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Subject: Bogdanoff update
From: International Institute of Mathematical Physics

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Dear Prof Woit,

Following a conference that was recently given by the Bogdanoffs in HKU
about their work in the field of riemannian cosmology, we got
interested and have since carefully read all the papers published by
them untill wed got a different view on their work and research. We
are convinced now that during the times of the Bogdanoff affair,
nobody had invested the requested time, energy and expertise to
seriously evaluate their publications. Since you issued a few
critical comments (SPR) and were quoted by newspapers (NY Times) as
attacking the Bogdanoffs, we send you the present message to convey
another opinion that we beleive is more coherent with the reality of
Bogdanoffs work. Not only -as everyone knows by now- they did not
commit any "hoax" (as they claimed since the very beginning) but they
also wrote deep and interesting papers about KMS condition as applied
to Planck's physics. These qualities are far from being reflected by
your comments. My colleagues and I think that you really should
reconsider your view and update it in a more appropriate way.

We sent the same letter to John Baez and some other mathematicians and
physicists who had a responsibility on the development of this affair.

In particular, in spite of many discussions, no one could see that
Bogdanoff started with the main objective to establish, in terms of
quantum groups, the existence of a natural link between
"q_deformation", quantisation of spacetime and "deformation" of the
signature of the metric. They showed that in dimension D = 4, the
Lorentzian and the Euclidean structures are related by twisting and
that the only natural signatures at the Planck scale are then the
deformations of the Lorentzian (+ + + - ) and Euclidean (+ + + +)

The validity of their approach and the originality of their results in
quantum groups theory has been confirmed by experts like S.Majid.

As far as we are concerned, in a few words, what we find sound and
interesting in Bogdanoffs work is their non expected way to apply,
witin the Planckian cosmological setting, some crucial properties of
tomita's modular theory (see KMS State of Spacetime at the Planck
Scale/ Chinese Journal of Physics and Thermal Equilibrium of Spacetime
at the the Planck Scale/ Chinese Annals of Mathematics). As all experts
in the field should know, temporal evolution of a non-dissipative
quantum system is described by a one-parameter group of automorphisms
of its algebra of observables. But it was a surprising discovery when
Tomita-Takesaki theory allowed us to naturally associate such a group
with each faithful normal state (or, more generally, weight) of the
algebra. In their papers (that apparently only a few ones understood
correctly) Bogdanoffs speculated that the modular group of
automorphisms of the equilibrium thermal state of the primordial
universe provides a "quantum dynamics" at a fundamental level, a
dynamics that defines, by itself, the very "existence of flow of
time". More important, they suggest that by a generalization of the
Tomita- Takesaki scheme natural semigroups of completely positive maps
can be associated to certain states of von Neumann algebras. If so,
then natural examples of EQT dynamics can be produced via pure
algebraic means (which Bogdanov developed in CQG paper). One can also
note in this group of papers that Bogdanovs propose a relevant
attempt to bridge the gap between physics and algebra in the
bicrossproduct (quantum groups) setting. Some of the examples they
provide (see their ArXiv quantum group article ( by the way a "proof"
that they did not wish to "fly under radars)) may have physical
interpretation and application to pre-Planck scale physics. This is
why we think that Bogdanoffs work is original and interesting.


Prof L. Yang
Theoretical Physics Laboratory
International Institute of Mathematical Physics
HKU/Clear Water Bay, Kowloon, Hong Kong