Cycles of Time: An Extraordinary New View of the Universe [ペーパーバック]

Many who wish to buy this book will be familiar with the other works of Professor Roger Penrose (such as The Road to Reality). Some will be curious to learn about a new theory of the origin of the Universe. This book presents a radical new idea which Penrose has been developing in the past few years on the Big Bang: essentially the idea is that there was a pre-Big Bang era and there will be a post-Big Crunch era too.

So one could review both the book and the idea itself. Firstly some will worry about the level of mathematics presented in this book. In the main chapters there are equations such as S = k log V - Boltzmann's Equation. If you are not comfortable with this, then maybe you will not get the most from the book. However if you are comfortable with this and similar physics equations and numbers then the first section of the book is readable. Of course there are plenty of diagrams too. There is some hard maths however and this has been relegated to the Appendix (30 pages). This maths is very advanced and another of Penrose's technical books (Penrose and Rindler Volume 2) would be needed to understand it fully - so that is only for the experts. Given that the reader wont be learning this material in the present book it shows that there is some more complex machinery behind the scenes needed to comprehend the full idea.

In the first section the book returns to an old concern of Penrose namely the entropy present in the early universe: less than today - but why so much less? The chapter then focusses in on the Big Bang described using "Conformal Diagrams". The key on page 115 is important for reading these diagrams.

Part 3 introduces the new idea called Conformal Cyclic Cosmology (CCC). Here we learn something about the idea that the Big Bang is merely a transition in the longer history of the universe. To get the most out of the mathematics in this section one needs to understand the idea of the conformal metrics introduced. Fortunately there are no calculations about it in the main text, but the idea needs to be understood. In order to develop the CCC hypothesis Penrose then needs to consider various physics issues: entropy, black hole information loss, the presence of mass in elementary particles. A novel use of other work in these areas provides for an interesting basis for the CCC hypothesis as we also study the far future of the Universe. Finally we close with some observational details from the Cosmic Background Data being gathered by satellites. So CCC is a physically testable theory!

If you are interested in another theory being presented at the forefront of Cosmology and Physics then this is for you. Also it provides another view of Penrose's approach to these subjects which is different from the mainstream. But beware that some of the mathematical ideas (of conformal infinity) go quite deep indeed - easily the subject of another book if this idea is successful!

Roger Penrose's latest book is an exposition of his latest cosmological speculations. As usual Penrose cheerfully overestimates the mathematical capabilities and accomplishments of the typical scientifically educated lay person his books are ostensibly aimed at. He presents what he sees as a baffling fact, the unusually low entropy state of the early universe, and gradually leads the reader up to his explanation of the nature of our universe. Though Penrose is coy throughout the book's first two sections about the details of his conjecture, the title gives it away and indeed this book is ultimately a speculation about cyclical universes. There are definitely some points of interest, and readers who enjoyed Penrose's earlier works such as The Emperor's New Mind will likely be intrigued by parts of the book. But while less overambitious than the author's sweeping Road to Reality, Cycles of Time is far denser than more accessible popular science works such as Stephen Hawking's A Brief History of Time, so those who found that bestseller to be of use mostly as bookcase filler might want to give Penrose a pass here.

The book is divided into three main sections: entropy and the Second Law of Thermodynamics; the Big Bang and the puzzling low-entropy state of the early universe; then the largest and most detailed concluding section. This section details Penrose's Conformal Cyclic Cosmology (CCC) model, a scheme whereby a tiny portion of a late-stage universe in its Big Rip phase becomes the seed of the next universe's Big Bang, and so on ad infinitum.

Also as the book progresses, the author goes through at least three voices: first the definite, lecturing one in which entropy and Big bang cosmology are presented. Then the speculative, theorizing one in which CCC is detailed. Finally he concludes on a tentative note with overtones of self-doubt. Here Penrose frankly muses aloud. He makes vague moves toward linking (A) the explosive late-stage expansion of the universe as the expansive cosmological constant lambda overwhelms the dwindling effects of gravity and (B) the similarly explosive growth of the very early-stage universe in its hypothetical inflationary phase. But up until that point, Penrose has expressed nothing but skepticism regarding inflation, and in fact one of the self-described strengths of his CCC proposal is that it obviates the need for inflation altogether!

Penrose raises up CCC as the latest rival to the plain linear time Big Bang. He admits to a youthful fondness for the old Continuous Creation (CC) model, and CCC is admittedly negatively motivated by an authorial distaste for the unadorned Big Bang. On the positive motivation side, Penrose has been so captivated by a mathematical model developed by his colleague Paul Tod that he has developed it into his CCC idea. There seems to be no direct evidence for CCC, it offers no possibility for experiment, and it is probably non-falsifiable. In other words, on its merits it has a great deal in common with string theory, which Penrose has always been openly skeptical of. I refer to his seduction by math because reading Penrose enthuse over Tod's conformal map and its implication of a pre-Big Bang universe is a little like reading about Edward Witten championing string theory on the grounds of its mathematical beauty.

The author is of course not the first to speculate about earlier and later Big Bangs, cyclical Big Bangs, infinite Big Bangs, Big Bounces, etc. He acknowledges as much and even devotes a brief chapter to previous pre-Big Bang theories. Oddly though, he is quite unsympathetic to rival ideas that on the surface have a great deal in common with his CCC; I am referring specifically to Andre Linde's infinite inflation model. Penrose is skeptical of inflation and the need for it and is no champion of string theory or any string-based ideas. But strings aside, anyone familiar with infinite inflation will be right at home with CCC.

So although I am left completely unconvinced by book's end about the usefulness of or the need for CCC, the foregoing thoughts should serve to demonstrate that the book has succeeded at least in getting one reader to consider Penrose's arguments and to ponder the issues he raises. If Cycles of Time can do as much for some key young physics and math students, then the author may be content.

I should mention that although the appendices are mostly repositories of even more advanced math than Penrose believed most of his readers would be comfortable with, the endnotes are of significant use while reading the text. Chore though it may be, it is a more rewarding read to keep one finger open to the notes while reading the text and flip between the two as needed. The notes explain and clarify points Penrose makes throughout the text; they are mostly not simply page references to cited works. I wish (American) publishers would realize that in many cases such as this one footnotes serve the purpose far better than endnotes; they are not just irrelevant distractions cluttering up the page margin. But this seems to be a losing battle, and Penrose's publisher, Knopf, has joined the majority in considering notes to be best tucked tidily into the back of the book, 200 pages away from the text they apply to.

Although the cover states that the book has no complex mathematical formulae in the main text (only on the appendix), the truth is that Penrose prefers to use mathematical language over physical language on most sections of the book. For instance, in the first chapter (of the three chapters of the book), Penrose talks about the Second Law of Thermodynamics and tries to mathematically argue that the Entropy on the Big Bang (or somewhen around that time) had to be very low. So it takes him about 50 pages to explain (not very successfuly) what Sean Carroll explains (very successfuly) in his entire book 'From Eternity to Here'.

Penrose tries to explain his theory of cyclic universes (aeons) from a mathematical point of view, based on conformal geometry, without giving a clear explanation of its physical meaning. I could not understand, physically, how his Conformal Cyclic Cosmology differs from other cyclic theories, such as 3-brane collisions or other theories (which Penrose hardly mentions).

Penrose his a brilliant mathematician and uses that talent on Relativity and Cosmology - the problem is that he forgets that not everybody (well, almost nobody) is as math genius. So, I will wait for some other author to write about Penrose's theory (translating it to common physical language) so that I can understand Penrose's idea...