Monday, October 03, 2005

Seriously about Bogdanoffs II

A fascinating book on the Bogdanoff affair and the rest of physics: click and buy
I was just asked to give my opinion about the Bogdanoff paper(s) on Wikipedia, so I replied with a neutral comment. It is surprising that some people who otherwise propose that everyone should study alternatives to string theory - such as Peter Woit - are so incredibly negative about the Bogdanoff paper(s).

Why? Because the Bogdanoff brothers are proposing something that has, speculatively, the potential to be an alternative story about quantum gravity. As a string theory believer, I would say "a new dual description of quantum gravity i.e. string/M-theory". What they are proposing is a potential new calculational framework for gravity. I find it unlikely that these things will work - but it is probably more likely than loop quantum gravity and other discrete approaches whose lethal problems have already been identified in detail.

In the previous article I focused on the creation of myths and their idea about the fluctuating spacetime signature. But let me now ask you about the following proposal that is included among their refreshing speculative ideas.

Usually we assume that the geometry completely breaks down at the sub-Planckian distances, together with the spacetime topology and all other things. It's because the excited string states and other states appear together with infinitely many higher-derivative corrections. But let us now believe that geometry is a useful picture despite all these effects.

Imagine that you start with a generic gravity action whose pure gravitational part has terms like
  • L = R / (16.pi.G) + alpha. R (wedge) R + beta . R^2 + gamma . R^3 ...

and so on. The topological term "R (wedge) R" would have to be replaced by something else in higher dimensions. At long distances, the first, Einstein-Hilbert term is important (after the vacuum energy, of course). At short distances, we usually assume that the infinite tower of higher-derivative terms takes over and we can't say anything; the metric is not a relevant degree of freedom anymore because we must really add a whole tower of new, equally important states predicted by string theory.

But try to assume, together with the Bogdanoff brothers, that it is not the case. Your task is nothing less :-) than to finish their work e.g.

  • find an appropriate theory of gravity in which the steps below can be justified
  • explain that the higher-derivative terms disappear or decouple in this theory at very short distances, or that they can be ignored for other reasons
  • isolate a topological term that does not disappear in this limit
  • write down the path integral as a summation over the actual quantum foam - different topologies of the Universe - in analogy with the quantum foam in topological string theory - where the contributions are labeled by "exp(-S)" where "S" is a combination of topological invariants of the d-manifold such as the Euler character
  • this will be your dual, sub-Planckian expansion of the partition sum or maybe just some important quantities in quantum gravity

Alternatively, prove that this picture by Bogdanoffs is impossible in any quantum theory of gravity. I can't do either.

1 comment:

  1. Lubos:
    Pretty soon people will all forget who are the Bogdanoff brothers and no one will care about super string theory any more because those are a bunch of crackpotists who will no longer have a job because governments will stop funding all such clueless researches and concentrate instead on alternative energy source researches.

    Don't you see, the bad news is already leaking out at faster pace than I expected. It's the government speaking, on CNN, not something I made up. They are not going to tell you the whole bad news in one piece, that that would be too bitter a pill to swallow. The oil crisis has started and it could only get worse, much worse, 6 months later.

    The matter of fact is if it were happening in an era of abundant oil, who gives a damn even if the while gulf of mexico oil production were wiped out, we could just import more from the rest of the world. But things are very different now because we have passed world peak oil. Every one is in short of oil and there is no possibility that the world can produce more barrels per day, than it's current production level.

    Why would any one expect the situation would return to "normal", six months later? The oil/gas production platforms and rigs are largely wiped out already. Those facilities were never designed to survive in a category 5 hurricane.

    We are talking about huge ocean waves, as high as 100 feet waves in the middle of the ocean. A wave that's 10 stories high, crashing the huge rigs like a toy. And those are very huge structures, containing 50 million kilograms of steel each. They are incredibly strong but when it comes to 10 stories high waves, nothing could survive.

    One would be naive to assume these things can be replaced or repaired within 6 months. Before the hurricanes, one would already have to wait until 2009 to get a new rig built. This is not something any one can built. 50 million kilograms of steel!

    Wait for more bad news to surface gradually in the main stream media. Mean time, if you live in a cold place, start to stock up some coals to try to keep yourself warm. This winter will be pretty miserable and you would wish the global warming has been under-estimated by one order of magnitude, instead of having been over-estimated by one order of magnitude.