Dialog with the Bogdanovs (Part 5)

John Baez

Here are two articles the Bogdanovs posted to the newsgroup sci.physics.research on November 6 and 11, 2002, in reply to an article of mine.

From: igor.bogdanov@free.fr (I/G.Bogdanoff)
Newsgroups: sci.physics.research,sci.physics
Subject: Re: Physics bitten by reverse Alan Sokal hoax?
Date: Wed, 6 Nov 2002 20:39:26 +0000 (UTC)
Organization: http://groups.google.com/
Message-ID: (e8e077d9.0211060607.59b42657@posting.google.com)

baez@galaxy.ucr.edu (John Baez) wrote in message 
news:(aq1uoo$sr2$1@glue.ucr.edu)...

> In article (aptbm5$rp6$1@panther.uwo.ca),
> igor.bogdanov (igor.bogdanov@free.fr) wrote:
 
We continue with our answers...

> 5) What does any of this have to do with Foucault's 
> pendulum or the origin of inertia?  Again, please describe
> the connection as precisely as possible.

Comment : The idea to apply topological field theory to some question
related to the F. Pendulum is (as indicated in the paper) of
conjectural nature.  What we had in mind is that topological fiel
theory might apply to the so called "0-scale of spacetime" (initial
singularity problem). We proposed to represent this euclidean 0-scale 
by 0-size gravitational instanton. In this conjectural paper, we have
written in the provocative conjecture 4.2 : "The inertial interaction
may be interpreted as a topological interaction, of which the source
is the topological charge of the  zero size singular gravitational  
instanton." By "topological interaction" we mean here a topological
amplitude whose source could be the singular gravitational instanton.
The charge Q of the  zero size gravitational instanton is detectable
at the boundary S3 of the singular gravitational instanton provided
with the topology of the B4 Euclidean ball of dimension D=4. We have
also conjectured that a possible model of the "propagation" of this
topological charge can be given by the conformal transformations of
the sphere S3.

>>>I appreciate the fact that to someone not expert in physics,
>>>this stuff may seem no weirder than any other paper in a physics
>>>journal. They are indeed using actual physics jargon - but I assure 
>>>you, it makes no sense.
  
>>Comment : OK.  However, we would prefer "not clearly understandable."
>>Perhaps for two reasons : 1) first it is a secondary paper written long
>>time after the "key paper"  (Classical&Quantum Grav.) where all our
>>ideas are exposed and developed in more details. 2) second : once more
>>it is conjectural paper. 
  
> Regarding these points:
> 
> 1) I was not able to find explanations of any of the relevant 
> concepts in your Classical and Quantum Gravity paper, either.

Some more detailed explanations are in the thesis (specially Grichka's
thesis). But the fundamental idea as exposed in CQG paper is that the
0-scale of spacetime should be considered as relevant for topological
field theory. We have suggested that the high temperature limit of
quantum field theory (corresponding to beta = 0 in the partition
function   Z = Tr (-1)s exp -H )  is a topological invariant. The
signature of the metric of the underlying 4-dimensional zero scale
manifold is therefore Euclidean (+ + + +).
 
> 2) It's okay to make conjectures, but there is little point
> in publishing conjectures that cannot be understood. 

OK. We will try to be clearer about our ideas and the way to express
them (with the help of the community).
 
> >John Baez text : How in the world could the plane of oscillation of a
> >pendulum be "aligned with the initial singularity", i.e. the big bang?
> >The big bang did not occur anywhere in particular; it happened
> >everywhere. 
> >  
> >Comment : Well, it is exactly what we wrote :  of course, there is no
> >"priviledged" point and the initial singularity is  -as you said-
> >everywhere. 
 
> Given this, what does it mean to say a given plane in 
> space is "aligned with the initial singularity"?  At best
> it is a vacuous statement.

> >It is precisely our view : in conjecture 4.9  (nothing more
> >that an conjecture, by the way) we have considered that the
> >2-dimensional plane of oscillation of the pendulum conserves the initial
> >singularity S for inertial reference, whatever the orientation of this
> >plane in physical space R3."
 
