This isn’t really a review of “Cycles of Time”: I’m not going to discuss the structure of the book or the quality of the writing. Instead I’ve tried for my own benefit to summarise what I learned from reading it. I hope I’ve done Professor Penrose justice. Any rubbish I’ve written is my responsibility, not his!

A big problem with our current best description of the evolution of the universe is the Big Bang. There are good theories and explanations about why the universe looks like it does 14 billion years on, but what Banged and why is rather vague. An explanation based on a random quantum event is about the best going but it does seem rather unsatisfactory. An associated problem comes from the second law of thermodynamics, which requires entropy (‘randomness’) to be always increasing, which implies it had a very low value at the moment of the Big Bang.

Roger Penrose’s latest book addresses the question “What came before the Big Bang?” For those who don’t know why Penrose’s thoughts are worth considering, I quote from Wikipedia:

Sir Roger Penrose OM FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. He has received a number of prizes and awards, including the 1988 Wolf Prize for physics which he shared with Stephen Hawking for their contribution to our understanding of the universe. He is renowned for his work in mathematical physics, in particular his contributions to general relativity and cosmology. He is also a recreational mathematician and philosopher.

Although he says he has relegated the difficult maths to appendices I admit I can’t even follow the mathematics (geometry) in the main text. Conformal scaling of tensors in field equations, if that makes sense, is more than I can cope with. But I think I get the general idea. The universe, or spacetime, has a geometry. Not the plane Euclidean geometry some of us learned at school but something much more complex. Penrose’s analysis is based on conformal geometry where shapes and angles are preserved when the underlying ‘fabric’ is distorted. In this geometry, infinity becomes a definite boundary rather than an unattainable end point always approached but never reached.

The universe as we know it is generally accepted to be about 13.7 billion years old. That’s 1.37×10¹⁰ years. Continue for all that time ten times over. It’s now 1.37×10¹¹ years old. Do all those 10¹¹ years ten times over and it’s 10¹² years. Penrose proposes that over an unthinkable timescale of the order of 10¹⁰⁰ years, which he calls an aeon, the universe comes to a final end which is the start of another.

He calls his theory Conformal Cyclical Cosmology. The length of an aeon is determined by the expansion and cooling of the universe, where long after the stars have died and become cold dwarfs or black holes spacetime consists of these cold massive objects and low-energy photons and gravitons. The black holes themselves lose mass by Hawking radiation, which takes place over these vast periods of time. Estimating the length of an aeon at 10¹⁰⁰ years is based on the time it would take for the universe to cool to a temperature at which the largest black holes would radiate their mass away and die with a final ‘pop’.

General relativity implies that massless particles (photons, gravitons) are oblivious to time. And if you can’t measure time you can’t measure distance (trust me on this). So the condition of the universe near the end of an aeon is such that time and distance no longer exist but conformal geometry will still apply. Penrose shows that in these circumstances there can be a smooth and continuous transition from ‘before’ a Big Bang to ‘after’. He even suggests a mechanism which could transfer observable effects from one aeon to the next which could be detectable in the cosmic background microwave radiation.

Penrose addresses the entropy problem I mentioned earlier and gives a fairly detailed analysis of how the far-future phase of the universe can lose entropy as matter is drawn into black holes. But there is one vital part of his analysis (if I understand anything at all about it) which is still purely speculative. His theory requires that over the length of an aeon all the mass of the universe disappears and is converted to massless radiation. There is no evidence to support this idea at the moment, but Penrose suggests that our observational timescale is so short relative to the 10¹⁰⁰ or so years of an aeon that the universe might just not have been around long enough for such a process to become evident.

Although Penrose explains mathematically how certain aspects of a dying aeon could make a smooth transition through a new Big Bang into the start of a new aeon I failed to find an account of what this might involve in physical terms. How does a cold, dark, radiation-filled universe transform into a violent exploding maelstrom of energy? It’s very hard to imagine. In my naive ignorance I feel it would be nice to find an answer in the maths of String Theory and Quantum Field Theory (see for example “The Elegant Universe” by Brian Greene) – which Penrose does not support. Here the universe has several more ‘hidden’ dimensions, and dimensions can have a strange symmetrical property such that whether a dimension’s radius of curvature is defined as R or 1/R its properties are the same. So perhaps at the ‘end of time’ when the radii of curvature of spacetime have become infinitely large the geometry transforms into infinitely small radii and the next Big Bang takes it from there. But this is just my whimsical fancy – don’t pay it any attention. Unless of course it turns out to be right, in which case please send the Nobel Prize invitation c/o this website.

I read this precursor of "The Fabric of the Cosmos" a couple of years after the later book, which was written 5 years after this one. It covers much of the same ground but has a slightly different purpose – this book is primarily a description of string theory as it stood in 1999, while the later book focuses more on setting string/M-theory in the historical context of our understanding of the fundamental nature of things from Einstein’s modifications of Newtonian mechanics through to the present day.

"The Elegant Universe" goes into more detail on some technical aspects of the theories, particularly the dualities of the different versions of string theory and their consequent unification under M-theory, and the curious result that the radii of the tiny hidden ‘curled up’ dimensions are somehow equivalent (symmetric) to their own inverses (i.e. a radius of R is in a sense equivalent to a radius of 1/R). Please don’t lose any sleep worrying about this, even if you start wondering whether the 4 extended dimensions (3 spatial, 1 time) with which we are familiar have their equivalent formulation as tiny curled up dimensions and if so what that might mean for the world (and us) as we know it.

There’s also more detail on black holes than in the later book, including the intriguing fact that they are not truly black (as proved by Stephen Hawking), and an explanation of why string theory needs 10 dimensions but M-theory needs 11. It’s all good stuff, and presented in the same non-mathematical way as "Cosmos". For the tiny minority of people (physicists and cosmologists) who understand (some of) all this, it must be an exciting time. There’s a feeling that we’re getting close to a theory of everything but one suspects the ultimate formulation, if it can be achieved, is still some way away and will probably look different again from what we have now.

Greene surveys our understanding of the nature of everything from the sub-atomic to the whole universe. He covers Einstein’s special and general relativity theories, quantum mechanics, entropy and the directionality of time. So far so good, and although some results are a bit weird he is probably in territory familiar to anyone with an amateur interest in modern science.

But if you thought that dark matter and dark energy were the latest topic in physicists’ café society, you’d be wrong. While such stuff is not exactly old hat (and definitely weird), it gets much weirder. Greene’s field is String Theory, aka M-Theory, and he gives a very readable account of where this all leads. Strings, branes (yes, the spelling’s right, and they come in different dimensions like 2-branes, 6-branes, and even p-branes and no-branes – physicist’s joke) and the tiniest chunks of reality beyond which space and time cease to be meaningful are paraded before you. There’s stuff on black holes, which because of their entropy are probably more important than you realised, time travel (forwards OK, backwards probably not) and teleporting (theoretically possible through quantum entanglement but completely out of reach with current technology).

If these are the sort of things that interest you this book is a good introduction. Greene is well-known for his "approachable" style, one feature of which is that what little maths he includes is relegated to the comprehensive chapter end-notes. You may find his prolific use of quirky, often Simpsons-related, illustrative examples becomes irksome, and I found myself wishing he would stick to just using notation like 10^-20 instead of insisting on writing "a hundred billion billionth". But these are minor quibbles. Greene combines enthusiasm and a deep knowledge of his subject with an ability to explain the origin, development and significance of the latest ideas in physics in a way that makes you think you might actually understand a bit of it.