|Subject: ... *only at a single instant in time*
Date: Fri, 24 Sep 2004 13:05:10 +0300
From: Dimi Chakalov <firstname.lastname@example.org>
To: Thomas A Roman <email@example.com>
CC: firstname.lastname@example.org, email@example.com,
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.
[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 . 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?
"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