mm-2019 i have a question to ask i have tried working on it but i am just getting no where with it. this is how it goes: i have before me three numeric palindromes. the first is two digits long; the second is three digits long; and when i add those two numbers together, i get the third number which is four digits long. what are the three palindromes? is the answer unique? it would be a great help i could get it solved. In other words, AA + BCB = DEED where each letter represents a digit, not necessarily all different. Can you work out what D and E must be? What about B? If you know those three, can you work out A and C? - Tim The only issue I am concerned with here is whether Lorentz invariance is universal and why. I don't know what you mean and neither do you. The question is ill-posed. In GR Lorentz invariance is a local symmetry not a global one because T(4) is locally gauged whose compensating field is the non-trivial part of the Cartan tetrad. This solves one of your problems, i.e. intrinsic vs coordinate. Do you mean there are exotic vacua where O(1,3) is wrong even locally? No evidence for that at all. G. E. Volovik has emergent O(1,3) at a fixed point low energy effective field theory in a renormalization group flow from a Galilean sub-stratum. Is that what you mean? I am not arguing against spontaneously broken symmetry. Obviously you can get preferred frames in a physical vacuum by breaking the underlying dynamical symmetry in the solutions at the macro-level, which I think is what you are saying. That's all the Cahill/Consoli data show, if they are real. Interesting and important to be sure - another triumph for PW Anderson's theory of emergent complexity! No change in paradigm needed. The mainstream paradigm 1. Symmetries 2. Locally gauging symmetries to get forces (complementary to geometrodynamics) 3. More is different emergence via spontaneously broken symmetries in the locally lowest energy valleys of the landscape of the parallel worlds of the multi-verse. This is all we need for the theory of everything from large-scale universe today to small-scale lepto-quarks & gauge force bosons. Higgs Ocean. Oil on Water. Einstein's gravity with anti-gravitating dark energy and gravitating dark matter emerges as phase and amplitude modulations of the post-inflationary calm Higgs Ocean (AKA Wilczek's multi-layered multi-colored cosmic superconducting field, AKA vacuum coherence of ZPF). I do not see what you are worried about. BTW the affine/vector space distinction for the space of Lorentz inertial frames is an elegant way to look at the contingent Einstein/Lorentz empirical significant difference. The alleged experimental anomaly is strictly isolated - no major damage control needed. Now if you could give me a counter example on that, then you would have something. At the moment you are charging windmills. Stop making vague statements. Simply write a review paper in complete detail with logic like Euclid step-by-step what you think Einstein says, what you think Lorentz says etc. Stop using polemics. Don't talk about it. Do it. Paul Of course I understand the data Cahill is alleging. But neither you nor Cahill understand the real meaning of that data! When there is a n =/= 1 (index of gas) v =/= 0 absolute velocity detected, that means a vacuum symmetry breaking of O(1,3). It does not mean a return to t' = t absolute time of Galilean relativity. You still must use O(1,3) to get from one inertial frame to another even though there is a preferred frame which is to O(1,3) as the ferromagnetic order parameter is to O(3). There is a local vacuum order parameter just like there is a ferromagnetic order parameter. Let Eve be in the preferred frame v = 0. This means that no fringe shifts on 90 degree rotations of the MM interferometer at rest in Eve's frame. If Alice (Bob) measures v(Alice(Bob)) that means the Lorentz boost between Alice(Bob) and Eve is via [1 - (v(Alice(Bob))/c)^2]^-1/2 with the usual Lorentz transformations! On the other hand the relative velocity between Alice and Bob (do 1 + 1 to keep it simple for now) directly measured in their Doppler radar is v(Alice - Bob) = - v(Bob - Alice) = [v(Alice) - v(Bob)]/[1 - v(Alice)v(Bob)/c^2] So that a direct boost between Alice and Bob (bypassing Eve) is via [1 - (v(Alice - Bob)/c)^2]^-1/2 There is no problem with reciprocity as you incorrectly allege. Apart from Alice and Bob seeing anomalous MM fringe shifts on 90 deg rotations if n =/= 1 and Eve seeing none, everything else is completely normal! Nothing else changes. The anomaly is truly isolated! It is contingent not fundamental. No change of paradigm is required. A spontaneous broken O(1,3) vacuum symmetry in a finite space-time region simply means that the space of inertial frames is a vector space with an origin rather than an affine space with no origin, i.e. no preferred inertial Eve frame. Ignoring GR curvature et-al for now, the kinematics of frame