Dear Dr. Garfinkle,

I read with great interest your recent pedagogical paper on the role of coordinate invariance [Ref. 1]. May I ask you for a decisive clarification of the affine parameter [lambda] in the context of the well-known statement by Kip Thorne [Ref. 2].

With respect to your affine parameter [Ref. 1, p. 3], what is the
difference between the electromagnetic waves that "propagate through spacetime" [Ref. 2] and the gravitational waves that "propagate" within themselves?

I couldn't find any difference whatsoever. If true, I'm afraid you've
'swept the garbage under the rug' with your analogies with the gauge
invariance of electrodynamics [Ref. 1].

Please correct me if I'm wrong.

See my essay on GW astronomy,

http://www.God-does-not-play-dice.net/gw.pdf

I have a lot more to say on your "pedagogical" paper, but will refrain
until I hear from you.

Looking forward to hearing from you at your earliest convenience,

Sincerely yours,

Dimi Chakalov

References

[Ref. 1] David Garfinkle, Gauge invariance and the detection of
gravitational radiation, gr-qc/0511083 v1, Wed, 16 Nov 2005 20:02:33 GMT,
http://arxiv.org/abs/gr-qc/0511083

Comments: This paper is a pedagogical treatment of the role of
coordinate invariance in explanations of how gravitational radiation
detectors work

Abstract: "The detection of gravitational radiation raises some subtle
issues having to do with the coordinate invariance of general
relativity. This paper explains these issues and their resolution by
using an analogy with the Aharonov-Bohm effect of quantum mechanics.
...

"It turns out that these questions can be answered by a careful
consideration of the role of coordinate invariance in general
relativity. Though coordinate invariance in general relativity is not a
subject easily at the command of most physicists, it turns out that it
is analogous to gauge invariance in electrodynamics. In fact the line of reasoning used to resolve the issue of the properties of gravitational wave detectors is the same as that used to understand the role of gauge invariance in the Aharonov-Bohm effect. In this paper, we will first look at the issues that come up for the Aharonov-Bohm effect and the resolution of those issues. We will then show how the same line of reasoning applied to gravitational wave detectors serves to resolve the issues raised here.
...

"At first sight, this equation seems crazy. There is no such thing as
*the* vector potential associated with ~B . Rather there is a class of
vector potentials, all equally good.
...

"The gauge invariance of electrodynamics is then not the byproduct of a particular mathematical trick to calculate the magnetic field. Instead gauge invariance is a rather deep property having to do with the local phase invariance of quantum mechanics.
...

p. 3: "We now consider the motion of material particles and light rays. We usually think of a trajectory as giving the spatial coordinates ~x as a function of time. For our purposes (Sic! - D.C.), it will be helpful to instead give all four coordinates x~ as functions of a parameter [lambda] called the affine parameter. For material particles this affine parameter will be the proper time, that is the time elapsed on a clock carried along that particle’s trajectory. For a light ray, the affine parameter will be the phase.

"Let an overdot denote derivative with respect to [lambda] and define [xxx]. Then the equation of motion is

(Eq. 9)
...

"Equation (18) is the main result of this paper. It expresses a
physically measurable quantity, the second time derivative of the phase difference, in terms of a gauge invariant quantity, the Riemann tensor. It is thus the analog for gravitational radiation of equation (7) for the Aharonov-Bohm effect."
 

[Ref. 2] K. S. Thorne, Gravitational waves, gr-qc/9506086 v1.

"There is an enormous difference between gravitational waves, and the electromagnetic waves on which our present knowledge of the Universe is based: Electromagnetic waves are oscillations of the electromagnetic field that propagate through spacetime; gravitational waves are oscillations of the "fabric" of spacetime itself."

