Subject: "... if such a frame exists, it must be very effectively concealed from view."
Date: Fri, 11 Jan 2008 06:11:58 +0200
From: Dimi Chakalov <>
To: Ted <>


RE your arXiv:0801.1547v1 [gr-qc], notice that such frame is not just "effectively concealed" but totally hidden,

I believe we will meet some day, and I wouldn't like to hear that you knew nothing about my web site.



Subject: The non-linear energy of aether
Date: Mon, 04 Oct 2004 14:41:10 +0300
From: Dimi Chakalov <>
To: Ted Jacobson <>
CC: Christopher Eling <>,
     David Mattingly <>,
     Michael Clayton <>,
     Stanley Deser <>,
     Charles Misner <>

Dear Professor Jacobson,

May I briefly comment on your "Spacetime Primer" [Ref. 1] and the
efforts to unravel the energy of ubiquitous aether [Refs. 2 and 3].

Please correct me if I'm wrong.

You employ the *linearized* Einstein-aether theory [Ref. 2], but the negative energy configurations "do not show up in the linearized limit" [Ref. 3].

It seems to me that the non-linear energy of aether is 'swept under the carpet' in your *linearized* Einstein-aether theory.

Hence the deep mystery of "the intrinsic time interval associated to any timelike displacement" [Ref. 1] may not be understood *in principle*.

We need to find a general solution to the so-called negative energy

First and foremost, I believe the intrinsic limitations of the linearized Einstein GR have been explained by Hermann Weyl in Amer. J. Math. 66 (1944) 591; see Angelo Loinger's physics/0407134,

NB: I believe "linearized gravity" is an oxymoron. The crux of the issue are these false tensors, also known as "pseudotensors" [Ref. 3].

I will appreciate the professional comments from your colleagues too. Will keep them strictly private and confidential.

My efforts at understanding the *non-linear* energy of aether can be read at

Your guess that "fundamental systems all march to the beat of the same drummer" [Ref. 1] is examined at

Regrettably, these efforts are still at purely conceptual (verbal) stage. I will be very happy if you and your colleagues use math to defend your viewpoint, hence shed light on the nature of gravity: is "linearized gravity" an oxymoron?


Dimi Chakalov


[Ref. 1]  T. A. Jacobson, A SPACETIME PRIMER (September 2, 2004),

pp. 18-19: "The existence of an intrinsic time interval associated to any timelike displacement is another deep mystery. The fact is that, in Nature, there are systems that can serve as clocks. It seems to be the case that fundamental systems all march to the beat of the same drummer, in the following sense: there is a large class of physical systems that mark time in a commensurate fashion."

[Ref. 2] T. Jacobson and D. Mattingly, Einstein-Aether waves,
gr-qc/0402005 v2; Phys. Rev. D 70, 024003 (2004),

"An important open question is the sign of the energy of the various
wave modes. To answer this, it is necessary to first determine the
expression for energy in the linearized Einstein-aether theory, which
has not yet been done. (...) Even without any direct coupling to matter, the extra modes will still be excited through their coupling to the time dependent  metric produced by the moving matter sources."

[Ref. 3] Christopher Eling, Ted Jacobson, David Mattingly,
Einstein-Æther Theory, gr-qc/0410001 v1

"Could there be an æther after all and we have just not yet noticed it?
By an "æther" of course we do not mean to suggest a mechanical medium whose deformations correspond to electromagnetic fields, but rather a locally preferred state of rest at each point of spacetime, determined by some hitherto unknown physics. (...) It is hard to imagine, both philosophically and technically, how we could possibly give up general covariance, the deep symmetry finally grasped through Einsteinís long struggle. Thus the question that interests us here is whether a generally covariant effective field theory with a preferred frame could describe nature.

"Another noteworthy feature of using a scalar is that, by construction, the 4-velocity of the preferred frame is necessarily hypersurface-orthogonal, i.e. orthogonal to the surfaces of constant T. Again, perhaps this is the way Nature works, but it is a presumption not inherent in the notion of a local preferred frame determined by microphysics.

