Cycles of Time – a new theory of cosmology

Cycles of Time, subtitled An Extraordinary New View of the Universe, is a very recent book by Roger Penrose; so recent that I pre-ordered it. Anyone who has followed my blog over the last few years will know that I’m a big fan of Penrose. Along with Paul Davies and Richard Feynman, I think he’s one of the top physics writers for laypeople ever. John Gribbin and James Gleick are also very good but not quite in the same league in my opinion. Davies, Feynman and Penrose all have different strengths so comparisons are not entirely fair. Feynman was the great communicator of some of the most esoteric theories in physics and if you want to grasp the physics, he’s the best. Davies is, in my view, the best philosophical writer and also covers the widest field: covering topics like astrophysics, the origin of life, cosmology, chaos theory, the nature of time and in The Goldilocks Enigma the meaning of life, the universe and everything.

Penrose is actually a mathematician and made significant contributions to tessellation (tiles, map boundaries etc), but he’s also won at least one award in physics (1988 Wolf Prize jointly with Stephen Hawking) and his dissertations on the subject of consciousness reveal him as an erudite and compelling polymath.

My favourite book of his is The Emperor’s New Mind(1989) where he first tackled the subject of consciousness and challenged the prevailing view that Artificial Intelligence would herald in a new consciousness equivalent to or better than our own. But the book also covers almost the entire field of physics, argues cogently for a Platonic view of mathematics, explains the role of entropy on a cosmic scale, and devotes an entire chapter to the contingent nature of ‘truth’ in science. A must-read for anyone who thinks we know everything or are on the verge of knowing everything.

Now I’m the first to admit that I can quickly get out of my depth on this topic, and I can’t defend all the arguments that Penrose delivers, because, quite frankly, I don’t understand all the physics that lay behind them, but he’s one of the few people, with the relevant intellectual credentials, who can challenge the prevailing view on our universe’s origins and not lose credibility in the process.

For a start, reading this book makes one realise how little we do know and how speculative some of our theories are. Many commentators treat theoreticians who challenge string theory, and its latest incantation, M theory, as modern-day luddites, which is entirely unfair considering that string theory has no experimental or observational successes to its name. In other words, it’s a work of mathematical genius that may or may not reflect reality. Penrose’s CCC (Conformal Cyclic Cosmology) is also a mathematically consistent theory with no empirical evidence to either confirm or deny it. (Penrose does suggest avenues of enquiry to rectify that however.)

I first came across CCC in a book, On Space and Time (2008), a collection of ‘essays’ by people like Alain Connes, Shahn Majid, Andrew Taylor and of course Sir Roger Penrose. It also included John Polkinghorne and Michael Heller to provide a theological perspective. Personally, I think it would have been a better book if it stuck to the physics, because I don’t think metaphysical philosophies are any help in understanding cosmology, even though one could argue that mathematical Platonism is a metaphysical philosophy. I don’t mind that people want to reconcile scientific knowledge with their personal religious beliefs, but it’s misleading to imply that religion can inform science. And science can only inform religion if one conscientiously rejects all the mythology that religions seem to attract and generate. Putting that personal caveat aside, I can highly recommend this book, edited by Shahn Majid, for an overview of current thinking on cosmology and all the mysteries that this topic entails. This is true frontier-science and that perspective should never be lost in any such discussion.

Getting back to Penrose, his latest book tackles cosmology on the grandest scale from the universe’s Big Bang to its inevitable demise. Along the way he challenges the accepted wisdom of inflation amongst other prevailing ideas. He commences with a detailed description of entropy because it lies at the heart of the conundrum as he sees it. It’s entropy that makes the Big Bang so very special, and he spends almost half the book on expounding why.

Penrose describes specific aspects of time that I referred to in a post last year (The enigma we call time, July 2010). He gives the same example I did of an egg falling off a table demonstrating the inherent relationship between entropy (the 2nd law of thermodynamics) and the arrow of time we are all familiar with. He even cites a film running backwards showing an egg reconstituting itself and rising from the floor as an example of time reversal and a violation of the 2nd law of thermodynamics acting simultaneously, just as I did. He also explains how time doesn’t exist without mass, because for photons (light rays), which are massless, time is always zero.