> I don't what it means for a plane to "conserve the initial
> singularity S for inertial reference".  You are using words
> in a rather strange way!
> 
> I know what it means for a process to conserve some quantity,
> e.g.: "nuclear fusion conserves charge".  It means that the 
> quantity doesn't change as the process happens.  I don't 
> know what it means for a plane to conserve something. 

Comment : it simply means in our mind that the oscillation plane of
the pendulum conserves its initial orientation (whatever this initial
orientation is). This is the whole point of the well known 1851
Foucault's experiment.

> And I don't know what it means for something to conserve 
> initial singularity. 

Comment : We admit that if we consider this expression ("...something
to conserve the initial singularity...") it does not make much sense.
What we would like to convey is simply that the more distant is the
inertial reference  the smaller is the angular deviation of the
oscillation plane of the pendulum regarding this reference. In this
perspective the most "distant" inertial reference can be seen as the
initial singularity of spacetime.
 
> I also don't know what the extra
> phrase "for inertial reference" is supposed to modify, and
> how it could modify anything in this sentence in a sensible
> way.  
 
Comment : As suggested above the "inertial reference" is identified in
our approach to the initial singularity of spacetime.

> So, could you please explain much more clearly what you mean
> here?
 
> >It is explicitly written  in conjecture 4.9

> >John Baez text : Indeed, nothing in the paper suggests that they really
> >understand N = 2 supergravity, Donaldson theory, or KMS states. For all
> >I can tell, they merely stuck together a patchwork of plausible-sounding
> >sentences on these subjects.  
>  
> >Comment : Once more, one should refer to the PRINTED VERSION (not the
> >PDF's) of CQG paper (and also to the 2 thesis) to get a clearer view of
> >what we say (and know) about N = 2 supergravity, Donaldson theory, KMS
> >states, etc.We have passed many years working on these topics and became
> >rather familiar with all these subjects.
> 
> Okay, I'll look at the printed version.  Exactly how does this
> differ from the version in the PDF file of your thesis?

Comment : We have noticed many misprints in the PDF version. But
regrettably it is also the case in the printed versions. Might be one
of the sources of the series of misunderstandings we have to cope
with. For instance (as noticed by Aaron Bergman in eq.19 of the CQG
paper) the /\ symbol in the Euler characteristic is missing. There is
somewhere in the introduction a Hodge star in F /\ F which should not
have been printed. We had ask the corrector of CQG to fix this but
those corrections were not applied to the final version.
 
> Anyway, it would be very reassuring to hear you say something 
> that demonstrates understanding of N = 2 supergravity, Donaldson 
> theory, KMS states, von Neumann algebras, or the other subjects 
> on which you write. 

Comment OK. But the subject is vast. But we welcome any precise
exchanges on those questions related to our work.
  
> >In our view,  the fact to
> >consider a topological field theory independent of the Hamiltonian is
> >just equivalent to consider the same theory as independent of the
> >metric. 
 
> This is clearly false, as explained below.
 
> >A theory independent of H is topological because it is - by
> >construction -  independent of any physical field.
 
> A theory with zero Lagrangian is independent of the fields
> appearing in that theory.  Such a theory has zero Hamiltonian:
> H = 0.  This is completely different from being "independent of H".
> If something is "independent of H", it doesn't matter what H
> is.  Here it matters a lot that H = 0.

Comment : Of course. We agree with you.  But when we write
"independent of H" the condition is beta = 0. It is only for beta = 0
that the theory becomes independent of H. Of course, it could look
like a sort of "tautology"; but in fact it is not. In this setting the
topological limit can be reached for beta = 0 (whatever the values of
H are). In other words, in the partition function of the theory, it is
equivalent to put H = 0 or beta =0 : one gets the same result. this is
all we suggest.