transforms is still O(1,3) and the dynamics is still O(1,3) covariant. A revolution is not called for. There is no impending paradigm shift overturning Einstein as Cahill professes. There is no return to Galilean relativity. One simply punches an isolated hole in Einstein's affine space of inertial frames. End of story. If you can find an inconsistency here show it. Cahill is the new Herbert Dingle even if his claims (and Consoli's in Catania) of the n =/= 1 Michelson-Morley fringe pattern shift on 90 degree rotations is confirmed. What he infers from that alleged fact is not justified by the evidence and the mainstream ideas of local gauge invariance with dynamics from compensating field and the More is different spontaneous breaking of vacuum (ground state) symmetries from the large-scale of cosmology to the shortest scales of high-energy physics. [Tim Peters] [Richard Henry] I wouldn't _need_ one, but I often enjoy my work. Besides, I'm not sure there's enough RSA challenge money to pay health insurance for the rest of my life. [JSH] See? You have to believe! I'm not going to all the bother of setting up a network of computers for perhaps a minute's work. Practical advice: when you're short on time, it helps to skip the first msg Cool! I think that's under-appreciated -- honest. There are, at times, some wonderfully lucid explanations of mathematical topics in these threads. They only seem to irritate James, but I too have profited from them. For example, what do I remember about algebraic integers? I had a vague recollection of the topic from college decades ago, and it was a delight to get reacquainted with some of the basics, and learn a bit more for the first time. OTOH, if there's something in particular you'd _like_ to learn more about, there are more efficient methods than waiting for JSH to announce that all the selective memory of age, but I seem to recall a lot more pleasant mutual exploration in the tech newsgroups in the late 1980's. Now it seems more a textbook example for the tragedy of the commons ... [...] [JSH] [Tim Peters] [David C. Ullrich] Of course! Remember that I was absent from USENET during our benefactors's formative years -- it would all be new to me, and I'm sure it would bring back so many pleasant memories for you. Besides, I'd like validation of my own short proof: suppose i^n+j^n=k^n, to Wiles. QED. I doubt even James can produce a correct proof shorter than that (although I wouldn't bet against him if he were judging the contest too). Are you kidding? Why go through the headaches? What I did was use one of the key techniques in the proof, which is non-polynomial factorization, and found an error that is over a hundred years old in what mathematician's have thought about certain numbers. It's actually kind of a neat story, as I used to argue out details of the FLT proof, and posters were focusing on one section. Well, I expanded out that short section of the full proof, and used the techniques introduced in a few paragraphs in that paper to do the analysis which became the paper Advanced Polynomial Factorization. Now do you get a little bit of a clue? Why do you think those sci.math'ers where so energetic in emailing the Southwest Journal of Pure and Applied Mathematics to attack the paper? They're not just blocking on the result itself--big as it is--but on the world knowing that a short FLT proof exists. Currently the Annals of Mathematics has a new paper, which is essentially a short section of the short FLT proof expanded out into a full paper. The FLT proof, while *mostly* simple to me, seems to simply leave everyone else befuddled, as it covers infinite sets, and there are posters who got really good about lying about its details, as well as making the most out of simply the *claim* of an FLT proof. You can get labeled a nut easily just with the claim without regard to what you can show, so I figure, why bother? And usually I don't, but this surrogate factoring has gotten me in a weird mood. And as for the short FLT proof not being known, well, I've gotten used to that fact, as it's just the way things are. And besides, it's not my loss. I have the proof and can consider it at my leisure. It's other people who don't. James Harris These Lorentz vs. Einstein arguments have already been made many times over. I mistakenly assumed you would be familiar with them. Jack, you don't seem to have any intuitive appreciation of the difference between a Lorentzian rubber-rod-and-clock model and an Einsteinian moving coordinates model of the Lorentz transformations. I am familiar. The argument is completely stupid as Kip Thorne says IF THERE IS NO EMPIRICAL DIFFERENCE. The Cahill difference is not relevant to that distinction. Didn't you read Feynman's Lectures on Gravitation? He explains the difference from the standpoint of a spin-2 quantum field model quite vividly. NO you completely MISUNDERSTAND Feynman. He is only talking about perturbation