The differentiable manifold concept: The Aristotelian Connection

Subject: The differentiable manifold concept
Date: Sat, 14 Apr 2007 20:19:40 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: Andrzej Trautman <andrzej.trautman@fuw.edu.pl>
CC: L Szabados <lbszab@rmki.kfki.hu>,
J Stachel <john.stachel@gmail.com>,
C Isham <c.isham@imperial.ac.uk>
BCC: [snip]

Thank you *very much* for your kind email from Sat, 14 Apr 2007 10:02:19 +0200 and for the pp123.pdf file attached (the scanned three pages from [Ref. 1], which I requested in my email from Sun, 8 Apr 2007 21:54:21 +0300).

As I mentioned in my preceding email, I am definitely sure that "the
brief account of the life and work of Andrzej Trautman" (Class. Quantum Grav. 14 (January 1997) A1-A8) is far from being completed. In your words, any changes in the assumption that spacetime can be represented by a 4-dimensional differentiable manifold "would result in a very profound revolution in physics" [Ref. 1].

You clearly demonstrated the need for new physical theories based on new assumptions about the structure of space and time, "but up to now, no such attempt has met with much success" [ibid., p. 102].

Q1: Can we suggest a new degree of freedom of the 4-dimensional
differentiable manifold, such that it could make the spacetime a
*dynamical entity*? Please see

If we succeed, Élie Cartan's 'La Géométrie des espaces de Riemann'
(The Geometry of Riemann Spaces, 1925) may have to be substantially modified, I suppose. I also believe that finding a "boundary" of spacetime is a challenge which might be resolved only by endowing the 4-dimensional differentiable manifold with a new degree of freedom from the outset (cf. the link above).

As an example of the need for new assumptions about the structure of space and time, consider the common belief in 'countable infinite'
(denumerably infinite) "points" in 3-D space, and recall its challenge
with Thompson's lamp paradox

As Henri Poincaré predicted, "point set topology is a disease from which the human race will soon recover",

Q2: Can we modify the Einstein-Cartan Theory [Ref. 2] by "inserting" the new degree of freedom in the Christoffel connection [Ref. 3, Eq. 1]? Given the totally unclear outcome from the first task, I can only offer some raw ideas about the "torsion" degree of freedom,

If we don't leave for India, how can we discover America? Perhaps this is at least a well-posed question :-)

[Ref. 1] A. Trautman, Foundations and current problems of general relativity, in Lectures on general relativity, ed. by Andrzej Trautman, F.A.E. Pirani, and Hermann Bondi, Englewood Cliffs: Prentice-Hall, 1965, Sec. 5.1, pp. 101-103

p. 103: "From now on we shall always assume that space-time can be represented by a 4-dimensional differentiable manifold. This is why the differentiable manifold concept was defined with care and discussed in detail in the preceding chapter. Any changes in this assumption would result in a very profound revolution in physics".

[Ref. 2] Andrzej Trautman, Einstein-Cartan Theory, in Encyclopedia of Mathematical Physics, Oxford: Elsevier, 2006, vol. 2, pp. 189-195; arXiv:gr-qc/0606062v1;
http://arxiv.org/abs/gr-qc/0606062

"It is possible that the Einstein-Cartan theory will prove to be a
better classical limit of a future quantum theory of gravitation than
the theory without torsion."

"We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context."

1. The deeper context: The 'grin of the cat without the cat' (cf. Alice) facilitates the negotiation (cf. the ontology of relational reality) with 'everything else in the universe', which "takes place" in the putative global mode of spacetime.

The putative 'local mode of spacetime' is a perfect continuum of already-negotiated (or linearized) facts cast in the absolute past of the universe. Stated differently, the main hypothesis here is that the relational ontology is the fundamental principle by which every "point" from a differentiable manifold is being identified dynamically (cf. dynamical determinism) by its transient and covariant physical content. In the classical limit of 'relational ontology' (classical mechanics and STR), the "negotiation" in the global mode of spacetime is spanned over the "immediate neighborhood" of the point, hence the effect of the Holon is vanishing small, the spacetime is "flat", and neither non-local nor quasi-local effects are present. In this highly contrived case, all "points" from the differentiable manifold are uniquely fixed/locked by their physical content, hence cannot be 'moved around' by what people call 'active diffeomorphism'. Consequently, by extending the "neighborhood" of the point and hence "extending" its Holon in the global mode, we introduce both "non-local" and quasi-local effects (cf. László Szabados) on the individuation of the points by their common Holon, as performed with the rules of relational ontology. The end result is again a perfect continuum of already-negotiated, linearized facts cast in the absolute past of the universe: the local mode of spacetime. The latter is a re-created (cf. Antonio Machado) continuum of points living on already linearized and "always flat" spacetime, with [lambda] tending asymptotically toward zero (otherwise you may lose your night sleep, like Ed Witten).

Also, the local mode of spacetime is a perfect continuum, because the Holon in the global mode of spacetime stays always in the absolute potential future of the whole universe as ONE, hence it is nonexistent in the absolute past of the universe -- there is nothing "in between" the points constituting 'the grin of the cat without the cat' (Alice), in the same way that there is no water in between two adjacent molecules of water. Hence the local mode of spacetime is "quantized" from the outset, and the law of continuity, as defined in the standard calculus texts of the 1800's, is fully obeyed: "the consecutive points of the same line succeed each other without any interval". Notice that the global mode "interval" is kept in the global mode of spacetime, and can indeed be eliminated in the local mode with the Aristotelian Connection.

Hence we have (i) a perfect continuum, (ii) locality, and (iii) global retarded causality (no CTCs nor CPP) in the local mode of spacetime: the EPR-like correlation of future potential events is being "inserted" in the gaps of the global mode of spacetime, thus making the local mode of spacetime an already-correlated "back bone" of the whole physical world, at all length scales. The 'global mode of spacetime' is a new degree of freedom in GR: read Matt Frank and bear in mind that it is not some "extra-dimension". Look at the ladder metaphor below:

The vertical shift in the global mode of spacetime is explained with the "GW lake" here; notice that its "direction" is omnipresent in the local mode of spacetime, as explained here. It is also completely hidden in STR, by the virtue of 'interactions on null intervals': light exists only as an already completed interactions on null intervals (Kevin Brown), hence the "proper time" of the flight "over" this null interval is zero to all 'passengers inside the train'; more here.

Thus, a relativistic observer confined inside the local mode of spacetime will "see" only one single instant dt of some scalar quantity called "time":

NB: Notice that t_1, t_2, t_3, ... , are like transparencies stacked one on top of one another (much like Photoshop layers), because in the local mode there is nothing that can reveal the "horizontal" nor "vertical" shift in the global mode: the "two" shifts are completely absent in the local mode, which in turn produces the illusion of some timeless "block universe", in which some scalar quantity called "time" refers to a time-reversible dynamics. This is as it should be, because in the local mode the "direction" in which the very 3-D space "moves", to produce the arrow of spacetime, is infinitesimal.

We may experience dt one-at-a-time, along the "vertical" red line of the global mode (the "explicit (but unmeasureable) time", W.G. Unruh), but in the local mode the "duration" of the elementary "horizontal" step -- the elementary timelike displacement -- is infinitesimal.

Perfect continuum, ladies and gentlemen! Its "quantization" is introduced in the global mode of spacetime -- ]between[ the "points" from the local mode -- with 'the universe as ONE' (the atom of Lucretius) and the Aristotelian First Cause; hence the name proposed to this connection is 'The Aristotelian Connection'. You can't find it in the caricature below.

Again, in the local ("horizontal") mode of spacetime, the "distance" dt between the "points" from the drawings above is [tending asymptotically toward zero], until it hits the ultimate cutoff -- the Aristotelian First Cause. Notice that the "absolute" time, along the "vertical" red line of the global mode of spacetime, "runs" simultaneously toward its two cutoffs, The Beginning and The End of the cosmological time: once created with two modes of spacetime, the universe has "already" become eternal in its local mode of spacetime.

NB: There is no other way to introduce a proper continuum. Its ontology requires a reference object -- global mode of spacetime -- such that it will (i) define discernible "points" on the continuum, and (ii) create them dynamically: Panta rei conditio sine qua non est.

