Subject: Two rows of arrows: The global mode of spacetime
Date: Fri, 07 Nov 2003 21:39:48 +0200
From: Dimi Chakalov <>
To: Merced Montesinos <>
CC: George F R Ellis <>,
     Jeff Murugan <>,
     Christos Tsagas <>,
     Roy Maartens <>,
     John Barrow <>,
     Janna Levin <>,
     Sigbjorn Hervik <>,
     Jean-Philippe Uzan <>, Alan Guth <>,
     Jaume Garriga <>,
     Alexander Vilenkin <>,
     Arvind Borde <>,
     Laurent Nottale <>,
     Ulrich Gerlach <>,
     Claus Kiefer <>,
     H Dieter Zeh <>,
     Don N Page <>,
     William G Unruh <>,
     Jorge Pullin <>,
     Andre Gsponer <>, Antoine Suarez <>,
     Hans Primas <>,
     Jean-Pierre Luminet <>,
     Paul Davies <>
BCC: [snip]

Dear Dr. Montesinos,

I read with great interest your beautiful paper on the double role of Einstein's equations, gr-qc/0311001 [Ref. 1]. I like very much your two rows of arrows, and since you stated that any comments on this issue are welcome, may I offer you seven comments.

You wrote [Ibid., pp. 4-5]:

"This means that for this type of observers, there is a balance between the 'content' of energy and momentum densities and stress associated with the matter fields [psi] (which is characterized in Tµv) and the 'content' of energy and momentum densities and stress associated with the gravitational field (which is characterized in [XXX])

                <---<---<---<---                                (23)

in a precise form such that both fluxes cancel, and thus leading to a vanishing 'flux', i.e., tµv = 0. Once again, the vanishing property of tµv for the system of gravity coupled to matter fields is just a reflection of the fact that the background metric is dynamical.

"More precisely, tµv = 0 tells us that the 'reaction' of the dynamical background metric is such that it just cancels the effect of 'flux' associated with the matter fields. It is impossible (and makes no sense) to have a locally non-vanishing 'flux' in this situation. If this were the case, there would be no explanation for the origin of that non-vanishing 'flux'. Moreover, that hypothetic non-vanishing 'flux' would define privileged observers associated with it (the ether would come back!)."

The ether might come back, but as a new feature of spacetime, which I call global mode of spacetime. Here's why.

1. I believe the ether is clearly present in your Eq. 23: it is the medium in which the cancellation due to diffeomorphism covariance (active diffeomorphism invariance) "takes place". We enjoy only the final product, with an *already* vanished flux tending *asymptotically* toward zero.

Last year, on 24 October 2002, I asked one of the leading experts in quantum gravity to explain what kind of "time" is tacitly involved in these 'moving points around' in Diff(M)-invariance, but I never got an answer,

Same story with Carlo Rovelli,

2. The ether (=global mode of spacetime) seems to be indispensable in discussing the cosmological constant problem,

3. The global mode of spacetime is needed for a "cut off" of the cosmological time,

4. The global mode of spacetime pops up in Cramer's Transactional Interpretation of QM, as two rows of arrows running in some atemporal hand-shaking medium,

5. The same global mode of spacetime has been re-discovered by Antoine Suarez in the so-called non-local interactions [Ref. 2]. He directed the Swiss think tank, Institute for Interdisciplinary Studies, from 1985 to 1993, and had an insight on Tuesday, June 26, 2001 [Ref. 3].

6. To the best of my knowledge, the global mode of spacetime has been first introduced by Raymond Ruyer in 1946 (in French only), as 'potentiel' and 'domaine trans-spatial',

To cut the long story short:

7. The global mode of spacetime is needed in both quantum physics and brain science, to "think globally and act locally",

The global "thinking" requires two rows of arrows, just like yours.

