Cycles of Time: An Extraordinary New View of the Universe

by Roger Penrose

Some physicists have argued that the ultimate maximum entropy achieved by our universe will arise not from clumping to black holes, but from the Berkenstein–Hawking entropy of the cosmological event horizon.

To make this more dramatic, let me write this out in more everyday notation. The entropy per baryon in the CMB is around 1 000 000 000, whereas (according to the above estimate), the current entropy per baryon is about 1 000 000 000 000 000 000 000, this being mainly in black holes. Moreover, we must expect these black holes, and consequently the entropy in the universe, to grow very considerably in the future, so that even this number will be utterly swamped in the far future. Thus, our conundrum takes the form of the question: how can this be squared with what has been said in the early parts of this section? What will ultimately have happened to all this black-hole entropy?

It seems to me to be much more plausible that the information contained in all processes whose future evolution is directed into such a space-time singularity is accordingly destroyed. However, there is an alternative suggestion,[3.49] frequently argued for, that somehow the information has been ‘leaking out’ for a long time previously, encoded in what are referred to as ‘quantum entanglements’, that would be expressed in subtle correlations in the Hawking radiation coming from the hole. On this view, the Hawking radiation would not be exactly ‘thermal’ (or ‘random’), but the full information that would seem to have been irretrievably lost in the singularity is somehow taken fully into account (repeated?) outside the hole. Again I have my severe doubts about any such suggestions. It would seem that, according to proposals of this kind, whatever information finds its way to the vicinity of the singularity, must somehow be ‘repeated’ or ‘copied’ as this external entanglement information, which would in itself violate basic quantum principles.

Indeed, for many years, Hawking himself has been one of the strongest proponents of the viewpoint that information is indeed lost in black holes. Yet, at the 17th International Conference on General Relativity and Gravitation, held in Dublin in 2004, Hawking announced that he had changed his mind and, publicly forfeiting a bet that he (and Kip Thorne) had made with John Preskill, argued that he had been mistaken and that he now believed[3.52] that the information must in fact all be retrieved externally to the hole. It is certainly my personal opinion that Hawking should have stuck to his guns, and that his earlier viewpoint was far closer to the truth! However, Hawking’s revised opinion is much more in line with what might be regarded as the ‘conventional’ viewpoint among quantum field theorists. Indeed, the actual destruction of physical information is not something that appeals to most physicists, the idea that information can be destroyed in a black hole in this way being frequently referred to as the ‘black-hole information paradox’. The main reason that physicists have trouble with this information loss is that they maintain a faith that a proper quantum-gravity description of the fate of a black hole ought to be consistent with one of the fundamental principles of quantum theory known as unitary evolution, which is basically a time-symmetric[3.53] deterministic evolution of a quantum system, as governed by the fundamental Schrödinger equation. By its very nature, in...

left to itself the quantum state ψ evolves with time according to the Schrödinger equation, this being unitary evolution, a deterministic, basically time-symmetric, continuous process for which I use the letter . However, in order to ascertain what value some observable parameter q might have achieved at some time t, a quite different mathematical process is applied to ψ, referred to as making an observation, or measurement. This is described in terms of a certain operation which is applied to ψ, providing us with a set of possible alternatives ψ1, ψ2, ψ3, ψ4, …, one for each of the possible outcomes q1, q2, q3, q4, … of the chosen parameter q, and with respective probabilities P1, P2, P3, P4, … for these outcomes. This entire set of alternatives, with corresponding probabilities, is determined by and ψ by a specific mathematical procedure. To mirror what actually appears to happen in the physical world, upon measurement, we find that ψ simply jumps to one of the given set of alternatives ψ1, ψ2, ψ3, ψ4 …, say to ψj, where this choice appears to be completely random, but with a probability given by the corresponding Pj. This replacement of ψ by the particular choice ψj that Nature comes up with is referred to as the reduction of the quantum state or the collapse of the wavefunction, for which I use the letter . Following this measurement, which has caused ψ to jump (to ψj), the new wavefunction ψj again proceeds according to until a new measurement is made, and so on.

I am thus asking the reader to accept information loss in black holes—and the consequent violation of unitarity—as not only plausible, but a necessary reality, in the situations under consideration. We must re-examine Boltzmann’s definition of entropy in the context of black-hole evaporation. What does ‘information loss’ at the singularity actually mean? A better way of describing this is as a loss of degrees of freedom, so that some of the parameters describing the phase space have disappeared, and the phase space has actually become smaller than it was before.

