In his latest book, Roger Penrose deals with three foundational problems of current physics from his particularly fresh perspective. He criticizes mainstream string theories, standard interpretations of quantum mechanics, and pre‐Big Bang cosmologies inasmuch as they aim to solve profound questions while glossing over equally deep issues in our understanding of nature. In this review, I analyze Penrose's main arguments, emphasizing his presentation of the Second Law conundrum as “the most profound mystery of cosmology”, and discuss his own proposals to overcome the impasse. I especially focus on the capabilities of conformal cyclic cosmology to illuminate the enigma of the extraordinarily low entropy at the Big Bang and review its capacity of success in stipulating a reset for the entropy of the universe. Even though one need not follow Penrose's tentative answers, which are not immune to serious critiques, much of his view can be shared as a sound starting point in search of “the new physics of the universe.”

INTRODUCTION

One part in ten to the power of 10¹²⁴. One divided by one followed by 10¹²⁴ zeros. A denominator which cannot be written down in decimal notation because there is no space enough in the known universe to set in a row 10¹²⁴ zeros of, say, one millimeter each. This is the ridiculous probability of a Big Bang like ours giving rise to the universe we inhabit, according to estimates of entropy. It is also the most astounding and controversial number that can be linked to Roger Penrose's scientific contribution. His most recent book (reviewed here) does not present much new material, but has the virtue of introducing the main conundrums in current physics from his vantage point. He has never been a mainstream physicist, but who should be, given the current impasse of cosmology? (Mangabeira Unger and Smolin ).

Fashion, Faith and Fantasy in the New Physics of the Universe follows the lectures offered by the author at Princeton University more than a decade ago in a nontechnical jargon (technicalities are reserved for the appendices). The tone is highly critical of the fashion for superstrings, of physicists’ faith in quantum mechanics, and of cosmological theories’ fantasies when trying to explain away the Big Bang for different reasons. And that is probably why one can often share Penrose's criticisms while occasionally remaining skeptical about his own proposals, especially when providing a solution obscurum per obscurius. Nevertheless, his insights should be made known to any physicist and philosopher who wishes to understand where the problems in our understanding of nature really lie. In this essay, I will review the three more relevant problems, in keeping with the book's structure, and focus on the Second Law puzzle.

FUNCTIONAL FREEDOM VS. STRING THEORIES

Penrose invokes functional freedom as the main setback haunting string theories. As is well known, string supporters devise a universe with 9 + 1 (or 10 + 1 in the case of M‐theory) dimensions which hopefully ease mathematical calculations and make room for finite answers. If one wishes to apply such view to our homely perception of a 3 + 1–dimensional world, some very good argument needs to be made on why one need not care about the remaining 6 (or 7) spatial dimensions. Let us listen to Penrose's strong interrogation in this regard: “How is it that the highly thermalized matter degrees of freedom in the very early 9‐spatial supra‐dimensional universe could somehow have adjusted themselves so as to leave the extra 6 dimensions so apparently completely unexcited, as string theory appears to demand? One must also ask what gravitational dynamics could have produced such an enormous discrepancy in the different spatial dimensions, and question especially how it could have so cleanly separated the 6 curled‐up unexcited dimensions from the 3 expanding ones” (197).

But that is not the only question related to arguments of functional freedom. “What happens to the floods of excessive degrees of freedom that now become available to the system, by virtue of the huge functional freedom that is potentially available in the extra spatial dimensions?” (41). One can raise serious doubts regarding their being under control. Moreover, “the logical implication of the string theorist's extra spatial dimensions would be a completely unstable universe, in which these extra dimensions would be expected to collapse dynamically, with disastrous consequences for the macroscopic space‐time geometry that we are familiar with” (69). Initial restrictions on the ground state—for example, use of Calabi‐Yau geometries for the extra dimensions—to avoid such instabilities cannot take over the general dynamics of space‐time. Curvatures are expected to become infinite at some point, precluding the emergence of any quasi‐classical space‐time. Even for string theories, the singularity theorems of general relativity—culminating in the work of Hawking and Penrose ()—loom large.

