Dear Dr. Henry-Couannier,

I'm reading your gr-qc/0404110 v2 [Ref. 1] with great interest. You
introduced a unique global privileged coordinate system [Ref. 1, p. 25] and two conjugated metrics that are exactly equal [Ref. 1, p. 30], and wrote: "This opens the fascinating perspective that then fields
(particles) may be able to jump from one metric to its conjugated
identical metric." [Ref. 1, p. 20]

I wonder if you can explore the time <--> space exchange,

http://www.geocities.com/optomaplev/programs/astro4.html#2.5

and describe a time-frozen luxonic world that stands "between" the two conjugated worlds, tachyonic and material [Ref. 2].

I think you can find this time-frozen world

http://God-does-not-play-dice.net/Ostermann.html#note

right above your neck,

http://God-does-not-play-dice.net/Azbel.html#self

I will appreciate the opinion of your colleagues as well.

Best regards,

Dimi Chakalov
--
http://God-does-not-play-dice.net
 

References

[Ref. 1] Frederic Henry-Couannier, Negative energies and time reversal in Quantum Field Theory and General Relativity, The Dark Side of Gravity, gr-qc/0404110 v2, Mon, 3 May 2004 13:18:27 GMT,
http://xxx.lanl.gov/abs/gr-qc/0404110

p. 4: "However, these antiparticles have nothing to do with genuine
negative energy states propagating forward in time, whose quanta are by construction of the conventional QFT fields never created nor
annihilated. Therefore, our deep understanding of the actual meaning of field negative frequency terms in QFT does not "solve" the negative energy issue since the corresponding solutions were actually neglected from the beginning. As we shall see, there is a heavy price to pay for having neglected the negative energy solutions: all those field vacuum divergences that unavoidably arise after quantization and may be an even heavier price are the ideas developed to cancel such infinities without reintroducing negative energy states.

p. 25: "Let us stress that our model is generally covariant and
therefore it respects Einstein’s principle of equivalence. Only did we
exhibited another (apart from the two inertial ones) privileged
coordinate system where a simple relation links our conjugated metrics. (...) Negative energy density is of course a good candidate to produce the universe acceleration that is actually observed."

p. 32: "Then it may be, as already Sakharov suggested in 1967 [6], that we are living in a left chiral positive energy world with its particles and antiparticles while the conjugated world is from our world point of view a right chiral negative energy world with its particles and antiparticles."

pp. 4-5: "2) A unitary time reversal operator

"Though our common sense intuition tells us that the interchange of
initial and final state stands to reason, a quick inspection of the
above pictures convinces us that the unitary picture (following the same usual procedure as for all other discrete and continuous symmetries in nature) is very natural as a time reversal candidate process. At the contrary there seems to be no clear reason for triggering time reversal starting from the final state as is the case in the anti-unitary picture.

"Both time reversal conjugated candidates are of course perfectly
mathematically coherent and there is no strong reason to prefer and
adopt the QFT T anti-unitary choice. We can even list several arguments in favor of the unitary choice:

" - Time irreversibility at macroscopic scale allows us to define
unambiguously our time arrow. But the microscopic time arrow may be not so well defined. (...) Therefore, in a certain sense, the running
backward movie picture appears just as a confusing and inappropriate concept obscuring our understanding of time reversal."

p. 20: "At last, considering that we have two metric fields, it is not
very surprising that there exists at least locally a third coordinate
system where g^µv = g_µv . We postulate that this is global so that this new coordinate system is essentially unique and we shall identify it to be the conformal cosmological coordinate system. So the model is not actually bi-metric and it is easily checked that the linearized
gravitational side of our new Einstein equation is the same as in General Relativity so that the number of physical degrees of freedom of the gravitational waves polarization tensor is still two. (...) This
opens the fascinating perspective that then fields (particles) may be
able to jump from one metric to its conjugated identical metric.

"The minus signs needed to interpret our new energy-momentum sources as negative sources naturally emerge from the extremum action and inverse metric mechanism, starting from a fully general coordinate, time reversal and parity scalar action. Therefore fields living in the reversed time arrow world are just seen from our world as negative energy fields. Last but not least, divergences cancel provided vacuum action terms are equal in the time conjugated inertial four-volumes. The solutions will be now derived and their physical consequences explored for the most important physical cases."

p. 30: "By the way, we were also led to a surprising and unexpected
result: finite radius singularity has disappeared from our final Schwarzschild metric solutions expressed in the most natural coordinate system. So what about black holes in this new context?
...

"As we have seen, negative energy virtual propagators would completely cancel positive energy ones if both were allowed to propagate the interaction with identical couplings. Suppose that such a connection between the two worlds is actually fully reestablished above a given energy threshold and that then loop divergences naturally get cancelled. (...) But a more realistic possibility as we already noticed is that such a transformation be triggered where our two conjugated metrics are exactly equal. Indeed, here our positive and negative energy fields live in the same metric."
 

[Ref. 2] Max Tegmark, On the dimensionality of spacetime, gr-qc/9702052
http://www.hep.upenn.edu/~max/dimensions.html
http://xxx.lanl.gov/abs/gr-qc/9702052

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)."
 

