|Subject: Does the vacuum "energy"
Date: Thu, 01 Dec 2005 06:29:26 +0200
From: Dimi Chakalov <firstname.lastname@example.org>
To: Alan Rendall <email@example.com>
CC: Varun Sahni <firstname.lastname@example.org>,
Yuri Shtanov <email@example.com>,
Alexei Starobinsky <firstname.lastname@example.org>,
Murli Verma <email@example.com>,
Michel Leclerc <firstname.lastname@example.org>,
Robert Wald <email@example.com>,
Chris Isham <firstname.lastname@example.org>,
Hermann Nicolai <email@example.com>
Dear Dr. Rendall,
Please correct me if I'm wrong.
In your latest gr-qc/0511158 v1, you wrote:
"This paper contains new results on the mathematical properties of solutions of the Einstein equations coupled to dark energy and other matter and concentrates on establishing a basis for the mathematical study of k-essence models. The k-essence Lagrangians give rise to a considerable variety of behaviour and the task of obtaining an overview of the possibilities is a challenge for the future."
To the best of my knowledge, the initial idea of Einstein, the lambda term, ran into insurmountable difficulties due to the problem of treating the vacuum in QFT as some real stuff that is subject to the rules of GR [Ref. 1].
Does the vacuum "energy" gravitate? Jain?
It seems to me that all these k-essence models, as well as all post hoc postulated scalar fields are 'sweeping the garbage under the rug', since they do not address the crux of the matter: Does the vacuum "energy" gravitate?
In the review article by Varun Sahni, astro-ph/0403324 v3, which appeared as ref.  in your gr-qc/0511158 v1, your colleague wrote (Sec. 2.1, p. 13): "It is important to note that there is no known fundamental symmetry in nature which will set the value of [lambda] to zero. In its absence, the small observed value of the dark energy remains somewhat of a dilemma which remains to be fully understood and resolved."
But we don't want [lambda] to be *exactly* zero, firstly, and secondly -- the beast should be able to *evolve* along the cosmological time arrow (the coincidence problem). In what "time", however? We can't use the cosmological time, because the intrinsic dynamics of the "dark" energy cannot be presented with its *product*, the cosmological time. It is an incredible error to consider the evolution of the dynamic dark energy (DDE) in the cosmological time. The latter *depends* on DDE. It is a *function* of DDE.
DDE *creates* the cosmological time (CT), hence it cannot "vary" IN THAT SAME cosmological time. We cannot write together
DDE = f(CT)
CT = f(DDE).
Do you agree?
I believe we need a new kind of "time", which brings us to the crux of the matter: how to treat the "energy" of the vacuum. Well, we simply need a new kind of time. This new kind of time is exactly the "time" in which DDE evolves. I called it 'global mode of spacetime', and invite you and your colleagues to try it with your brain. Why the brain? Because there is a state of the human brain, which does *not* change in the cosmological time. It has an entirely different dynamics, since it evolves/vary in the putative global mode of spacetime. In psychological terms, this state of the human brain is called 'human self',
Please follow the link above, and if you cannot understand the nature of this "time", please write me back.
To sum up, it seems to me that we need to upgrade Einstein's GR from the outset,
Unless, of course, you or some of your colleagues can
Note: In addition to [Ref. 1] above, see: D.W. Sciama, The
Physical Significance of the Vacuum State of a Quantum Field, in The
Philosophy of Vacuum, ed. by Simon W. Saunders and Harvey R. Brown,
Clarendon Press, Oxford, 1991, pp. 137-158, and John Baez (25 August 1999),
What's the Energy Density of the Vacuum?
creates time, and at the same time evloves in that same time?
Dear Professor Frampton,
May I ask you and your colleagues to help me understand the following conundrum: the so-called dark energy of [X] creates time, and at the same time evolves in that same time [Ref. 1].