======

Subject: Re: The affine parameter [lambda]
Date: Thu, 17 Nov 2005 17:41:05 +0200
From: Dimi Chakalov <dimi@chakalov.net>
To: garfinkl@oakland.edu
CC: kip@tapir.caltech.edu, adler@ias.edu

On Thu, 17 Nov 2005 09:08:15 -0500 (EST), garfinkl@oakland.edu wrote:
>
> Dear Mr. Chakalov,
> Kip Thorne is certainly right about the nature
> of gravitational waves. However, weak gravitational waves,
> the only kind treated in my paper, are such a small
> disturbance of the spacetime that they can be treated as
> propagating in the fixed spacetime of special relativity.
> In this sort of treatment, the only residue of the special
> nature of gravitational waves is the effect of coordinate
> invariance, and this shows up as just the sort of gauge
> invariance that I mention.
> --David Garfinkle

Dear David:

I believe have specifically asked your for a *decisive clarification* of
the affine parameter [lambda] in the context of the well-known statement by Kip Thorne. Please elaborate. My preceding email can be read at

http://www.God-does-not-play-dice.net/Garfinkle.html

I know that you treat weak gravitational waves as "propagating" in FAPP fixed spacetime of special relativity. In your linearized approximation of GR, this is inevitable. Hence you cannot -- even in principle -- design an experimental setup that could detect the *qausi-local* wave strain of GWs. That's the problem IMHO.

See again p. 7 in my essay on GW astronomy,

http://www.God-does-not-play-dice.net/gw.pdf

I wrote: "However, if somebody from LIGO Scientific Collaboration is genuinely interested in detecting GWs, the first off task is to design
an experimental setup which would account for the quasi-local nature of gravitational field: (...)."

See the references on p. 7. They too are pedagogical.

Once I receive a *decisive clarification* of the affine parameter
[lambda], as requested in my preceding email, I will be more than happy to comment on your *analogy* with the Aharonov-Bohm effect, which too is non-local. Very briefly, in non-relativistic QM, the class of *the* vector potentials, all "equally good", is subject to the collapse rule, correct? Have you discovered some relativistic presentation of the collapse? If yes, can your affine parameter [lambda] describe the class of *the* vector potentials "during" the collapse?

Looking forward to hearing from you,

Dimi
--
http://www.God-does-not-play-dice.net
http://www.God-does-not-play-dice.net/download.html

====

Subject: The gravitational-wave background
Date: Fri, 18 Nov 2005 05:04:27 +0200
From: Dimi Chakalov <dimi@chakalov.net>
To: Domenico Giulini <giulini@physik.uni-freiburg.de>
CC: norbert.straumann@freesurf.ch

Dear Dr. Giulini,

In physics/0507107 v2, p. 26, footnote 24, you and Prof. Straumann
wrote:

"Though it is considered to be unlikely, it is not impossible that the
gravitational-wave background -- once it is observed -- ‘moves’ relative to the CMB frame and therefore defines another potentially preferred frame."

I'm highly interested in your speculations on the "sliding"
gravitational-wave background. But how can we observe its sliding? Also, how can we observe "the phases in which most of the gravitational radiation is generated" (Ibid., p. 45)? The task reminds of the way Baron von Münchhausen pulled himself and his horse out of the swamp, as explain by Karl Friedrich von Münchhausen. More at

http://www.God-does-not-play-dice.net/Garfinkle.html#note

Regards,

Dimi Chakalov
 

Note: For those who haven't captured the crux of my argument, let me try to elaborate.

The linearized approximation of Einstein's GR is not applicable for treating the "ripples" of spacetime metric, for a number of reasons. Regardless of how "weak" the Gravitational Waves (GWs) are, they cannot in principle evade the quasi-local nature of the metric field, hence we need to construct an appropriate experimental setup for their detection (cf. p. 7 in gw.pdf). LIGO and all other "detectors" are manifestly deaf and blind to the quasi-local nature of GWs. In fact, we need quantum gravity to design a proper measurement setup for GWs, because the current understanding of these matters inevitably leads to contradiction. The interaction of GWs with a quantum system would either lead to a "collapse" of the wave function, in which case the momentum conservation breaks down, or there would be no "collapse", in which case signals must propagate faster-than-light [Ref. 3]. If you insist on the "collapse", see [Ref. 4]. If you don't like it, see Chris Isham here.

Moreover, the linearized approximation of Einstein's GR can only describe a frozen, static snapshot of already-correlated values of physical quantities over a finite volume of 3-D space (cf. ref. [19] and the shoal of fish metaphor on p. 7 in gw.pdf). This correlation is intrinsically quasi-local and holistic, as explained by L. Lusanna and M. Pauri in gr-qc/0503069 v1. The problem here is that LIGO and all other "detectors" cannot, even in principle, detect two successive holistic snapshots of already-correlated, diff-invariant values of the metric and its derivatives over the whole spacelike surface. The latter does not move. In the linearized approximation of Einstein's GR, it is frozen. Hence LIGO and all other "detectors" are manifestly deaf and blind to the intrinsic dynamics of the metric field. Last but not least, the linearized approximation of Einstein's GR smears the essential difference between 'propagating through spacetime', as in the case of EM waves, and 'oscillations of the "fabric" of spacetime itself', as explained eloquently by Kip Thorne [Ref. 2].

