Subject: ... *only at a single instant in time*
Date: Fri, 24 Sep 2004 13:05:10 +0300
From: Dimi Chakalov <>
To: Thomas A Roman <>

Dear Professor Roman,

In connection with my email sent in the past four years, let me briefly comment on your recent "Some Thoughts on Energy Conditions and Wormholes", gr-qc/0409090 v1 [Ref. 1].

You said that "the energy density can be made arbitrarily negative over an arbitrarily large compact spatial region, *only at a single instant in time* [Ref. 1].

I believe *inside* a 'single instant in time' one can reveal many interesting things, such as imaginary time,

The meaning of "inside" is explained at

Regarding "5) Dark energy with a (-) energy density?" [Ref. 1], see

Contrary to the ideas in refs [66, 67, 68] in your paper [Ref. 1], I believe (-) energy densities cannot be observed by *any* physical observer, since the so-called imaginary time pertains to a holistic state of the whole universe (see the first link above), and requires an absolute reference frame for its physical detection. You can find this absolute reference frame with your brain only; the experiment is at

Finally, let me address your 'key unsolved problem': "Although there is evidence for the existence of spacetime-averaged QIs in 4D, no explicit simple analytic forms have yet been written down. This is a key unsolved problem."

I'm afraid neither you nor any of your colleagues will be able to write down QIs in 4D. From your perspective, this task is impossible. Never. You need to find out the elementary increment of time (see the second link above). It pertains to 'a single instant in time', too.

I will appreciate your professional comments, as well as those from your colleagues. Will keep them private and confidential.

Sincerely yours,

D. Chakalov


[Ref. 1] Thomas A. Roman, Some Thoughts on Energy Conditions and Wormholes, gr-qc/0409090 v1

"Energy conditions tell us what are "physically reasonable" distributions of mass-energy, which in turn tell us what are physically reasonable spacetime geometries. They are also crucial in proving many theorems using global techniques in general relativity, such as singularity theorems and the topological censorship theorem [15]. However, the energy conditions are not derivable from GR.

"One might ask what are the possible reasons for the existence of negative energy in nature? Two thoughts come to mind. The first is the stability of flat spacetime. We know from quantum field theory (QFT) that the energy density undergoes quantum fluctuations even in the vacuum. In order for the expectation value of the stress-tensor to be zero in the Minkowski vacuum state, the sign of the energy density must be allowed to fluctuate both negatively and positively [L. Ford, private discussion].

"If there are no restrictions on (-) energy, then the semiclassical Einstein equations would have almost no physical content. One could produce "designer spacetimes." Write down any spacetime geometry you like, "plug it in" to the Einstein equations, and find the corresponding mass-energy distribution which generates that geometry. Since any solution of the Einstein equations corresponds to some distribution of mass-energy, with no restrictions (such as some form of energy condition) you can get anything you like. Therefore a key fundamental question is: does QFT impose any constraints on (-) energy?

"5) Dark energy with a (-) energy density?

"Recently there have been several models and arguments which propose that the dark energy driving the acceleration of the universe may have an equation of state which allows (-) energy densities, at least as seen by some observers [66, 67, 68]. This (-) energy component would grow with time and would not seem to be limited by the QIs. If true, this would seem rather puzzling and a bit disturbing. This would seem to allow the possibility that an observer holding a box could see it fill up with an arbitrarily large amount of negative energy as the universe expanded.

"It is thus important to emphasize here that, in our example, the energy density can be made arbitrarily negative over an arbitrarily large compact spatial region, *only at a single instant in time*.

"Although there is evidence for the existence of spacetime-averaged QIs in 4D, no explicit simple analytic forms have yet been written down. This is a key unsolved problem. The techniques used to prove the worldline QIs do not seem to easily generalize to the spacetime-averaged case. Even simple explicitly constructible states involving (-) energy densities, e.g., squeezed vacuum states of a massive scalar field, can exhibit a subtle intertwining of the (-) with the (+) energy. How generic is this behavior?

"How seriously should one take classical fields with (-) energy? If such fields are truly physical, then why does Nature bother to enforce QIs at all? The fascinating mysteries and subtleties of negative energy should keep us all busy for a while yet."



Subject: Scientific communism
Date: Wed, 13 Oct 2004 19:34:35 +0300
From: Dimi Chakalov <>
To: Serguei Krasnikov <>

Dear Serguei,

Thank you for your reply.

I'm interested in facts, and nothing but facts. I believe the facts listed below are true. Please correct me if I'm wrong.

1. In your gr-qc/0409007 v2 (Tue, 12 Oct 2004 11:22:58 GMT), you wrote:

"Its renormalized stress-energy tensor in W is readily found by formula (6.136) of [13]"
[13] N.D. Birrel and P.C.V. Davies, Quantum Fields in Curved Space (Cambridge: Cambridge University Press, 1982).

That nice yellowish 24-year old Cambridge Monograph on Mathematical Physics deals with Minkowski space QFT and Minkowskian metric tensor (pp. 10-11).

That's "scientific communism". Its Ch. 2.2, Quantization, is "scientific communism", too.

2. You also wrote (gr-qc/0409007 v2): "The part preceding the counter example proper is substantially rewritten", but you again chose to limit your considerations to a *free* field in *two* dimensions.

I personally haven't seen "free fields" in "two-dimensional de Sitter spacetime", and consider them "scientific communism", too.

Again, please focus on QIs in 4D. Plain and simple.

I agree with your Latin saying, only I believe the correct expression is 'Sapientibus sat', not 'Sapientibus sati'. It comes from 'Verbum sapientibus sat est'.

Again, please use math in deriving QIs in 4D. I prefer math, not Latin.

I'm afraid neither you nor any of your colleagues in the CC: list can derive these QIs in 4D, because you're dealing with 'relational reality',

Needless to say, I'll be more than happy if you prove me wrong. With math.

Kindest regards,