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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 (+ + + +)

signatures.

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.

Sincerely,

Prof L. Yang

Theoretical Physics Laboratory

International Institute of Mathematical Physics

HKU/Clear Water Bay, Kowloon, Hong Kong