theory to finite order from a flat background and there you can maybe make the distinction you want to make implicit in Puthoff's PV Tables I & II. As Penrose explains YOU CANNOT DO IT for the complete GR, which in Feyman's terms is a INFINITE SUM of flat diagrams! This is like in BCS theory gap energy ~ (Debye Energy)e^-1/V(binding)(Density of Fermi Sea States Per Unit Energy at Fermi Surface) You cannot get this SPONTANEOUS BREAKING of the VACUUM SYMMETRY from a FINITE NUMBER of flat background diagrams. Penrose distinguishes the linear graviton of Feynman here, also of Puthoff's Yilmazian PV from the nonlinear graviton in the book Geometric Universe. So your basic error here Paul is to take a limited approximate idea BEYOND its proper domain of validity. Feynman's approximation and your distinction above violates what all the Big Boys today like Ashtekar, Smolin et-al call BACKGROUND INDEPENDENCE closely connected to the full meaning of the equivalence principle that your distinction essentially violates. That is NO RIGID BACKGROUNDS that act without direct back-reaction. Everything is a player. No stages. No fixed arenas - not even in quantum theory, hence the signal nonlocality of consciousness! remove 3 dots for e-mail This is mathematically correct! O'Barr comments: This is mathematically correct for boosts between frames! O'Barr comments: But if this were true, that those moving in the ether would see these anomalous fringes, and those who were not moving in the ether would not, then it does not matter whether anything else were different or not. The above would be more than sufficient to remove SR, and put LET up as a superior theory to SR, if any experiment could be found to demonstrate this. O'Barr comments: What you say is mainly a mathematical examination of what would change if such occurred. SR math would remain very useful whether we have the results given above or not. But math is only math. Once we have any of the above, the physical interpretation of the math would change by an terrific amount! And it should do this whether we have this data or not. There is no other way that SR can physically work, except by the physical interpretations of LET. O'Barr comments: Mathematically speaking, you are very correct. The math for the kinematics of frame transforms, and the dynamics, will still be the same math. But the physical understanding, the physical explanation of what is really occurring, will not be the same. And you are not a physicist when you are not able and/or not willing to say all this! Shame on you! O'Barr comments: Yes again, the math is very solid, whether SR is there or whether LET is there. These theories are the same theory, mathematically. The differences are not worth the trouble to talk about. But physically, the physical understanding and the physical explanations as to what is really happening will be miles apart. The story, physically, will just be beginning. And you know it! O'Barr comments: Do you mean mathematically, or do you mean physically? If physical rulers and material clocks really do change their physical lengths and their rates, then that is sure physically different than having only changes in our perspective being involved. The math might be the same, but the explanations will not. O'Barr comments: And what happened to Hoyle? I have no real idea as to what we will get with n not equal to 1. But I do believe that the need for an absolute reference is already here, in terms of the physical need to establish a physical correlation between physically separated material frames, as observed in SR. In other words, LET provides to us a physical explanation to SR, and SR has no means of rejecting this physical explanation. Unless SR is able to provide a better physical explanation, a simpler physical explanation, then LET is superior. SR is unable to provide any physical explanation at all. All that SR can do is just to verbally say that math is the physics, and this is only a laugh to anyone who really listens to what is being said. No multidimensional space, unless physical evidence is provided. No such physical evidence exists, and cannot exist as long as LET is a viable approach. remove 3 dots for e-mail Anyone following this discussion will find much of interest at: http://www.Agora.demon.co.uk/dynamics.txt where a wide range of alternatives is examined. Tony Hollick I have reviewed your works, and have found them to be without merit. Sorry. You are trying to gain peer approval via internet newsgroup, If you really think you have something consider publishing in a refereed Journal. My best advice to you is to consider making wood toothpicks for a living. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + A minor point -- but should respectfully be respectively instead? and is the inverse function of f and g respectfully Aristotle Polonium + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + begin 666 Image174.gif