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239 of 245 people found the following review helpful
on October 16, 2010
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!
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167 of 177 people found the following review helpful
on May 6, 2011
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.
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53 of 56 people found the following review helpful
on November 1, 2011
Penrose puts forth an old idea, that the end of our universe is the start of a new one, in a beautiful new way. That is, eventually the universe will lose track of the scale of space and time. So the whole giant universe turns into a Big Bang of about zero size!
Astronomers have recently found out that the expansion of the universe is accelerating, so it doesn't look like it will ever recollapse in the ordinary way. But in Penrose's theory, this apparently depressing reality is essential for a cyclic universe, because it means that the universe at the end of time is a spacelike surface, so its geometry can match the geometry of the Big Bang singularity in the next eon.
He offers a partial answer for an old puzzle: why did the Big Bang have such incredibly low entropy? The second law of thermodynamics tells us that entropy never decreases. The low entropy of the Big Bang defines the arrow of time, since entropy has been increasing since then, and life wouldn't be possible without a low-entropy state to start from. But where did the very low-entropy Big Bang come from?
Penrose's answer (or part of it) is that black holes destroy the information that goes into them (whether black holes destroy information is a big controversy in physics). That means that when the black hole eventually evaporates by Hawking radiation, the entropy that was in the matter that fell in has been permanently destroyed. I don't know if this can destroy enough entropy to explain the next very low entropy Big Bang.
Penrose doesn't believe the inflation theory, which is that space expanded incredibly rapidly right after the Big Bang. He says his conformal cyclic cosmology theory explains the things that inflation was invented to explain: it explains correlations in temperature in the cosmic microwave background between areas that are separated by large angles, and the scale invariance in the temperature fluctuations. The CCC theory also requires Weyl curvature to be zero at the Big Bang. This apparently explains why we don't see magnetic monopoles, another thing that inflation is invoked to explain, although Penrose doesn't discuss this in his book.
The CCC theory seems much more appealing than the inflation theory. It's more parsimonious, not requiring extra fields or an incredibly rapid expansion of spacetime. The universe would have expanded at the normal rate, only over a very very long time before the Big Bang.
The big hole in Penrose's theory is that our universe can only lose track of the scale of space and time if rest mass disappears. Rest mass gives a scale to spacetime. So it's necessary that all particles should eventually decay into massless particles like photons, or lose their rest-mass some other way. He hasn't come up with any good explanation for how this would happen. His best attempt at a theoretical framework for the decay of rest mass is:
"A standard procedure for addressing the idea of an 'elementary particle' is to look for what are termed the 'irreducible representations of the Poincare' group'. Any elementary particle is supposed to be described according to such an irreducible representation. The Poincare' group is the mathematical structure describing the symmetries of the Minkowski space M, and this procedure is a natural one in the context of special relativity and quantum mechanics. The Poincare' group possesses two quantities referred to as Casimir operators, these being rest-mass and intrinsic spin, and accordingly the rest-mass and spin are deemed to be 'good quantum numbers', which remain constant so long as the particle is a stable one and does not interact with anything. However, this role of M appears to be less fundamental when there is a positive cosmological constant L (Greek letter Lambda in the book) present in physical laws (as L=0 for M), and it would seem that, when we are concerned with matters related to cosmology, it should be the symmetry group of de Sitter space-time D, rather than of M, that should ultimately be our concern. However, it turns out that rest-mass is not exactly a Casimir operator of the de Sitter group (there being a small additional term involving L), so that its ultimate status is more questionable in this case, and a very slow decay of rest mass seems to me to be not out of the question."
I don't know how convincing this is. Does rest mass need to be a Casimir operator of the spacetime, to be a good quantum number, so that it's conserved for a particle as long as it exists? Apparently nobody's worked out what becomes of quantum mechanics and the Standard Model of particle physics in de Sitter spacetime. Until they do, and rest mass really does turn out to fade away in the expanding universe, Penrose's theory will limp badly.
Perhaps the above quote will tell you whether you'll find Cycles of Time to be readable, or whether it'll make your eyes glaze over. I found it readable, but I'm somewhere between the "intelligent layman" and a real expert. I loved Penrose's earlier book The Road to Reality, and worked all the exercises in it that looked challenging, except for one.
In Cycles of Time, unlike in Road to Reality, Penrose relegates almost all equations and mathematics to a couple of appendices, where he explains the transition from the scale free geometry at the end of the previous eon, to the Big Bang. The dynamics of the earlier universe propagate through the Big Bang. There's a loose end: unwanted freedom in the spacetime metric right after the Big Bang, so it isn't fully determined by the universe before the Big Bang. Penrose proposes various ways of eliminating this freedom.
Penrose tends to throw around technical language without much explanation. Road to Reality might be a good reference; or Google it. He mentions "gravitational degrees of freedom" early in the book. What concretely ARE gravitational degrees of freedom, I wondered? I asked online, then noticed he defines them later in the book!
Even though he uses technical language, he's very good at making advanced physics accessible. I found Road to Reality to be intellectually nurturing. It stimulated me to learn multivariable complex analysis, which he uses in his work.
Penrose is a maverick who disagrees with much of the contemporary physics consensus. He dislikes many contemporary physics theories that are science-fictiony or kludgish, like string theory with its extra dimensions, and inflation. But as Mark Twain said, "Whenever you find yourself on the side of the majority, it is time to reform (or pause and reflect)." Penrose has done it again in this book: come up with a wonderful and beautiful idea for Penroseland, his mirror of reality. Perhaps his mirror focuses better than the consensus mirror.
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60 of 73 people found the following review helpful
on May 7, 2011
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...
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12 of 13 people found the following review helpful
on June 23, 2012
Alright. I'm not completely dim. I have an MBA, lots of work in quantitative analysis, statistics, integral and differential calculus and this book was almost unreadable for me.

