Subject: The "speed" of gravity: w.r.t. what?
Date: Thu, 27 May 2004 15:46:20 +0300
From: Dimi Chakalov <>

Serëzha dorogoi,

If possible, please send me a copy from

S.M. Kopeikin, The speed of gravity in general relativity and theoretical interpretation of the Jovian deflection experiment, Classical and Quantum Gravity, June 2004

I believe 'speed of [whatever]' requires an answer to the question 'with respect to what?'. We might eventually be able to say something on 'speed of gravity in general relativity' if only we can imagine how those gravitational waves can propagate within themselves, and with respect to themselves.

That's very tough, which is why I'm very curious to see how you have bypassed the problem. If you have managed, see another problem waiting for you at

Best regards,


Note: The paper by Sergei Kopeikin appeared as gr-qc/0310059, currently v2 of Monday, 29 March 2004 04:45:48 GMT. The trick to bypass the problem above is explained in the abstract: "To this end we work out the speed of gravity parameterization of the Einstein equations (cg-parameterization) to keep track (emphasis mine - D.C.) of the time-dependent effects associated with the geometric sector of general relativity and to separate them (emphasis mine - D.C.) from the time-dependent effects of the matter sector."

But how can you separate the left hand side of Einstein's equation from the right hand side, and say "shut up, please, don't "talk" for a moment, coz I want to keep track of something very interesting." Everything and anything you can possibly measure is already the end-result from this bi-directional "talk", so I really don't know how can you "insert" your curiosity "between" the two sides of Einstein's equation.

The idea to separate two time-dependent effects and keep this separation for a finite time interval in order to measure the speed of gravity, cg , is quite a challenge.

Sergei Kopeikin also wrote: "We emphasize that the speed of gravity  cg  pertains to all time-dependent gravitational phenomena but not only to the propagation of gravitational waves in vacuum."

I wasn't able to understand those "time-dependent gravitational phenomena" in the past thirty years, but probably Sergei will shed some light on his mysterious phrase. With math.

Meanwhile, if you prefer math, you can find it here.

D. Chakalov
May 28, 2004

P.S. Sergei Kopeikin's gr-qc/0310059 v3, "The Speed of Gravity in General Relativity and Theoretical Interpretation of the Jovian Deflection Experiment", has been published in Class. Quantum Grav. 21 (2004) 1-36.

To understand why I don't like the current version of the theory of gravitational field, see the motivation of Huseyin Yilmaz to propose his theory, as explained by Jason Douglas Brown.

June 1, 2004

Subject: T_µv <--> g_µv
Date: Tue, 01 Jun 2004 15:10:22 +0300
From: Dimi Chakalov <>

Dear Sergei,

Thank you for your postscript file of your paper published by Class.
Quantum Grav.

You wrote (p. 7): "However, the metric tensor  g_µv  is not simply a geometrical object but represents one of the most fundamental objects in physics -- the gravitational field. For this reason, the constant c  in the Einstein tensor characterises the speed of gravitational field and has to be associated with the speed of gravity rather than with the speed of light which has an electromagnetic nature and is physically irrelevant for the Einstein tensor.

"On the other hand, the stress-energy tensor  T_µv  is defined locally as a special relativistic object and can not physically depend on the speed of gravity in a direct way because gravitational field is not localized. Nonetheless,  T_µv  can depend on the speed of light indirectly through the metric tensor  g_µv ."

What I really love in your papert is that it helps me identify the reason why I wasn't able to understand the inperplay of  T_µv  <-->
g_µv  in the past 30 years: the gravitational field is not, cannot, and
*should not* be localized.

You want to move further, by elaborating on some *indirect* connection between these apples and oranges,  T_µv  <-->  g_µv . I can't. I'm not that smart; that's it.

I perefer to zoom on the crux of the puzzle, after Hermann Weyl,

Besides, there is a striking similarity b/w the main idea of Einstein's GR,  T_µv  <-->  g_µv , and the mind-brain problem,

Can we catch two birds in one stroke?