Mathematicians will probably hate these statements and will ignore them, only they can't do better: see Paul Ehrlich's "the wonderful elementary limit" due to the Aristotelian Connection. As to theoretical physicists, they very seldom admit the generic pathologies in present-day GR: see Matt Visser, The quantum physics of chronology protection. In: Gibbons GW, Shellard EPS and Rankin SJ, The Future of Theoretical Physics and Cosmology, Cambridge: Cambridge University Press, 2003; gr-qc/0204022, p. 3: "What general relativity does not do is to provide any natural way of
imposing global constraints on the spacetime — certainly the Einstein
equations provide no such nonlocal constraint."

2. We want to understand the idea of the proof: Place the elephant's trunk in the Holon (global mode of spacetime), and let it choose one state of all sub-systems for their next explication as 'facts' in the local mode of spacetime. Such 'one state' will be unique, since 'the chooser' is the whole universe as ONE: God is flexible.

Notice that we can address the non-linear quasi-local dynamics of both gravitational and quantum systems, thus providing a unification of GR and QM from the outset as well. The key idea is a new kind of determinism, dubbed 'dynamical determinism', which exploits the inherent flexibility of quantum and gravitational systems.

Notice also the affine connection puzzle: "The affine structure is a further primitive (not definable from mere differential structure) structure" (Graham Nerlich). We simply postulate that the Hausdorff topological space is "connected", but cannot derive this connection from any physical stuff, because it isn't there yet. We are still working with pure math, yet we tacitly introduce by hand the fundamental connection originating from the Aristotelian First Cause: the Beginning is that which does not have anything necessarily before it, but does have something necessarily following from it [Poetics VII 1450b27-29].

NB: This is the Aristotelian connection which binds the "points" from the geometry of spacetime: 'the grin of the cat without the cat' (cf. Alice). It is also the reference fluid, as sought by Hilbert and Einstein. In simple words, the physical world ends with its own geometry. Even Kurt Gödel can't go further.

The implications from this story are that we cannot define any 'elementary step' on the differentiable manifold unless we have defined it 'as a whole', which means fixing the "boundary" of spacetime. It's a package. In plain words, the Cosmological Principle reads:

The ONE is an unbroken ring with no circumference, for the circumference is nowhere (no direction in the local mode of 3-D space leads to the "boundary" of spacetime) and the "center" is everywhere (no direction in the local mode of 3-D space leads to the source of DDE).

There is no need to postulate some brand new scalar filed that interacts with all types of matter, like the so-called phi-field in Brans-Dicke theory or the Higgs field. What we have instead are effects of the Holon -- the universe as ONE -- and a generalized Mach’s Principle for the dynamics of quantum and gravitational systems in the local mode of spacetime: 'think globally, act locally'. For if the universe possesses a Holon state as ONE, it can and will be self-determined by 'dynamical determinism'.

This is the bootstrap ontology of Geoffrey Chew, applied to the whole universe. Obviously, the self-determination of the whole universe will be a bona fide self-action: the universe as ONE entity will act on itself. Such self-action, performed by the whole universe as Aristotelian First Cause, will inevitably look "dark" to all sub-systems, simply because its "origin" cannot be traced back to any sub-system. Isn't that simple?

Why is this so difficult to understand, I wonder. Even my teenage daughter knows how to calculate the circumference of a circle, so all we need is to reveal the reference fluid [Ref. 1], which identifies uniquely the "points" from the circle, and then think of such 'continuum of points' as matter fields coupled to gravity, and finally explain the dynamics of GR: from one "point" to the "nearest" one. Basically, all we need is to find the reference fluid in GR -- provided it is there.

Subject: AoC
Date: Thu, 31 May 2007 19:58:37 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: <spaans@astro.rug.nl>

Dear Dr. Spaans,

I wonder if you plan so address the Cauchy problem for Einstein equations with what "appears to be a rich topology hiding in Einstein gravity" (grXiv:0705.3902v1 [gr-qc]).

Regards,

Dimi Chakalov

Subject: Re: AoC
Date: Fri, 1 Jun 2007 00:06:11 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: <spaans@astro.rug.nl>

Dear Professor Spaans,

Thank you for your prompt reply. Suppose the topology can impose a three-torus as a spatial section, with some "nice consequences for isotropy", as you put it. Would you imagine that this would eventually help removing the geodesic incompleteness?

Best regards,

Dimi Chakalov
--

Note: The rich topology hiding in Einstein gravity comes from a "bare" topological manifold that is not (yet) endowed even with metric; it is just a three-dimensional topological manifold, denoted with Q . Marco Spaans explains (arXiv:0705.3902v2, p. 4):

"A priori, there is nothing physical about Q. It is merely a means to pick out all the different three-space regions in a four-dimensional space. Still, the logic that leads to Q holds for any physical property of the three-space regions. Given that there is no metric at this stage, one cannot assess the sizes of different regions, i.e. one is dealing with socks because there are none of the physical properties yet that define Einstein gravity."

And finally (ibid., p. 9): "Although Einstein-Cartan theory is beyond the scope of this derivation, it is obvious that Q possesses a topological analog because the three-tori are not simply connected."

But to avoid the Axiom of Choice (AoC) and hence construct a genuine background-free theory such as Einstein GR, "one needs a distinguishing quality," says Marco Spaans. Here's the full excerpt (ibid., p. 3):

"For self-consistency of the procedure one can then best ask the following question: Is it possible, for a connected set of three-space regions (in a four-dimensional space-time), to choose a region from that set through a choice process that is defined solely in terms of the three-space regions in the space-time itself? If such a construction can be found then it is self-contained and does not require the AoC.

"The starting point is formally a set S that contains objects. These objects are taken to be infinitesimal space-time regions, or one can even think of points for simplicity. Note then that, in order to choose an object x, one needs to select it and to distinguish it from another object y. That is, one does not know, a priori, whether two selections have not just singled out the same object. This is basically the difference between having an infinite collection of socks versus one of shoes in Russell’s apt quote on the necessity of the AoC.

"Thus, to avoid the AoC one needs a distinguishing quality."

Which brings us to the fundamental article by A. Trautman [Ref. 1] and the reference fluid in GR, provided by the Aristotelian connection. The latter can be unraveled (not without difficulties) in the following quote (ibid., p. 3, emphasis added):

"Because the region is infinitesimal, one can take it to be a simply connected region, i.e. one assumes that the region has no prior properties other than continuity. The assumption of continuity, although plausible, is a necessary one."

The very presence of continuity -- from one 'selected' object x to the 'distinguishable' object y -- is the manifestation of Aristotelian connection. It is the fundamental structure enabling quasi-local interactions in GR. It is a genuine fundamental structure that cannot be derived from the physical stuff we introduce later in GR. Hence it looks "dark". You can only notice that x and y are somehow "self-connected" by pure math called "the assumption of continuity". There is no intermediate object "between" x and y. The latter are "self-acting" like Baron Munchausen, because are defined in a background-free manner, without the Axiom of Choice (AoC) but "solely in terms of the three-space regions in the space-time itself."

I shall wait to see if Marco Spaans can suggest a new topological structure that is 'rich enough' to remove some of the generic pathologies of classical spacetime manifold, such as the geodesic incompleteness. Highly unlikely, I'm afraid. Notice that M. Spaans considers pairs of three-space regions [x, y], which yields two (one for x and one for y) three-tori and three "handles" (arXiv:0705.3902v2, p. 4). If I was in his shoes, I would start with a triplet of three-space regions [x, y, z], and would search for some "handles" that can provide for a time-orientability of y with respect to its neighbors x and z . I mean, we should lay out a topological structure that would enable the 3-D space to acquire its "time", otherwise the very assumption of continuity (see above) wouldn't be justified. Notice that neither the topology nor time-orientability can be derived from GR, so we may explore this 'freedom of choice' and try to fix many problems before they appear in GR equations from textbooks.

Last but not least, I wish to stress that I have great respect for the work by Prof. M. Spaans. Anyone can drop suggestions, but he does the hard work, and I sincerely wish him full success.