Sec 3, p. 6: "Another flaw with the Maxwell-like case is that it admits negative energy configurations, as shown by Clayton [9] using the Hamiltonian formalism in the decoupling limit where gravity is neglected. [The argument in Ref. 9 has a minor flaw, but the conclusion is correct. The negative energy configuration described there is a time-independent pure gradient u_i = (XXX). This initial data with vanishing time derivative u_i,t = 0 indeed has negative energy, however the equation of motion implies that the time derivative does not remain zero (unless u_i = 0).]

"6.2. Positivity

"Perhaps a total divergence term that leaves the energy unchanged must be removed before positivity can be seen. Also, since the asymptotic value of the unit vector selects a preferred frame, it might be that the energy is always positive only in that particular frame. We can make no definite statement about the non-linear energy at this time, based on general formal grounds.

"6.2.1. Linearized wave energy

"It is useful to examine the linearized theory to begin with. The energy density of the various wave modes has been found [19] using the Einstein or Weinberg pseudotensors, averaging over oscillations to arrive at a constant average energy density for each mode. The energy density for the transverse traceless metric mode is always positive. (...) The negative energy configurations discussed in section 3 do not show up in the linearized limit."
[19] 19. C. Eling, and T. Jacobson, Einstein-Æther energy, in preparation.


Subject: The stability of naked singularities, if any
Date: Mon, 04 Oct 2004 16:16:52 +0300
From: Dimi Chakalov <>

Dear Colleagues,

May I ask some questions about how "the two energies are related by a divergent boundary term", as r* --> 0 (hep-th/0409307 v1, Eq. 42).

You wrote: "We might therefore ask whether there is any relation between these two expressions for the energy. Indeed there is."

The first expression of energy is the energy associated with the
Schrödinger equation (ibid., Eq. 33). I wonder what is this "other"
expression of energy, and where does it come from. From some unphysical divergence in the Schrödinger potential?

Besides, why would  r*  go down to zero in Eq. 42? To satisfy our
"positive mass theorems"? See Tom Roman,


D. Chakalov

Note: Let me comment on the quasi-local energy and the non-covariant pseudo-tensors from [Ref. 4]: "Each expression has a geometrically and physically clear significance associated with the boundary conditions".

Each expression depends on, and is being derived under, strictly formulated initial and boundary conditions valid for the specific case studies. No general solution is known, and you get a total mess. Why? Because the gravitational field cannot be entirely detected/projected at a point; more from R. Penrose here. And because the "intrinsic time interval associated to any timelike displacement" [Ref. 1] requires at least two "points", plus the metaphysical postulate of 'locality', we need precise, non-divergent, locally-defined values of the gravitational energy to understand this 'intrinsic time interval'. But the beast that defines the 'intrinsic time interval' is utterly non-local. Hence the "deep mystery" [Ref. 1] remains unsolved.

To understand why in Einstein's GR the conservation laws for energy, momentum, and angular momentum are meaningless (if not impossible), read the introductory sections of Anatoly Logunov's book here. In the context of the so-called gravitational waves, read H.-J. Schmidt here.

If all this has somehow created the impression that I understand Einstein's GR, let me immediately correct it by declaring that I don't understand it. But since [Ref. 3] is based on a talk given by T. Jacobson at the Deserfest, and Ted Jacobson and Stanley Deser teach GR, it is reasonable to suppose that they understand it. Probably they will reply to my question above: is 'linearized gravity' an oxymoron?

I believe it is indeed an oxymoron, but we have to understand the reason why it works as calculation tool.

The notion of 'flat space' can only be obtained by instructing the Riemann curvature to vanish completely -- go to zero. Zilch. Gone forever, dead, period. In classical mechanics, we know that can obtain similar idiosyncratic situations of 'instantaneous velocity' or 'point-like mass', which are pure fiction, and yet they work amazingly well for calculating purposes. Nobody claims, however, that if we toss a banana, there would be some point-like state from the trajectory of the banana with such unphysical state. It's pure idealization, which we use for purely calculating purposes. And yet in the so-called linearized version of Einstein's GR we not only use such totally unphysical "limit" for calculating purposes, but claim that it corresponds to some real physical situation, for example, some "black hole". Well, if you really get to the point at which "all geodesics are straight lines and all covariant derivatives are ordinary derivatives", as explained by G. 't Hooft, there is no way back to Einstein's GR. This is a pure idealization, pure fiction, which should never be considered to represent physical reality. See again the seminal paper by Hermann Weyl of 1944, mentioned above.

