the process, the addition becomes too large and > only subtraction can be used (this happens when one side or the other of > the +/- must contain enough factors to make it greater than the next prime > squared). Even so, all primes (so far) can be found with subtraction > alone. > The size of the exponents needed seems to grow very, very slowly. Maybe if > you DON¹T use every partition, you might require very large exponents. > I believe, based only on the experience of having solved so many of these, > that it WILL be possible to put upper bounds on the exponents that depend > only on the size of the prime. Let me illustrate what seems to be a > natural phenomenon when doing these computations. > abs(15+/-2^x) > 13,11,7,1,17,49stop subtracting > 17,19,23,31,47,79stop adding > Now increment exponent on 3: > abs(45+/-2^x) > and keep going, incrementing exponents on the 3 and 5 as needed. > At some point, you will increment an exponent on 3 or 5 to get the next > larger size on the left, and you will get NO OUTPUTS less than 49, > particularly with subtraction. I call this the beginning of a desert, > where no outputs are to be found. > At that point, you could stubbornly try higher exponents on the left, > until you Þnd a power of 2 on the right that produces more solutions > within 49. It might be possible to Þnd all primes in this fashion, BUT... > The interesting thing that I¹ve discovered is that, so far, this isn¹t > necessary. At the point you reach this desert, simply repartition the set > and continue: > abs(10+/-3^x) and abs(6+/-5^x) > incrementing powers on the left as needed. So far, this has been > sufÞcient to Þnd all primes in the given range. > There are a staggering number of variables to consider when looking for > large primes. The fact that I haven¹t found an exception (a skipped prime) > so far is encouraging, particularly when you consider how unlikely it > seems that I would get any sufÞciently small solutions at all for some of > the larger primes. The highest I¹ve gone so far included partitioning > and exponentiating primes from the set {2,3,5,7,11,13,17,19,23,29, and 31} > and I found every prime from 37 to 37^2=1369, without going beyond the > natural desert that I mentioned. > One way I¹ve thought about proving no primes are skipped is the following: > 29, 30, 31, 32, 33, 34, 35, ...... ,58, 59, 60, 61, 62 > 0, 1, 2, 3, 4, 5, 6, ........,29, 30, 31, 32, 33 > subtract a bottom number from the corresponding top number to get 29. Now, > to Þt my abs( +/- ) scheme, every top/bottom pair must have a 2, a 3, and > a 5 in it, along with no other primes. Now, 2 is in every pair. 3 is in > two-thirds of the pairs, and 5 is in two-Þfths of the pairs. So to Þnd a > pair that has 2,3, and 5 in it, we only need to look at 2/3 * 2/5 = 4/15 > so out of 15 such pairs, four of them will have 2,3, and 5 as factors of > one number or the other. It get¹s trickier when we try to eliminate higher > primes from the pairs, but notice that Þve-sevenths of them will NOT have > a seven as a factor, nine-elevenths will NOT have 11, eleven-thirteenths > will NOT have 13, Þfteen-seventeenths will NOT have 17, etc. So multiply > all of these by the 4/15 that we found above. Where do we cut it off? I¹m > still working out the details, but it looks like if our fraction is > greater than 1/n, and we¹ve considered less than n pairs so far, we can > say there exists a representation o! > f the prime that Þts the form given. Or something like that, like I said > I¹m still looking at it. > To all interested, I suggest working out all of the primes less than 121 > this way, doing the process may answer questions more efÞciently than I > can, and if you still don¹t have faith in this process after trying it > out, I¹ll be very, very surprised. To start out, look at > f(x)=abs(105+/-2^x), it is a fascinating exponential expression, with > reþection where it becomes negative, and every prime that it puts out > occurs on integer values of x. Graphing some of these things in three > dimensions is interesting, also, though adjustments are needed because the > exponents are all positive, and the plus gets graphed separate from the > minus, etc. If you all have a spare minute, please try a couple, you¹ll > be surprised at how easy it is to Þll the whole range from 11 to 121. > Remember, I did all primes to 1369 in my head, Þrst checking odds by > division to see if they were prime, and then Þnding a form that Þts the > procedure given. > You will also get a single output that isn¹t usually considered prime, the > number 1. 1=3-2=10-9=15-14 etc. all come from the correct form. I believe > it wouldn¹t be too hard to prove that you can always get the number 1. > Also, I note the similarity with the theorem that says you can get every > multiple of the gcd of two numbers by using linear combinations of them. I > wonder if you can get all RELATIVELY PRIME multiples of the gcd of the > left and right sides, i.e. all multiples of 1 that are relatively prime to > the left and right, using linear combinations of the left and right with > the coefÞcients restricted to factors already present in that side. Ex: > Left->15, Right->2 now use a coefÞcient having only 1,3,5 as factors, to > multiply by the left, and a coefÞcient having only 1,2 as factors to > multiply by the right, then subtract the two results. Can we Þnd all > multiples of 1, relatively prime to 15 and 2, with this restricted linear > combination? Good question, I think the a! > nswer is yes, at least if we use the other two partitions in the same > way. > Given, there is no perfect formula to Þnd the xth prime by inputting x. > However, my algorithm does satisfy the one requirement that it Þnds > primes without any undue checking of composite numbers. All else being the > same, if a test Þnds primes without hours being wasted on numbers that > are not prime, it will be more efÞcient. Say your favorite testing > algorithm is testing a number that will prove to be prime, it may be a > little faster than mine, BUT if you are testing one hundred numbers, of > which only one is prime, mine will Þnd several primes before yours Þnds > that one. > comments you may add. Happy prime hunting! > Aaron The short, simple answer to your question is that if you choose x at random, the probability of it being prime is 1/ln(x), and you must check of the order of ln(x) numbers to Þnd the next prime. So for numbers of the order of 10^60 (the size you nominated), about each 145th number is prime, so you may have to check 70 on average. Taking out those divisible by 2,3,7 and 7 probably reduces this to about 20 or so. The efÞciency of checks for primality for the remaining numbers varies according to how big the numbers are, and how certain you need to be that the number is prime. Many tests (and all the fast tests) indicate that a number is likely or almost certain to be prime; they don¹t guarantee it. For many applications, that may be sufÞcient. If you haven¹t found it, http://www.utm.edu/research/primes/ is an excellent reference.