Subject: GW parapsychology?
Date: Mon, 16 Apr 2007 18:25:55 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Josh Goldberg <goldberg@phy.syr.edu>
Cc: saulson@physics.syr.edu,
sdpenn@physics.syr.edu,
Leszek Sokolowski <uflsokol@th.if.uj.edu.pl>,
Andrzej Staruszkiewicz <staruszkiewicz@th.if.uj.edu.pl>,
D Sigg <sigg_d@ligo.caltech.edu>,
D Shoemaker <dhs@ligo.mit.edu>,
bombelli@olemiss.edu,
brett.bolen@wku.edu,
Bernard.Schutz@aei.mpg.de,
gerhard.heinzel@aei.mpg.de

Dear Professor Goldberg,

Some colleagues of yours claim that "we will all be working hard to
take advantage of whatever Nature sends us in the meantime",

http://www.ligo.caltech.edu/LIGO_web/0312news/0312one.html

Perhaps you can speed up the process by explaining exactly how LIGO would detect a physical force from the "ripples" of metric field,

http://www.god-does-not-play-dice.net/Xiao.html#Wigner_1960

Please explain the "localization" of GW strain. Your colleagues have completely ignored Hermann Weyl and Angelo Loinger, but I sincerely hope they won't ignore your arguments.

Kindest regards,

Dimi Chakalov

Subject: Re: GW parapsychology?
Date: Mon, 16 Apr 2007 21:15:51 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Joshua Goldberg <goldberg@physics.syr.edu>

Dear Professor Goldberg,

> Before I respond, please tell me something about your background so
> that I can understand at what level of knowledge to put my
> explanation.

I've been struggling to understand GR since 1972.

Please choose your level of knowledge, with your meticulous precision and perfectionism. If, for some reason, I cannot follow it, I will not bother you again, but will do my homework.

The text to consider is at

http://www.god-does-not-play-dice.net/Xiao.html#Wigner_1960

Kindest regards,

Dimi Chakalov

Note: I am eagerly expecting to hear from Prof. J. Goldberg, because I don't believe he can explain the "localization" of GW strain and vindicate the scope of "GW astronomy", because such joint solution would lead to the wrong conclusion that "the points occurring in the base sets of differentiable manifolds, with which general relativity models spacetime" (cf. Butterfield & Isham), were physically real. The contradiction between these two totally incompatible tasks is obvious: in the second case, the "background" is the flat metric of Minkowski spacetime (with respect to which each point/event is individuated with localized physical content of matter fields), while in the first case there can be no background whatsoever nor localized GW energy along a trajectory of some "test particle" (LIGO's arms, say). In a background-free theory such as GR, the individuation of points/events is a brand new dynamical process (cf. dynamical determinism) associated to extended domains rather than to points. Namely, the tensorial quantities (e.g., the four non-vanishing invariants of the Riemann tensor, cf. John Stachel and Mihaela Iftime) are indissolubly connected to the "non-tensorial" ones (cf. Hermann Weyl): "even if we start with genuine tensorial variables, then certain important physical quantities turn out to be non-tensorial" (Laszlo Szabados). Thus, I believe we need to (i) endow the underlying differentiable manifold with a new degree of freedom, then (ii) extend the group Diff(M) with a new symmetry group that could include the quantum vacuum, and finally (iii) produce a brand new kind of "background" with respect to which each point/event is individuated relationally, by acquiring localized physical content of matter fields: one-at-a-time and on a perfect continuum (local mode of spacetime). This (iii) is the "context" of the Holon. Put it differently, quantum gravity --> new physics --> new assumptions about the structure of space and time --> new differentiable manifold --> new math. I hope this can answer the question from Professor Goldberg about my "background" (see above). But let's go back to "GW astronomy".

Joshua Goldberg will immediately notice the main problem from the "linearized approximation" of Einstein's GR: it is like building an antennae that can only detect very weak TV signal, because the "linearized approximation" itself cannot cope with any strong TV signal whatsoever.

Surely we can use approximations, such as the Schrödinger equation, which does not take into account any effects from the quantum vacuum. Only LIGO Scientific Collaboration (490 distinguished scholars) does not have any theory combining strong gravitational effects of both GWs and spacetime curvature, from which one can derive the theory of detecting GWs in the case of vanishing small "dimensionless amplitude". Their expectations for "increased sensitivity" with the Enhanced LIGO and Advanced LIGO make them look like some harum-scarum kids who claim that can measure the room temperature in their house, but their home-made "theory of thermometers" cannot be applied to the surface of the Sun even with a Gedankenexperiment, which in turn obliterates their "theory of thermometers" (LIGO 'n LISA) and the initial "theory of temperature" (the quadrupole approximation). It is not surprising that LSC failed to measure any "temperature" at all, since they in fact measure the dipole mode, and no "increasing of sensitivity" can help.

Most importantly, in a universe dominated by Dynamic Dark Energy (DDE), the mass-energy (cf. Eq. 10 in B. Schutz' article in Encycopedia of Astronomy and Astrophysics here) cannot be conserved: there is indeed energy radiated due to the "dipole" and "monopole" effects in general relativity, only it is totally "dark". It is most likely pertaining to the energy associated with the elementary timelike displacement, which is not an observable in GR (see Slide 29 in Bolen.zip).

How do we detect "the time changing quadrupolar distribution of mass and energy" (cf. Scott A. Hughes below), given the fact that 'time changing distribution of mass and energy densities in GR' is totally unknown?

Let's briefly recall the basic basics of gravitational energy: we must take into account "nonlocal interactions between the T_uv's at different points" (R. Penrose). "At least two ideal observers are needed to detect gravitation, but only one is enough to detect an electromagnetic field. In this sense gauge fields are local, and gravitation is not" (J. Pereira et al.). Thus, we need at least two observers/test particles, such that they could detect the gravitational energy only by being EPR-like correlated, like a shoal of fish. Locally, they must not "feel" any gravitational energy contributions (H. Weyl).

p. 467, emphasis added: "(T)he gravitational wave energy has to be measured in some other way that is not locally attributable to an energy ‘density’. Gravitational energy is a genuinely non-local quantity."

p. 458: "The contributions of gravity to energy-momentum conservation should somehow enter non-locally as corrections to the calculation of total energy-momentum. (...) From this perspective, gravitational contributions to energy-momentum, in a sense, ‘slip in through the cracks’ that separate the local equation [XXX] = 0 from an integral conservation law of total energy momentum."

Therefore, LIGO's arms are totally incapable of detecting GWs from the outset. This conclusion shouldn't be surprising, since you don't need non-local interactions in the "linearized approximation" of GR -- it can only "detect" very week GW strain. Again, it is like building an antennae that can only detect very weak TV signal, because the "theory" itself cannot cope with any strong TV signal whatsoever.

Here's an elucidating quote from B. Schutz' book "GRAVITY from the Ground Up: An Introductory Guide to Gravity and General Relativity":

p. 317: "But if the geometry is strongly distorted, the distinction between
wave and background has little meaning. In such cases, physicists do not speak about waves. They only speak about the time-dependent geometry."

And again from p. 317 (emphasis added): "To arrive at a conserved energy that can be exchanged between the detector and the wave, we have to treat the wave and detector together. This is not so easy in general relativity, because it is not easy to define the wave separately from the rest of the geometry. (...) Energy is only conserved in situations where external forces are independent of time. For weak waves, it is possible to define their energy with reference to the "background" or undisturbed geometry, which is there before the wave arrives and after it passes."

Which is why V. Faraoni (see below) tried very hard to dismiss the objections by Steven Weinberg. But if you introduce some fictitious "background" or undisturbed geometry, which "is there before the wave arrives and after it passes" (B. Schutz), you can play with GR as much as you wish, as long as you manage to separate the undisturbed "time parameter" of the "undisturbed geometry" from the other time parameter pertaining to the "waveforms" that "carry detailed information about the source" (cf. Kip Thorne's slide 5, from Caltech's Physics 237-2002).

NB: In other words, the proponents of "GW astronomy" (currently 490 physicists) split the metric field into two parts: one that has become (in their imagination) an 'undisturbed background', with respect to which they hope to detect the temporal and spatial disturbances of the other part of the same metric field, the "disturbed" one (see the drawing below).