If some physical quantity evolves with time, then 'time' is a *background* parameter. For example, I can plot the color of my hair to my age, and can predict that after 10 years there will be no more "pepper" in it.
If some entity, call it [X], is the source of the "dark" energy, then [X] creates the cosmological time. There is no background parameter here. None. Zilch.
Thus, if we claim that [X] creates time, and at the same time [X] evolves in that same time, we are talking like Baron Munchausen, who managed to pull himself out of the swamp by his own hair, as explained eloquently by Karl Friedrich von Münchhausen.
Moreover, as you stressed in astro-ph/0211544, the ultimate fate of the universe is undecidable [Ref. 2], hence we cannot rely on the textbook prescription of some "global coordinate t ",
The fate of the universe is *undecidable* because the cosmological time *arrow* employs a non-unitary dynamics: "Time is Nature's way to keep everything from happening all at once" (John Wheeler). Our potential future is open up to the 'unknown unknown', hence our possible/propensity states do not, and can not form a *set*. These possible states exist in the form of potentialities which cannot be normalized. Hence there exists a window for totally new things to emerge in the future by creatio ex nihilo: everything is possible [Ref. 2].
GR simply doesn't work here, which isn't surprising at all, given the fact that the cosmological "constant" was introduced by hand,
The way I see it, the crux of the problem is, and has always been, in the following: does the vacuum "energy" gravitate? Regrettably, many people have ignored this crucial problem and have complied a huge zoo of post hoc postulated "scalar fields" [Ref. 1]. More at
Looking forward to hearing from you and your colleagues,
"The cosmological Coincidence Problem
stems from the observation that the present-day ratio of dark matter (or
total matter) to dark energy is near unity despite the fact that these
two species are thought to evolve with time in different ways."
"Our dreadful conclusion is that
no amount of data from our past light-cone can select between these future
is the wrong EoS of the current universe?
Dear Professor Beck,
I just read your very intriguing astro-ph/0512327 v1, in which you elaborated on a new dynamics of vacuum fluctuations (or a new cancellation process of vacuum energy), grounded on a fictitious time variable: "just a helpful fifth coordinate to do 2nd quantization" (astro-ph/0310479 v4, Sec. 2).
I agree with your colleagues that "Dark Matter and Dark Energy could be considered as "shortcomings" of General Relativity since no definitive proof of their existence has been given, up to now, at some fundamental level" (Capozziello et al., hep-th/0512118 v1, p. 6), and am wondering what could be the wrong EoS of the current universe. If it contains a grave mathematical error, it will be wrong, I suppose. For example, if we consider f(x) = y and f(y) = x together, we're heading to a dead-end. Please see
If you agree, I wonder if you could fix this error with your fictitious time variable. The opinion of your colleagues will be greatly appreciated, too.
You also wrote (astro-ph/0512327 v1, p. 4): "Since zero-point fluctuations produce experimentally measurable effects in Josephson junctions, it is natural to conjecture that the energy density associated with the underlying primary fluctuations has physical meaning as well: It is a prime candidate for dark energy, being isotropically distributed and temperature independent."
I'm a bit skeptical, since my "fictitious time" is quite different,
Subject: Re: What is the wrong EoS
of the current universe?
Dear Professor Beck,
Thank you for your prompt reply.
It seems to me that the problems are rooted on some well-known limitations of non-relativistic QM; please see Larry Horwitz' quant-ph/0507044 v4.
If you can suggest a solution that is easier/simpler than my ansatz,
please drop me a line.
"For example, Ludwig [Ref. 3] has pointed out that the time variable cannot be a quantum observable, since there is no imprimitivity system (i.e., no operator exists that does not commute with \t in the nonrelativistic theory) involving this variable. Note that the Hamiltonian of the standard theory evolves quantum states in time, but does not act as a shift operator since it commutes with \t.
