Well, my mind has been well and truly boggled this evening.

I started the day by driving over the North Downs at Gatton early this morning. The main roads were all clogged up so, although I was in an area I don’t really know, I took to the back roads. The curves of the Downs were still white with dew, the sky was blue and the sun was shining. It was a lovely morning.

I’ve been sorting through a few thousand books someone is needing moved, so I spent a dusty morning heaving boxes of books to the car. On the way back home I stopped at Fanny’s Farm Shop for an early lunch – a savoury tea (like a cream tea except savoury). Some frantic parcel packing and posting in the afternoon, and then I was off to London to see Roger Penrose at the Royal Institution, promoting his new book Cycles of Time: an Extraordinary New View of the Universe.

Roger Penrose is a mathematical physicist, known for his theories in general relativity and cosmology, and also producing the Moore-Penrose Inverse, the Penrose triangle, twistor theory, Penrose tiling, work in loop quantum gravity, proving black holes could exist, the cosmic censorship hypothesis, and his theory that animal consciousness is a quantum effect.

I took my son (then not yet having started GCSE physics or maths) to see him at the Ri last February, giving a Friday Evening Discourse called Aeons Before the Big Bang (my son found the discourse quite entertaining, but unfortunately this was in the main due to Roger Penrose’s technique of using an overhead projector and getting his slides muddled up; of the discourse itself he understood not a word). This was the precursor to the current talk, as it discussed the possibility of a cyclically expanding universe, using the geometry of space-time to show that the universe never contracts. There were no formulae, unlike most of Prof. Penrose’s books, but lots of diagrams including light cones.

Much the same could be said of this evening’s lecture – although there were a few formulae. Penrose started off by saying that he didn’t like the concept of inflation immediately after the Big Bang. He then moved straight on to discussing the Second Law of Thermodynamics (I have had an interest in the 2nd Law for a long time,ever since I wrote an A-Level essay on the Second Law of Thermodynamics’ relation with the nature of time) and explaining the nature of entropy and its connection with quantum mechanics. After talking about coarse-graining regions, thermal equilibrium, pots of paint, and eggs falling off tables, he said that the greatest mystery of entropy is that the tendency of entropy in the universe is for it always to increase as time progresses, yet at the Big Bang it was in a state of maximum entropy – therefore it is starting at its greatest but then increasing. It is possible to show that the early universe was at thermal equilibrium as the Cosmic Microwave Background (CMB) shows agrees exactly with the Planck spectrum, which means it is at high entropy (although gravity at this time was low entropy).

A quick excursion into M C Escher and hyperbolic negative geometry ensued, then an explanation of how the earth receives energy from the sun (the reradiated, infrared photons are less energetic and therefore higher in entropy, than the incoming photons).

Black Holes were next up, and the problem raised by the 2nd Law of why the Big Bang didn’t involve any white holes (time reversed black holes), this apparently isn’t answered by inflation or by any (current) theory of quantum gravity which are time symmetrical.

Gravitational fields and Weyl curvature was next – the gravitational lensing of light from distant galaxies – and then Prof Penrose explained that at the Big Bang the gravitational field was effectively zero, because it was so extremely hot (the kinetic energy in the particles’ motions would have been so big that it would have overwhelmed their small rest energies, and so the rest-mass would have become irrelevant (E=mc^{2}).

There’s a problem, too, with a cyclic universe (big bang/big crunch), because if there were to be a wildly chaotic black-hole-riddled collapse, this shouldn’t have produced a conformally smooth big bang. And he doesn’t like the thought of an exponentially expanding universe with eventually supermassive black holes slowly becoming victim to Hawking radiation (and taking Googol years or so before going ‘pop’).

So, Penrose’s answer is a conformal cyclic cosmology, which also removes the information paradox from black holes. In this theory phase space volumes are reduced in black holes, degrees of freedom are lost, and entropy is gone. The thermodynamics of black holes involves the 2nd Law, but if the phase space is flattened then you have to subtract the information lost in black holes, and therefore the entropy, so the entropy of the universe can be said to exclude the entropy within the event horizon.

If there has been and will be a (possibly) infinite succession of aeons between big bangs this theory may be able to explain the anthropic cosmological problem and preclude the need for a multiverse (which theory Penrose dislikes). And it may be possible to make observations to see through into the previous aeon: colliding massive black holes would produce huge bursts of gravitational waves, carrying enormous amounts of energy, and which should be detectable in the CMB by statistical analysis*.

At the end he explained that it is possible to mathematically work through the transition using classical equations – you don’t need quantum mechanical equations.

Well, I think that’s what he said. As I mentioned at the beginning of this post, my mind is a bit boggled. I’ve started on the book (which will be published next week), have got to page 44, and I think I’ve comprehended enough to keep going. Although most of the maths has been banished to the Appendices, there’s still a little bit in the text, and the diagrams depicting multiple dimensions in two dimensions are sometimes a little hard to get your head round, but I think when I get to the end I will have a pretty good understanding of what he’s saying in the book. His forté as far as the lecture goes is being able to explain something so difficult in such an entertaining way, such that he overran the hour by fifteen minutes and I could still have listened to more – not bad for a 79-year-old.

