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                                The Nature of Space and Time
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Two relativists present their distinctive views on the universe, its evolution
and the impact of quantum theory
by Stephen W. Hawking and Roger Penrose
       
Introduction
In 1994 Stephen W. Hawking and Roger Penrose gave a series of public lectures
on general relativity at the Isaac Newton Institute for Mathematical Sciences
at the University of Cambridge. From these lectures, published this year by
Princeton University Press as The Nature of Space and Time, Here are excerpts
that serve to compare and contrast the perspectives of the two scientists
Although they share a common heritage in physics-Penrose served on 
Hawking's Ph.D. thesis committee at Cambridge-the lecturers differ in their
vision of quantum mechanics and its impact on the evolution of the universe.
In particular, Hawking and Penrose disagree on what happens to the information
stored in a black hole and on why the beginning of the universe differs from
the end.
One of Hawking's major discoveries, made in 1973, was that quantum effects
will cause black holes to emit particles. The black hole will evaporate in
the process, so that ultimately perhaps nothing of the original mass will be
left. But during their formation, black holes swallow a lot of data-the types,
properties and configurations of the particles that fall in. Although
quantum theory requires that such information must be conserved, what finally
happens to it remains a topic of contentious debate. Hawking and Penrose both
believe that when a black hole radiates, it loses the information it held.
But Hawking insists that the loss is irretrievable,
whereas Penrose argues that the loss is balanced by spontaneous measurements
of quantum states that introduce information back into the system.
Both scientists agree that a future quantum theory of gravity is needed to
describe nature. But they differ in their view of some aspects of this
theory. Penrose thinks that even though the fundamental forces of particle
physics are symmetric in time-unchanged if time is reversed-quantum
gravity will violate time symmetry. The time asymmetry will then explain
why in the beginning the universe was so uniform, as evinced by the microwave
background radiation left over from the big bang, whereas the end of the
universe must be messy.
Penrose attempts to encapsulate this time asymmetry in his Weyl curvature
hypothesis. Space-time, as Albert Einstein discovered, is curved by the
presence of matter.  But space-time can also have some intrinsic bending, a
quantity designated by the Weyl curvature. Gravitational waves and black
holes, for example, allow space-time to curve even in regions that are empty.
In the early universe the Weyl curvature was probably zero, but in a
dying universe the large number of black holes, Penrose argues, will give rise
to a high Weyl curvature. This property will distinguish the end of the
universe from the beginning.
Hawking agrees that the big bang and the final "big crunch" will be different,
but he does not subscribe to a time asymmetry in the laws of nature. The
underlying reason for the difference, he thinks, is the way in which the
universe's evolution is programmed. He postulates a kind of democracy,
stating that no point in the universe can be special; therefore, the universe
cannot have a boundary. This no-boundary proposal, Hawking claims,
explains the uniformity in the microwave background  radiation.
The physicists diverge, ultimately, in their interpretation of quantum 
mechanics. Hawking believes that all a theory has to do is provide predictions
that agree with data. Penrose thinks that simply comparing predictions with
experiments is not enough to explain reality. He points out that quantum theory
requires wave functions to be "superposed," a concept that can lead to 
absurdities. The scientists thus pick up the threads of the famous debates
between Einstein and Niels Bohr on the bizarre implications of quantum
theory.
 Stephen Hawking on quantum black holes:
The quantum theory of black holes...seems to lead to a new level of
unpredictability in physics over and above the usual uncertainty associated
with quantum mechanics. This is because black holes appear to have intrinsic
entropy and to lose information from our region of the universe. I should say
that these claims are controversial: many people working on quantum gravity,
including almost all those who entered it from particle physics, would
instinctively reject the idea that information about the quantum state of a
system could be lost. However, they have had very little success in showing
how information can get out of a black hole. Eventually I believe they will
be forced to accept my suggestion that it is lost, just as they were forced to
agree that black holes radiate, which went against all their preconceptions...
The fact that gravity is attractive means that it will tend to draw the
matter in the universe together to form objects like stars and galaxies.