Now, let's see what happens if we ignore this very old story: total mess. Why? Because you would then have to choose between two alternatives, 'either ... or',

The latest example is "The Emergent Universe: An Explicit Construction", by George F.R. Ellis, Jeff Murugan, and Christos G. Tsagas, gr-qc/0307112 [Ref. 4]. Drop the space-time singularity, "with all that that entails" [Ibid.], and you're facing a fine-tuning of the initial conditions that is just absolutely miraculous!

Miracles, however, lead to dead-end. Or to the New Age of the so-called anthropic principle,

With the global mode of spacetime, you can 'have your cake and eat it': the universe would have a dual age. Finite, some 13.7B years, in the *local* mode of spacetime, and infinite (indecisive) in the *global* mode of spacetime.

I will appreciate your feedback, as well as the critical comments from all your colleagues, from both CC: and BCC: lists.

More in my White Paper,

and in the manuscript "From the Human Brain to Quantum Gravity: Biocausality",

Possible practical applications are briefly mentioned in

Kindest regards,

Dimi Chakalov


[Ref. 1] Merced Montesinos, The double role of Einstein's equations: as equations of motion and as vanishing energy-momentum tensor, gr-qc/0311001 v1, 31 October 2003.

Comments: 7 pages, no figures, latex file. Contribution to the meeting in honor of Plebanski. Any comments on this issue are welcome

"'Anybody who looks for a magic formula for "local gravitational energy-momentum" is looking for the right answer to the wrong question' is, for instance, a quotation found in page 467 of Ref. [1].

[1] C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation (W. H. Freeman and Company, New York, 1973).

"Therefore, it is conceptually not possible to neglect gravity effects and thus all observers must conclude that the background metric is always dynamical and that its effects can not be neglected. Thus, conceptually,  tµv = 0  always. If, by hand (Einstein’s equivalence principle) the dynamics of the background metric is neglected then this fact leads to the arising of non-vanishing energy-momentum tensor associated with matter fields only.

"Alternatively, one could say that the vanishing property of  tµv  is another manifestation of the so-called ‘the problem of time’ which, of course, is not a problem but a property of generally covariant theories."

[Ref. 2] Antoine Suarez, Entanglement and Time, quant-ph/0311004 v1, 2 November 2003.

"The dependence expressed by the term Pr(a|b) (or Pr(b|a)), actual though it is, it doesn't correspond to any real temporal ordering, it doesn't have any observable counterpart."

[10] "There is no way of defining a relativistic proper time for a quantum system which is spread all over space", A. Peres, Classical interventions in quantum systems. Relativistic invariance, e-print quant-ph/9906034.

[Ref. 3] Antoine Suarez, The Center for Quantum Philosophy,

"I was strongly convinced that it should be possible to give a time-ordered causal explanation of nonlocal correlations, in terms of "before" and "after".

"On Friday, the 22nd of June 2001 in the morning, I was in Geneva for the Colloquium where André Stefanov presented the first results he was obtaining. These refuted multisimultaneity, and I got the impression I was assisting to my burial. (...) On Tuesday the 26th at 19:15, I suddenly became aware that my confidence in beating quantum mechanics was the product of a prejudice: I was assuming that causality always sticks to time. But nothing speaks against the idea of phenomena being produced by causes that are not bound to the limits of space and time. I then understood that this is the kind of causality behind the formalism of quantum mechanics."

[Ref. 4] George F.R. Ellis, Jeff Murugan, Christos G. Tsagas, The Emergent Universe: An Explicit Construction, gr-qc/0307112 v2.

"However, the reader will probably by now have noted the large degree of fine-tuning that went into setting up the initial state from which the universe emerges. Indeed, the emergent model is a very special trajectory in the space of possible inflationary evolutions. We have shown existence of such models, but not that they are probable.

"Some may regard this as a deadly blow to these models, but we believe the case is wide open.

"This may be the real philosophical choice facing us: to decide which is worse, a space-time singularity, with all that that entails, or a fine tuning of initial conditions. (...) Models of the kind presented here are useful in terms of making clear the alternatives facing us: we can indeed avoid both a singularity and the quantum gravity regime, without introducing any exotic physics; but there is a price to pay in terms of fine-tuning."