"Dirac [Ref. 2] has argued that if
\t were an operator, then the resulting t,E commutation relation would
imply that the energy of the system is unbounded below, from which he concluded
that the time cannot be an observable in the nonrelativistic quantum theory
(note, however, that in a relativistic theory, negative energies correspond
to antiparticle states, and are not excluded)."
[Ref. 2] P.A.M. Dirac, Quantum Mechanics, First edition, pp. 34-36, Oxford Univ. Press, London (1930); Lectures on Quantum Field Theory, Academic Press, New York (1966). See also W. Pauli, General Principles of Quantum Mechanics, p. 63, Springer-Verlag, Heidelberg (1980); E. Schrödinger Berl. Ber., p. 238 (1931); P. Carruthers and M.M. Nieto, Rev. Mod. Phys. 40, 411 (1968), and references therein.
[Ref. 3] G. Ludwig, Foundations of
Quantum Mechanics I, p. 295, Springer-Verlag, New York (1983).
Subject: Time-dependent [lambda]?
Dear Dr. Bauer,
I'll be happy to elaborate.
full quantum gravity, is the singularity resolved?
RE: Sean A. Hayward, gr-qc/0504037
v1, p. 3: "In full quantum gravity,
Dear Dr. Hayward,
It seems to me that, with minimal
assumptions about "correct" quantum gravity, the so-called singularity
could be replaced with 'potential
Prerequisites in [Ref. 1].
If you can (i) completely eliminate the possibility for a time-like Naked Singularity (R. Goswami et al., gr-qc/0410041) and (ii) include the dynamic "dark" energy on the so-called marginal surfaces ("as time develops, the marginal surfaces generate a hypersurface in space-time", gr-qc/0504037 v1, p. 1), please do write me back.
Subject: Black holes and naked singularities, if any
Dear Dr. Rendall,
Please don't send me your report AEI-2005-046, "The nature of spacetime singularities", as requested in my preceding email from Mon, 28 Mar 2005 20:01:19 +0300. I got it today from arXiv server, gr-qc/0503112 [Ref. 1], and am reading it with great interest.
You wrote: "It is important for the predictive power of
"There has been much study of the Einstein equations coupled to dust. It is not clear that they teach us much. In flat space dust forms shell-crossing singularities where a finite mass of dust particles end up at the same place at the same time. The density blows up there. In curved space this leads to naked singularities . These occur away from the centre in spherical symmetry. Finite time breakdown of self-gravitating dust can also be observed in cosmological spacetimes . This shows the need for restricting the class of matter considered if a correct formulation of cosmic censorship is to be found. In a more realistic perfect fluid the pressure would be expected to eliminate these singularities."
Your ref.  is from 1973, and I wonder if you know the recent status of naked singularity research,
It seems to me that black holes and naked singularities form a 'package' which demonstrates the breakdown of Einstein's GR: "a singularity in general relativity cannot be a point of spacetime, since by definition the spacetime structure would not be defined there." [Ref. 1].
Hence it is important for the predictive power of general relativity that both black holes and naked singularities be ruled out.
I wonder if you agree.
I like you paper very much, and will soon write some brief comments at
On Mon, 28 Mar 2005 20:01:19 +0300, Dimi Chakalov wrote:
[Ref. 1] Alan D. Rendall, The nature of
"In the case of a field theory in Newtonian physics or
special relativity we can say that a solution becomes singular at certain
points of spacetime, where the basic physical quantities are not defined.
Each of these points can be called a singularity. On the other hand, a
singularity in general relativity cannot be a point of spacetime, since
by definition the spacetime structure would not be defined there."
Note: There are many fictional stories about the so-called black holes, but perhaps the best source is the Harvard-Smithsonian Center for Astrophysics. See the Black Hole Animation, from NASA/SAO/CXC/D.Berry, at the web page here, and download the clip (MPEG, 4.3 MB) from here. It's all about the famous Sagittarius A*, and the explanatory text reads:
"This sequence begins with a 600,000-second exposure of Sgr A* made with NASA's Chandra X-ray Observatory. Next, it zooms into the precise location of the central supermassive hole, and then dissolves into an artist's rendition of the system."