It sounds like a stupid joke à la Baron Munchausen, only costs billions. The same type of error is made by those who claim that the so-called Dynamic Dark Energy (DDE) produces the cosmological time, and at the same time evolves in that same time.

True, every measurement is relational by its nature, so we need a new referential background, but LIGO Scientific Collaboration had made an incredible error of "producing" it from the very stuff (the metric field) they were supposed to measure.

If we are serious about the dynamics of GR and the wave of the spacetime metric (Caldwell & Kamionkowski), I believe we need to clarify the status of "dipole radiation", since the common, and convenient, belief that it is nonexistent (see above) is not valid anymore. And here we enter a terra incognita, because of the unknown nature of the much-needed gravitational shielding: "any manipulation of matter acting as a source of gravitational field will introduce an additional stress-energy tensor as a source of gravitational field" (J. Stachel). Thus, it seems that the only option we may have is to manipulate matter in the global mode of spacetime, before it becomes localized in the local mode of spacetime as "positive matter" (P. Joshi).

And that's a whole new ball game. The first 'rule of the game' is the structure of spacetime. The simplest way to explain the latter is to recall the hypothetical (and wrong) non-relativistic case in which there would be no 'global mode' nor 'local mode' of spacetime: this is the case depicted with the picture below, in which there is a preferred center of the universe in 3-D space, and subsequently a preferred "location" of The Beginning in 3-D space.

See the train metaphor here, and recall that we eliminated such preferred origin/Big Bang and preferred reference frame by "multiplying" The Beginning across an imaginary instantaneous "cut" of 3-D space, in which all observers would have measured/observed the same value of the cosmological time: 13.7 billion years, called 'modern universe' (cf. above).

Again, the picture above is a highly misleading, non-relativistic presentation of the Cosmological Principle: the instantaneous "cut" called 'modern universe' is just a mental imagery of the global mode of spacetime, corresponding to an imaginary 'now-at-a-distance' reference frame, in which the "distance" can be stretched to infinity (like a transcendental tachyon that is absolutely everywhere in "no time"), to exhaust the whole 3-D space. If we think of the "balloon center" in the expanding balloon metaphor (courtesy of Ned Wright), we can easily visualize such instantaneous "cut" of the expanding balloon, corresponding to the current surface of the balloon, because we can compare it to a "cut" that was smaller in the cosmological past with a "cut" that will be larger in the cosmological future, as depicted in the picture above; all these 'past' and 'future' would have absolute values, since we'd have an absolute "center" of the balloon (a.k.a. big bang) and an absolute empty space "outside" the balloon, waiting patiently for the balloon to expand into. We would also be able to settle the old dispute about who walks upside down, Matt Visser in New Zealand or the author of these lines in Europe (the way I see it, Matt will win, because he is so good in math!).

Mother Nature is smarter, however, because in the real, relativistic case the very "surface of the balloon" -- the 3-D space itself -- is composed of infinitely many "centers" of the balloon: (i) the "center" has been multiplied and spanned absolutely everywhere and evenly inside the 3-D "balloon surface" (cf. again the Cosmological Principle above), and (ii) the "boundaries" of spacetime are being dynamically fixed by 'the universe as ONE' -- the Aristotelian First Cause.

Not surprisingly, then, some "remnants" from 'the universe as ONE' will show up in its relativistic presentation (e.g., the omnipresent cosmic microwave background (CMB) radiation and the smooth DDE), and even become observable (the cosmic equator).

Once we switch to this relativistic presentation (which is, I believe, the only possible alternative to the misleading non-relativistic picture above), the global mode of spacetime "shows up" in the gaps "between" the infinitely many "centers" of the balloon placed on the balloon "surface", only we cannot directly observe this "dark shift" due to the "speed" of light. Thus, all "dynamic dark energy" effects, all acausal, inflation-like interactions across the expanding "rubber band" (see Fig. 24.3 from B. Schutz' book here), all quasi-local contributions of gravity to energy-momentum conservation (see R. Penrose's book above, p. 458), and the very nature of gravity -- "the whole universe must know about everything instantaneously" (see M. Zucker below) -- are vivid evidence for the "dark", or rather holistic effects of gravity, produced in the global mode of time.

Briefly, in the relativistic case both 'the center of the balloon' and 'the empty space before and after the current balloon surface' are converted into 'global mode of spacetime': see again the white area in Fig. 3.1 here. This is a concise, but incomplete, outlook of the structure of spacetime, suggested at this web site. See also the GW lake metaphor here, and on the hypothetical GWs here and here.

I am sure Josh Goldberg can elaborate extensively on these issues. Back in 1955, he published a landmark article on gravitational radiation (Phys. Rev. 99 (1955) 1873-1883). From 1956 to 1963, he was responsible for US Air Force support of research in GR, based at the Aeronautical Research Lab at Wright-Patterson Air Force Base in Ohio, and managed to support the 1957 Chapel Hill conference "Conference on the Role of Gravitation in Physics", organized by Bryce De Witt in January 1957, with US Air Force money. At that conference, Sir Hermann Bondi had stressed the following:

"The analogy between electromagnetism and gravitational waves has often been made, but doesn’t go very far, holding only to the very questionable extent to which the equations are similar. The cardinal feature of electromagnetic radiation is that when radiation is produced the radiator loses an amount of energy which is independent of the location of the
absorbers."

Thus, when EM radiation is produced, it is like a letter sent to all recipients which can "absorb" it; the simplest example with the emission of light from the Sun can be read here. The whole "postal service" with emission and absorption is perfectly local, obeys STR, and energy conservation laws.

Contrary to this simple picture, recall that the metric of spacetime has been "expanding" during the inflation in a totally acausal fashion (cf. Edward W. Kolb), being driven by DDE ever since the first instant "right after" The Beginning:

If we trust the inflationary scenario, the conversion of gravitational energy into physical energy is precisely the puzzling "localization" of normal-plus-dark gravitational energy, which we don't understand at all, because it had somehow evaded STR during the inflation, and also because in GR there is no tensorial presentation of it. All we can say is about what this "localization" is not: read Mike Zucker here.

We cannot accommodate any acausal process à la inflation nor action-at-a-distance in GR, yet "somehow the whole universe must know about everything instantaneously", as Mike Zucker put it. Therefore, it shouldn't be surprising that GR explicitly forbids any 'simple localization of energy' similar to the case of EM radiation, as is well known since 1917, thanks to Tullio Levi-Civita. Ninety years later, we've only coined a very peculiar term for the gravitational energy: Quasi-Local Energy (QLE), as explained by Bjoern Schmekel [Ref. 1]. Since the localization of GW energy is not a 'simple localization of energy at a point', we also call it "non-localizable" [Ref. 2].

NB: We can't use any finite domain of 3-D space either, so the only option left is to define a "boundary" at infinity [Ref. 1], which is nothing but the main issue raised here and elaborated on here. We simply do not have any other choice -- "His thoughts" can only be produced by the Aristotelian Connection, as the quasi-localized conversion of "His thoughts" constitute the putative local mode of spacetime.

If Kip Thorne or any of his LSC colleagues had made a professional effort to explain the puzzle demonstrated by Tullio Levi-Civita in 1917, they might have had a chance to gain respect and admiration on behalf of GR community. Instead, "Kip Thorne had no difficulty in 1981 in finding a taker for a wager that gravitational waves would be detected by the end of the last century. The wager was made with the astronomer Jeremiah Ostriker, one of the better-known critics of the large detectors then being proposed. Thorne was one of the chief movers behind the largest of the new detector projects, the half-billion-dollar Laser Interferometer Gravitational Wave Observatory, or LIGO. He lost the bet, of course." (Daniel Kennefick, Traveling at the Speed of Thought, Princeton University Press, Princeton, 2007, p. 1.)

Twenty-six years later, Kip Thorne has not yet encountered any difficulties in spending taxpayers' money for his juvenile dream. He just keeps quiet. And so does Josh Goldberg, regrettably.

But because Josh Goldberg was involved with these problems for more than fifty years, and also because I consider him a real professional, it is my hope that he will not stay quiet forever.

If some day Josh Goldberg decides to teach LSC a lesson in contemporary (after 1960s) gravitational physics, he will do it professionally, and they might eventually read it and start thinking.