Perturbations of space‐time lead to singularities irrespective of supersymmetry arguments. Of course, one may always resort to symmetry‐breaking arguments to cope with the departure from exact supersymmetry actually observed in nature. However, such selection procedures seem to be hardly justified. The huge number of inequivalent vacua (available ground states) in M‐theories—10⁵⁰⁰ possibilities for the moduli of Calabi‐Yau spaces—paves the way for recurring to dubious selection arguments in the string community, as invoking some sort of anthropic principle (119). Even though it is not immediately evident how to address the functional freedom issue in a general quantum context, the odds are more unfavorable, because “the wave function involves a functional freedom that is far higher than that which manifests itself in reality, or at least in that aspect of reality that is revealed as the result of a quantum measurement” (198). Apart from instability problems, string theories must face up to a noted trouble in philosophy of science: there is no isomorphism between our most basic theories and nature, so that further prescriptions and selection rules need to be introduced almost by fiat.

BEYOND QUANTUM MECHANICS

This situation leads to Penrose's consideration of quantum mechanics and physicists’ faith in it, perhaps because “there are no observations whatever, to date, which contradict the expectations of the theory” (124). As is well known, the standard interpretation of quantum mechanics considers two basic, fundamentally irreducible, processes: the deterministic evolution of the wave‐function according to the Schrödinger equation, once the initial conditions have been settled (U‐process); and the indeterministic wave‐function collapse into one of the possible outcomes, after performing a specific measurement (R‐process). This is the measurement paradox. Penrose shows the inconsistencies and insufficiencies of trying to develop an R‐process in the macroscopic world from an allegedly more basic U‐process in the microscopic realm. Contextual and cognitive aspects appear as essential ingredients in our interpretation of quantum mechanics. For instance, “the particle‐like aspects of photons do not come about from their wave functions having … a highly localized nature. They come, instead, from the fact that the measurement being performed happens to be one that is geared to observing their particle‐like characteristics” (157). In null measurements, on the other hand, the state of the system necessarily “jumps” even when it does not disturb the measuring device (172). There seems to be something very subtle regarding how our cognition deals with nature. The wave‐function presents ontic and epistemic features which must be considered together at the same time, if one wants to make sense of what is going on out there.

None of this is solved with alternative quantum mechanics interpretations conducive to double ontologies, as the Bohmian picture or the resort to environment‐induced decoherence. Nor with many worlds interpretations, where “we may definitely question why human experiences are to be allowed to un‐superpose a given quantum state into two parallel world states, rather than maintaining just one superposed world state—which is what the U‐description actually provides us with” (207). Accordingly, “to get a proper solution to the measurement paradox, we need a change in the physics, not just some clever mathematics, brought in to cover the ontological cracks” (206). And he sets out to work: with clever mathematics, as provided by his twistor theory using non‐localities of holomorphic cohomology possibly linked to the puzzling non‐local aspects of quantum entanglement and measurement; and with new physics, making current quantum mechanics and its linearity a provisional theory until gravity may properly be taken into account. For Penrose, the final answer must give precedence to the principles of relativity theory. His cue is that “[A]ll quantum state reductions arise as gravitational effects. … In many standard situations of quantum measurement, the main mass displacements would occur in the environment, entangled with the measuring device, and in this way the conventional ‘environmental decoherence’ viewpoint may acquire a consistent ontology” (215). In other words, environment‐induced decoherence may become ontologically univocal only when subsumed into gravity‐induced objective reduction of the wave‐function.

STRUGGLING WITH THE SECOND LAW

All in all, the most ambitious new physics conjured up by Penrose aims to answer “the most profound mystery of cosmology” (258): the extraordinarily tiny entropy at the Big Bang as represented by the number with which this review begins. There are many other cosmological problems and many other proposals which try to extend standard Big Bang cosmology to inflationist or pre–Big Bang scenarios, as suggested by the presence of correlations in the small deviations from uniformity of the cosmic microwave background which extend over wide angles of the sky (307). Fantasy is needed for the new physics, but current proposals fall short of solving the singularity problem, singularities remaining even in the quantized theory. The claim that singularities would not persist when asymmetrical generic perturbations are introduced turned out not to be correct because “for local situations of gravitational collapse, once a trapped surface has occurred, singularities cannot be avoided, for physically reasonable classical material, quite irrespective of any assumptions of symmetry” (239). Singularities are but a generic feature of gravitational collapse.

