Subject: NATO ARW
Date: Wed, 27 Feb 2002 16:57:39 +0200
From: "Dimiter G. Chakalov" <dchakalov@surfeu.at>
To: George.Jaroszkiewicz@nottingham.ac.uk
CC: Mark Stuckey <stuckeym@etown.edu>,
     Abner Shimony <shimony@bu.edu>, "Zafiris, E" <e.zafiris@ic.ac.uk>,
     "John D. Fearns" <j.fearns@ic.ac.uk>,
     Saul Youssef <youssef@bu.edu>,
     Giuseppe Vitiello <vitiello@sa.infn.it>
BCC: [snip]
 

Dear Dr. Jaroszkiewicz,

Regarding NATO Advanced Research Workshop "The Nature of Time: Geometry, Physics & Perception": I will be very grateful to you if you could send me your paper "Analysis of the Relationship Between Real and Imaginary Time in Physics" (24 May 2002, 08:00 ~ 08:45) or any other paper of yours relevant to this crucial issue. I suppose you will examine with great details the complex time introduced by D. Sokolovski and L. Baskin [Ref. 1] and the challenge of exotic probabilities,

http://members.aon.at/chakalov/Youssef.html

My interest in your research stems from my (certainly not original) hunch that the way time is treated in physics, as a special classical observable outside QM and hence the impossibility for its quanization [Ref. 2], encodes the absence of *transience* [Ref. 3] and the lack of correct geometrical presentation of the infinitesimal,

http://members.aon.at/chakalov/Zafiris.html#below

I suspect that if we model the infinitesimal with a dimensionless "point", we're stuck on a road toward a dead-end: the structure of spacetime could be either continual or discrete, and thus the road toward quantum gravity is confined by two possibilities only, leading to causets or loop quantum gravity, none of which can recover the 3+1-D world of tables and chairs from which it started,

http://members.aon.at/chakalov/Smolin.html

I believe there is a diametrically opposite possibility: start from the outset with a correct geometrical presentation of the infinitesimal, which would encode the duration of transience [Ref. 3] and the way Mother Nature is hiding the infinitesimal,

http://members.aon.at/chakalov/Fearns.html

If true, the structure of spacetime would be both continual and discrete,

http://members.aon.at/chakalov/PHI.html#dark_room

and hence we would have to introduce two modes of time for its proper geometrical modeling. I intend to explain this in my talk on Tuesday, 21 May 2002, 16:35 ~ 17:00,

http://members.aon.at/chakalov/dimi.html

I will have 20 min only, and just 5 min left for discussion, and would very much like to be well-prepared by studying your papers relevant to the real and imaginary time in physics. I very much hope that if I quote your papers I would eventually manage to squeeze my paper into seven pages, as required. At this point I definitely can't meet this stringent requirement.

I will also appreciate help from your colleagues, for I really have no clue how a length of a table or a duration of a time interval measured with a clock can be presented with anything but a real number,

http://members.aon.at/chakalov/Zafiris.html#GPP

Perhaps some cancellation procedure is going on in the infinitesinmal, wiping out all imaginary parts/tails from this much deeper level of (physical?) reality.

Regards,

Dimi Chakalov
http://members.aon.at/chakalov
(last update 25.02.2002)
 

References

[Ref. 1] D. Sokolovski and L.M. Baskin, Phys. Rev. A 36, 4604 (1987).
 

[Ref. 2] A.S. Wightman, Rev. Mod. Phys. 34, 845 (1962).
 

[Ref. 3] A. Shimony, Implications of Transience for Spacetime Structure, in: S.A. Huggett, L.J. Mason, K.P. Tod, S.T. Tsou, and N.M.J. Woodhouse (eds.), The Geometric Universe: Science, Geometry, and the Work of Roger Penrose. Oxford: Oxford University Press, 1998, pp. 161-172.

Abner Shimony: "Even more problematic is the role of transience in physical theory. Classical mechanics, special relativity, and general relativity differ profoundly in their assumptions about spacetime structure, but in all three the structure is characterized without any reference to the slipping away of the present moment into the past."
 

