Equations don't sell. Pop science editors tell us that each equation added to a book halves its sales figure. If this is true, Sir Roger Penrose's Cycles of Time, which was recently released in the US, and which I can testify sold at least one copy, would have sold by the billions if only the editor would have scrapped half of the equations.

With his 2004 book The Road To Reality Penrose has shown to be capable of blurring the distinction between textbooks and pop science writings. Cycles of Time continues in this tradition. I applaud Renrose's non-populistic attitude, and admire his style. Reading 'The Road' and 'Cycles' is like listening to talks by Penrose himself. A Penrose who does not shy away from in-depth explanations and who dives deep into the beauty of mathematical physics. Penrose boldly presents spinors, twistors, Clifford algebras and conformal diagrams to the general public. I know of no other pop-science writer who dares to tread into this territory. 

Yet, one might wonder who is Penrose's audience. Lay persons mostly find his books mathematically too dense. A casual reader will prefer Hawking's The Grand Design over Penrose's math heavy Cycles of Time. Physicists on the other hand, are critical towards Penrose's pop science writings and dismiss his idiosyncratic views. Where other science popularizers see it as their task to dumb down generic ideas and the state of understanding in their field of science, Penrose aims for nothing less than to convince the reader of his latest theories. This is particularly the case with Cycles of Time in which he aims to explain his Conformal Cyclic Cosmology (CCC) model of the universe. No small task. 


The inventor of (clockwise): the Penrose triangle, Penrose tilings, Penrose diagrams, and the Penrose graphical notations. For this guy math equates to doodling!

The good thing is that Penrose's wish to convey the CCC model, forces him to educate the reader on concepts such as entropy, the arrow of time, Hubble expansion, space-time metrics, conformal geometries, and conformal diagrams. In the first two parts of Cycles of Time, he explains these abstract concepts in a very clear way using lots of hand drawings. This is Penrose's strength. Penrose, inventor of the Penrose triangle and the Penrose tilings is a geometrist at heart. He doesn't hide his love to visualize theoretical concepts, and all his books - Cycles of Time included - contain a large number of pen drawings that illustrate abstract theoretical concepts and enlighten the reader. 

The bad news is that Penrose's CCC theory, presented in the third and last part of Cycles of Time, is most likely wrong. The simple reason is that Penrose has to make too many leaps of faith to arrive at his CCC model. Moreover, his key motivation to construct this CCC model is flawed. CCC provides a solution to a non-issue. More about that later. Let's first look into CCC itself.

CCC in a nutshell

Penrose's line of reasoning roughly goes as follow. Our universe consists of matter (massive particles) and radiation (massless particles). With time, the matter in our universe will be drawn into black holes. Over even longer timescales, these black holes will evaporate. The end result is a universe filled with uniform radiation. This featureless universe is indistinguishable from a big bang, apart from the fact that the end stage of the universe is cold and filled with long-wavelength low-energy radiation, while the big bang is hot and filled with short-wavelength high-energy radiation.

Penrose continuous by making the key observation that in a universe filled with only radiation time seizes to exist. Reason being that a universe without massive particles can not contain a clock of any form. And without a clock there is also no ruler. Time and distance have disappeared. But if this is the case, there is literally nothing that distinguishes the end state of our universe from it's starting point. After ages of expansion, Penrose argues, our universe will be reduced to the big bang for the next universe. According to Penrose, our universe is a bead in a necklace of universes. A necklace in which the death of each universe represents the birth of the next universe. An attractive thought.

What's Wrong With CCC?

So what is the problem with CCC? Two key issues are discussed in Penrose's book, but in my opinion these are too easily brushed aside by the author. The first is that Penrose has to assume that black holes with time manage to 'clean out' the whole universe from massive particles. In a universe like ours that undergoes an accelerated expansion, this is extremely unlikely. There is absolutely no reason to assume that every isolated electron will be sucked up in a black hole and spit out in the form of radiation. 

Even if we give Penrose the benefit of the doubt and assume that with time all massive particles including the last electron will disappear - if not by being digested by black holes, then by some other process - a second issue gives a killing blow to Penrose's theory: the CCC theory does not pass the Eddington test. 

Penrose's motivation to come up with CCC is founded in the realization that the arrow of time and the very existence of life are all rooted in the fact that the universe started off in an ultra low entropy state. For this state to have such a low entropy it must have been very special and highly ordered. This, Penrose argues, requires an explanation. 

But for the CCC theory to explain a low entropy starting point of a universe, the previous universe in Penrose's chain of universes must have ended in a low entropy state. A highly ordered and therefore unlikely state. This goes smack in the face of the second law of thermodynamics that stipulates that entropy can only increase. 



Penrose seeks rescue in the black hole information paradox and postulates that the debate whether information is conserved in black holes has tilted to the wrong consensus. Penrose postulates that black hole evaporation is irreversible and effectively eliminates gravitational degrees of freedom from the system. The end result is that the entropy of the universe drops due to this evaporation process. 

The strongest proponent of this 'information loss assumption', Stephen Hawking, has years ago redefined his position and conceded his bet with John Preskill on this issue. This bet and how the scientific community settled the black hole information paradox in favor of information preservation is the subject of Lenny Susskind's book 'The Black Hole War'. 

Penrose might not be entirely alone in defending black hole information loss, but certainly scientific consensus is not in his favor. Although Penrose tries to argue that the elimination of degrees of freedom does not mean that the second law of thermodynamics gets violated, it should be noted that the net effect is the same. The total entropy of the universe drops. Unless one accepts highly speculative ideas like baby universes splitting off from within black holes and carrying away entropy, CCC goes against the second law of thermodynamics. I only need to quote Arthur Eddington to get a clear and final ordeal on the CCC theory:

Solution To A Non-Problem

But there is more to be hold against CCC. The whole CCC model is flawed from the start due to the simple fact that it is entirely motivated by a non-issue. As stated above, Penrose's motivation to work on CCC is the issue of the ultra low entropy starting point of the universe. This ultra-low entropy state equates to a very special, highly homogeneous configuration. Such a special state, Penrose argues, requires an explanation. Physics Blogger Sean Carroll agrees with him and words these thoughts eloquently on his website as follows:

"In the late 19th century, Boltzmann and Gibbs figured out what entropy really is: it's a measure of the number of individual microscopic states that are macroscopically indistinguishable. An omelet is higher entropy than an egg because there are more ways to re-arrange its atoms while keeping it indisputably an omelet, than there are for the egg. That provides half of the explanation for the Second Law: entropy tends to increase because there are more ways to be high entropy than low entropy. The other half of the question still remains: why was the entropy ever low in the first place?"

I have blogged about this issue before, but I did so in a somewhat cryptically way. In my next blogpost I will come back to this subject and argue that a low entropy big bang emerges naturally in an infinite universe driven by a reversible dynamics. This eliminates the need for any CCC theories. Stay tuned.

Finally, the verdict: should you buy Penrose's latest book Cycles of Time? Based on the above, you might conclude that my answer would be a resounding 'no!'. That is not the case. While I dismiss Penrose's CCC model as too speculative and most likely wrong, I am appreciative of the fact that this book contain loads of information on undisputed subjects, all presented in the clearest way. I recommend buying the book for readers interested in an in-depth discussion on entropy and cosmological models presented (parts 1 and 2 of the book). Where Penrose elects to discuss his untested ideas (part 3 of the book), he is very clear and upfront about the speculative nature of these. Be skeptical when arriving at these sections.