These can support themselves for a time against further contraction by
thermal pressure, in the case of stars, or by rotation and internal motions,
in the case of galaxies. However, eventually the heat or the angular momentum
will be carried away and the object will begin to shrink. If the mass is less
than about one and a half times that of the Sun, the contraction can be
stopped by the degeneracy pressure of electrons or neutrons. The object will
settle down to be a white dwarf or a neutron star, respectively.
 However, if the mass is greater than this limit there is  nothing that can
hold it up and stop it continuing to contract. Once it has shrunk to a
certain critical size the gravitational field at its surface will be so
strong that the light cones will be bent inward.... You can see that even
the outgoing light rays are bent toward each other and so are converging
rather than diverging. This means that there is a closed trapped surface....
Thus there must be a region of space-time from which it is not possible
to escape to infinity. This region is said to be a black hole. Its
boundary is called the event horizon and is a null surface formed by the
light rays that just fail to get away to infinity.... Computer animations
help clarify some of there peculiar phenomena
Large amount of information is lost when a body collapses to form a black hole.
The collapsing body is described by a very large number of parameters. There
are the types of matter and the multipole moments of the mass distribution.
Yet the black hole that forms is completely independent of the type of matter
and rapidly loses all the multipole moments except the first two: the monopole
moment, which is the mass, and the dipole moment, which is the angular momentum.
This loss of information didn't really matter in the classical theory. One
could say that all the information about the collapsing body was still inside
the black hole. It would be very difficult for an observer outside the black
hole to determine what the collapsing body was like. However, in the classical
theory it was still possible in principle. The observer would never actually
lose sight of the collapsing body. Instead it would appear to slow down and
get very dim as it approached the event horizon. But the observer could still
see what it was made of and how the mass was distributed.
However, quantum theory changed all this. First, the collapsing body would
send out only a limited number of photons before it crossed the event
horizon. They would be quite insufficient to carry all the information about
the collapsing body. This means that in quantum theory  there's no way an
outside observer can measure the state of the collapsed body. One might not
think that this mattered too much, because the information would still be
inside the black hole even if one couldn't measure it from the outside.
But this is where the second effect of quantum theory on black holes comes
in....
Quantum theory will cause black holes to radiate and lose mass. It seems that
they will eventually disappear completely, taking with them the information
inside them. I will give arguments that this information really is lost and
doesn't come back in some form. As I will show, this loss of information would
introduce a new level of uncertainty into physics over and above the usual
uncertainty associated with quantum theory. Unfortunately, unlike Heisenberg's
uncertainty principle, this extra level will be rather difficult to confirm
experimentally in the case of black holes.
 Roger Penrose on quantum theory and space-time:
The great physical theories of the 20th century have been quantum theory,
special relativity, general relativity and quantum field theory. These
theories are not independent of each other: general relativity was built
on special relativity, and quantum field theory has special relativity and
quantum theory as inputs.
It has been said that quantum field theory is the most accurate physical
theory ever, being accurate to about one part in about 1011. However, I
would like to point out that general relativity has, in a certain clear
sense, now been tested to be correct to one part in 10^14 (and this
accuracy has apparently been limited merely by the accuracy of clocks on
Earth). I am speaking of the Hulse-Taylor binary pulsar PSR 1913+16, a
pair of neutron stars orbiting each other, one of which is a pulsar.
General relativity predicts that this orbit will slowly decay (and the
period shorten) because energy is lost through the emission of
gravitational waves. This has indeed been observed, and the entire
description of the motion...agrees with general relativity (which I am taking
to include Newtonian theory) to the remarkable accuracy, noted above, over an
accumulated period of 20 years. The discoverers of this system have now rightly
been awarded Nobel Prizes for their work. The quantum theorists have always
claimed that because of the accuracy of their theory, it should be general
relativity that is changed to fit their mold, but I think now that it is
quantum field theory that has some catching up to do.
Although these four theories have been remarkably successful, they are not
without their problems....General relativity predicts the existence of
space-time singularities. In quantum theory there is the "measurement problem"
-I shall describe this later. It may be taken that the solution to the various
problems of these theories lies in the fact that they are incomplete on their
own. For example, it is anticipated by many that quantum field theory might
"smear" out the singularities of general relativity in some way....