In conclusion for today : we are aware of the fact that our papers are
"difficult to decipher"  (misprints, typos, elliptic definitions, ill
defined objects, etc).But as written by Robert Coquereaux 


http://www.cassiopaea.org/cass/bogdanovs.htm, 

is our papers that different from many other papers in the same field? 
Hopefully, with the help of the community, we will improve the written 
material ( as suggested by D.Sternheimer

http://www.cassiopaea.org/cass/bogdanov3.htm, 

our former thesis advisor.This has already began with the precious help 
of Ark Jadczyk).  Are there some interesting ideas to discuss in these 
papers? We think that's the case. But it is our personal view and we 
are sincerely looking forward to get some feedback from all interested 
members of the community.


From: igor.bogdanov@free.fr (I/G.Bogdanoff)
Newsgroups: sci.physics.research,sci.physics
Subject: Re: Physics bitten by reverse Alan Sokal hoax?
Date: Mon, 11 Nov 2002 18:13:17 +0000 (UTC)
Organization: http://groups.google.com/
Message-ID: (e8e077d9.0211101049.b640c0@posting.google.com)

> >>> John Baez wrote:

> >>>>For example, here's the beginning of [Igor's] paper "Topological Origin
> >>>>of Inertia:

> >>>>>We draw from the above that whatever the orientation, the plane of 
> >>>>>oscillation of Foucault's pendulum is necessarily aligned with the 
> >>>>>initial singularity marking the origin of physical space S^3, 
> >>>>>that of Euclidean space E^4 (described by the family of instantons
> >>>>>I_beta of whatever radius beta), and, finally, that of Lorentzian 
> >>>>>space-time M^4. 

> Note that I am still waiting for an explanation of this sentence. 

Answer : Let's be simple and heuristic : if we consider (as you wrote
yourself in your webpage) that Big Bang occured "everywhere",  then FP
oscillation plane intersects the Initial singularity "everywhere"
(naively speaking).

> In particular, what does it mean to say the plane of oscillation 
> of a pendulum is "aligned with the initial singularity"?   This 
> was your previous attempt at explanation:

> >>>in conjecture 4.9 (nothing more
> >>>that an conjecture, by the way) we have considered that the
> >>>2-dimensional plane of oscillation of the pendulum conserves the initial
> >>>singularity S for inertial reference, whatever the orientation of this
> >>>plane in physical space R3."

> This attempt did not help at all.
> 
> I still don't what it means for a plane to "conserve the initial
> singularity S for inertial reference".  What does it mean?

Answer : It means that (at the pole) whatever the intial direction of
the oscillation plane P is,  there is always a geodesic that belongs
to P  up to the "everywhere"  Initial singularity (that is the reason
why the pendulum oscillation plane does not "rotate" and conserves its
average initial direction).In (slightly) more technical terms,  there
is a theorem  (Hawking/Penrose) showing that in the standard Roberton
Walker model,  all past directed timelike as well as null geodesics
>from a point P converge within a compact region  (initial
singularity). In this case any 2-dimensional spacelike surface will
intersect the cosmological past lightcone at the origin.

> But let's continue with my questions and your answers:

> >> 1) Could you please define "at 0 scale"?  

> >Answer : Let's begin first with a heuristic definition. In the FLRW
> >cosmology the scale factor R of the Universe can be reduced to R = 0.
> >On this singular region, the scale = 0 (O scale).  This point is the
> >"initial singularity" in the cosmological standard model. 

> Okay, that makes sense.  We are studying the usual Friedman-LeMaitre-
> Robertson-Walker "big bang" solution of Einstein's equations, and
> you're referring to the big bang itself, where the scale factor R 
> equals zero.  Strictly speaking only the limit R -> 0 makes sense,
> not R = 0.  But I'll treat you as physicists and accept a little
> sloppiness.
> 
> The trouble starts here:
> 
> >As far as our own model is concerned
> 
> Which model is that???

Answer : The model based on what we call the " quantum superposition"
of Lorentzian and Riemannian metrics.

> >we have established that at the vincinity of this "singular point" 
> >(0 scale) the 4 dimensional metric must be considered as positive 
> >definite (euclidean signature ++++).

> Ah!  You say you have *established* this.  That means you have
> some sort of definite proof or calculation, at least at the physical 
> level of rigor.  I would like to understand what you actually did.
> So:
> 
> Firstly, tell me what model you are talking about.  

