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on 2 January 2011
After being delighted with Penrose's "Road to Reality" (2004) I couldn't wait to see what he would say about cosmology. Penrose's whole argument revolves around the consideration of the constraints put on cosmological theories by the Second Law of Thermodynamics, constraints he hinted at in the "Road to Reality".

These constraints he elaborates in a deep discussion of the nature of entropy, and what is so very special about the Big Bang. The book has three parts, "The Second Law and its Underlying Mystery", "The Oddly Special Nature of the Big Bang"; and the speculative proposal he concludes with : "Conformal Cyclic Cosmology".

Penrose takes no hostages : this is a deeply mathematical book, as is "The Road to Reality". He is a Platonist, he believes there is something there to tell us about! The first two sections of the book are "standard physics", But, as Seth Lloyd said in his Physics World review of the previous book, "When he represents the well established, nailed-down parts of mathematics and physics, Penrose is a joy to read. ... Penrose's treatment is ... deep; he is witty; he provides elegant insights." So his first section, which covers Bolzmann's definition of entropy, Liouville's Theorem, and similar matters, manages to explain the gigantic nature of phase space, the remarkable fact that although the equations of motion are symmetrical with time the path taken though phase space is definitely time-asymmetrical, and the robustness of the definition of entropy despite its apparent subjectivity in the details of counting states in phase space; all in only 45 rather small pages.

The second section now takes this "elementary" treatment and systematically applies it at a cosmological scale. There is a very strange peculiarity here which becomes very obvious in this Part. I think that Penrose thinks that his explanations could be followed by Everyman with a little application, since he carefully explains the difference between natural logarithms and logarithms with base 10. But he then launches into an intricate exposition of conformal geometry as it applies to the metric tensor of General Relativity! His purpose here, never mind who can understand it, is to use the constraints implied by the Second Law on a cosmological scale to constrain the geometry of space-time at the Big Bang.

And it appears that the constraints are very real. Because the entropy at the Big Bang is of necessity extraordinarily low, it must be (it seems) that gravitational degrees of freedom cannot have been excited. More explicitly, he draws a mathematical analogy between the electromagnetic field tensor F and the charge-current vector J in the Maxwell equations on the one hand, and (respectively, from General Relativity) the conformal Weyl tensor C and the Einstein or Ricci tensor E on the other; where E provides the source of the gravitational field (involving the mass-energy density tensor) and C characterises the curvature of space-time. Penrose asserts the "Weyl curvature hypothesis" C=0 at the Big Bang to represent its special low-entropy state.

But, and now here is the trick, a smooth C at the Big Bang invites a mathematical expression of this assertion that implies a smooth C prior to the Big Bang. Prior? Fear not! This is only a mathematical fiction. Or is it? Penrose then opens his third section where he piles speculation upon speculation to show that it is not irrational to consider the possibility of continuity "before" the Big Bang and "after" the what I shall call the Big Crunch for brevity. The background of this is the old belief of physicists, nearly universally held since Newton, that the Universe (the totality of everything physical that is) is really infinite in time. Today, it is conventional to say that spacetime itself originated at the Big Bang, and to speak of events prior to the Big Bang is to speak literal nonsense. But, Penrose suggests, this may not be necessarily true. And, he goes further to suggest, it is the detailed structure of the irregularities in the cosmic microwave background that may enable us to look behind the Big Bang without invoking inflation theories.

I must confess to being way out of my depth in this section. What is clear though is that Penrose believes that quantum theory, despite its magnificent observational successes, is still only a provisional theory; a position for which he claims the support of no less than Dirac himself. Everyone knows that a quantum theory of gravity is yet to be achieved, so that it is clear, even without the embarrassing anomalies of the mysterious dark matter and dark energy, that our ignorance is still profound. Central to Penrose's case in this third section is his account of information loss in black holes, and the consequent necessary non-unitary nature of Nature, a consequence that he has no hesitation in linking with the quantum mechanical problem of the collapse of the wave function during observations (the problem of Schrödinger's cat).

I am personally disposed to believe that the Universe is finite in time, at least towards the past. Perhaps this is something beyond observational proof, but in any case I think that Penrose's discussion, whether you believe him or not, is elegant and profound, and I sincerely hope that the new generation of mathematical physicists will take him very seriously. I think he is pointing to the next revolution in physics, with the development of quantum gravity, a consequent revolution in cosmology, and progress at last in some glimmer of appreciation of what consciousness could possibly be. The Universe is intelligible, and the systematic demand for intelligibility has always stimulated revolutions in our understanding.
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on 18 June 2017
This is Penrose explaining the entropy problem with the Big Bang theory. Ít could have been shorter. It is nevertheless interesting, if controversial. There is a good deal of spin-off cosmological knowledge in it. It does make one gasp at the scale of the known universe and the deductive power of the brains on our insignificant earth. Overall an enjoyable and quotable read.
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on 28 February 2012
Reflecting other reviews here, the level of Maths required to appreciate this book is high. Not just maths, but maths particular to understanding the type of physics relevant to multidimensional physics! I am up to Engineering degree Maths and this is way beyond that. Trying to hang on to Penrose's coattails through the maths parts really turned me off I'm sad to say. Plus it really lacks the type of explanation required for the lay-man like me, so that the theme gradually becomes more and more confusing as more and more little pieces come and go unexplained. So I am not quite sure at what level this book is aimed. If I were a student of physics at Princeton I think I would find it enjoyable.