Wishing you all the best in your work,


On Mon, 31 May 2004 20:24:55 -0500, Sergei Kopeikin wrote:
> Dear Dimi,
> attached is a postscript file of my paper published by Class. 
> Quantum Grav.  The speed of gravity has been measured with
> respect to the speed of light from the quasar used for observation
> of the retardation of gravity effect.  I agree with your formulation
> that any measurement of whatever must be done with respect to
> some standard which is known. The statements of my opponents
> that I have measured the speed of light are absurd from this point
> of view. It is not possible to measure the speed of light with respect
> to the speed of light.
> Best wishes,
> Sergei


Subject: Within themselves, and with respect to themselves
Date: Sun, 16 May 2004 02:02:03 +0300
From: Dimi Chakalov <>

RE: Prof. Kip Thorne - "Probing the Universe and Black Holes with Gravitational Waves", GR17, Dublin, Monday 19th July 8.00pm RDS Concert Hall

Dear Professor Thorne,

I wonder how would those gravitational waves propagate within themselves, and with respect to themselves.

Your insights and those from your colleagues will be highly appreciated, and will be kept strictly private.


D. Chakalov

July 27, 2004: So, how would those gravitational waves propagate within themselves, and with respect to themselves?

I haven't yet heard from Kip Thorne, who hasn't replied to my email of Sunday, 30 March 2003 either. In this email I asked him to get professional -- nothing else, and nothing more.

Let me help Kip Thorne with the following excerpt from "Lectures on Mathematical Cosmology" by Hans-Jürgen Schmidt (gr-qc/0407095, p. 35), Sec. 4.2, Why do all the curvature invariants of a gravitational wave vanish?

"The energy of the gravitational field, especially of gravitational waves, within General Relativity was subject of controversies from the very beginning, see Einstein [66]. Global considerations - e.g. by considering the far-field of asymptotically flat spacetimes - soon led to satisfactory answers. Local considerations became fruitful if a system of reference is prescribed e.g. by choosing a timelike vector field. If, however, no system of reference is preferred then it is not a priori clear whether one can constructively distinguish flat spacetime from a gravitational wave. This is connected with the generally known fact, that for a pp-wave, see e.g. Stephani [250] especially section 15.3. and [65] all curvature invariants vanish, cf. Hawking and Ellis [107] and Jordan et al. [123], but on the other hand: in the absence of matter or reference systems - only curvature invariants are locally constructively measurable."
[66] Einstein, A.:
1914, Sitzungsber. Akad. d. Wiss. Berlin, 1030.
1916, Sitzungsber. Akad. d. Wiss. Berlin, 688.
1918, Sitzungsber. Akad. d. Wiss. Berlin, 154.
1921, Sitzungsber. Akad. d. Wiss. Berlin, 261. 35, 145

[65] Ehlers, J., Kundt, W.: 1962, in: Witten, E., ed., Gravitation, an introduction to current research, Wiley New York, 49. 36

[107] Hawking, S., Ellis, G.: 1973, The large scale structure of space-time, Cambridge University Press. 36

[123] Jordan, P., Ehlers, J., Kundt, W.: 1960, Abh. Akad. Wiss. Mainz, Math./Nat. Kl. 2, 21. 36

[250] Stephani, H.: 1982, General Relativity, Cambridge University Press. 7, 36, 164; section 15.3.

Prof. Hans-Jürgen Schmidt hasn't yet replied to my email of Thursday, 20 February 2003 either. I asked a very simple question:

"Isn't it true that the *necessary* condition for detecting gravitational waves is that the distribution of energy-momentum of a physical system in the gravitational field must be uniquely defined on a continual trajectory, not just in one instant of measurement?"

Now, since Hans-Jürgen Schmidt believes that global and local considerations had "soon led to satisfactory answers" (cf. above), may I refer the reader to a well-known problem of the ambiguities in the definition of gravitational energy here and here.

I regret that was not able to attend GR17, but will try next year at GR18. Bottom line is the puzzle of 3-D space in GR and the "mysterious time" of Bill Unruh. Should you find this too complicated, try T. Levi-Civita of 1917 and H. Weyl of 1922.

D. Chakalov
Tuesday, July 27, 2004


Subject: There could be surprises
Date: Tue, 31 Aug 2004 17:24:09 +0300
From: Dimi Chakalov <>
To: Alessandra Buonanno <>

RE: Alessandra Buonanno, TASI Lectures on Gravitational Waves from the Early Universe, gr-qc/0303085 v2, 29 August 2004

"If nature is kind with us, we will not wait for a long time. There could be surprises."

