Subject: Dark Matter and Potential fields
Date: Tue, 21 Dec 2004 14:02:49 +0200
From: Dimi Chakalov <>
To: Ivanhoe Pestov <>
BCC: [snip]

Dear Dr. Pestov,

I wonder if you could find some spare time to help me grasp the main ideas in your newest paper "Dark Matter and Potential fields", gr-qc/0412096 v1, December 21, 2004. Please correct me if I'm wrong.

People talk about dark matter since 1933, after Franz Zwicky [Ref. 2].

We infer its existence by studying the *deviation* of the dynamics of luminous matter from what we would expect to be its 'normal dynamics', had the latter been determined exclusively by the luminous matter. The challenge of understanding the nature of this so-called dark matter is in reconciling two seemingly incompatible requirements: the dark matter does interact with the luminous matter, but its action is NOT directly observable. Only the net effect is observable, but this "net effect" can be inferred only from the peculiar dynamics of the luminous matter, firstly, and secondly -- we know nothing about the "recoil" (if any!) from the the luminous matter on the dark one, since the latter is unobservable.

I speculate that the action of dark matter is "dark" due to the very nature of relativistic observations: we can observe (with inanimate measuring devices) changes in the physical world *post factum* only, after they have been recorded in our past light cone. Once this happens, we can say -- retrospectively -- that the interaction between the luminous and dark matter has produced an event that has been already embedded in the spacelike hypersurface.

Do you see the catch? We can say *nothing* about the dark matter *immediately prior* to the embedding of the event of its interaction with the luminous matter. That's what makes this "matter" dark, IMHO.

Please note that we face the same problem with the relativistic "collapse", as explained with Wheeler's 'cloud',

Now, let me comment on your "Dark Matter and Potential fields", gr-qc/0412096 v1, from today, 21 December 2004. You wrote:

"The general conclusion is that a dark matter gravitate but there is no actually direct interactions of this new form of matter with known physical fields that represent luminous matter."

Same with dark energy. It should gravitate but there is no *direct* interactions of this dark energy and dark matter with known physical fields that represent luminous matter and are studied in Einstein's GR,

You also wrote: "According to the modern viewpoint a fundamental physical theory is the one that possesses a mathematical representation whose elements are smooth manifold and geometrical objects defined on this manifold. Most physicists nowadays consider a theory be fundamental only if it does make explicit use of this concept. It is thought that curvature of the manifold itself provides an explanation of gravity."

Hence we need a new theory that is "more fundamental":-) I mean, we can embed the dark matter and dark energy in that smooth manifold only *after* its interaction with the luminous matter, and only *after* this interaction we have the net effect represented with some "curvature of the manifold".

In other words, the dark matter/energy stands before/above/outside your smooth manifold, in the sense that its *direct* interaction with the good old luminous matter is not observable. This "dark" stuff is the equivalent of Wheeler's 'cloud' (please see above) that determines "later on" some curvature of the manifold, as you put it.

I agree with you that there is matter "outside" spacetime
(gr-qc/0308073, p. 21),

My efforts to understand the two "dark" components of the universe, which make up to 96 per cent of our world, is outlined at

I'm writing these lines because I still hope to hear from you regarding my proposal from December 12, 2003,

Kindest regards,

Dimi Chakalov

Download the whole web site, 4.4MB, from


[Ref. 2] Australia Telescope Outreach and Education, December 17, 2004,

"Vera Rubin in the early 1970s measured the rotation rate of over 60 galaxies. Her analysis showed that they must have a lot of invisible matter in them to hold them together as they were rotating too fast to be gravitationally bound by the visible mass. The first mention of this so-called dark matter was by Franz Zwicky in 1933. By measuring the velocities of galaxies in the Coma cluster he was able to conclude that about 90% of the mass of the cluster must be some form of dark matter in order to hold the cluster together."