As it was , the book came and went and I felt bereft of information I could digest. I quickly turned to Michio Kaku "Hyperspace" for comfort and someone who actually takes time to explain complicated ideas and knows that the lay-man is interested but needs the information to be distilled.
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on 8 October 2010
Before reading this review, keep in mind this is a review of the book and how well it reads rather than the science of the book:

If like me you are an avid reader of popular science and feel the best way to communicate complex theories to the layman is through clever analogies, then I would be careful before delving into this book. What Penrose sets up is a bewildering array of algebraic equations and somewhat vague diagrams with little warning beforehand. The vagueness does not come about because Penrose doesn't know what he's talking about -he clearly does- but rather that as a reader, to understand his descriptions on an intuitive level, you need to have some familiarity and grounding in algebra. For those that do, I'm sure this book will provide an interesting, if still challenging, read. For those, like me, who have banished all algebra since school, it proves very hard to grasp onto any narrative. It's very hard to understand exactly where Penrose is taking his argument since it's clearly important to understand the relevance of the countless equations and diagrams he provides. Blink, and you'll miss the point of the whole book.

The main problem is that Penrose assumes far too much on the part of the reader. On the inside of the book cover, the words 'basic ingredients are introduced...without any complex mathematical formulae' sting like salt to a wound. It's a horribly misleading introduction once you've become a little familiar with the pages thereafter. 'Cycles of Time' is seemingly written as though intended for his peers rather than the general public, and as someone who has a keen interest but limited knowledge in physics, this is very frustrating. Penrose is a great scientist and, from what I can gather from various interviews and lectures available online, a very kind, friendly and ultimately likable chap. But compared to the friendly reassuring prose and lucid style of popular science authors like Leonard Susskind, John Gribbin and Brian Greene, Penrose's book reads more like a textbook and no amount of charm on his part can make up for this fact. It's a shame really, because Penrose's ideas deserve to be heard by as many people as possible.

I think this book should really come with a warning: Reader must have knowledge and competent handle on algebra. If not a warning, then at least a free gift certificate for 'Algebra for Dummies'.
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on 25 October 2010
I read Hawking's "The Grand Design" about two weeks before picking this up. I'd been quite disappointed with that one, as I felt it to be so dumbed down that the arguments lost cohesion and descended into a rather confused and impregnable morass. What a refreshing contrast Roger Penrose's book has been! The explanations are clear with good examples and Roger builds his arguments logically and coherently. I never knew the second law of thermodynamics was so interesting! It's not for the faint-hearted though - the mathematics in this book are essential to make sense of it, and I suspect they will be hard going for anyone without exposure beyond A-level. I think this point will be devisive. But personally, I enjoyed the maths and it was nice to finally understand why Hawking was conjecturing about why we don't remember the future in "A Brief History of Time"!
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on 24 September 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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on 6 December 2011
I honestly cannot figure whether this book is to be taken literally or as a fantasy history of the universe(s) consistent with (mostly) established scientific knowledge: along the lines of The Hitchhiker's Guide To The Galaxy, perhaps?

Don't get me wrong. It is quite a good read, largely redeemed by a host of diagrams - hand-waving made manifest - which convey obscure and multidimensional ideas in artistic form.

The theme is an old chestnut about whether our universe is merely one in an infinite succession. The issue used to turn upon expansion eventually ceasing, followed by collapse, a singularity and a fresh start. The second law of thermodynamics raised problems about the slew of entropy to be disposed of at change-over. And since the 1998 detection of a sizable cosmological constant the collapse process is ruled out anyway.

Both the second law and accelerating expansion aspects are addressed here. A lot of stuff on tensors went way over my head, but the author manages to hold the narrative together even when detail becomes a bit obscure.

Around forty pages in, ambiguity surfaced. The relentless second law, which had smashed a carelessly-placed egg so irreversibly, sometimes behaved subtly, said Sir Roger, as exemplified by the amazing un-mixing of dye by reversing the stirrer in a special apparatus. It raised "profound issues", even "confusing issues of subjectivity..."