Update 17th September: – I’m now about halfway through the book (I would have been further but irritating working keeps taking up time) and by the time I’ve finished I should be able to see how all the bits of the lecture fit together to make the argument somewhat more coherent. I think the problem last Wednesday was the lack of enough time to expand on the subject for long enough. As it was he overran by about ten minutes – an hour wasn’t long enough by any means.

The talk from last week is available to listen to now on the Royal Institution website, by the way.

25 September : Having had a chance to read more of the book now (although I have been very busy and haven’t had much of a chance to do any reading lately, I went to the Royal Institution Friday Evening Discourse [Empathy and the Human Brain] last night and was able to spend the train journey reading) certain of the points raised at the lecture have become much clearer. To give Roger Penrose his due, at several times he did say ‘you’ll have to read the book’ – there just wasn’t enough time for him to get everything across.

The inflation field was introduced to explain the uniformity in the state of the universe at the time the CMB was produced, but may there have been enormous irregularities at the time? The inflation field is supposed to make this highly improbable. If the universe is time-reversed to a hypothetical collapse, it would produce a mess of congealing black holes – if this is then time-reversed it produces multiply bifurcating white holes, and this didn’t happen.

At the end of the universe, after a googol (10^{100}) years and all the black holes have evaporated due to Hawking radiation, the physical content of the universe will consist of photons (from the Hawking radiation and from red-shifted starlight and CMB radiation), and also gravitons (which are also massless and therefore cannot be clocks); there will also be ‘dark matter’, which interacts only with the gravitational field and can therefore, presumably, not be used as a clock either.

After the last supermassive black hole has popped, all there is left for the universe to do is a relentless exponential expansion, cooling, and thinning out, and if there are only particles with no rest mass, there is no way of measuring time (and also, therefore, distances).

There may be the odd massive particle (particularly electrons or positrons), and they will be isolated within their own cosmological event horizons, and therefore won’t be able to undergo pair annihilation. Penrose wonders whether, over the enormous time scales involved, these particles rest mass may fade away, perhaps converted into kinetic energy.

At the end of the universe, therefore, radiation would cool down to zero temperature, and there would be zero density; the very remote future and the very remote past are very similar to each other – in the sense of the use of the word in Euclidean geometry, i.e. the distinction between the two is just an enormous scale change. Conformal stretching at the Big Bang brings ∞ density and temperature down to finite values; conformal squashing at ∞ brings zero density and temperature up to finite values.

Or, to put it another way, at 10^{-32}s the early universe’s state is dominated by conformally invariant physics, inhabited by effectively massless particles; gravitational degrees of freedom are largely suppressed; a conformal stretching out gives a smooth non-singular state inhabited by massless entities largely photons and ‘dark matter’). At the other end of the time-scale, the ultimate exponentially expanding universe is largely inhabited by massless ingredients (photons).

This then suggests the universe is an extended conformal manifold consisting of many (∞?) successive aeons. The maths of the theory actually requires the existence of ‘dark matter’ and ‘dark energy’; it also requires information loss in black holes, or rather the loss of degrees of freedom. I imagine that this may be a little contentious with physicists.

I only have two short sections left to read – one about the implications of quantum gravity and the other on observational implications. Although there are the appendices to which most (but by no means all) of the maths has been banished – this is the least formula-filled book of Penrose’s that I have seen.

It’s not possible to do the book justice in a short post like this one – as he said several times throughout the lecture: ‘You’ll have to read the book’. Read this one – not Hawking’s The Grand Design, which I found very tedious and unenlightening – see my post.

*Update 27 November: There’s a paper posted on the Arxiv website, by Penrose and V. G. Gurzadyan of Yerevan Physics Institute and Yerevan State University, *Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity* (arXiv:1011.3706v1), which apparently provides supporting evidence gleaned from the CMB. It’s early stuff (12 locations out of 11,000 studies showed the concentric circles), and they’re looking for more (Penrose said at the RI talk that his difficulty was finding someone who could spare the time needed to do the statistical analysis).

The paper hasn’t been peer-reviewed, and I’m in no way qualified to tell whether what it purports is credible, but I’m sure there must be the odd cosmologist or so out there in the blogosphere who is.

There’s also a short article at the BBC News website; and a short recording of Penrose talking about the theory on the BBC Today news programme from September.

Further update 26 December: spending a small part of Boxing Day morning browsing arXiv, there are three papers there refuting Penrose and Gurzadyan’s paper: A search for concentric circles in the 7-year WMAP temperature sky maps; No evidence for anomalously low variance circles on the sky; Are There Echoes From The Pre-Big Bang Universe? A Search for Low Variance Circles in the CMB Sky; plus a second paper in response from Penrose & Gurzadyan, More on the low variance circles in CMB sky.

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