The Cycles of Time. An extraordinary new vision of the Universe

Author: Javier Sánchez Cañizares
Published in: yearbook Filosófico 44/2 (2011), 416-418.
Date of publication: 2011

review expanded from Roger Penrose, Cycles of Time. An Extraordinary New View of the Universe, The Bodley Head, London 2010, 304 pp, ISBN 978-0-224-08036-1

The existence of the Second Law of Thermodynamics is one of the greatest enigmas of physics today. The evolution of the universe entails an increase in entropy that cannot be deduced from the fundamental laws of physics as we know them today, nor can it be explained on the basis of purely statistical arguments. The Second Law distinguishes between past and future time.

Roger Penrose is a master at tackling this paradox and leading us to its deepest roots: the existence of the Second Law has to do with cosmology and, specifically, with the special character -from the point of view of physics- of the Big Bang. Contrary to what superficial views of the cosmic soup may suggest, the initial states of the universe were characterised by a great uniformity in the distribution of subject, which meant an exceptionally high entropy leave compared to today.

Curiously, almost none of the "pre-Big-Bang" cosmological models (those that postulate a universe prior to the initial big bang that gave rise to the one we know today) usually enter into the discussion of the fundamental problem posed by the Second Law. The author of "The Road to Reality" does, presenting in Cycles of Time an explanation of the universe that confronts the problem of entropy.

Penrose "explores" pre-Big Bang physics from an essentially geometrical perspective, exploiting the scale invariance of spaces whose topology is determined solely by the light cones of each point in space-time. Specifically, he suggests "that the universe as a whole should be viewed as an extended conformal manifold, consisting of a (possibly infinite) succession of eons, each of which gives rise to a complete history of the expanding universe" (p. 147). This is what he calls "conformal cyclic cosmology" (CCC).

Such a proposal does not need the speculations of a currently unknown quantum theory of gravity, since each Big-Bang (which will take place at the transition from one aeon to another) would be treated in an essentially classical way, with deterministic differential equations similar to those governing the behaviour of systems within the framework of general relativity (cf. p. 204).

The close relationship between the Second Law, the gravitational Degrees of freedom and the Big-Bang prohibits a backward continuation of the former similar to a space-time bounce, either classical or quantum. The CCC, however, postulates a smooth geometrical transition between eons through a change of scale that leaves the conformal topology of space-time invariant. But how does the CCC become compatible with a Second Law that implies a continuous increase of entropy from one eon to the next? The solution of such a problem is the central question of the book (cf. p. 174).

The core topic of the solution lies in black holes - the highest entropy objects in the universe - and their evaporation process due to Hawking radiation. What Penrose proposes is that black holes are large entropy sinks. Those "places" devised by nature to resize its increase, so that, according to the CCC, a smooth transition can be made from the end of one aeon to the beginning of another. In the evaporation process of each black hole a loss of Degrees of freedom would take place, so that the phase space becomes much smaller than it was at the beginning (cf. p. 186). This destruction of information causes the entropy according to Boltzmann's definition to be resized without a violation of the Second Law (cf. pp. 188-189).

Undoubtedly, Penrose's proposal raises a long series of questions that are difficult to answer. Regarding the proposal itself, it must be said first of all that there is no consensus among experts about the destruction of Degrees of freedom inside black holes. For such space-time singularities, a quantum theory of gravity is needed, which is currently beyond our reach. On the other hand, the feasibility of CCC requires that no particle with a non-zero rest mass lasts forever (cf. p. 180). A decay process of the rest mass would have to take place, which is more than debatable with the present experimental data (cf. p. 212).

One may also wonder about the physical interpretation of the transition between eons. In particular, about the geometrical meaning of the extremely high temperature and density at each Big-Bang. Penrose seems to solve this problem geometrically, by means of the scaling procedures allowed by conformal geometry (cf. pp. 148-149). This is legitimate but incomplete, as a physical description of the process is missing.

Finally, there are a number of questions that are not answered in the work. For example, since entropy reduction seems to occur in each black hole, within one eon and not in its transition to another: is it possible to compare entropies between two eons? If so, is entropy still increasing? Do not forget that the volume of phase space is invariant to the CCC (p. 148). Penrose manages to present a scenario of a succession of eons that could be compatible with the Second Law and respectful of relativistic causality, since it does not admit closed timelines. But, even if we were eventually taking a step forward in the understanding of the universe according to the CCC, the problem of the physical origin of the Second Law has not been solved. In other words, the problem of the arrow of time and the growth of entropy remains an enigma for physics.

These objections do not detract from the brilliance of proposal which has the merit of presenting a possible experimental test of itself. The impacts between black holes in the previous eon would be the ultimate cause of the irregularities in the energy distribution observed in our present universe (cf. pp. 212ff). A proper statistical analysis of the fluctuations in the microwave background radiation (CMB) should be able to discern whether these fluctuations are due to this subject of shocks or have another origin. In particular, CCC predicts a circular outline for the basic perturbations in the CMB, but the presence of Weyl curvature in the universe distorts the circular shapes. Experimental analysis of the available data gives still very preliminary results.

Cycles of Time is a brave work, which seeks to go beyond the Big-Bang theory from a scientific point of view. Certainly, his proposal is highly speculative. Penrose is a mathematician who is committed to a geometrical interpretation of fundamental realities, so his theory may surprise those who still hold a naïve view of the methodology of current theoretical physics. However, the CCC maintains a high level of internal coherence, respecting most of the requirements that current cosmological theories must satisfy, according to the data available to us.

Penrose's proposal does not explain the Second Law, but it is able to partially circumvent it thanks to its redefinition of those cosmic sinks - not only of light and subject, but also of Degrees of freedom - called black holes. The universe would start again and again in a manner respectful of the Second Law, which does not become cancerous. Black holes - through this cleansing of information - cure each aeon of the risk of being the last of its kind. However, although Penrose is silent about it, it seems difficult to escape a global growth of entropy between eons.

To Penrose's credit, there is also the fundamental distinction in the way he understands the Big Bang as opposed to incomplete inflationary cosmologies. The latter rely on the effects of quantum gravity, but do not account for the problem of the existence of the Second Law. For Penrose, however, there is a basic physical difference between Weyl and Ricci curvature in the geometry of space-time, which allows the Big Bang to be treated classically if the Weyl curvature is zero or finite. This allows him to advance a pre-Big-Bang cosmological theory which, in principle, can be refuted experimentally.

Beyond its high Degree of physico-mathematical speculation and the questions that remain unanswered, Penrose has the merit of presenting at the end of the book a concrete prediction of the CCC in relation to the statistical analysis of the data of the CMB, which proves to be a priority for current cosmology. But Penrose also has the added merit of not making statements of a philosophical nature, which would be out of place in this subject work. Although this may make him less media-friendly than other scientists, it undoubtedly increases his well-deserved prestige as a researcher searcher for an explanation of the universe and entropy.