Penrose may be smart, but he surely isn't interested in writing for anyone not completely comfortable with advanced math and physics and the technical jargon associated with it.

He seems to start his books with a little story to sucker you in; make you think he's going to try and explain things to you like Carl Sagan might. Then, wham! You're in to hyperbolic geometry, tensor fields and Schrodinger's cat. And when he explains his technical jargon ... it's with more technical jargon.

After a while I just found myself skipping around trying to find something written in english that I could understand.

The book might as well be written in a foreign language for most of us.
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10 of 11 people found the following review helpful
VINE VOICEon July 27, 2012
I read popularized physics books. I make no pretense of understanding every point and especially every mathematical equation but I do try to comprehend the basics. Well written books of this nature, for example "Warped Passages" by Lisa Randall, help the reader understand the latest ideas about the nature of the universe. The badly written ones, not so much. Others have complained about the heavy math understanding required for "Cycles of Time." I can't add anything to that, except to agree. However, I would have been okay with that if Penrose had been, otherwise, convincing in his basic premise. I'll try to summarize, but please forgive me if I don't get it quite right:

There was very low entropy in the universe at the instant of the big bang.
The above seems to violate the second law of thermodynamics.
The expansion of the universe in a very short interval of time soon after the big bang makes no sense.
There does seem to be an expansion but maybe it wasn't immediately after the big bang. Maybe it was before the big bang.
Our universe is presently seen to be expanding and entropy is increasing as it expands.
Given enough time, even the most basic building blocks of matter will evaporate into massless particles.
At that point, there will be a new big bang, and everything starts all over again.
By the same argument, there was a "before" to our big bang. Thus the "conformal cyclic cosmology" of the book.

Somehow I missed any conjecture of what causes the big bang in each cycle: how a flat, fully heat-dead universe could produce a low-entropy big bang and start everything over again. If you see it, please bring it to my attention. Without that, the whole argument is just flat.
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10 of 12 people found the following review helpful
on December 31, 2011
I did not know what to expect from this book when it was purchased. So far it is becoming a work horse of my cosmology trips i.e. the only nit I have with it, is that it effectively precludes the multiverse. The refinement I have presented in conferences, the last being ICGAC 10, is that the multiverse is a feed into the conformal mapping , and that black holes are de facto 5 dimensional , whereas our present universe is four dimensions. That is a horrendous over simplification, but in a general sense Penrose got the basic mechanics right.

The section on the enormous specialness of the big bang is an eye opener. The best part of the book has to do with its treatment of entropy, and initial conditions, which is a must read.