The prevailing view, according to almost everything I read on this subject via science magazines, is that we live in a multiverse where universes pop out like exploding bubbles, of which the Big Bang and its consequent ‘inflation’ was just one. In the Christmas/New Year edition of New Scientist (25 December 2010/1 January 2011, p.9) there is an article that claims we may have ‘evidence’ of ‘bruising’ in the CMB (Cosmic Microwave Background) resulting from ‘collisions’ with other universes. (The cosmic background radiation was predicted by the Big Bang and discovered purely by accident, which makes it the best evidence we have that our universe did indeed begin with the Big Bang.)

Some people also believe there is an asymmetry to the universe, implying there is an ‘axis’, which would be consistent with us being ‘joined’ to a ‘neighbouring universe’. But be careful with all these speculative scenarios fed by inexplicable and potentially paradigm-changing observations – they just confirm how little we really know.

The multiverse in conjunction with the ‘anthropic principle’ appears to be the most widely accepted explanation for the how, why and wherewithal of our hard-to-believe existence. Because we live in possibly the only universe of an infinite number then naturally it is the only universe we have knowledge of. If all the other universes, or almost all, are uninhabitable then no one will ever observe them. Ergo we observe this universe because it’s the one that produced life, of which we are the ultimate example.

Paul Davies, in The Goldilocks Enigma, spends a page and a half discussing both the virtues and pitfalls of the multiverse proposition. In particular, he discusses what he calls ‘...the extreme multiverse model proposed by Max Tegmark in which all possible worlds of any description really exist…’ In other words, whatever mathematics allows can exist. Quoting Davies again: ‘The advantage of the extreme multiverse is that it explains everything because it contains everything.’ However, as he also points out, because it explains everything it virtually explains nothing. As someone else, a theologian (I can’t remember who), once pointed out, in a discussion with Richard Dawkins, it’s no more helpful than a ‘God-of-the-gaps’ argument, which also explains everything and therefore ultimately explains nothing.

Stephen Hawking has also come out with a new book with Leonard Mlodinow titled The Grand Design, which I haven’t read but read reviews of, in particular Scientific American. Someone in America (Dale, who has a blog, Faith in Honest Doubt) put me onto a radio podcast by some guys under the name, Reasonable Doubts, who ran a 3-part series on Buddhism. At the end of one of their programmes they took Hawking to task for making what they saw as the absurd claim that the universe could be ‘something from nothing’.

I left a comment on their blog that this was not a new idea:

I'm not sure why you got in a tiz about Hawkings' position, though I haven't read his latest book, but I read an editorial comment in Scientific American under the heading, Hawking vs God. The idea that the universe could be 'something for nothing' is not new. Paul Davies discussed it over 20 years ago in God and the New Physics (1983) in a chapter titled: Is the universe a free lunch? He says almost exactly what Hawking is credited with saying (according to Scientific American): the universe (according to the 'free lunch' scenario) can account for itself, the only thing that is unaccountable are the laws of nature that apparently brought it about. Davies quotes physicist, Alan Guth: "It's often said that there is no such thing as a free lunch. The universe, however, is a free lunch."

Davies, Hawking and Penrose are not loonies – they are all highly respected physicists. We’ve learned from Einstein and Bohr that nature doesn’t obey rules according to our common sense view of the world, and, arguably, the universe’s origin is the greatest of all unsolved mysteries. Why is there something instead of nothing? And is there any reason to assume that there wasn’t nothing before we had something?

What, may you ask, has any of this to do with Penrose’s CCC theory? It’s just a detour to synoptically describe the intellectual landscape that his theory inhabits.

As I alluded to earlier, Penrose focuses on the biggest conundrum in the universe, being entropy, and how it makes the Big Bang so ultra-ultra special. Few discussions I’ve read on cosmology even mention the role of entropy, yet it literally drives the entire universe’s evolution – Paul Davies doesn’t shy away from it in God and the New Physics - but otherwise, only Penrose puts it centre stage from my reading experience.