I should now like to talk about information loss in black holes, which I claim
is relevant to this last issue. I agree with nearly all that Stephen had to
say on this. But while Stephen regards the information loss due to black holes
as an extra uncertainty in physics, above and beyond the uncertainty from
quantum theory, I regard it as a "complementary" uncertainty.... It is
possible that a little bit of information escapes at the moment of the
black hole evaporation...but this tiny information gain will be much smaller
than the information loss in the collapse (in what I regard as any
reasonable picture of the hole's final disappearance).
If we enclose the system in a vast box, as a thought experiment, we can
consider the phase-space evolution of matter inside the box. In the region of
phase space corresponding to situations in which a black hole is present,
trajectories of physical evolution will converge and volumes following these
trajectories will shrink. This is due to the information lost into the
singularity in the black hole. This shrinking is in direct contradiction to
the theorem in classical mechanics,  called Liouville's Theorem, which says
that volumes in phase space remain constant....Thus a black hole space-time
violates this conservation. However, in my picture, this loss of phase-space
volume is balanced by a process of "spontaneous" quantum measurement in which
information is gained and phase-space volumes increase. This is why I regard
the uncertainty due to information loss in black holes as being "complementary"
to the uncertainty in quantum theory: one is the other side of the coin to the
other....
Let us consider the Schroedinger's cat thought experiment. It describes the
plight of a cat in a box, where (let us say) a photon is emitted which
encounters a half-silvered mirror, and the transmitted part of the photon's
wave function encounters a detector which, if it detects the photon,
automatically fires a gun, killing the cat. If it fails to detect the photon,
then the cat is alive and well. (I know Stephen does not approve of 
mistreating cats, even in a thought experiment!) The wave function of the
system is a superposition of these two possibilities....But why does our
perception not allow us to perceive macroscopic superpositions, of states such
as these, and not just the macroscopic alternatives "cat is dead" and "cat
is alive"?...
I am suggesting that something goes wrong with superpositions of the
alternative space-time geometries that would occur when general relativity
begins to become involved. Perhaps a superposition of two different geometries
is unstable and decays into one of the two alternatives. For example, the
geometries might be the space-times of a live cat, or a dead one. I call this
decay into one or the other alternative objective reduction, which I like as a
name because it has an appropriately nice acronym. How does the Planck
length 10^-33 centimeter relate to this? Nature's criterion for determining
when two geometries are significantly different would depend upon the Planck
scale, and this fixes the timescale in which the reduction into different
alternatives occurs.
Hawking on quantum cosmology:
I will end this lecture on a topic on which Roger and I have very different
views-the arrow of time. There is a very clear distinction between the
forward and the backward directions of time in our region of the universe.
One only has to watch a film being run backward to see the difference.
Instead of cups falling off tables and getting broken, they would mend
themselves and jump back on the table. If only real life were like that.
The local laws that physical fields obey are time symmetric, or more
precisely, CPT (charge-parity-time) invariant. Thus, the observed difference
between the past and the future must come from the boundary conditions of
the universe. Let us take it that the universe is spatially closed and that it
expands to a maximum size and collapses again. As Roger has emphasized, the
universe will be very different at the two ends of this history. At what we
call the beginning of the universe, it seems to have been very smooth and
regular. However, when it collapses again, we expect it to be very
disordered and irregular. Because there are so many more disordered
configurations than ordered ones, this means that the initial conditions would
have had to be chosen incredibly precisely.
It seems, therefore, that there must be different boundary conditions at the
two ends of time. Roger's proposal is that the Weyl tensor should vanish at one
end of time but not the other. The Weyl tensor is that part of the curvature of
space-time that is not locally determined by the matter through the Einstein
equations. It would have been small in the smooth, ordered early stages but
large in the collapsing universe. Thus, this proposal would distinguish the two
ends of time and so might explain the arrow of time.
I think Roger's proposal is Weyl in more than one sense of the word. First, it
is not CPT invariant. Roger sees this as a virtue, but I feel one should hang
on to symmetries unless there are compelling reasons to give them up. Second,
if the Weyl tensor had been exactly zero in the early universe, it would have
been exactly homogeneous and isotropic and would have remained so for all time.