I urge non specialists and also theorists to read the book. This has been the best 29 USD spent on a purchase in 2011.
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12 of 15 people found the following review helpful
VINE VOICEon October 6, 2011
Sir Roger Penrose, Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, has written another marvellous book. Once again, he manages to discuss topics in modern physics in a way that will educate and enthuse the intelligent layman while retaining enough substance to engage the more sophisticated reader. This time, the topic is (in Penrose's words) "an extraordinary new view of the universe," a theory that he calls "Conformal Cyclic Cosmology (CCC)."

As in his previous efforts, Penrose's success derives from his ability to actually teach some fundamental concepts before entering the more speculative domains. Hence, the first third of the book is devoted to an informative explanation of entropy and the second law of thermodynamics, and their place in describing the evolution of the universe. In the second third, Penrose emphasises the unique character of the low entropy state of the early universe before gravitational degrees of freedom had been activated. In this part, he also introduces the notion of "strict conformal diagrams" that provide a graphical description of the rather involved maths.

The final portion of the book is devoted to an intriguing summary of CCC. This is based largely on Penrose's earlier introduction of the Weyl Curvature Hypothesis that requires the Weyl curvature tensor to vanish at the conformal hypersurface of the Big Bang. CCC proposes that beyond the distant future of the current universe lies another Big Bang and, conversely, before the Big Bang of the current universe lies the future infinity of a previous one, with space-time being merged at the boundary of each "aeon" by a conformal rescaling of the metric tensor. How this is reconciled with the continuing increase in entropy, consistent with the second law, is quite interesting and I won't spoil the surprise by revealing it here. The book concludes with a mathematical appendix that more fully describes some of the basic notions. This, in conjunction with the notes and cited references, will help the student on his way.

To be sure, this book will challenge even the brightest and most motivated layman. Understanding just the elementary exposition of the basic ideas requires some serious thinking. And Penrose cannot help dropping terms like "tensor field" and "tangent space" that will baffle the novice. There are even a few equations. In addition to thinking, one should be prepared to consult additional references and ask many questions. But, after all, that is what learning is all about.

Enthusiastically recommended!
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4 of 4 people found the following review helpful
on July 13, 2012
This book has problems.

To a layman, one problem of the book is that this book discusses the writer's theory which are not broadly accepted. If you are looking for a mainstream book, to find out what is going on with modern physics I would suggest looking elsewhere.

Another problem is that I think I know much more of physics and mathematics then I think the average reader of this book would yet I confess I was struggling to get through it. There are large sections that I needed help and had to bypass.

To be fair the subject is complex and it is not simple. The writer is trying to do the best he can and in that he only partly succeeds.

Overall, I suggest giving this book a miss unless you really know your stuff and you are interested in this writer's theories.
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3 of 3 people found the following review helpful
on June 11, 2012
"Cycles of Time" by Roger Penrose. Roger Penrose is an erudite and acclaimed mathematical physicist who has written a book about cosmology that a vanishingly small number of people will actually be able to read, but we can all gain some glimpses into modern physics and some visions of cosmology, according to our preparation and our concentration level. Basically, he proposes an old-new cosmology of repeating cycles, or aeons, of 10**100 (ten raised to the 100 power) years or so, in a very loose sense intermediate between the older steady-state model and the more recent big bang model. He motivates the need for a new model in order to reconcile cosmology with the Second Law of thermodynamics, namely the inexorable increase in entropy, or disorder, in the universe. Penrose provides an intuitive picture of entropy as a measure of disorder, which will be helpful to people at all levels in understanding this murky concept. It is when he "explains" the need for his new model in terms of the conformal geometrical structure of the universe that he will lose most readers, but those that bear with it will be rewarded by an edifying summary of other cosmological models and their implications for the ultimate future of the universe. According to the current favorite big bang model, the mass of the universe will accrete into black holes at the center of galaxies and Hawking radiation will slowly convert this mass to radiative energy, and the universe will end in a series of small pops of dead black holes producing a sea of massless photons and gravitons. But not to worry, because this will be another 10**100 years, which raises the question why so many talented physicists are spending their time working on cosmology when there are so many nearer term problems.
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