Note: I have serious doubts about the mechanism of separation of the two worlds, as suggested by Frederic Henry-Couannier. The problem is well-known (Sheldon Glashow has elaborated in early 1980s) but highly non-trivial: the two worlds have to be both totally separated, to avoid their mutual destruction, and safely linked, to enable their joint elimination of divergences in QFT. We face the same non-trivial task in the mind-body problem and the "talk" between matter and geometry. The solution proposed above is to place their nexus in the potential future of the putative universal time arrow. Physically, we can determine/calculate only one instant from this arrow, which is why it shows up only as some atemporal luxonic world ("its proper time would stand still").

Perhaps the idea of joint evolution of two mirror/conjugated worlds (see above) can be amended with the Chronon theory of Erasmo Recami and Ruy H.A. Farias (quant-ph/9706059 and quant-ph/0206117). In other words, we have to start with the mechanism of creating wave amplitudes by these two conjugated worlds, bearing in mind that the proper time of this creative process is zero, since it "takes place" at the apex of the light cone ('interactions on null surfaces', Kevin Brown). Perhaps we can gain some hints from John Cramer and Yakir Aharonov, bearing in mind that 'at the end of the day' we should add the gravitational field, hoping that this brand new quantum theory will be renormalizable. This is going to be a tough challenge, for at least two reasons. Firstly, I cannot see how the Hilbert space could be made compatible with the proposal of Kevin Brown, and secondly -- the very transition from classical to quantum regime is still unknown. And then, of course, comes the problem with the gravitational field: these two mirror worlds show up in Kruskal-Szekeres diagram, but we don't know how to formulate some common state space for both quantum and gravitational fields. Tough.

To sum up, the main idea of creating wave amplitudes is to keep the two mirror worlds, and allow them to interact in some atemporal luxinic medium that stands "between" them. Note that in E. Recami's quant-ph/9706059, there are three Schrödinger equations: retarded, symmetric, and advanced. Again, all this pertains to the realm of possibilities, not probabilities. The Born rule is valid only for the case of [tau] tending asymptotically toward zero.

What else but the two mirror worlds could eventually explain the cancellation of all but one part in 10¹²⁰? I think the right way to start is with the unitary time reversal operator, as suggested by Frederic Henry-Couannier. It's a long way to go, however.
 

D. Chakalov
May 15, 2004

==========

Subject: Re: Living in the same metric?
Date: Tue, 25 May 2004 19:07:12 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: Frederic Henry-Couannier <henry@cppm.in2p3.fr>
CC: oldstein@math.rutgers.edu, don@phys.ualberta.ca,
unruh@physics.ubc.ca, duerr@mathematik.uni-muenchen.de,
hartle@physics.ucsb.edu, piet@ias.edu, adler@ias.edu


Dear Frederic,

Regarding my comments,

http://God-does-not-play-dice.net/Frederic.html#note

I wonder if you have thought about virtual and negative probabilities [Ref. 3] to describe the "intermediate steps" of the cancellation process. The aim of the cancellation process is to replace the collapse in standard QM with some real quantum ontology, and to explain the occurrence of events/spacetime points.

Hear the recent lecture by Prof. Sheldon Goldstein at the Perimeter
Institute, it's all about what he dubbed X or "something else" [Ref. 4],
and pay attention to what he said about the timeless evolution of the
wave function of the universe (56th min). My whole web site is about
this "something else", known also as the Gap of Zen,

http://God-does-not-play-dice.net/1.html

Best regards,

Dimi
--


[Ref. 3] James B. Hartle, Linear Positivity and Virtual Probability,
quant-ph/0401108, Sec. V

"Since recording outcomes is usually taken to be an essential part of a measurement process[8], we can say that sets of histories with virtual probabilities cannot describe the outcomes of measurements. Extending the notion of probability to include virtual values thus does not risk assigning a virtual value to the probability of anything measured or recorded exactly.
...

"Feynman [28] explored the uses of negative probabilities in intermediate steps in a variety of circumstances in physics. These included the probabilities for position and momentum defined by the Wigner distribution, for the emission of virtual non-transverse photons in electrodynamics, in two-state systems, and in the two-slit experiment. He concluded that extending the notion of probability to negative values was useful provided these negative values are interpreted to mean that the situation is "unattainable" or "unverifiable". We take the same viewpoint here.
--
[28] R.P. Feynman, Negative Probability in Quantum Implications: Essays in Honor of David Bohm, ed. by B.J. Hiley and F.D. Peat, Routledge and Kegan Paul, London (1987).

[Ref. 4] Sheldon Goldstein, Rutgers
Title: What is quantum theory?
Date: Wednesday May 19, 2004, 2:00 PM

Abstract: Despite the fact that quantum theory has been widely accepted as fundamental for more than 70 years, it is still not entirely clear what makes a physical theory a quantum theory. I shall explore this question, coming perhaps to no definite conclusion. In doing so, I shall provide my own personal perspective on the lay of the quantum mechanical landscape.

http://www.perimeterinstitute.ca/activities/scientific/seminarseries/
alltalks.cfm?CurrentPage=2&SeminarID=331

http://www.perimeterinstitute.ca/activities/scientific/seminarseries/
data/331/audio/SheldonGoldstein05192004.rm

Length: 1:06:41, Size: 24,686,841 bytes