What is the meaning of "zero curvature" of some absolutely flat spacetime, such as that of STR? If we talk about 'zero curvature of flat spacetime', we inevitably imply something that has already disappeared in the Minkowski limit, being converted into some "linearized" stuff "localized" in our past light cone.

This conversion is irreversible: not only an infinitesimal piece of spacetime "looks flat", but is being converted into some abstract mathematical point with zero dimensions and zero curvature: we instruct an observable to 'get down to zero', just as we do in classical mechanics with 'instantaneous velocity' at some 'point from the trajectory'. There is no way to get a tangent vector but to a "point", as we know from Leibnitz' differential calculus. There is no way back to Einstein's GR, however.

Just as in the case of von Neumann's projection postulate, we "project" an instantaneous snapshot from the bi-directional talk of matter and geometry in the so-called Minkowski limit of Einstein's GR. Then we wrongly assume that have described the intrinsic dynamics of the coupled geometry-matter system by calculating the instantaneous state of 'one banana', as if we have found the "instantaneous velocity" at some "point" from the trajectory of the banana in classical mechanics. Not surprisingly, we get black holes & naked singularities, closed time curves, and many other ridiculous consequences from this blind application of the Hamiltonian classical mechanics on Einstein's GR.

Okay, we have calculated one linearized localized state of our banana, as seen in our past light cone, but where are the rest of the non-linear and non-local bananas (=nonlocal diffeomorphism-invariant observables)? They "go back" in the spacetime "gaps" and re-join the set of potential states that are invariant under Diff(M) action. That's how you pass to the limit of 'flat space' (equivalent to that of 'points' in classical mechanics) and use the linearized version of Einstein's GR for purely calculating purposes. It works because of the gaps of potential reality embedded in the perfect (not coarse-grained) continuum of events that we observe in our past light cone. Needless to say, this perfect continuum needs the gaps, too. They are the source of all brand new events in the future state of the universe, the 'unknown unknown' included. (It is very difficult to construct such a set of potential states, unless we use the idea of creatio ex nihilo and 'make room' for non-unitary evolution of the universe along the cosmological time arrow, as well as non-unitary deflation time resembling "information loss" back to The Beginning [John 1:1]. Perhaps there is no need for any ad hoc scalar filed that would be "minimally coupled to Einstein gravity" but "non-minimally coupled to matter" (S. Carroll et al., astro-ph/0410031). The pool of potential states residing in the spacetime gaps may explain the inflation and its "twin elephants", too. No doubt Stanley Deser will love this!)

To prove me wrong, try to "constructively distinguish flat spacetime from a gravitational wave", as stressed by Hans-Jürgen Schmidt here. Aren't we chasing a ghost living on a null-plane only? Any other result will prove my ideas wrong, and I will offer you my sincere apologies for wasting your time.

It would be nice if Ted Jacobson and Stanley Deser put their cards on the table, too. Since they teach GR, I'm sure they understand it. I will highly appreciate some falsifiable statement in the format 'if  A  is true, then linearized gravity is indeed an oxymoron'. For if we cannot formulate falsifiable statements, we aren't doing science but philosophy. Are Ted Jacobson and Stanley Deser teaching philosophy?

No, they do science. Stanley Deser's research involves the study of quantum fields, gravitational theories, and their generalizations. He is widely known for his pioneering work applying quantum field theory to Einstein's GR, demonstrating that this theory is not renormalizable, as well as for elucidating the inherent problems of supergravity described as the "Dirac square root" of Einstein theory (S. Deser, gr-qc/0301097). He knows the history of the problem with the linearized GR, and stated that "the first, and completely isolated, attempts at treating (linearized) GR as a dynamical system were probably those of the early thirties by Rosenfeld [2], and by Bronstein [3] in the USSR" (ibid.). He is also one of the authors of the famous ADM paper in which serious attempts at treating the linearized GR as a "dynamical system" were made. The ADM paper was published in 1962 (The Dynamics of General Relativity, gr-qc/0405109), but we still don't have a complete theory of quantum gravity. Obviously, something very important is missing, and I'm sure Stanley Deser has a professional opinion on the oxymoron issue above.