Answer : The model of  superposition (as quoted above).  Again, at the
Planck scale, we consider that the spacetime metric and its signature
are subject to some "quantum fluctuations". The quantum fluctuation of
the signature implies that the lorentzian signature +++- should be
extended to +++(+,-).
The "space of oscillation" between the lorentzian and the euclidean 
metrics can be described -as we did- by the separated quotient
topological space sigma =  R3,1 cross R4 diagonally quotiented by
SO(3)   (the slicing being here given by the orbits of the action of
SO(3) on R3,1 cross R4). This of course suppose an extention to a
5-dimensional underlying space. By the way :  the topological space
sigma is constructed from the symmetric homogeneous space SO(3,1)
cross SO(4) diagonally quotiented by SO(3). In terms of generators,
this homogeneous space is 9-dimensional; but sigma (considering the
orbits of the action of SO(3) is 5-dimensional.

> Secondly, tell me what mean by saying the 4-dimensional metric
> "must be considered as" positive definite.  Are you saying it
> *is* positive definite?  That would be very odd if you were 
> talking about the FRLW cosmology, because here the metric is
> never positive definite, not even in any vicinity (neighborhood)
> of the initial singularity.  So, what's going on?

Answer : The superposition model is NOT anymore the FRLW model (which
only valid up to the Planck scale). In the framework of superposition
space of the metric it is easy to show (as proved in prop. 2.2.4 of
Grichka's thesis) that sigma top has the structure of a convex cone
endowed with a singular origin.  On this origin (and only on this
singular point), the metric is euclidean.

> Thirdly, tell me how you *established* that the metric must be
> considered as positive definite.

Answer : There are different kinds of arguments (possible
demonstrations). Some belongs to  algebraic topology or Lee groups
theory, some others to quantum groups theory or van Neumann algebra,
and still some others have a more physical content. But all are very
long to expose. The best is to see chap 2, 3, 4, 5, 7 of Grichka's
thesis. In one sentence and on physical basis, we could say that KMS
condition applied to spacetime system at the Planck scale necesseraly
implies  complexification  of the timelike direction of the metric.
This involves (in terms of factors) a III-lambda factor able to be
decomposed into a semi-direct product of R and a II-infinite factor (M
0,1). One can then show that at the origin t goes to 0,  the
one-parameter automorsphism  group of the "residual" II-infinite
factor M 0,1 is an euclidean automorphism semi-group of the form :
exp - beta h  M O,1  exp +beta h. This gives a "pseudo evolution" in
imaginary time (euclidean metric).
The question here : do we have a Lagrangian corresponding to thie
"superposed state" of the metric at the Planck scale?  The answer is
yes, but only in the framework of an extension of classical gravity. A
good toy model of this extended lagrangian is :
  
L sugrav = beta hat R + 1 over g squared times R squared + alpha R R
dual.

Here, beta is the compactification radius of the theory, 1 over g
squared the dilaton (g being the coupling constant) and alpha the
axion (super partner of the dilaton field). We have shown that this
lagrangian has an infrared and an ultraviolet limit.  For g goes to
arbitrary large values  (infrared limit corresponding to beta > to
Planck scale) the extended lagragian is reduced to the Einstein term
beta R. In this case, of course, the underlying metric is
4-dimensional lorentzian. On the contrary, for g goes to 0.  (ie.beta
goes to 0, ultraviolet limit ) the Einstein term becomes neglectible.
Moreover, as the theory becomes self dual on this limit, the only
relevant term is the topological term alpha R R dual. This limit
represents the instantonic pole of the theory.   In this case, the
timelike direction is compactified on the circle S1 of radius beta=0. 
 Dually, the spacelike direction (whose the compactification radius in
an inverse function of beta) is decompactified on the straight line R
for beta=0. The underlying theory is 4-dimensional endowed with an
euclidean metric.

> >This topic is described by topological field theory.

To be continued...