Nevertheless, all these problems point to the deep connection between the Second Law of Thermodynamics and the nature of the singularities in space‐time structure. Paying heed only to statistics, one would obtain a contradiction with the Second Law if the procedure is applied to the past direction of time. Quite the contrary, the Second Law works because of the existence of an extraordinarily macroscopically organized initial state of the universe (250). Beware! The entropy of the universe does not increase because the universe is expanding—this expansion being essentially adiabatic. In fact, one could have a big crunch with a final state in a very tiny scale with huge entropy. “The answer lies in the fact that there can be an enormous entropy gain once we allow significant deviations from spatial uniformity, the greatest gain resulting from those irregularities leading to black holes. A spatially uniform Big Bang, therefore, can indeed be of hugely low entropy, relatively speaking, despite the thermal nature of its contents” (255).

Whereas the universe can be partially thermalized at the very beginning in its non‐gravitational degrees of freedom—as the black‐body shape of the cosmic microwave background suggests—it is completely out of equilibrium regarding gravity. “[T]he entropy was low in a very particular way, and apparently only in the way, namely that the gravitational degrees of freedom were, for some reason, completely suppressed. … To my mind, this is perhaps the most profound mystery of cosmology and, for some reason, it is a still a largely unappreciated mystery!” (258). Contrary to many cosmologists that gloss over the Second Law, Penrose rightly points out where the conundrum really lies: the unknown origin of the Second Law and the impossibility of its stemming from ordinary physical evolution, defined by time‐reversible equations and random initial conditions.

Some corollaries must then be underscored. First, the emergence of life on the Earth does not need whatsoever such absurd smallness in the Big Bang entropy. It is much less expensive—in entropic terms—to make lots of small habitable universes than it is to make just one big universe like ours—also habitable, as a matter of fact. The emergence of brains—the so called Boltzmann brain paradox—out of sheer randomness is thermodynamically much cheaper than the cost of an evolving universe with galaxies, stars, and planets, where life and evolution may eventually appear. The anthropic argument is thus futile and can be made redundant. Gravity on its own, via star formation, seems capable of getting low entropy photons necessary for the emergence and sustainability of life, for which one does not need the thermalized cosmic microwave background relic. Consequently, our universe's bio‐friendliness possesses a highly non‐local character, a feature very seldom recognized or tackled by most physicists and biologists.

Second, even though inflationary models succeed in predicting the right fluctuations in the cosmic microwave background, they become wanting in giving an answer to the existence of the Second Law. They use it, but they cannot explain it. Moreover, none of the current proposals for extending cosmology beyond the standard Big Bang theory “explains the fantastic discrepancy between (a) the wild high‐entropy geometry of black‐hole singularities and (b) the extraordinarily special geometry of the Big Bang” (333). The Big Bang singularity cannot be understood whatsoever as a time‐reversal black‐hole singularity, and perhaps that is what inspires Penrose for leaving aside quantum theory and thinking in terms of the type of geometry that must have held sway in the vicinity of the Big Bang. The upshot is his conformal cyclic—or crazy, in his words—cosmology.

Penrose's proposal is highly geometrical in motivation, aiming at compliance with the Weyl curvature hypothesis. “The Weyl curvature hypothesis asserts that any space‐time singularity of past type—i.e. from which timelike curves can emerge into the future, but not enter from the past …—must have vanishing Weyl tensor, in the limit as the singularity is approached inwards from the future along any of these timelike curves” (373). Benefitting from Tod's mathematical argument—that our Big Bang can be conformally represented as a smooth spacelike 3‐surface, across which the space‐time is, in principle, extendible into the past in a conformally smooth way—the author assigns physical reality to the pre–Big Bang region, from which massless particles such as photons could pass through the Big Bang from before to after it, that is, from the previous aeon to the next one. At the Big Bang, the rest masses of all particles become insignificant. The conformal extension gives them a past. Rescaling the space‐time metrics with a global factor, different for each aeon but leaving invariant the null‐cone structure at each point of space‐time, the transition at the Big Bang can be made smooth. Some more technical points linking the rescaling factors with the emergence of mass (and dark matter) need to be introduced, but the procedure seems clear enough without the need for invoking subtle quantum gravity effects. “What would have been the inflationary phase of each aeon is replaced by the ultimate exponential expanding phase of the previous aeon (382). Circular correlations at the cosmic microwave background—a very controversial issue at the moment (see, e.g., Moss, Scott, and Zibin, ; Gurzadyan and Penrose ; )—should provide traces of pre–Big Bang activity—e.g., inhomogeneities in the supermassive black‐hole distribution—in previous aeons.