Ted Jacobson has included his Spacetime Primer [Ref. 1] as prerequisite to many of the courses he teaches at the University of Maryland, College Park, and I think his students should feel very happy to have such a brilliant teacher. Not only is he fluent in math, but can think as physicist. Proof: Back in February 1986, Ted Jacobson and Lee Smolin were working together in Santa Barbara, looking for some exact solutions to the full equations of quantum gravity (Lee Smolin, "Three Roads to Quantum Gravity", p. 40). But Ted Jacobson didn't slide toward "spin networks". He knows very well that we cannot recover the asymptotically flat 3-D space from the quantum mesh of those bubbles in loop quantum gravity, nor from any "upgrade" of the aging standard model: the number of possible vacua is in the range of googles (a google, G, is defined to be ten to the power one hundred, G = 10100), which annihilates the "predictive power" of the standard model. Sad but true (Lenny Susskind, hep-th/0302219). Ted Jacobson can think as physicist, and I'm sure he also holds a professional opinion on the oxymoron issue above.

Last but not least, let's not forget that both physicists teach students and shape their thinking. Students are kids, they have the right to know everything. This is their ultimate right, and we should tell them everything we know, even if it includes some "unpleasant" problems known from Hermann Weyl since 1944.

So, is 'linearized gravity' an oxymoron?

I believe the answer to this question will help us understand a very real mystery that is happening in the center of Milky Way galaxy. It's name is Sagittarius A*. See slide 23 below, from Ted Jacobson's public talk "Relativity, Time and Black Holes".

The capture of Ted Jacobson's slide 23 reads: "Elliptical orbit of a star around the super-massive black hole in the center of the Milky Way galaxy".

Here almost everything correspond to facts, except that, if 'linearized gravity' is an oxymoron, there are no black holes. No stellar black holes, no 'intermediate-mass' black holes, no supermassive black holes, no 'linearized gravity'. Mother Nature is smarter.

Again, is 'linearized gravity' an oxymoron? I believe it is indeed an oxymoron, and it seems to me that the only way to circumvent the problems with these "points" is to reformulate Einstein's GR, say, in the framework of Synthetic Differential Geometry (SDG) or in some other mathematical framework that will preserve the "regions" while we get "points" from them, as tried by Chris Isham. Or maybe we should try something brand new.


D. Chakalov
October 4, 2004
Last update: October 10, 2004


[Ref. 4] M. Sharif, Tasnim Fatima, Energy-Momentum Distribution: A Crucial Problem in General Relativity, gr-qc/0410004 v1

"The point is that the gravitational field can be made locally vanish and so one is always able to find the frame in which the energy-momentum of gravitational field is zero while in the other frames, it is not true. Unfortunately, there is still no generally accepted definition of energy-momentum for gravitational field. The problem arises with the expression defining the gravitational field energy part.

"The lack of a generally accepted definition of energy-momentum in a curved spacetime has led to doubts regarding the idea of energy localization. According to Misner et al. [10], energy is localizable only for spherical systems. Cooperstock and Sarracino [11] came up with the view that if energy is localizable for spherical system, then it can be localized for any system. Bondi [12] argued that a non-localizable form of energy is not allowed in GR. After this, an alternative concept of energy, called quasi-local energy, was developed.

"5 Summary and Discussion

"The problem of energy-momentum localization has been a subject of many researchers but still remains un-resolved. (...) It is worth mentioning that the results of energy-momentum distribution for different spaceimes are not surprising rather they justify that different energy-momentum complexes, which are pseudo-tensors, are not covariant objects. This is in accordance with the equivalence principle [10] which implies that the gravitational field cannot be detected at a point.

"These examples indicate that the idea of localization does not follow the lines of pseudotensorial construction but instead it follows from the energy-momentum tensor itself. This supports the well-defined proposal developed by Cooperstock [42] and verified by many authors [29-33,43]. In GR, many energy-momentum expressions (reference frame dependent pseudo-tensors) have been proposed. There is no consensus as to which is the best. Hamiltonian's principle helps to solve this enigma. Each expression has a geometrically and physically clear significance associated with the boundary conditions."