Both Davies and Penrose discuss it in terms of ‘phase space’ which is really hard to explain and really hard to envisage without thinking about dimensional space. But effectively the equation for entropy is the logarithm of a volume of phase space multiplied by Boltzmann’s constant: S = k log(V). The use of a logarithm allows one to differentiate between entropies in a dynamic system. Significantly, one can only ‘take away’ entropy by adding it to somewhere else that’s external to the ‘closed’ environment one is studying. The most obvious example is a refrigerator that keeps cold by dumping heat externally to the ambient air in a room (the fridge loses entropy by adding it externally). As Penrose points out, the only reason the Sun’s energy is ‘useful’ to us is because it’s a ‘locally’ hot spot in an otherwise cold space. If it was in thermal equilibrium with its environment it would be useless to Earth. ‘Work’ can only be done when there is an imbalance in energy (usually temperature) between a system and its environment.

But more significantly, to decrease the entropy in a ‘closed’ system (like a refrigerator or Earth) there must be an increase in entropy externally. So ultimately the entire universe’s entropy must always be increasing. The corollary to that is that the universe must have started with a very small entropy indeed, and that is what makes the Big Bang so very special. In fact Penrose calculates the ultimate phase space volume of the entire universe as e raised to the power of 10 raised to the power of 123, (e¹⁰)¹²³, or, if it’s easier to comprehend, take 10 raised to the power of 10 (10 plus 10 noughts) raised to the power of 123 (10 x 123 noughts). So That’s 1 with 123 x 10 noughts after it. To reverse this calculation, it means that the precision of the big bang to create the universe that we live in is one part in 10 to the 10 to 123, (1^-10)^-123. So that’s a precision of 0.00…(123x10 0’s)1.

Penrose takes the universe in its current state and extrapolates it back to its near-origin at the so-called inflationary stage between 10^-35 and 10^-32 seconds from its birth. He also extrapolates it into its distant future, making some assumptions, and finding that the two states are ‘conformally’ equivalent. One of his key assumptions is that the universe is inherently hyperbolic so it has a small but positive cosmological constant. This means that the universe will always expand and never collapse back onto itself. Penrose provides good arguments, that I won’t attempt to replicate here, that a ‘Big Bounce’ scenario could not produce the necessary entropic precision that we appear to need for the Big Bang. In other words, it would be a violation of the 2nd law of thermodynamics.

Penrose’s future universe assumes that the universe would consist entirely of black holes, many of which exist at the centre of all known galaxies. As these black holes become ‘hotter’ than the space that surrounds them, they will evaporate through Hawking radiation, so that eventually the entire universe will be radiation in the form of electromagnetic waves and gravitons. Significantly there will be virtually no mass therefore no clocks, and, from what I can understand, that’s what makes the universe conformal. It will have a ‘conformal boundary’. Penrose’s bold hypothesis is that this conformal boundary will become the conformal boundary that we envisage at the end of the inflationary period of our universe. Hence the death of one universe becomes the birth of the next.

What of the conundrum of the 2nd law of thermodynamics? Penrose spends considerable time discussing whether or not information is lost in black holes, which is a contentious point. Hawking once argued that information was lost, but now argues otherwise. Penrose thinks he should have stuck to his guns. Many scientists believe it’s a serious flaw in cosmological thinking to consider that information could be lost in black holes. Many scientists and philosophers argue that ‘everything’ is information, including us. There’s an argument that teleportation is theoretically achievable, even on a macro scale, because everything is just information at base. I’ve never been convinced of that premise, but leaving that aside, I think that information could be lost in black holes and so does Penrose. If this is true then all information regarding our universe will no longer exist after all the black holes evaporate, and, arguably, entropy will be reset, along with time. I’ve simplified this part of Penrose’s treatise, so I may not be doing him justice, but I know that the loss of information through multiple black hole evaporation is crucial to his theory.

When I first came across this thesis in On Space and Time I admit that it appealed to me philosophically. The idea that the end of the universe could be mathematically and physically equivalent to its beginning, and therefore could recycle endlessly is an intellectually attractive idea. Nature is full of beginnings and endings on all sorts of scales, why not on the cosmological scale? Infinity is the scariest concept there is if you think about it seriously – the alternative is oblivion, nihilism effectively. We have a life of finite length that we are only aware of while we are living it, yet we know that existence goes on before we arrive and after we’re gone. Why should it be any different for the universe itself?

I admit I don’t understand all the physics, and there still seems to be the issue of going from a cold universe of maximum entropy to a hot universe of minimum entropy, yet Penrose seems to believe that his ‘conformal boundary’ at both ends allows for that eventuality.