Roger's Weyl hypothesis could not explain the fluctuations in the background
nor the perturbations that give rise to galaxies and bodies like ourselves.
Despite all this, I think Roger has put his finger on an important difference
between the two ends of time. But the fact that the Weyl tensor was small at
one end should not be imposed as an ad hoc boundary condition but should
be deduced from a more fundamental principle, the no-boundary proposal....
How can the two ends of time be different? Why should perturbations be small
at one end but not the other? The reason is there are two possible complex
solutions of the field equations.... Obviously, one solution corresponds
to one end of time and the other to the other.... At one end, the universe
was very smooth and the Weyl tensor was  very small. It could not, however,
be exactly zero, for that would have been a violation of the uncertainty
principle. Instead there would have been small fluctuations that later grew
into galaxies and bodies like us. By contrast, the universe would have been
very irregular and chaotic at the other end of time with a Weyl tensor that was
typically large. This would explain the observed arrow of time and why cups
fall off tables and break rather than mend themselves and jump back on.
Penrose on quantum cosmology:
From what I understand of Stephen's position, I don't think that our
disagreement is very great on this point [the Weyl curvature hypothesis]. For
an initial singularity the Weyl curvature is approximately zero....
Stephen argued that there must be small quantum fluctuations in the initial
state and thus pointed out that the hypothesis that the initial Weyl curvature
is zero at the initial singularity is classical, and there is certainly some
flexibility as to the precise statement of the hypothesis. Small perturbations
are acceptable from my point of view, certainly in the quantum regime.
We just need something to constrain it very near to zero....
Maybe the no-boundary proposal of [James B.] Hartle and Hawking is a good
candidate for the structure of the initial state. However, it seems to me that
we need something very different to cope with the final state. In particular,
a theory that explains the structure of singularities would have to violate
[CPT and other symmetries] in order that something of the nature of the
Weyl curvature hypothesis can arise. This failure of time-symmetry might be
quite subtle; it would have to be implicit in the rules of that theory which
goes beyond quantum mechanics.
Hawking on physics and reality:
These lectures have shown very clearly the difference between Roger and me.
He's a Platonist and I'm a positivist. He's worried that Schroedinger's cat is
in a quantum state, where it is half alive and half dead. He feels that can't
correspond to reality. But that doesn't bother me. I don't demand that a theory
correspond to reality because I don't know what it is. Reality is not a quality
you can test with litmus paper. All I'm concerned with is that the theory
should predict the results of measurements. Quantum theory does this very
successfully....
Roger feels that...the collapse of the wave function introduces CPT violation
into physics. He sees such violations at work in at least two situations:
cosmology and black holes. I agree that we may introduce time asymmetry in the
way we ask questions about observations.  But I totally reject the idea that
there is some physical process that corresponds to the reduction of the wave
function or that this has anything to do with quantum gravity or consciousness.
That sounds like magic to me, not science.
Penrose on physics and reality:
Quantum mechanics has only been around for 75 years. This is not very long if
one compares it, for example, with Newton's theory of gravity. Therefore it
wouldn't surprise me if quantum mechanics will have to be modified for very
macroscopic objects.
At the beginning of this debate, Stephen said that he thinks that he is a
positivist, whereas I am a Platonist. I am happy with him being a positivist,
but I think that the crucial point here is, rather, that I am a realist.
Also, if one compares this debate with the famous debate of Bohr and Einstein,
some 70 years ago, I should think that Stephen plays the role of Bohr, whereas
I play  Einstein's role! For Einstein argued that there should exist something
like a real world, not necessarily represented by a wave function, whereas
Bohr stressed that the wave function doesn't describe a "real" microworld but
only "knowledge" useful for making predictions.
Bohr was perceived to have won the argument. In fact, according to the recent
biography of Einstein by [Abraham] Pais, Einstein might as well have gone
fishing from 1925 onward. Indeed, it is true that he didn't make many big
advances, even though his penetrating criticisms were very useful. I believe
that the reason why Einstein didn't continue to make big advances in quantum
theory was that a crucial ingredient was missing from quantum theory. This
missing ingredient was Stephen's discovery, 50 years later, of black hole
radiation. It is this information loss, connected with black hole radiation,
which provides the new twist.
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