The fantasy of the artist (D. Berry?) is stunning, but let's see what Alan Rendall says on this subject. He might have read Lewis Carroll's "The Hunting of the Snark", but there are no fictional creatures in his paper [Ref. 1], maybe because he has omitted, deliberately or not, the perplexing puzzle of naked singularities. The issue is 'on the table' since 1991, if not earlier. Combined with the well-known puzzle of closed time curves (CTCs), we face a truly paradoxical situation of an enormous catastrophe which hasn't happened in the past 13.7 billion years, much like the ultraviolet catastrophe discovered by Lord Rayleigh in 1900.
To explain the conceptual resolution of these problems, let's go back to Alan Rendall's paper [Ref. 1]. He wrote: "A spacetime which is a solution of the Einstein equations is said to be singular if it is timelike or null geodesically incomplete. Informally we say in this case that the spacetime ‘contains a singularity’ but the definition does not include a description of what a ‘singularity’ or ‘singular point’ is. There have been attempts to define ideal points which could be added to spacetime to define a mathematical boundary representing singularities but these have had limited success."
Since we expect that a solution may be found only in a complete theory of quantum gravity, it is important to seek similar cases of 'geodesic incompleteness' in quantum theory, all of which should be resolved en bloc. I have elaborated on such "geodesic incompleteness" here, stressing the need for global mode of spacetime (or ideal points, if you prefer). Note that we need to unravel a special case of virtual reality in GR, which can match the virtual reality in QM.
To move further along these lines, imagine a leather jacket with a zip, and picture the dynamics of GR shaped like 'Y'. The zipped part corresponds to what we can observe in the past, and surely we can see there the pattern of the cosmological "gravitational waves" as well (more on the GWs here and here). As the sliding tab of the zip follows the cosmological time arrow and moves toward your neck, it takes two "channels" of virtual reality: one from the virtual/potential states of the system in consideration, and the other from 'the rest of the universe', in line with the rule 'think globally, act locally'. This is the dynamics of the 'relational reality', plain and simple. I'm very brief here, because all this has been said many times.
Now, one question remains unsettled: why do we care about black holes (BH) but ignore their inevitable counterparts, the naked singularities? The Holon state of the universe is always in the "unzipped" part, but it casts two "opposite" blueprints on the fixed history of the universe, as explained here. I strongly believe that the whole mess around the "cosmic censorship" and the unobserved naked singularities requires new physics, and it seems to me that the only viable option is to consider the blueprint from the Holon, which is "opposite" to the cosmological time arrow: we cannot observe naked singularities (NS) in the zipped part of our universe (local mode of spacetime), because NS effects originate from the virtual component of the Holon in which "time" runs "against" the time parameter of the local mode of spacetime. Consequently, we do observe BH effects, because they originate from the other virtual component of the Holon, in which "time" runs "along" the time parameter of the local mode of spacetime. Neither BH nor NS are real in the zipped part of your jacket, however. Hence we're alive and well, and will never see our great-grand-son coming from the future and asking some tough questions, such as 'what did you do for Einstein's GR, grandpa'? Kids can be cruel, you know.
I very much like Alan Rendall's paper [Ref. 1], he writes with clear short sentences which contain incredible amount of information. It is a real joy to communicate with his sharp mind. Let me quote again from his paper:
"It remains to be seen whether the Einstein equations have further types of singularities in store for us.
"New things can happen if we go beyond
the usual framework of the singularity theorems. The cosmological acceleration
which is now well-established by astronomical observations corresponds
on the theoretical level to a violation of the strong energy condition
and suggests that a reworking of the singularity theorems in a more general
context is necessary. Exotic types of matter which
have been introduced to model accelerated cosmological expansion go even
further and violate the dominant energy condition. (...) The study of these
matters is still in a state of flux."