[Ref. 1] Bjoern S. Schmekel, Quasi-local definitions of energy in general relativity, arXiv:0708.4388v1 [gr-qc]

p. 2: "Because of the problems associated with defining a local energy density it may be easier to make sense of the energy enclosed by a boundary. For regions of finite extend we expect non-zero values because in general a coordinate transformation can make the connection coefficients vanish at only one point. Therefore, it seems the only sensible way to define energy is by defining energy itself and not energy density.

"Of course this may seem ugly because a local covariant and tensorial formulation depends on densities evaluated at a point and its infinitesimally small neighborhood (in order to compute derivatives). A point remains a point under a Lorentz transformation, but needless to say the size of a finite region depends on the observer, so obviously such an energy will depend on the chosen coordinate system. It is therefore maybe not surprising that the first useful notions of energy were defined at infinity, i.e. they enclosed the whole system (cf. ADM mass [4], Bondi mass [5]). Like a point an infinitely large box does not change its size under a change of observer."

[Ref. 2] Daniel Kennefick, Controversies in the History of the Radiation
Reaction problem in General Relativity, gr-qc/9704002 v1.

p. 10: "At the Bern conference Rosen, returning to the cylindrical wave solution of his 1937 paper with Einstein, adduced evidence backing up Scheidegger’s position by proposing the possibility that gravitational waves did not transport energy (Rosen 1955). It is a peculiar characteristic of general relativity that the energy contained in the gravitational field, and thus the energy in gravitational radiation, is not described in a coordinate invariant way. This energy is considered to be real enough, and can be converted into other forms of energy which can be expressed invariantly, but the principle of equivalence prevents one from doing this for field energy in gravity. The reason is that any observer in a gravitational field is always entitled to imagine himself in a locally Lorentz (that is zero gravity) freely falling frame of reference which, locally, contains no field energy. Of course, one is not free to transform away the entire field energy of a planet but one can always choose co-ordinates on an infinitesimally small portion of its surface so as to eliminate the field energy in that region. Thus it is said that gravitational field energy is non-localizable."

Subject: GW parapsychology?
From: Dimi Chakalov <dchakalov@gmail.com>
Date: Tue, 09 Oct 2007 06:40:10 -0700
Message-ID:
<1191937210.856214.257330@r29g2000hsg.googlegroups.com>
Newsgroups: sci.physics.research
Cc: baez@math.ucr.edu

I believe can offer a simple Gedankenexperiment to verify the status
of Gravitational Wave (GW) astronomy,

http://www.god-does-not-play-dice.net/Trautman.html#proposal

A penny for your thoughts!

Dimi Chakalov

Date: Tue, 9 Oct 2007 23:20:04 +0300
Message-ID:
<bed37360710091320p18da558fi2434100b85781f82@mail.gmail.com>
From: Dimi Chakalov <dchakalov@gmail.com>
To: Phillip Helbig <helbig@astro.multivax.de>
Subject: Re: GW parapsychology?

Dear Mr. Helbig,

I have not posted an "article".

If you believe my argument at the URL below is "too speculative", please provide at least 1 (one) argument.

Please get professional.

Sincerely,

D. Chakalov

====================================================

Date: Tue, 9 Oct 2007 19:42:07 +0200 (MET DST)
Message-Id: <07100919420714_2520023A@multivax.de>
From: helbig@astro.multivax.de (Phillip Helbig)
To: dchakalov@gmail.com
Subject: Re: GW parapsychology?

> Unfortunately, the article you posted to sci.physics.research is
> inappropriate for the newsgroup because it is too speculative.
[snip]

> Phillip Helbig, sci.physics.research co-moderator

====================================================
>
> I believe can offer a simple Gedankenexperiment to verify the status
> of Gravitational Wave (GW) astronomy,
>
> http://www.god-does-not-play-dice.net/Trautman.html#proposal
>
> A penny for your thoughts!
>
> Dimi Chakalov
>

Subject: Re: Netiquette
From: dimi@chakalov.net
Date: Thu, 6 Sep 2007 00:45:31 +0200 (CEST)
To: Daniel Kennefick <danielk@uark.edu>

Hi Dan:

> I read your articles with interest.

Which particular argument against the very possibility for detecting GWs attracted your attention?

> It will certainly be interesting to see whether gravitational wave
> detectors see anything in the coming years, given the historical
> controversies over their existence or non-existence.

Instead of waiting, I've suggested a number of tasks for clarifying the artifacts from the linearized approximation by LSC (420 physicists). Please see my question above.

> However, I do not think it is fair to imply that Kip Thorne and others
> have wantonly spent tax-payer's money is pursuit of a dream, as if little
> thought had gone into it.

Just watch the video lecture by Kip Thorne, about the "invariance angle" that determined the L-shape of LIGO. The physics is from 1960s. See again my question above.

> While it is always possible that those who believe in the existence
> of detectable gravitational radiation are wrong, they have spent
> several decades and much of their own working career trying to
> establish whether or not they do exist. I suspect that you will find few
> other government expenditures which have been quite so thoroughly
> debated and analysed.

I quoted Cliff Will on that matter, and cannot agree with you. Will be happy to elaborate, with facts.

> If government funding of research is to be continued at all, it must be
> on the understanding that, in science, a null result is always a
> possibility, and may even be a particularly fruitful one.

Dan, this is a VERY serious business, so please get professional. There is
nothing fruitful in wasting billions of dollars and Euro for LIGO and LISA. You can't catch a dimensionless ghost, GW "amplitude". If you succeed, you'll ruin the whole GR.

Again, which particular argument against the very possibility for detecting GWs attracted your attention?

Looking forward to hearing from you,

Best - Dimi

> On Wed, 5 Sep 2007, Dimi Chakalov wrote:
>
>> Dear Dr. Kennefick,
>>
>> I quoted from your gr-qc/9704002 v1 at
>> http://www.god-does-not-play-dice.net/Trautman.html#dipole
>>
>> Regards,
>>
>> Dimi Chakalov
>>

Note: Suppose that, for the sake of the optimistic remark of Daniel Kennefick, some day LSC somehow detects GWs with their "linearized approximation". Such result will ruin the whole GR, for the following reasons.

Unlike in STR, where the metric acts as a background structure given a priori, in Einstein GR the metric is treated as a field which not only affects, but also is affected by, the other fields present. This non-linear, bi-directional "talk" (J. Wheeler) continues at every instant from the non-tensorial "time" [tau] (cf. C. Rovelli and B. Bolen), as depicted with the lake metaphor here. Due to the active diffeomorphism freedom, the geometrical "points" cannot be identified by any fixed material content of 'objective reality out there', as explained by J. Stachel and Butterfield & Isham.

Now, if LIGO detects some "wave" of the metric field, such "wave" could only "propagate" on a set of geometrical points that are already-fixed by their physical content, which of course contradicts GR:

To clarify this issue, I will draw 1-D wave pattern snapshots of the GW lake below, at two instants of time, t_m and t_n , depicting the periodic wobbling of the metric field:

t_m: [ xxxxx x x x x x xxxxx x x x x x xxxxx x x x x x ]

t_n: [ x x x x xxxxx x x x x x xxxxx x x x x x xxxxx ]

Notice that a rigorous description of the wobbling of the metric field requires (i) well-defined distribution of energy densities at each instant x , and (ii) knowledge of the nature of Cold Dark Matter. The first is impossible in GR; the second is totally unknown. Hence the drawing above can at best be summarized with Murphy's Law No. 15: Complex problems have simple, easy-to-understand wrong answers.

According to the "linearized approximation" of GR (cf. Scott A. Hughes, [Ref. 1]), your wristwatch and LIGO's arms can read these instants of time: "A passing gravitational wave would change the distance between the weights, first in one arm, then in the other arm, which is arranged at a right angle to the first" (reference here).

Which in turn requires that the GW energy should be localized during a finite time interval during which the spacetime "points" x possess fixed content obtained from the right-hand side of Einstein equation (the material stuff of the GW lake), which is, of course, pure fantasy: read again Angelo Loinger.