In the latter case, you need a bird's eye view on the whole spacelike surface and its "boundaries" (r --> [infinity]; cf. ref. [19] in gw.pdf). In other words, you need to position LIGO in the reference frame in which you can identify the "direction" of the expansion of 3-D space due to the "dark" energy. Only then you can think of LIGO's arms as some fishing rod float that is patiently waiting for the GW "push" toward the "edges" of the the 3-D lake. Of course, all this doesn't make sense in the linearized approximation of Einstein's GR. Just click on the lake below.

I thank Kip Thorne for his illuminating remark [Ref. 2]. If you believe can detect any of the effects of the dynamic "dark" energy -- either GWs or the cosmic equator -- then you certainly believe in Father Christmas' beard. More in gw.pdf.

In practical terms, the question is this: what can we make from these long, dark, air-conditioned, L-shaped tunnels of LIGO? I suggest we convert them to wine cellars. The sooner, the better.

D. Chakalov
November 18, 2005
Last update: December 2, 2005

[Ref. 3] Kenneth Eppley and E. Hannah, The necessity of quantizing the gravitational field, Found. Phys. 7 (1977) 51-68.

[Ref. 4] D.V. Ahluwalia. Three Quantum Aspects of Gravity, gr-qc/9711075 v1.

"The second observation that I wish to report here is that the collapse of a wave function is associated with the collapse of the energy-momentum tensor. Since it is the energy-momentum tensor that determines the spacetime metric, the position measurements alter the spacetime metric in a fundamental and unavoidable manner. Therefore, in the absence of external gravitating sources (which otherwise dominate the spacetime metric), it matters, in principle, in what order we make position measurements of particles [cf. Quantum Measurement, Gravitation, and Locality, gr-qc/9308007]. Quantum mechanics and gravity intermingle in such a manner as to make position measurements non-commutative. This then brings to our attention another intrinsic element of gravity in the quantum realm, the element of non-locality."

========

From: Dimi Chakalov <dimi@chakalov.net>
To: Lindy Blackburn <lindy@ligo.mit.edu>
Cc: <kudoh@utap.phys.s.u-tokyo.ac.jp>,
<ataruya@utap.phys.s.u-tokyo.ac.jp>,
<hiramatsu@utap.phys.s.u-tokyo.ac.jp>,
<himemoto@utap.phys.s.u-tokyo.ac.jp>,
<ando@granite.phys.s.u-tokyo.ac.jp>,
<r.cashmore1@physics.ox.ac.uk>,
<j.al-khalili@surrey.ac.uk>,
<s.rowan@physics.gla.ac.uk>,
Robert M Wald <rmwa@midway.uchicago.edu>
Subject: The unknown unknown of GW astronomy
Date: Tue, 29 Nov 2005 05:40:45 +0200

Dear Dr. Blackburn,

I think the "logic" of U.S. Secretary of Defense Donald Rumsfeld tallies
exactly to your enterprise [Ref. 1]. More at

http://www.God-does-not-play-dice.net/gw.pdf

At least you don't kill people; just waste money.

Sincerely,

Dimi Chakalov
--
[Ref. 1] LIGO Scientific Collaboration, Search for gravitational wave bursts in LIGO's third science run. Sun, 27 Nov 2005 22:13:06 GMT, gr-qc/0511146 v1.
http://arxiv.org/abs/gr-qc/0511146

LIGO Laboratory document number P050043-A-R, to be published in Classical and Quantum Gravity.

LSC (395 distinguished scholars): "Gravitational-wave bursts may also result from sources that are completely unknown or not anticipated.
..
"No gravitational wave burst event is observed during the 8 days of LIGO's S3 data that we analyze."
--

"There are known knowns. There are things we know we know. We also know there are known unknowns. That is to say, we know there are some things we do not know. But there are also unknown unknowns, the ones we don't know we don't know."

Secretary of Defense Donald Rumsfeld, news briefing on February 12, 2002