From: igor.bogdanov@free.fr (I/G.Bogdanoff)
Newsgroups: sci.physics.research,sci.physics
Subject: Re: Physics bitten by reverse Alan Sokal hoax?
Date: Wed, 6 Nov 2002 20:39:26 +0000 (UTC)
Organization: http://groups.google.com/
Message-ID: (e8e077d9.0211060607.59b42657@posting.google.com)


baez@galaxy.ucr.edu (John Baez) wrote in message news:(aq1uoo$sr2$1@glue.ucr.edu)...

> In article (aptbm5$rp6$1@panther.uwo.ca),
> igor.bogdanov (igor.bogdanov@free.fr) wrote:

We continue with our answers... 

> 5) What does any of this have to do with Foucault's 
> pendulum or the origin of inertia?  Again, please describe
> the connection as precisely as possible.

Comment : The idea to apply topological field theory to some question
related to the F. Pendulum is (as indicated in the paper) of
conjectural nature.  What we had in mind is that topological fiel
theory might apply to the so called "0-scale of spacetime" (initial
singularity problem). We proposed to represent this euclidean 0-scale 
by 0-size gravitational instanton. In this conjectural paper, we have
written in the provocative conjecture 4.2 : "The inertial interaction
may be interpreted as a topological interaction, of which the source
is the topological charge of the  zero size singular gravitational  
instanton." By "topological interaction" we mean here a topological
amplitude whose source could be the singular gravitational instanton.
The charge Q of the  zero size gravitational instanton is detectable
at the boundary S3 of the singular gravitational instanton provided
with the topology of the B4 Euclidean ball of dimension D=4. We have
also conjectured that a possible model of the "propagation" of this
topological charge can be given by the conformal transformations of
the sphere S3.


> >>I appreciate the fact that to someone not expert in physics,
> >>this stuff may seem no weirder than any other paper in a physics
> >>journal. They are indeed using actual physics jargon - but I assure 
> >>you, it makes no sense.
 
> >Comment : OK.  However, we would prefer "not clearly understandable."
> >Perhaps for two reasons : 1) first it is a secondary paper written long
> >time after the "key paper"  (Classical&Quantum Grav.) where all our
> >ideas are exposed and developed in more details. 2) second : once more
> >it is conjectural paper. 

> Regarding these points:
> 
> 1) I was not able to find explanations of any of the relevant 
> concepts in your Classical and Quantum Gravity paper, either.

Some more detailed explanations are in the thesis (specially Grichka's
thesis). But the fundamental idea as exposed in CQG paper is that the
0-scale of spacetime should be considered as relevant for topological
field theory. We have suggested that the high temperature limit of
quantum field theory (corresponding to beta = 0 in the partition
function   Z = Tr (-1)s exp -H )  is a topological invariant. The
signature of the metric of the underlying 4-dimensional zero scale
manifold is therefore Euclidean (+ + + +).

> 2) It's okay to make conjectures, but there is little point
> in publishing conjectures that cannot be understood. 

OK. We will try to be clearer about our ideas and the way to express
them (with the help of the community).

> >John Baez text : How in the world could the plane of oscillation of a
> >pendulum be "aligned with the initial singularity", i.e. the big bang?
> >The big bang did not occur anywhere in particular; it happened
> >everywhere. 
> >
> >Comment : Well, it is exactly what we wrote :  of course, there is no
> >"priviledged" point and the initial singularity is  -as you said-
> >everywhere. 

> Given this, what does it mean to say a given plane in 
> space is "aligned with the initial singularity"?  At best
> it is a vacuous statement.
 
> >It is precisely our view : in conjecture 4.9  (nothing more
> >that an conjecture, by the way) we have considered that the
> >2-dimensional plane of oscillation of the pendulum conserves the initial
> >singularity S for inertial reference, whatever the orientation of this
> >plane in physical space R3."

> I don't what it means for a plane to "conserve the initial
> singularity S for inertial reference".  You are using words
> in a rather strange way!
> 
> I know what it means for a process to conserve some quantity,
> e.g.: "nuclear fusion conserves charge".  It means that the 
> quantity doesn't change as the process happens.  I don't 
> know what it means for a plane to conserve something. 

Comment : it simply means in our mind that the oscillation plane of
the pendulum conserves its initial orientation (whatever this initial
orientation is). This is the whole point of the well known 1851
Foucault's experiment.

