Subject: Re: gr-qc/0109061
Date: Wed, 19 Dec 2001 14:23:33 +0200
From: "Dimiter G. Chakalov" <dchakalov@surfeu.at>
To: ford@cosmos.phy.tufts.edu
CC: roman@ccsu.edu, arvind.borde@liu.edu,
     adam@godel.math.missouri.edu, questions@niac.usra.edu
BCC: [snip]
 

Dear Professor Ford,

In connection with my email from Thu, 20 Sep 2001 21:28:18 +0200 (attached): I read the revised version of your paper, from Tue, 18 Dec 2001 00:25:35 GMT, and thought again about the Garfinkle result (Fig. 1, p. 3 of your PDF file "Constraints on Spatial distributions of Negative Energy", gr-qc/0109061).

As you have surely noticed, since my first email to you sent nearly three years ago, I do not have a theory of the putative global mode of time but just a few very general ideas and speculations. I will first try explain them, and then will formulate a wild guess about the method of spacetime averaging. As you wrote (ibid., p. 14): "We have given some explicit examples of spacetime averaged quantum inequalities in two-dimensional spacetime. However, the problem of finding similar results in four-dimensional spacetime is unsolved."

Postulate

P1. The putative global mode of time, as explained at my web site, refers to a hypothetical propensity-state of all quantum systems spanned across the entire Universe, which can not be observed by means of *inanimate* physical devices due to the speed of light.

Physically, we observe the net effect from the 'dialogue' between the global and local modes of time, as seen in our past light cone. The global mode of time contains potential outcomes of all measurements in the future [Ref. 3], which will be inevitably 'filtered' through the apex in Minkowski's cone and will thus take some point-like values from the *local* mode of time.

[I will skip the highly speculative issue of some non-perturbative measurements of the quantum realm, which may be performed with the human brain only; the so-called 'physics of human intention' or PHI.]

2. Hypotheses

H1: The quantum world can be modeled with two worlds with inverted spacetime basis, as in Kruskal-Szekeres diagram, or with 'material' and 'tachyonic' worlds, as in the diagram of Tegmark,

http://www.hep.upenn.edu/~max/dimensions.html

H2: The intrinsic nonlocality of the quantum world, pertaining to the putative global mode of time, can be modeled with a parameter  [delta] , which can take real values in the open interval  (0, [infinity]) , and describes the overlapping of the two worlds in the global mode of time (H1). Three qualitatively different cases can be outlined: [delta] approaching zero (classical world), [delta] taking some finite value sufficiently bigger than zero (quantum world), and [delta] approaching infinity (a totally new case of effectively ONE entity).

H2.1: In the case of [delta] tending asymptotically toward zero, we have the macro-world of classical mechanics, with objects localized in sharp, "point-like" locations in space and time (no Schrödinger's cats). This is the case of four-dimensional spacetime, which has to be recovered as a classical limit.

H2.2: In the case of [delta] taking some value "sufficiently bigger than zero" (the meaning of this phase needs to be explained by a relation including Planck constant), the effects of the global mode of time must be taken into account.

Example: the Garfinkle result (p. 3 from your PDF file). You wrote:

p. 3: "Consider first the Garfinkle box. We can understand the unboundedness of the total energy  E  in this box as arising from two factors: (1) The energy is measured at a precise instant in time, and (2) the walls of the box are sharply defined.

p. 4: "These considerations might suggest that the Garfinkle and Helfer results arise by methods of spatial averaging which manage to capture large amounts of (-) energy while ignoring larger amounts of (+) energy which are really very close by."

You also stressed that  (-) energy is "propagating" along spacelike trajectories (p. 9), and wrote: "Another analogy is an Einstein-Podolsky-Rosen state in which two photons are generated in an  entangled state such that a measurement of the spin of one photon allows  one to determine the spin of the other photon even at spacelike separations. This process cannot be used for superluminal signaling because there is no way to know ahead of time what the spin of the first photon will be before it is measured, which is what one would need to send Morse code type messages. The two photons are in some sense two parts of one single "object".

Now, what if you try to model space averaging over "spacelike separations" with  [delta] ? It is a "spacetime" of all propensities a la Aharonov [Ref. 3].