=========

Subject: Re: NATO ARW
Date: Fri, 01 Mar 2002 17:01:55 +0200
From: "Dimiter G. Chakalov" <dchakalov@surfeu.at>
To: "Dr G. A. Jaroszkiewicz" <George.Jaroszkiewicz@nottingham.ac.uk>
CC: Mark Stuckey <stuckeym@etown.edu>,
     Abner Shimony <shimony@bu.edu>, "Zafiris, E" <e.zafiris@ic.ac.uk>,
     "John D. Fearns" <j.fearns@ic.ac.uk>,
     Saul Youssef <youssef@bu.edu>,
     Giuseppe Vitiello <vitiello@sa.infn.it>
BCC: [snip]
 

Dear George,

Thank you very much for your reply.

Regarding the imaginary time, I didn't mean Wick rotation nor changing the signature a la Hawking, but a peculiar implication of two worlds with "inverted" spacetime basis, as in Kruskal-Szekeres conformal map and in Tegmark's gr-qc/9702052 [Ref. 4]. It seems to me that the most important things "take place" on a null hypersurface (the putative 'global time mode'), as in [Ref. 4, Footnote 4] and [Refs. 5 and 6].

Perhaps there is a tachyonic "copy" of the material world, such that if you are in one of the worlds, the other one would be seen as "tachyonic", i.e., none of the worlds is neither material nor tachyonic 'per se'. The conversion should be via luxonic "matter", the same atemporal hand-shaking medium in Cramer's Transactional Interpretation of QM. In other words, I'm talking about the so-called pseudo-time of Cramer's transaction, which I prefer to call 'global time mode'.

My wild and certainly uneducated guess is that *if* we have a finite duration 'now', in both the human brain and the quantum world,

http://members.aon.at/chakalov/dimi.html  ,

these two worlds would be sort of 'running against each other' [Ref. 7].

If so, there should be some transformation mapping one of the world to the other, but this putative transformation is hidden in the case of a singular 'now'. To zoom on it, we need an extended 'now' or [tau], as in [Ref. 7].

Does that ring some bells? I get a headache from it, and can only think of a big and very real (not imaginary) gin tonic:-)

Best wishes,

Dimi
 

[Additional references]

[Ref. 4] M. Tegmark. On the dimensionality of spacetime.
http://www.hep.upenn.edu/~max/dimensions.html
http://xxx.lanl.gov/abs/gr-qc/9702052

Max Tegmark, Footnote 4: "The only remaining possibility is the rather contrived case where data is specified on a null hypersurface. To measure such data, an observer would need to "live on the light cone", i.e., travel with the speed of light, which means that it would subjectively not perceive any time at all (its proper time would stand still)."
 

[Ref. 5] K.S. Brown. Quantum Interactions on Null Surfaces.
http://www.mathpages.com/home/kmath238.htm
 

[Ref. 6] K.S. Brown. Spacetime Mediation of Quantum Interactions.
http://mathpages.com/rr/s9-11/9-11.htm

Kevin S. Brown: "An interesting feature of this interpretation is that, in addition to the usual 3+1 dimensions, spacetime requires two more "curled up" dimensions of angular orientation to represent the possible directions in space. The need to treat these as dimensions in their own right arises from the non-transitive topology of the pseudo-Riemannian manifold. Each point [t,x,y,z]  actually consists of a two-dimensional orientation in space, which can be parameterized (for any fixed frame) in terms of ordinary angular coordinates  q  and  f . Then each point in the six-dimensional space with coordinates  [x,y,z,t,q,f ]  is a terminus for a unique pair of spacetime rays, one forward and one backward in time."
 

[Ref. 7] R.H.A. Farias, E. Recami. Introduction of a Quantum of Time (chronon), and its Consequences for Quantum Mechanics.
http://xxx.lanl.gov/abs/quant-ph/9706059

R. H. A. Farias and E. Recami: "There are three equations, -- retarded, symmetric, and advanced Schrödinger equations, all of them transforming into the (same) continuous equation when the fundamental interval of time (that now can be called just tau) goes to zero."