> And I don't know what it means for something to conserve the
> initial singularity. 

Comment : We admit that if we consider this expression ("...something
to conserve the initial singularity...") it does not make much sense.
What we would like to convey is simply that the more distant is the
inertial reference  the smaller is the angular deviation of the
oscillation plane of the pendulum regarding this reference. In this
perspective the most "distant" inertial reference can be seen as the
initial singularity of spacetime.
 
> I also don't know what the extra
> phrase "for inertial reference" is supposed to modify, and
> how it could modify anything in this sentence in a sensible
> way.  

Comment : As suggested above the "inertial reference" is identified in
our approach to the initial singularity of spacetime.

> So, could you please explain much more clearly what you mean
> here?

> >It is explicitly written  in conjecture 4.9
 
> >John Baez text : Indeed, nothing in the paper suggests that they really
> >understand N = 2 supergravity, Donaldson theory, or KMS states. For all
> >I can tell, they merely stuck together a patchwork of plausible-sounding
> >sentences on these subjects.  
 
> >Comment : Once more, one should refer to the PRINTED VERSION (not the
> >PDF's) of CQG paper (and also to the 2 thesis) to get a clearer view of
> >what we say (and know) about N = 2 supergravity, Donaldson theory, KMS
> >states, etc.We have passed many years working on these topics and became
> >rather familiar with all these subjects.

> Okay, I'll look at the printed version.  Exactly how does this
> differ from the version in the PDF file of your thesis?

Comment : We have noticed many misprints in the PDF version. But
regrettably it is also the case in the printed versions. Might be one
of the sources of the series of misunderstandings we have to cope
with. For instance (as noticed by Aaron Bergman in eq.19 of the CQG
paper) the /\ symbol in the Euler characteristic is missing. There is
somewhere in the introduction a Hodge star in F /\ F which should not
have been printed. We had ask the corrector of CQG to fix this but
those corrections were not applied to the final version.

> Anyway, it would be very reassuring to hear you say something 
> that demonstrates understanding of N = 2 supergravity, Donaldson 
> theory, KMS states, von Neumann algebras, or the other subjects 
> on which you write. 

Comment OK. But the subject is vast. But we welcome any precise
exchanges on those questions related to our work.

> >In our view,  the fact to
> >consider a topological field theory independent of the Hamiltonian is
> >just equivalent to consider the same theory as independent of the
> >metric. 

> This is clearly false, as explained below.

> >A theory independent of H is topological because it is - by
> >construction -  independent of any physical field.

> A theory with zero Lagrangian is independent of the fields
> appearing in that theory.  Such a theory has zero Hamiltonian:
> H = 0.  This is completely different from being "independent of H".
> If something is "independent of H", it doesn't matter what H
> is.  Here it matters a lot that H = 0.

Comment : Of course. We agree with you.  But when we write
"independent of H" the condition is beta = 0. It is only for beta = 0
that the theory becomes independent of H. Of course, it could look
like a sort of "tautology"; but in fact it is not. In this setting the
topological limit can be reached for beta = 0 (whatever the values of
H are). In other words, in the partition function of the theory, it is
equivalent to put H = 0 or beta =0 : one gets the same result. this is
all we suggest.

In conclusion for today : we are aware of the fact that our papers are
"difficult to decipher" (misprints, typos, elliptic definitions, ill
defined objects, etc).But as written by Robert Coquereaux
http://www.cassiopaea.org/cass/bogdanovs.htm, is our papers that
different from many other papers in the same field? Hopefully, with the
help of the community, we will improve the written material ( as
suggested by D.Sternheimer http://www.cassiopaea.org/cass/bogdanov3.htm,
our former thesis advisor.This has already began with the precious help
of Ark Jadczyk).  Are there some interesting ideas to discuss in these
papers? We think that's the case. But it is our personal view and we are
sincerely looking forward to get some feedback from all interested
members of the community.  
To read my reply and that of Russell Blackadar, click here.


baez@math.ucr.edu © 2002 John Baez

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