Fare well, what happens next with the Second Law? Quite surprisingly, in my opinion, Penrose relies on the loss of dynamical degrees of freedom inside black holes—which will eventually evaporate due to Hawking radiation roughly after 10⁹⁰ years—to postulate a redefinition of the universe phase space, and accordingly of entropy, in the transition zone between aeons (382–83). Somehow, the loss of information is possible because the U‐linear process of quantum mechanics no longer rules when gravity does take over deep inside black holes. Then, the Second Law is transcended: “[B]y the time all the black holes have completely evaporated away in an aeon …, the entropy definition that would initially be employed as appropriate would have become inappropriate after that period of time, and a new definition, providing a far smaller entropy value, would have become relevant some while before the crossover into the next aeon” (386).

Unfortunately, it is difficult to avoid the impression that Penrose is sweeping under the rug. At this point, one can at least reveal the following drawbacks and inconsistencies:

• (1)

  Such a line of reasoning contradicts what the phase space of the universe means, turning useless Boltzmann's definition of entropy. If one fully endorses Penrose's conformal cyclic cosmology, there is no possible comparison of entropies among aeons. Or is there? It is highly unclear how a smooth transition between aeons can be maintained in parallel with a strong discontinuity in the definition of entropy for each aeon.

• (2)

  Is the (alleged) redefinition of entropy a local (dependent on each black‐hole evaporation, with a local end of time) or a global phenomenon occurring in the universe “some while before the crossover into the next aeon”? What is the meaning of “while” in such a statement, when time itself becomes meaningless? Is not the rescaling in the space‐time metrics affecting the counting of microstates and the global entropy of each aeon? Little is known about the physics inside black holes and invoking an overall loss of information tries to find out an explanation obscurum per obscurius. Indeed, for the information loss paradox to ensue, additional speculative assumptions are necessary, there being a strong link between black holes, the issue of information loss, and the very measurement problem (Okon and Sudarsky ).

• (3)

  Last but not least, a methodological point seems relevant here. One cannot base all reasons supporting the extremely low entropy at the Big Bang on the calculation of black holes’ entropy, providing an entropy value of around 10¹²⁴ as a possibility for the space‐time singularity constituting the initial state of the universe as stated by the Bekenstein‐Hawking formula, whereas later rejecting the black‐hole entropy to make conformal cyclic cosmology work. Even though “there is still no totally convincing and unambiguous procedure for obtaining the Bekenstein‐Hawking black‐hole formula from the general Boltzmann entropy definition” (106), the figure 10¹²⁴ may not be neglected. If black holes’ entropy cannot even be ignored in the ekpyrotic crunch‐to‐bang transition (332–33), neither should it in conformal cyclic cosmology!

CONCLUSIONS

The easy summary of Penrose's search of a new physics of the universe is this: string theories must be replaced with twistor theory, standard quantum mechanics with gravity‐induced objective reduction of the wave‐function, and beyond‐Big‐Bang cosmologies with conformal cyclic cosmology. Easy, but unfair to a physicist who succeeds in conveying his worries regarding excessive fashion, faith, and fantasy in current scientific endeavors. Are there ulterior reasons for his criticisms? Yes, there are. String theory's requirements of extra spatial dimensions get along badly with the beautiful links between our experienced universe and Lorentzian 4‐space, so much beloved to Penrose (393). There should also be a limit to our quantum faith (126): the underlying duality of quantum mechanics could be superseded paying heed to the principles of relativity, because the principle of equivalence should be more basic than the principle of linear superposition (395). Quantum gravity is, according to the author, not really what cosmologists should be looking for; one reason among others being that no quantum‐gravity theory is necessary to understand the Big Bang and its extraordinarily low entropy.

Do these reasons suffice to follow Penrose? Probably not. But he is to be followed in his scientific honesty, acuteness, and humility in dealing with current problems in the foundations of physics without dodging them. Actually, he has already been defined as “a scientist who transcends the boundaries of science, seeking the ultimate meaning of things, and thus he behaves like a philosopher” (Herce , 692). A physicist who continues endlessly struggling to reach some truth, instead of ill‐founded opinions, and a natural philosopher who acknowledges his epistemic shortcomings. Does it all mean to take a step forward to religion and transcendence? Not necessarily, but it shows how the house of science itself possesses open windows inviting scientists to see through them. In the end, “how does one wade through the multitude that is there largely because it is a multitude, rather than because it contains ideas, either new or old, that have genuine substance, coherence, and truth? It is a difficult question and I can supply no clear answer” (394). Nor can I, but gratitude and recognition among scientists and believers are well‐deserved for Penrose and his proposals.