Once the black holes have all evaporated away, we find that the zero of the entropy measure must be reset, because of this great loss of degrees of freedom, which means, in effect, that a very large number gets subtracted from the entropy value, and the allowable states in the ensuing big bang for the following aeon find themselves greatly restricted, so as to satisfy a ‘Weyl curvature hypothesis’, this providing the potential for gravitational clumping in the succeeding aeon.

Rindler observers[3.67]

it is frequently argued that a natural interpretation of the cosmological constant is that it is this vacuum energy,

even the ordinary closely flat space-time of our experiences, if it were to be examined at the minute Planck scale, would be found to have a turbulent chaotic character, or perhaps a discrete granular one—or have some other kind of unfamiliar structure better described in some other way. Wheeler presented the case for quantum effects of gravity causing the space-time at the Planck level to curl up into topological complications that he viewed as a kind of ‘quantum foam’ of ‘wormholes’.[3.70] Others have suggested that some kind of discrete structure might manifest itself (like entangled, knotted ‘loops’,[3.71] spin foams,[3.72] lattice-like structure,[3.73] causal sets,[3.74] polyhedral structure,[3.75] etc.[3.76]), or that a mathematical structure, modelled on quantum-mechanical ideas, referred to as ‘non-commutative geometry’[3.77] might become relevant, or that higher-dimensional geometry might play a role, involving string-like or membrane-like ingredients,[3.78] or even that space-time itself might fade away completely, where our normal macroscopic picture of space-time arises only as a useful notion derived from a different more primitive geometric structure (as happens with ‘Machian’[3.79] theories and with ‘twistor’ theory[3.80]). It is clear from this multitude of very different alternative suggestions that there is no agreement whatsoever as to what might actually be going on in ‘space-time’ at the Planck scale.

The point of view of CCC is to agree that when radii of curvature approach the Planck scale, the madness of quantum gravity (whatever it is) must indeed begin to take over, but the curvature in question must be Weyl cuvature, as described by the conformal curvature tensor C. Accordingly, the radii of curvature involved in the Einstein tensor E can become as small as they like, and the space-time geometry will still remain essentially classical and smooth so long as the Weyl cuvature radii are large on the Planck scale

It might have been thought that any evidence concerning a putative ‘aeon’ existing prior to our Big Bang must be well beyond any observational access, owing to the absolutely enormous temperatures arising at the Big Bang that would seem to obliterate all information, thereby separating us from all that supposed previous activity. We should bear in mind, however, that there has to be an extreme organization present in the Big Bang, as a direct implication of the Second Law, and the arguments of this book point to this ‘organization’ having the character that allows our Big Bang to be extended conformally to an aeon prior to ours, this extension being governed by a very specific deterministic evolution.

The ultimate behaviour of these matter distributions, taking the form of massless radiation (in accordance with CCC’s §3.2 requirements), can then leave its signature on the crossover 3-surface, and then perhaps be readable in subtle irregularities in the CMB. Our task would be to try to ascertain what, in this regard, would be the most important processes taking place in the course of the previous aeon, and to try to decipher the signals hidden in such tiny irregularities in the CMB.

resulting exponential expansion of that earlier aeon would bear a tantalizing similarity to the supposed inflationary phase of the currently favoured picture of the very early history of the universe, although this currently conventional picture has the exponential expansion taking place between around 10–36 s and 10–32 s in our own aeon (see §2.1, §2.6), closely following the Big Bang itself. On the other hand, CCC would place this ‘inflationary phase’ before the Big Bang, identifying it with the exponential expansion of the remote future of the previous aeon.

we see that the surface of last scattering , (decoupling; see §2.2) occurs much too close to the Big-Bang 3-surface for effects that are seen from our vantage point to be more than about 2° apart in the sky ever to have been in causal contact. This assumes that all such correlations arise from processes occurring after the Big Bang, and the different points of are in fact completely uncorrelated. Inflation is able to achieve such correlations because the ‘inflationary phase’ increases the separation between and in a conformal diagram,[3.82] so that much larger angles seen from our vantage point are brought into causal contact;

Various other possible interpretations of the red shift have been put forward from time to time, one of the most popular being some version of a ‘tired light’ proposal, according to which the photons simply ‘lose energy’ as they travel towards us. Another version proposes that time progressed more slowly in the past. Such schemes turn out to be either inconsistent with other well-established observations or principles, or ‘unhelpful’, in the sense that they can be re-phrased as being equivalent to the standard expanding-universe picture, but with unusual definitions of the measures of space and time.

B. Carter (1974), ‘Large number coincidences and the anthropic principle in cosmology’, in IAU Symposium 63: Confrontation of Cosmological Theories with Observational Data, Reidel, pp. 291–8. John D. Barrow, Frank J. Tipler (1988), The anthropic cosmological principle, Oxford University Press.