Hang on! He must have used examples like this to see if students had been listening to that clause in the entropy rule which specifies "in an isolated system". Is he suggesting the universe is not an isolated system? Outside agencies to turn the handle? Surely not!

But no, it later turns out that the entropy largely disappears in black holes, according to Steven Hawking. Never mind that S. H. changed his mind on this in 2004 and duly paid up on bets, as described in The Black Hole War by Leonard Susskind.

The author's way of getting rid of hadronic matter in the late universe also seems dubious. Most could go into black holes which evaporate over 10^100 years or so (with a final "pop") as Hawking radiation; colliding black holes could produce massless gravitons; but what of the rest? "Protons ... might eventually, over vast periods of time, decay into less massive particles"; (positrons in the end). And "something to be considered seriously is that rest-mass is not the absolute constant that we imagine it to be". Same with dark matter. Also, "over the reaches of eternity, all electric charge could eventually vanish away", with electrons and positrons ending up as neutrinos. Lack of evidence for any of this is acknowledged; but, given time...?

The great thing is that when all particles are massless there can be no measure of time, so all the hanging around for an eternity until the changeover to the next big bang will not be so interminable. And evidence for the theory might eventually be seen in raindrop patterns on our CMB where graviton bursts from the yester-universe impinged on what became the final scattering horizon. Eventually, but not just yet...

I wouldn't mind all this fanciful stuff; it is quite like Douglas Adams's use of concepts that almost make sense, like superluminal travel via the infinite improbability drive, or the invisibility cloak of the SEP field (Somebody Else's Problem); but it is then a bit inconsistent to go off into realms of hyper science that have absolutely no bearing on the issue.
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on 3 February 2013
This book is best regarded as an appendix to the author's Road to Reality. This means that it does not spare you some difficult maths. Even with my A level maths I found some of this to be difficult. Some of this is perhaps not explained well enough for this layman. However, one does get an idea of the issues that have troubled this distinguished mathematician especially the second law of thermodynamics.

He views quantum theory as a provisional theory and is not impressed by string theory. He is troubled by the predicted end of the universe. I am not sure about his proposed solution but it is good to have such an intelligent appraisal of the evidence. I only wish it had been easier to follow.

One stylistic note too many sentences end with an ! which is irritating as this is neither a chess match nor a girl's magazine. There are some spelling mistake such as council when counsel is meant.
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on 8 December 2011
This book centres on the role of entropy in discussing the evolution of the Universe. In essence the author allows for entropy to be low in the beginning, and to increase as the universe expands without limit. He then goes on to theorise that entropy is lost when matter enters a black hole, and then, in the far future, when all matter has been be absorbed leaving nothing but faint radiation, something will then be able to form the next 'Big Bang'.

His text is not easy to read, even simple concepts like logarithms are poorly defined, and often key facts are quoted without any justification. He uses abstract mathematics at random, interspersed with rambling text. Even so I felt I could grasp the conclusions he was making, which from a philosophical viewpoint were interesting. You just have to believe his maths is correct !
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on 25 February 2011
This is a very interesting read on Penrose's new hypothesis: conformal cyclic cosmology. Before he gets to this in the third part of the book, he first needs to give the reader the background to his thinking. To that end, the first part of the book looks at the Second Law of Thermodymanics, which plays a pivotal role in this work. So if you don't yet have any idea what this is, I would recommend a little preliminary reading before tackling Cycles of Time.

If you are not familiar with Penrose's writings, then this perhaps is not the best starting point. He jumps straight into the Second Law and doesn't shy away from the necessary maths. For a science graduate, this is relatively easy reading, though those without a formal background in maths or physics may struggle, although Penrose's styles of diagrams are immensely helpful. One thing that is helpful is that even if you haven't grasped all the detail in a given section (and I certainly didn't) then that doesn't mean you cannot grasp any of the later concepts.

No one could ever accuse Penrose of patronising his audience, and though many topics will be familiar to scientists, Penrose's particular style always stretches you and makes you think in a slightly different way; so that which you thought you knew quite well suddenly has a few extra question marks posed against it. One thing that is very praiseworthy in this book is Penrose's modesty and his clearly laying out of what is well evidenced scientific consensus and what is his own minority view, as well as pointing out the drawbacks in his own theory. This style contrasts greatly with the brash optimism that Hawking & Mlodinow put forward in their book, The Grand Design, published within a few weeks of Cycles of Time. The fact that Penrose does this raises some interesting questions. For example, he does state that in order for his hypothesis to be correct, we would have abandon many well-established theories, such as the invariability of rest-masses of fundamental particles.

I could not claim to have fully understand all the nuances and detail of this book at the first, but that does not diminish my enjoyment of it or my ability to get the overall gist of it. I will be re-reading this book, going over each line in more detail in order to get the complete picture.
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