Note: See the version of 'dark matter/energy problem' in brain science here; general considerations here and here. Note that we talk about a physical stuff: the effect of the Holon called 'context' and 'relational reality'.

D. Chakalov
December 21, 2004



Subject: Is there matter outside the time?
Date: Fri, 29 Aug 2003 01:01:49 +0300
From: Dimi Chakalov <>
To: Ivanhoe Pestov <>

Dear Dr. Pestov,

In your recent paper "Time and Energy in Gravity Theory", gr-qc/0308073 [Ref. 1], you suggested that there is matter outside the time, and provided the equations for the gravity field and the electromagnetic field "exterior" to time [ibid., p. 21].

I've been trying to comprehend the nature of time for many years, and it seems to me that all efforts to tackle this issue are inevitably doomed to resemble the old story of how Baron von Münchausen managed to pull out himself and his horse out of the mire (=smooth differentiable manifold). This is the reason for my efforts to introduce two modes of spacetime needed for the *emergence* of both time and 3-D space, but since you didn't reply to my previous email, I won't delve into my speculations but will try to understand yours.

May I ask three questions.

Q1: How are you going to separate the two "times"?

Q2: Do you need a third "time" that will time the switching from the physical "time" to the "exterior time" and back?

Since you acknowledged that "it is very important to understand the nature of the emergence of time" [Ref. 1], my last question is about the good old 3-D space:

Q3: Is there 3-D space in classical GR  ?

I hope to hear from you, and will appreciate the opinion of your colleagues on Q3 above.

Thank you for your time, as read by your clock.

Yours sincerely,

Dimiter G. Chakalov

[Ref. 1] Ivanhoe Pestov, Time and Energy in Gravity Theory, Fri, 22 Aug 2003 10:45:41 GMT,

Abstract: "A new concept of internal time (viewed as a scalar temporal field) is introduced which allows one to solve the energy problem in General Relativity. (...) Theory of time presented here predicts the existence of matter outside the time.

"However, till now in the framework of these principles there is no adequate solution to the energy conservation problem [2-5]. In presented paper we give the simple solution of the problem in question, which is based on the connection between the time and energy and necessarily follows from the first principles of General Relativity if one puts them into definite logical sequence. The energy conservation means that total energy density of gravity field and all other fields does not vary with time and hence represents the first integral of the system.

"New understanding of time presented here may have implications for the problem of time in quantum gravity. In fact, a major conceptual problem in this field is the notion of time and how it should be treated in the formalism. The importance of this issue was recognized at the beginning of the history of quantum gravity [6], but the problem is still unresolved and has drawn recently an increasing attention (see, for example [7],[8] and [9] and further references therein).

"We put forward the idea that the time is a scalar field on the manifold. By this we get a simple answer to the question with long standing history "What is time?" It should be emphasized, that temporal field (together with other fields) designs manifold as it was explained above but it has also another functions which will be considered below.

p. 21: "From the theory of time presented here it follows directly that there is matter outside the time. For example, the gravity field and the electromagnetic field exterior to time are described by the equations


"In this context it is very important to understand the nature of the emergence of time."


Faute de mieux, on couche avec sa femme. We don't have a complete theory of quantum gravity, so let us assume that General Relativity (GR) is the proper gravity theory, only we should not waste our time with quantizing the gravitational field: quantum fluctuations of the metric tensor is not a good idea, as explained by Chris Isham in October 1992. He has suggested seventeen years ago that, instead of quantizing gravity, one should seek a new quantum theory which yields GR as its classical limits. "So the kind of theory envisaged here would somehow be still more radical than that; presumably by not being a quantum theory, even in a broad sense -- for example, in the sense of states giving amplitudes to the values of quantities, whose norms squared give probabilities" (Jeremy Butterfield and Chris Isham, gr-qc/9903072).

