Date published: 2008/06/27

Roger Penrose gave the second annual Andrew Chamblin Memorial Lecture today in Cambridge. (Chamblin got his Ph.D. in Cambridge but, as it happens, before that also briefly worked in Penrose's twistor group in Oxford.) The title of the talk was "Deep Questions of Cosmology: Did Something Happen Before the Big Bang?".

Penrose is in his mid-70s (so at an age when most people are past any productive work in maths) and quaintly used an overhead projector during the talk with hand-scribbled slides. Apparently he's been doing the rounds with pretty much this talk.

Penrose said that three years ago he would have considered the question in the talk title to be a "ridiculous" and a "crazy" question. He said that indeed it is "crazy", but that "perhaps the universe is crazy".

Before the 1980s the "standard" cosmological model was pretty much the one a physicist by the name of Friedman (also spelled Friedmann) came up with in 1922. He solved Einstein's equations of gravity assuming that the universe was homogeneous and isotropic (a reasonable first approximation). It turns out that the solutions can be characterised by a parameter K, where K < 0, K = 0 or K > 0. In all three cases the universe started in a Big Bang. In the K = 0 and K < 0 cases the universe just expands forever whereas in the K > 0 case the universe eventually re-collapses into a Big Crunch.

Back in the 1980s it was deemed that the standard model had some problems. So it seemed (although the evidence was thin) that the value of K might be nearly or even exactly 0, and why should that be the case. Further, there were allegedly acausal correlations in the Cosmic Microwave Background. A postulated (and currently fairly accepted) way out of these "problems" was something called inflation, which allegedly resulted in an exponential increase in the size of the universe in the early stages just after the Big Bang. Penrose still doesn't seem to have accepted inflation.

Penrose mentioned several theoretical physicists (Friedman, Tolman, Wheeler, etc.) had come up with the idea that if K > 0 perhaps the universe oscillates (forever) between singularities, so a Big Crunch is the next Big Bang. Well, this is a bit fanciful (or "crazy") but a variant on this idea is what Penrose was claiming.

All of this was pretty much assuming that the so-called cosmological constant was 0. In the last decade it seems there is growing evidence that it is not 0. In this case even the K > 0 universe expands forever.

Penrose talked quite a bit about the Second Law of Thermodynamics. Although it has a reputation of being something very difficult to understand, he joked that it was simple because it just said that things always get worse. Anyway, the Second Law says that something called entropy (which somehow measures "disorder") was always increasing. Well, the laws of Newtonian mechanics are time reversible so this seems contradictory. If entropy increases into the future why doesn't it increase into the past. Well, the Second Law only works into the future.

If you look into the past the entropy of the universe must be decreasing, and Penrose claimed this meant that there was an enormous constraint on the spacetime geometry at the Big Bang. In particular, the Weyl tensor (part of the Riemann tensor which describes the curvature of spacetime) must be approximately zero (allegedly to 1 part in 10 to the 10 to the 123). This is back to the usual problem that our universe is allegedly *very* special.

Anyway, Penrose has always had something about the Weyl tensor, because it describes the conformal curvature of spacetime. The fundamental object in Einstein's view of the world is the metric tensor, which describes the distance between points in spacetime. But if instead of considering distance you only consider angles, then that is the conformal structure. Light rays (photons) only care about the conformal structure.

The fundamental claim of Penrose was that you only had to consider the conformal information near the Big Bang, and you could (presumably analytically) continue the geometry to before the Big Bang if you just considered the conformal structure. Well perhaps. Penrose claimed this led to a new view of a "conformal cyclic cosmology" (so even though the universe is expanding forever it turns out you can always compactify the infinite future in terms of its conformal structure). Well perhaps.

It was supposed to be a popular lecture (although anyone who didn't know a fair amount of 20th century relativity would have been pretty lost) so he didn't give any details. But he claimed at the end that he could make predictions based on his ideas, and that these were not only testable, but that someone had sent him some experimental data just today. Unfortunately he had not had time to study the data before he gave his lecture, so it's possible he has made a revolution discovery or it's possible his theory will soon be in the trash. (Well, making any prediction which is somewhat verified by experiment does not really prove very much. But making any prediction which is negated by experiment sinks the theory pretty conclusively.)

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