- Grichka Bogdanov and Igor Bogdanov, Topological field theory of the initial singularity of
spacetime,
*Classical and Quantum Gravity***18**(2001), 4341-4372. - Igor Bogdanov, Topological origin of
inertia,
*Czechoslovak Journal of Physics*,**51**(2001), 1153-1236. -
Igor Bogdanov,
The KMS state of spacetime at the Planck scale,
*Chinese Journal of Physics*,**40**(2002).

The latter two reports mainly confine themselves
to summarizing the paper and correcting spelling errors, typos,
and stylistic mistakes. The *Classical and Quantum Gravity*
referee's report also demands many clarifications, which presumably
the Bogdanovs provided.

From: Eli Hawkins Date: May 13, 2003 1:54:12 PM EDT To: John Baez Subject: Old Controversy John, Journal of Physics A finally sent me a copy of the referee report I wrote for "THE KMS STATE OF SPACE-TIME AT THE PLANCK SCALE". It is definitely in contrast to the other referee reports you show on your web page. Feel free to distribute this if you want to. - Eli This paper is built around the idea that "at the Planck scale, the "space-time system" is in a themodynamical equilibrium state". It is not quite clear what the author means by this, but on page 4 he seems to be referring to a Friedman model of a homogeneous universe with thermal matter. He may mean that when the matter is at the Planck temperature, it is in thermodymanic equilibrium with the geometry. He does not explain why there should not be thermal equilibrium at all temperatures. It may be simply that the author does not know what he is talking about. The main result of this paper is that this thermodynamic equilibrium should be a KMS state. This almost goes without saying; for a quantum system, the KMS condition is just the concrete definition of thermodynamic equilibrium. The hard part is identifying the quantum system to which the condition should be applied, which is not done in this paper. It is difficult to describe what is wrong in Section 4, since almost nothing is right. The author seems to believe that just because an analytic continuation of a function exists, the argument "must" be considered a complex number. He also makes the rather obvious claims in eq's 6 and 7 that complex numbers should be the sums of real and imaginary parts. The remainder of the paper is a jumble of misquoted results from math and physics. It would take up too much space to enumerate all the mistakes: indeed it is difficult to say where one error ends and the next begins. In conclusion, I would not recommend that this paper be published in this, or any, journal.

© 2004 John Baez baez@math.removethis.ucr.andthis.edu