Think of a typical 2-D bell-shaped distribution, where the "wave amplitude" takes values from the *global* mode of time. Hence you might get a global 2-D spacetime, maybe. Perhaps you could also try another mystery, that of the cosmological constant. Since gravity couples all forms of energy, what kind of action, and what sort of symmetries would explain the cancellation of all but one part in 10^(120)? We need new physics, and I believe it can be unraveled with an infinite-dimensional global spacetime. It should also be the solution to the basis problem in QM. All the rest comes from imposing constraints, such as boundary conditions pertaining to some concrete physical case, like the Casimir effect.

Just a wild guess.

Regards,

Dimiter G. Chakalov
http://members.aon.at/chakalov
http://members.aon.at/chakalov/dimi.html
--

[Ref. 3] Yakir Aharonov, Lev Vaidman. The Two-State Vector Formalism of Quantum Mechanics.
http://xxx.lanl.gov/abs/quant-ph/0105101

"One of us (YA) is not ready to adopt the far reaching consequences of the MWI. He proposes another solution. It takes the TSVF even more seriously than it was presented in this paper. Even at present, before the "future" measurements, the backward evolving quantum state (or its complex conjugate evolving forward in time) exists! It exists in the same way as the quantum state evolving from the past exists. This state corresponds to particular outcomes of all measurements in the future."

    ---------------------------------------------------------------------

Subject: gr-qc/0109061
Date: Thu, 20 Sep 2001 21:28:18 +0200
From: "Dimiter G. Chakalov" <dchakalov@email.com>
To: Larry Ford <ford@cosmos.phy.tufts.edu>
CC: arvind.borde@liu.edu, roman@ccsu.edu,
     adam@godel.math.missouri.edu

Dear Professor Ford,

I'm reading your recent article [Ref. 1] with great interest. May I ask you to help me understand some basic implications for the phenomenon of entanglement.

Would you agree with Adam Helfer [Ref. 2] that negative energy states may exist as long as no one is "looking" at them?

If that is the case, what could be the mechanism restricting the production of negative energy densities? Would it be some cancellation mechanism that can eliminate all but 1 part in 10^(120), as in the case of cosmological constant problem?

My speculations on these issues can be read at my web site.

With kind regards,

Dimiter G. Chakalov
http://members.aon.at/chakalov
(last update 3 September 2001)
 

References

[Ref. 1] Arvind Borde, L.H. Ford, Thomas A. Roman. Constraints on Spatial distributions of Negative Energy. Wed, 19 Sep 2001 02:19:54 GMT,
http://xxx.lanl.gov/abs/gr-qc/0109061

"It might appear from this example that the  $(-)$  energy is "propagating" along spacelike trajectories. However, a relativistic quantum field theory incorporates causality in its construction. So what is going on? One must remember that these are rather special states which have correlations built into them. These built-in correlations cause the energy density to vary in a manner that looks like acausal propagation. At each point, the energy density is moving in such a way as to create the effect of peaks and troughs of energy that are constant along spacelike lines.

...
"Another analogy is an Einstein-Podolsky-Rosen state in which two photons are generated in an entangled state such that a measurement of the spin of one photon allows one to determine the spin of the other photon even at spacelike separations. This process cannot be used for superluminal signaling because there is no way to know ahead of time what the spin of the first photon will be before it is measured, which is what one would need to send Morse-code type messages. The two photons are in some sense two parts of one single "object".
...

"We have given some explicit examples of spacetime averaged quantum inequalities in two-dimensional spacetime. However, the problem of finding similar results in four-dimensional spacetime is unsolved."
 

[Ref. 2] A. Helfer. 'Operational' Energy Conditions. Fri, 13 Feb 1998 22:41:21 GMT,
http://xxx.lanl.gov/abs/gr-qc/9709047

"Too, it is something of a puzzle why such states do not interfere with the dynamics of the quantum fields: why do not perturbations (which are always present) send the field cascading through these negative-energy states, with a corresponding release of positive-energy radiation? It is a matter of common experience that such effects do not occur, or at least not often, and therefore there must be some mechanism restricting the production of negative energy densities, their magnitudes, durations, or interactions with other matter.
...

"The present results suggest that any attempt to understand the consequences of negative energy densities for gravity (Hawking evaporation; effect on singularity theorems, area theorem, positivity of Bondi and ADM energies) must take into account quantum measurement issues."