Trouble is, we don't have it. The Principle of Equivalence in GR inevitably requires the notions of locality and trajectory, which are not compatible with Quantum Mechanics (QM). Hence in order to keep "the good parts" of GR and QM, which work perfectly well, and to develop a theory of quantum gravity, we should perhaps seek a new theory of spacetime that would allow us to recover GR and QM (say, by setting some of its parameters to approach zero). Briefly, we do not want to modify GR nor QM, or at least not until we work out the challenges from 'things we know that we don't know'. Then will see. Quantum gravity may very well be in the realm of 'things we still do not know that we don't know'. The future is somehow 'open', in the sense that the spectrum of all future possibilities cannot be normalized (this assertion cannot be falsified, however).

 But how to identify the "good parts" of GR and QM, which should be unified by the new theory of spacetime, and the "bad parts" which lead to paradoxes, hence set the task of quantum gravity? Let's focus on this first crucial step.

There is a common saying that the strength of a chain equals the strength of its weakest link. If this philosophy were applicable to QM and GR, none of them would have worked at all, ever. There are many paradoxes in both theories, which clearly indicate the "bad parts". These paradoxes predict horrible pathological events, such as "smearing" of the localization of objects around us (A. Sudbery, quant-ph/0011082; A. Bassi and G-C. Ghirardi, quant-ph/0009020) and non-localization of the gravitational energy (I. Pestov, gr-qc/0112045), and yet we have never observed any catastrophes, at least not at the macro-scale of tables and chairs. (However, we observe GRBs on a daily basis, which too calls for new physics beyond GR.)

The situation is deeply puzzling: on the one hand, QM and GR work flawlessly in their respective fields, but, on the other hand, we have no idea how Mother Nature has managed to cancel all catastrophic events predicted by the same theories. Back in 1924, David Hilbert wrote (Die Grundlagen der Physik, Mathematische Annalen, Heft 92, S.1-32, 1924): "I assert that for the general theory of relativity, i.e., in the case of general invariance of the Hamiltonian function, energy equations corresponding to the energy equations in orthogonally invariant theories do not exist at all. I could even take this circumstance as the characteristic feature of the general theory of relativity." This truly peculiar feature of Einstein's GR is well-known since November 1917. A few years later, in 1922, Hermann Weyl (H. Weyl, Space-Time-Matter, Dover Publications, New York, 1951, p. 270) stressed that the quantity proposed by Einstein for the gravitational field stress-energy is not, and can not be a tensor. It is manifestly pointless to expect some weird non-tensorial quantity to "obtain" a fixed, point-like, and hence numerical value, much like the case of "points" in QM, as explained succinctly by Asher Peres. Moreover, the conservation laws for energy, momentum, and angular momentum are in principle impossible in GR, as shown by Anatol Logunov; more references here. Even the weakest energy condition, ANEC, must be severely violated (C. Barcelo and M. Visser, gr-qc/0205066). Strangely enough, the cancellation of "negative" energies works flawlessly and with incredible precision, but we have no idea how to employ it (or should we?) for solving the cosmological constant puzzle, as acknowledged by Richard Feynman and Steven Weinberg in Dreams of a Final Theory.

These are some of the "bad parts" of QM and GR. They are not problems nor miracles but paradoxes. We have to find a common solution to all of them, without any exception. The next requirement is to keep the "good parts" from GR and QM. We want to keep (i) the notions of trajectory and continuum (smooth differentiable manifold is a must), (ii) the principles of locality and general covariance, and (iii) the principles of superposition, linearity, and unitary evolution.

In general, any efforts to suggest new quantization recipes (e.g., by freezing to zero two Grassmannian partners of time, A.A. Abrikosov Jr et al., quant-ph/0308101, pp. 5-6) should be bound to the measurement (macro-objectification) paradox in QM. Last but not least, we want our new theory of spacetime to make sense. Steven Weinberg told a story, in his book mentioned above, about a young and talented student who tried to understand QM, then of course failed, and decided to quit his promising career in theoretical physics. This must never happen again! We have to help kids do better than us.

