Infinities at Cambridge

The ‘Infinities and Cosmology’ conference  (see last post) got off to a great start here at Cambridge today. The first surprise was that DAMTP, Cambridge’s Department of Applied Mathematics and Theoretical Physics, is now housed in a beautiful modern building with lots of light, wide open spaces and a great canteen. The building forms part of the new Centre for Mathematical Sciences, most impressive. I couldn’t resist taking a few other photos after breakfast on my way to the conference, nearly missed registration!

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The Department of Applied Maths and Theoretical Physics at Cambridge

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 Clare College (where I’m staying) in the mist at breakfast this morning

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Walking through Clare College on the way to the conference

After registration and coffee, the conference started with a ‘brief introduction’ by John Barrow . This comprised a succinct but comprehensive overview of problems posed by infinities in mathematics, classical physics, quantum physics and particle physics, finishing with a discussion of specific problems in cosmology. There’s nothing quite like an overview like this by an expert, all sorts of connections between diverse phenomena become apparent. I took copious notes which will keep me busy over the next few days. Indeed, I suspect that if no other speaker had turned up, Prof Barrow could have expounded further on the topics he touched on for the duration of the conference.

George Ellis then took the podium for the first installment of his talk ‘Infinities of age and size, including global topology issues’. He set a no-nonsense tone by starting with a pet peeve – that physicists routinely confuse inconceivably large numbers with infinity, a very different beast. He expounded on this theme at length and then set about an interesting argument: that talk of infinities in physical systems is meaningless unless one can verify that they are truly infinite – which cannot be done, as pointed out by David Hilbert. Thus, the hypothesis of an infinite universe is dubious science and dubious philosophy. George then postulated a general test (the Ellis/Hilbert fork) for theories; any hypothesis that no longer works when infinite quantities are replaced by arbitrarily large numbers is bunk!

We were still pondering this opening salvo when Anthony Aguirre took the podium after coffee to talk about ‘Infinite and finite spacetimes’. This started with a succinct review of the ‘initial conditions’ problem in the big bang model, the theory of cosmic inflation and the main inflationary models of today. In particular, Anthony explained why inflation leads naturally to the concept of the multiverse  (essentially, quantum tunneling or equivalent processes are simply far too slow to compete with the still-inflating universe, leading to separate bubble universes). Personally, I once hoped that some mathematician would one day prove that inflation either happened to all or the universe or not at all, but this is looking increasingly unlikely. Anthony then went on to describe the model of eternal inflation and explained how Hoyle’s famous ‘steady-state universe’ could be right after all (at least on the global scale of the multiverse, as he explained in response to a silly question from yours truly).

After lunch, string theorist Michael Douglas presented the first installment of his talk ‘Can we test the sting theory landscape?’. This was the most technical talk so far, nothing less than a brief review of fundamental ideas in string theory and the famous problem of the landscape. A very basic argument Michael made chimed with me, namely that “almost all physical theories have a landscape of possible solutions” (there are dozens of example of this in solid-state physics). After some more general points, Michael went on to address the problem of dark energy, describing how his recent work on the flux vacua hypothesized by Bousso and Polchinski might deliver a mechanism for the cancellation necessary to reduce the quantum energy of the vacuum to the tiny ‘dark energy’ value we see today. I need to read around this area before Michael’s follow-up talk tomorrow so I’ll stop there!

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