While quite a few obviously cranky papers on high energy physics are published (and ignored) regularly, either electronically or in print, for some reason John Baez noted that the articles and PhD theses of I. Bogdanov and G. Bogdanov were such an impressive example of nonsensical science that they were maybe nothing but a deliberate hoax, maybe in the same spirit as the famous hoax by Alan Sokal.
In the sudden explosion of public attention that followed, the authors of these papers did not seize the opportunity to do high energy physics a painful favour and become world famous as the the ones who showed that some parts of this research area are emperors without clothes. Instead, suprising to some, they persistently maintained the seriousness of their claims.
In the long discussion that followed on sci.physics.research, several people tried hard to figure out from the answers of the two brothers what the precise content of their papers actually was supposed to be. While following this conversation I was increasingly getting the impression that the central ideas - and, I think, the mistakes - in these papers were actually way simpler than it may have appeared from the experts' questions and comments.
Therefore I wrote a short mail, reproduced below, in which I tried to
summarize what I figured was the essential line of reasoning that lies
behind the Bogdanov & Bogdanov articles. I was pleased, and somewhat
surprised, when on the 27th of Febuary 2003 I received an email from I.
Bogdanov and G. Bogdanov themselves in which they wrote the following:
So here is what I had written:
Viewing message <aqdan4$dum$1@rs04.hrz.uni-essen.de>
From: Urs Schreiber (Urs.Schreiber@uni-essen.de)
Subject: Re: Physics bitten by reverse Alan Sokal hoax?
Newsgroups: sci.physics.research, sci.physics
Date: 2002-11-10 16:41:04 PST
John Baez wrote:
> In article <e8e077d9.0211041841.bba684e@posting.google.com>,
> I/G.Bogdanoff <igor.bogdanov@free.fr> wrote:
[...]
>>This topic is described by topological field theory.
>
> That might be interesting if true, but until you've explained
> what you're talking about it's probably not worthwhile going
> into this further.
I think this is their line of reasoning:
They look at the general form of any partition function Z(beta) =
Tr(exp(-beta H)). They set beta equal to zero and find, lo and behold,
Z(0)
= Tr(1). They notice that the Hamiltonian has disappeared in this
expression! They conclude that Tr(1) must be the partition function
of a
topological field theory, because they think you obtain the partition
function of a topological field theory by setting the Hamiltonian in
exp(-beta H) equal to zero.
Let me call this "result" A.
Next they want to apply this insight to something and search for a setup
that justifies setting beta -> 0, thereby arriving at the FRW cosmology,
where beta->0 as the scale factor R->0.
(At this point they mention the word, just the word, "Hagedorn temperature",
not noticing that, considering the role the Hagedorn temperature plays
in
string cosmology, this is bordering on self-parody.)
They reason as follows: "At the initial singularity we have beta=0,
therefore physics 'at the initial singularity', by result A, is described
by topological field theory."
This is "result" B.
(By the generality of "result" A it does not matter _which_ field theory
they are considering. But they are thinking of their H's as the
Hamiltonians of field theories on fixed FRW backgrounds, not of the
Hamiltonian constraint of some theory of gravity.)
The next step is to assert, C, that a topological field theory is a
field
theory defined on a Riemannian manifold. Since, by result B, "every
field
theory is a topological field theory 'at the initial singularity'"
it
thereby follows that the metric of spacetime "at the initial singularity"
must be Riemannian, which is "result" D.
Next, they realize that D is in contradiction to the original assumption
of
an FRW cosmology with pseudo-Riemannian metric! Being confronted with
a
paradox they invoke quantum mechanics and postulate that the signature
of
the metric must be subject to quantum fluctuations "at the initial
singularity". That's "result" E.
It remains to be understood how the Foucault pendulum comes into play
now.
Even more so, since this doesn't fit the pattern of using modern
termionology.
Just to make sure: I do not think that any of the above is valid reasoning.
I am writing this just to point out what I think are the central "ideas"
the authors had when writing their articles and how this led them to
their
conclusions.
--
Urs.Schreiber@uni-essen.de