Let's start with the first requirement, which boils down to the paradox of continuum. How do we get "points"? Recall the famous Thompson's lamp paradox of 1954, after James Thompson, and try to answer the following question posed by Robin Le Poidevin (Travels in Four Dimensions, Oxford University Press, New York, 2003, p. 121):

If between any two points in space there is always a third point, can anything touch anything else?

Paradoxes are often based on our thinking. We are conditioned to think in terms of alternatives, 'either - or', namely, the "third" point can either exist in the way its two neighbors exist, or not exist at all. We believe that are dealing with two, and no more than two, alternative cases. We also take for granted that this "third" point is indistinguishable from its two neighbors. Hence we can not crack this paradox: if we remove the "third" point, we immediately lose the identity of its two neighbors (hence the cardinality of the set of points on a finite line interval will collapse into one), but if we decide to keep it, 'nothing could ever touch anything' and there will be again no more than one "point". A bona fide self-referential logical paradox à la Liar paradox. The story of this "third" point goes back to Lucretius, some 2060 years ago, but still creates tough mathematical quandaries (O. Yaremchuk, quant-ph/0204090). See also three beautiful papers by John L. Bell, (1) DISSENTING VOICES: Divergent Conceptions of the Continuum in 19th and Early 20th Century Mathematics and Philosophy, in: Ramifications of Category Theory. A Workshop including a featured lecture series by F.W. Lawvere, University of Florence, Florence, Italy, November 18-22, 2003, Dissenting Voice1.pdf, (2) INFINITESIMALS, Unpublished encyclopedia article, INFINITESIMAL1.pdf, and (3) Infinitesimals and the Continuum, New lecture on infinitesimals.pdf.

Briefly, the "third" point refers to the global mode of spacetime in which everything is ONE. It is the source and the cause of the phenomenal performance of actual infinity that enables us to use differential calculus and obtain finite things in the local mode of spacetime, as made by 'infinitely many infinitesimals'. Do we use the notions of 'point mass', 'instantaneous velocity at a point from a trajectory', and the like? If yes, please read my FAQ and "think deeply of simple things", as advocated by John Baez (no pun intended).

Maybe the time has come to change our thinking. The idea of two modes of spacetime is the only possible solution to the paradox of continuum. In the local mode of spacetime, we can have all the "good parts" of GR and QM, requirements (i) through (iii) above, safe and secure. (Perhaps quantum gravity will then modify GR and QM, but right now it is still in 'the unknown unknown'.)

Why is this solution the only possible one? Because it enables us to 'have our cake and eat it': we have exhausted all possible cases by unifying the two seemingly alternative ideas about the nature of spacetime. It is both perfectly continual (local mode) and utterly discrete (global mode).

Isn't this simple and beautiful? As a bonus, we can have a theory of the human brain and its mind, since the theory of spacetime, based on two modes of spacetime, has been suggested to explain the human brain in the first place. I'm not a physicist, but it seems to me that the universe can indeed be modeled as a brain. If quantum gravity must involve in some way a quantum interaction of the gravitational field with itself, as proposed by Jeremy Butterfield and Chris Isham in 1999, then we should keep in mind that the only physical system empowered with such unique self-acting faculty is the human brain: we think about our brain, with our brain. This is not a "miracle" nor some story told by Baron von Münchausen. No. This is an effect of the Holon living in the global mode of spacetime. Everything that exists "inside the universe" pertains to the local mode of spacetime, while its complement, the Holon, exists in the global mode of spacetime. Otherwise we can never have "points" and nothing could touch anything, for any finite time interval.

Of course, I could be all wrong, since I "do not know enough theoretical physics to help with any research in that area." This is the final and irreversible opinion of a highly respected theoretical physicist and one of the leading experts in quantum gravity.

If you, my dear reader, do not endorse this opinion, or wish to make some corrections, please drop me a line. No rush, we have plenty of time until 2007.

Dimi Chakalov,

August 30, 2003
Latest update: December 12, 2003