Dear Dr. Buonanno,

I like your review, and agree that there could be surprises,

Suppose you keep a bottle of Coca Cola in your fridge. One day you open your fridge and see a new, huge bottle of Coca Cola, due to the local change of spacetime metric inside your fridge, which has not affected you, miraculously. Then you'd say that you've been shrunken, or, equivalently, that your old bottle has been expanded. You wouldn't know which one is "true", and will be deeply surprised, I suppose. Perhaps you'd even question the basic principle of GR, and will check out whether the two states are indeed indistinguishable: [you normal size & expanded bottle] and [you being shrunken & normal size bottle]. Or a mixture of the two states, say, 50/50. Or maybe a superposition of the two states, like the Schrödinger's cat?

If you notice such effect in your fridge, please drop me a line. Please also write to Steven Weinberg, since he is a bit pessimistic,


Dimi Chakalov


Subject: Gravitational waves and massive black holes, if any
Date: Fri, 03 Sep 2004 18:39:12 +0300
From: Dimi Chakalov <>

RE: Leor Barack, Curt Cutler, LISA Capture Sources, gr-qc/0310125 v3; Phys. Rev. D69 (2004) 082005

"Most, if not all, nucleated galaxies harbor MBHs in their centers [12,13]."
[12] D. Richstone et al., Nature 395, A14 (1998).
[13] J. Kormendy and K. Gebhardt, in Proceedings of 20th Texas Symposium on Relativistic Astrophysics, eds. H. Martel and J. C. Wheeler, AIP (2002); astro-ph/0105230.

Dear Colleagues,

I will appreciate your comments on


Dimi Chakalov


Subject: Re: Gravitational waves and massive black holes, if any
Date: Sat, 04 Sep 2004 15:39:08 +0300
From: Dimi Chakalov <>

Dear Dr. Mitra,

Thank you for your feedback.

> However since I have never worked on the problem of gravitational
> waves, I am in no position to make any comment on it.

Perhaps you may wish to see Angelo Loinger and Hermann Weyl, denouncing the linearized version of Einstein's GR, which is the standard textbook lore,

and of course the fundamental paper by T. Levi-Civita,

> If there is any definitive development, I would be glad to know.

I'm not aware of any definitive development, and I'm afraid there is too much politics and money involved with the so-called "gravitational wave astronomy",

Needless to say, I like very much your papers. Perhaps you can elucidate the question of what kind of GW can be emitted by some *non-rotating* BHs only, what kind of energy they can impose on some measuring device so that we can detect them, and what kind of recoil they will get from the measuring device by the act of measurement. All these events have to occur in line with the principles of locality and relativistic causality. I hope that all LIGO/LISA/etc researchers will agree.

All this sounds to me like astrology,

My guess is that those GW are bona fide empty waves "living" on a null-plane only,

Qui vivra, verra.

Best wishes,

Dimi Chakalov

Note: To read some of the papers by Abhas Mitra, click here. Don't miss "Why the astrophysical Black Hole Candidates may not be black holes at all", astro-ph/0409049, and "Why the astrophysical Black Hole Candidates are not rotating black holes", astro-ph/0407501.

It is not at all clear to me whether one can "constructively distinguish flat spacetime from a gravitational wave", as stressed by Hans-Jürgen Schmidt above.

Aren't we chasing a ghost living on a null-plane only?

See the recent paper by B. Abbott et al. (The LIGO Scientific Collaboration), Limits on gravitational wave emission from selected pulsars using LIGO data, gr-qc/0410007 v1.

The sensitivity of the LIGO interferometers has been improved by more than a factor of ten lower than what was previously achieved [cf. B. Abbott et al. (The LIGO Scientific Collaboration), Phys. Rev. D 69 082004 (2004); gr-qc/0308050].

To quote from the recent LIGO Scientific Collaboration paper, gr-qc/0410007 v1: "No such triggers occurred in the analysis of these data, and we therefore simply present upper limits."

However, they show some mystical optimism: "Once the detectors operate at design sensitivity for a year, the observational upper limits will improve by more than an order of magnitude."

Nobody from 368 co-authors of gr-qc/0410007 v1 has mentioned the smashing rejection by Angelo Loinger. He examined their previous data [B. Abbott et al. (The LIGO Scientific Collaboration), Phys. Rev. D 69 082004 (2004); gr-qc/0308050], and found them wrong. See A. Loinger's "Gravitational waves and ether's wind", physics/0309039.

Improving LIGO sensitivity "by more than a factor of ten lower than what was previously achieved" won't help. Neither by a factor of google lower than what was "previously achieved". Why? Click here.

Again, aren't we chasing a ghost living on a null-plane only?

D. Chakalov
September 4, 2004
Last update: October 5, 2004