Notice that we can ponder on such "wave pattern" only by taking a bird eye's view on the whole spacetime, that is, by taking the stand of some meta-observer placed in an absolute reference frame. The bold reality of Einstein GR is entirely different: your wristwatch and LIGO's arms are immersed into the GW lake, such that there is no fixed background nor meta-observer "outside" the GW lake. Steven Weinberg was right: “all lengths are stretched at the same rate by the gravitational wave”.

Valerio Faraoni tried very hard to compare "the variation of the proper length of the interferometer arm with the variation in wavelength", and argued that "the gravitational wave “treats in a different way” the wavelength of light and the length of the interferometer’s arm" (reference here, pp. 7-8), but all his beliefs about physical wavelength of the gravitational wave are expressed in the context of the "linearized approximation" of GR.

You can't enjoy a physical GW wavelength paired with a dimensionless, yet "slowly evolving", GW amplitude. The whole mess of "GW astronomy" begins with the "time parameter" pertaining to the "waveforms" that "carry detailed information about the source" (cf. Kip Thorne's slide 5, from Caltech's Physics 237-2002), which is a ghost that shows up only in the "linearized approximation" of GR: see NB above. Moreover, if GWs had genuine physical "phase", there should be a way to cancel it by Gedankenexperiment, similar to the real experiment with canceling the phase of EM waves.

First, some history. As Richard M. Jones reminded, in late summer of 1991, the House Science Subcommittee passed a bill prohibiting LIGO construction funding, but on 27 September 1991 "conference action on the NSF bill was completed, and LIGO had the full $23.5 million the Bush Administration had requested."

I was in the United States in 1991, but cannot recall any major discovery in the late summer of that year, which could have changed drastically the course of action set by the House Science Subcommittee, prohibiting LIGO construction funding.

Such 'major discovery' can be explained with an old joke from Martin Gardner: two people whose ship sank were left on an island for many years, and one day they found on the beach a big Coca-Cola bottle (they knew only the small ones). Then one of them said: "Holy cow, we got shrunken!" Suppose they were instead "stretched 'n squeezed" by some local GW passing locally over their island.

What could possibly constitute the referential background with undisturbed metric that defined the dimensions of the small/undistorted Coca-Cola bottle? And how would the two guys keep track on it, so that they can at the same time realize that were indeed "stretched 'n squeezed"? It really requires a major discovery to explain such schizophrenic observation.

With a delay of sixteen years, during which at least $500 million taxpayers' money have been "spent", may I offer to LIGO Scientific Collaboration a simple task regarding the GW phase and amplitude, which, if completed successfully, would clear their reputation.

It is just a Gedankenexperiment, so all they need is blank notebooks and sharp pencils.

Please don't miss the details explained above and the main objection explained here. In a nutshell, the measuring device will be "stretched and squeezed" by zero distortion: there is no undisturbed background.

Why? Because we cannot "split" the metric field into two parts: undisturbed background metric vs. "disturbed" metric (cf. A. Buonanno in [Ref. 1]).

In GR, you can't produce a referential background from the very stuff you're supposed to measure, and then measure "it" with respect to itself.

In the context of the story from Martin Gardner above, our island is 'the whole spacetime', hence the alleged effect depicted with the drawing from Kip Thorne

Again, there was no major discovery in the late summer of 1991, which would have recovered the dimensionality of GW "amplitude", h .

Should anyone has doubts about the statements above, there is a simple way to refute them and vindicate the scope of LSC research: write down the dynamics of strong GWs in the case when "the geometry is strongly distorted" (cf. B. Schutz above), and then choose a parameter in GR -- your choice -- that could enable you to recover -- reversibly -- the linearized approximation of GR valid for negligible distortion of geometry, and then go back to the initial case when "the geometry is strongly distorted". If you succeed, you will demonstrate the correctness of the linearized approximation, hence clear the reputation of LSC as people doing science (not parapsychology). Needless to say, the rest of the world will learn about such discovery from CNN Breaking News, and we might get a clue how to build classical spacetime 'from scratch', that is, from nonlocal Diff(M)-invariant observables (cf. Steve Carlip and Chris Isham).

Notice how LSC member Valerio Faraoni tried to obscure both the crucial issue explained above and Steven Weinberg's objection, by arguing that "the gravitational wave “treats in a different way” the wavelength of light and the length of the interferometer’s arm".

But LSC don't have any detected GW in the first place, to prove that it indeed “treats in a different way” the wavelength of light and the length of the interferometer’s arm. They can only offer speculations about some "linearized approximation", and five consecutive failures to detect GWs.

"I agree that much of what one reads in the literature is absurd. Often it is a result of bad writing, rather than bad physics. I often find that people who say silly things actually do correct calculations, but are careless in what they say about them."

The "silly things" in question are the statements of many LSC members regarding the phase and amplitude of GWs. Let's hope this time they will act professionally, and not be careless in what they say about them.

To begin with, let us recall some basic prerequisites from Kip Thorne (see his slide 4 below):

By comparison, recall the cancellation of the EM phase with two Polaroid filters, as explained by B. Schutz (reference here):

"You can prove that light is a transverse wave by using Polaroid, the semi-transparent material that is used in some sunglasses. If you take two pieces of Polaroid and place them over one another, then if they are oriented correctly they will pass about half the light through that falls on them. But if you rotate one piece by 90^o, then the two pieces together will completely block all the light (propagating along the Z axis - D.C.)."

To perform the Gedankenexperiment with GW's phase, I believe LSC will need some object that can be mapped onto itself by 180^o rotation ("force pattern invariant under 180^o rotation", see Kip Thorne's slide 4 above), in 3-D space and by using Cartesian coordinates. And also keep in mind that "each polarization has its own gravitational-wave field", as Kip Thorne stated in slide 5 from his course Caltech's Physics 237-2002, so you'll have to fit those two independent "gravitational-wave fields" in the same 3-D space as well, and finally ensure that all this happens "with reference to the "background" or undisturbed geometry, which is there before the wave arrives and after it passes", as Bernard Schutz eloquently explained.

Once you complete this task, not only will you pass Caltech's Physics 237-2002, but also discover the "direction" of GW propagation along the Z axis, and of course recover the dimensionality of GW "amplitude" projected on x/y axes (in meters or bananas, whichever comes first). That's all.

NB: Notice that the "direction" of GW propagation is a very subtle issue, because if we picture it as a 'simple displacement along a particular direction in 3-D space' (say, from a fixed location at the center of the Galaxy towards the Earth, cf. Marie-Anne Bizouard et al., gr-qc/0701026 v1), it turns out that the "displacement" of spacetime from GWs is zero, as demonstrated by Angelo Loinger (physics/0506024 v2, pp. 2-3): "if we displace a mass, its gravitational field and the related curvature of the interested manifold displace themselves along with the mass." Thus, if you claim that the "displacement" or distortion of the metric from GWs were not zero, you would need an absolute reference frame (as shown in the non-relativistic cosmological picture above), such that you can look at the GW pond (click the picture below) and be able to record the 3-D component of the GW "push" on your 'fishing rod float' (LIGO's arms).

Notice also that the "direction" of GW propagation can only be determined relationally, with respect to some other direction in 3-D space, in which the same GW does not propagate. For EM waves in Minkowski spacetime, this task is trivial, because we can determine the direction of light propagation with respect to the undisturbed spacetime "grid", and define the volume of 3-D space ahead, in which the photons have not yet arrived, as well as some alternative direction in 3-D space, in which the same EM waves do not propagate.

In the case of GWs, however, such exercise does not make sense at all, since it requires a non-relativistic presentation of 'the whole spacetime' -- see the non-relativistic cosmological picture above. Read also my email to Kip Thorne from Sun, 16 May 2004 02:02:03 +0300 here.

Moreover, if GWs propagate along the "direction" of the global expansion of 3-D space as well, there will be no "direction" left in 3-D space in which they would not propagate, and subsequently there will be no unique direction singled out by GWs, on which LIGO or LISA would stick to measure the GW strain. They just can't detect an omnipresent stuff like GWs and DDE.

These crucial conceptual problems of "GW astronomy" should have been discussed in February 2003, at the American Association for the Advancement of Science's 2003 Annual Meeting (17 February 2003, Denver, Colorado; reference here). What happened instead was that Kip Thorne and his LSC colleagues got additional US$150 million to "discover" the "desired sensitivity" of LIGO, since all their failures to detect some effect from the dimensionless GW amplitude have been interpreted as useful hints for obtaining the "desired level of LIGO sensitivity". The latter was certainly not clear even to Kip Thorne, since in 1981 he bet that GWs will be detected "by the end of the last century" (Daniel Kennefick, Traveling at the Speed of Thought, PU Press, Princeton, 2007, p. 1).

The insane quest for detecting GWs continues. Surely we can use a linearized approximation of GR for task-specific purposes, for example, to fix Global Positioning System (GPS) coordinates in Minkowski space (C. Rovelli, arXiv:gr-qc/0110003v2), but detecting GWs is an entirely different challenge. For example, can you detect your "local coordinates" in the reference frame of the equator of the universe? If you can, you might discover the local "push" from the omnipresent Dynamic Dark Energy, and perhaps the "waves" of the spacetime metric. Go ahead, only use your own savings.

Again, the answer to the key question 'with respect to what?' cannot be 'locally, and with respect to itself' (see above). Only in a non-relativistic presentation of GW radiation one could "envisage" an unphysical, gauge-dependent "global reference frame" (cf. Butterfield & Isham), as depicted in the (very misleading!) picture above ("Seeing back into the cosmos", cf. above). In order to detect the perturbations of the quasi-local gravitational energy densities caused by the impact from the quasi-local GW energy, we need a unique 'referential background' that can only be provided by 'the whole spacetime', which in turn requires brand new kind of quasi-local GW detectors, resembling the human brain (read a historical remark from 1984 here).

As to the "linearized approximation" of GR, it produces artifacts totally incompatible with the full, non-linear GR. If the Schrödinger equation (see above) were the same kind of fake "approximation", it would have predicted effects that contradict QFT.

Another comparison with quantum theory goes as follows: There are quantum effects that are quite week too (e.g., Josephson effect), but nobody would treat them classically. Most importantly, nobody would search for some "weak" quantum effects with some classical mechanics approximation, given the indisputable fact that such "weak" quantum effects cannot exist in quantum theory in principle. Now, replace 'quantum theory' with 'full non-linear GR', and 'classical mechanics approximation' with 'linearized approximation', and you will get the full coverage of "GW astronomy".

It is indeed GW parapsychology.

Daniel Kennefick believes that Kip Thorne and his group have not "wantonly spent tax-payer's money is pursuit of a dream", but I haven't read any effort to clarify the status of the dipole radiation in "GW astronomy", despite the facts that the dark energy problem has been established since 1998 (see J.A.S. Lima).

Which reminds me of a somehow cruel experiment my son did with our cat two years ago: he boiled her milk in the microwave, and poured it in her cup. Poor thing, she was running around her milk cup but couldn't touch it. But at least she showed genuine interest and dedication.

Not so with Kip Thorne and his LSC collaborators, perhaps because they get their "cat food" from us anyway, since we all pay for their totally irresponsible dream.

Again, if we interpret the spacetime "points" x (see my clumsy drawing above) as 'EPR-like correlated dice on the table' (local mode of spacetime), then there is indeed a genuine GW, but it cannot in principle be detected with LIGO and the like: read Roger Penrose on the quasi-local gravitational energy above. Hence one day we may have to convert LIGO and the other interferometer-based "GW detectors" to wine cellars, as suggested previously, but LISA will remain a totally unusable piece of junk.

To finish this discussion, let me comment on two excerpts from Flanagan & Hughes, The basics of gravitational wave theory, New J. Phys. 7 (2005) 204, gr-qc/0501041 v3:

p. 9: "We begin by defining the decomposition of the metric perturbation h_ab, in any gauge, into a number of irreducible pieces. Assuming that h_ab --> 0 as r --> [inf], we define the quantities (...) together with the constraints (...) and boundary conditions (...) as r --> [inf]."

To clarify this crucial assumption of the "linearized approximation", I hope Prof. J. Goldberg will define rigorously r --> [inf] and its "boundary conditions" (cf. Sijie Gao). See also Bjoern Schmekel, and recall the 'finite infinity' proposal by George F.R. Ellis.

And on p. 12, Eq. 2.70: "Although the variables [X1], [X2], [X3], and hTT_ij have the advantage of being gauge invariant, they have the disadvantage of being non-local. Computation of these variables at a point requires knowledge of the metric perturbation h_ab everywhere. (...) Thus, at least certain combinations of the gauge invariant variables are locally observable."

NB: I hope Prof. J. Goldberg will (i) clarify the crucial limitations from not knowing the metric perturbation h_ab everywhere, and (ii) disentangle the alleged gauge invariant variables that were "locally observable" from those which aren't simply because they can't be "locally observable" in the first place (cf. Larry H. Ford and Steve Carlip), hence eliminate the poetry in the seemingly innocent expression "certain combinations".

And an excerpt from LISA International Science web site (last modified 2006-11-29 14:05): "gravitational waves - disturbances of the fabric of space travelling through the cosmos like ripples on a pond (notice the poetry - D.C.).
...
"In order to detect gravitational waves, scientists search for tell-tale signs of the stretching and squeezing of space which heralds (notice the poetry - D.C.) the passing of such waves. To this end, LISA will be using laser light to monitor the distances between its three satellites, which orbit the sun in a triangular formation."

Notice that the main reference in Flanagan & Hughes' article is ref. [51], which is an article by Richard A. Isaacson (Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio) from 1968. Notice also that their Ph.D. Advisor, Kip Thorne, also relies on "crucial" articles from 1960's (the mythical "gravitons" and the "invariance angle" that determined the L-shape of LIGO's arms).

Again, there was no breakthrough in the summer of 1991, which would have changed the opinion of the House Science Subcommittee, prohibiting LIGO construction funding. Instead, I guess Kip Thorne and his colleagues and friends have convinced some influential people to play poker with taxpayers' money.

So far all these people are keeping quiet, included Josh Goldberg, who was responsible for US Air Force support of research in GR, based at the Aeronautical Research Lab at Wright-Patterson Air Force Base in Ohio, where all this mess started to evolve, up to this day.

It will be highly embarrassing to LSC scholars in USA, UK, Germany, Italy, Australia, Japan, Canada, India and Spain if it turns out that some outsider has been repeatedly showing their errors, while they were ignoring Hermann Weyl and Angelo Loinger and wasting money earned with hard labor by their fellow citizens, until -- and finally -- fail miserably again, this time with their "Advanced LIGO".

[Ref. 1] Chris L. Fryer, Daniel E. Holz, Scott A. Hughes, and Michael S. Warren, Stellar collapse and gravitational waves,
http://arxiv.org/abs/astro-ph/0211609v1

"GWs are tensor perturbations to the metric of spacetime, propagating at the speed of light, with two independent polarizations. As electromagnetic radiation is generated by the acceleration of charges, gravitational radiation arises from the acceleration of masses. Electromagnetic waves are created (at lowest order) by the time changing charge dipole moment, and are thus dipole waves. Monopole EM radiation would violate charge conservation.

"At lowest order, GWs come from the time changing quadrupolar distribution of mass and energy; monopole GWs would violate mass-energy conservation, and dipole waves violate momentum conservation.

"GWs act tidally, stretching and squeezing objects as they pass through. Because the waves arise from quadrupolar oscillations, they are themselves quadrupolar in character, squeezing along one axis while stretching along the other."

See also: Alessandra Buonanno, Gravitational waves, arXiv:0709.4682v1 [gr-qc], 50 pages, 13 figures; to appear in the Proceedings of Les Houches Summer School, Particle Physics and Cosmology: The Fabric of Spacetime, Les Houches, France, 31 Jul - 25 Aug 2006

See also: Chris J. Isham, Canonical Quantum Gravity and the Problem of Time, Lectures presented at the NATO Advanced Study Institute "Recent Problems in Mathematical Physics", Salamanca, June 15-27, 1992; Imperial/TP/91-92/25, 3 October 1992, gr-qc/9210011 v1.

"Yang-Mills transformations occur at a fixed spacetime point whereas the diffeomorphism group moves points around. Invariance under such an active group of transformations robs the individual points in M of any fundamental ontological significance. (...) In the present context, the natural objects that are manifestly Diff(M)-invariant are spacetime integrals like, for example,

[XXX]

"These implications of Diff(M)-invariance pose no real difficulty in the classical theory since once the field equations have been solved the Lorentzian metric on M can be used to give meaning to concepts like 'causality' and 'spacelike separated', even if these notions are not invariant under the action of Diff(M). However, the situation in the quantum theory is very different. For example, whether or not a hypersurface is spacelike depends on the spacetime metric g . But in any quantum theory of gravity there will presumably be some sense in which g is subject to quantum fluctuations. Thus causal relationships, and in particular the notion of 'spacelike', appear to depend on the quantum state."

See also: Jörg Frauendiener, Conformal Infinity, 2 February 2004,
http://www.livingreviews.org/lrr-2004-1

Sec. 2.3, Asymptotically flat space-times

"In summary, our qualitative picture of asymptotically flat space-times is as follows: Such space-times are characterized by the property that they can be conformally compactified. This means that we can attach boundary points to all null-geodesics. More importantly, these points together form a three-dimensional manifold that is smoothly embedded into a larger extended space-time. The physical metric and the metric on the compactified space are conformally related. Smoothness of the resulting manifold with boundary translates into asymptotic fall-off conditions for the physical metric and the fields derived from it. The boundary emerges here as a geometric concept and not as an artificial construct put in by hand. This is reflected by the fact that it is not possible to impose a “boundary condition” for solutions of the Einstein equations there. In this sense it was (and is) not correct to talk about a “boundary condition
at infinity” as we and the early works sometimes did."

See also: Alan Rendall, Approximation methods for gravitational radiation,
http://www.aei.mpg.de/~rendall/approx.html

"One of the characteristic predictions of general relativity is that of gravitational waves. Up to now these could only be observed indirectly in astrophysical systems, but very soon detectors for gravitational waves on earth will come into operation. In obtaining detailed predictions about gravitational waves from general relativity, the only way we know how to proceed is to apply approximation techniques. For a long time I have been interested in putting these approximate methods on a mathematical basis which is as solid as possible. Earlier I studied post-Minkowskian and post-Newtonian approximations, with some success.

"However the description of radiation only starts at the point where considering these approximations separately ceases to be sufficient. Recently Markus Kunze and I have obtained results which can be seen as a first step in the direction of a mathematical understanding of the approximation techniques used to describe radiation (math-ph/0012041, gr-qc/0105045)."

See also: M. Kunze and A.D. Rendall, Simplified models of electromagnetic and gravitational radiation damping, Classical Quantum Gravity 18 (2001) 3573-3587; http://arxiv.org/abs/gr-qc/0105045

"None of the results mentioned above prove anything about matching the two approximations and until this can be done the possibilities of understanding anything about radiation (even at the quadrupole level) in a rigorous way are very limited. In the following these limits will not be
removed."

See also: Alan D. Rendall, Theorems on Existence and Global Dynamics for the Einstein Equations, http://www.livingreviews.org/lrr-2005-6
(Section 9.6, the geodesic hypothesis, was published on 18 October 2005)

9.6 The geodesic hypothesis

"In elementary textbooks on general relativity we read that the Einstein equations imply that small bodies move on geodesics of the spacetime metric. It is very hard to make this into a mathematically precise statement which refers to actual solutions of the Einstein equations (and
not just to some formal approximations).

9.5 The initial boundary value problem

"In most applications of evolution equations in physics (and in other sciences), initial conditions need to be supplemented by boundary conditions. This leads to the consideration of initial boundary value problems. It is not so natural to consider such problems in the case of
the Einstein equations since in that case there are no physically motivated boundary conditions. (For instance, we do not know how to build a mirror for gravitational waves.)"

See also: Alan D. Rendall, General Relativity, June 20, 2005,
http://www.aei.mpg.de/~rendall/gr2.pdf

p. 2: "A beautiful mathematical property of the Einstein equations is that they are independent of the choice of coordinates. It is however the case that when we have to choose coordinates in order to solve a specific problem this beautiful abstract property often leads to headaches.

"Since we can in principle choose any coordinate system we are in the uncomfortable situation of being forced to make a choice. We will encounter many examples of this in the following."

See also Alan D. Rendall's web site,
http://www.aei.mpg.de/~rendall

"I have a collection of useful equations related to the 3+1 decomposition of the Einstein equations. I have put a lot of effort into trying to ensure that these equations are correct. If you nevertheless find a mistake please report it to me."

Subject: The correct answer to the wrong question
Date: Mon, 17 Sep 2007 21:54:39 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: <rendall@aei-potsdam.mpg.de>

Dear Dr. Rendall,

I quoted from your GR Lecture Notes at
http://www.god-does-not-play-dice.net/Trautman.html#Rendall

You stated at your web site: "I have a collection of useful equations
related to the 3+1 decomposition of the Einstein equations. I have put a lot of effort into trying to ensure that these equations are correct. If you
nevertheless find a mistake please report it to me."

I believe you did put a lot of effort into trying to ensure that these
equations are 'the correct answer to the wrong question'. I'm afraid you may never recover the dynamics of GR with the "3+1 decomposition" of the Einstein equations, and regret that you did not answer any of my email
messages sent since 30 March 2005.

Sincerely,

D. Chakalov

Note: Regarding the decomposition of the Einstein equations, Donato Bini and Luca Lusanna (arXiv:0710.0791v1 [gr-qc]) mentioned in a footnote:

Actually, the “3+1” approach requires the knowledge of the data on a whole space-like hyper-surface which is not factual; similarly the “1+3” is not factual because it requires the knowledge of the data on a whole world line, i.e. also in the “future.”

The reason why the splitting of spacetime does not and cannot produce any factual presentation of the physical reality can be explained by zooming on the nature of continuum (see above).

When people ponder on GR and claim that "the simplest differential identities of the theory, namely the Bianchi identities, implied the existence of conservation laws", and then envisage "match between geometrical (Einstein tensor) and physical (energy-momentum tensor) quantities" (C. G. Böhmer, arXiv:0710.0752v1 [gr-qc]), they ignore a hidden, directly unobservable (recall the quark confinement and my prediction about LHC dated January 9, 2003) entity called here 'global mode of spacetime'.

The impact of the latter on the quasi-localized constituents of the local mode of spacetime is "dark" in the sense that it comes from the Holon of the universe (cf. the Cosmological Principle above), hence it cannot be traced back to its origin. Only it is a bit too much: up to 96% from the stuff in the universe is considered "dark".

Going back to the forest metaphor, each tree lives in the local mode of spacetime, and gets EPR-like corrections/contributions to its instantaneous state from 'the forest' (the Holon in the global mode of spacetime), due to which the whole forest exhibits wave-like pattern (read a story about a centipede here, and a note on the "dark" brain dynamics here). However, it is manifestly pointless to try to detect such quantum-gravitational "wave" with local interactions: the "amplitude" of the wave can only be dimensionless, as we know from QM textbooks.

Besides, in order to eventually understand the quasi-localized gravitational "energy", we need to define the 'whole spacetime', from each arbitrary "point" up to "infinity", in such way that the "dynamic dark energy" will be poured into it. And because "any non-constancy in [lambda] would have to be accompanied by a compensating non-conservation of the mass-energy of the matter" (R. Penrose), the twice-contracted Bianchi identities can only be relevant to the current GR, as "a low energy effective field theory description of something else" [Ref. 1].

One question immediately arises: Can we unravel the 'entry points' of the "dark" impact from the Holon? Of course we can. They are called non-trivial/non-Gaussian fixed points [Ref. 1], and are perhaps made of "unparticles" [Ref. 2]. And that is not a poetry.

[Ref. 1] Assaf Shomer, A pedagogical explanation for the non-renormalizability of gravity, arXiv:0709.3555v1 [hep-th].

p. 7, Footnote 20: "Some recent discussion of possible physical signatures of a non-trivial fixed point are discussed e.g. in [5].
...
p. 8: "... path integrals are by definition descriptions of quantum field theories that are perturbations by relevant operators of Gaussian fixed points.
...
p. 10: "It seems that gravity is a low energy effective field theory description of something else that is not a quantum field theory."

[Ref. 2] Howard Georgi, Unparticle Physics, arXiv:hep-ph/0703260v3.

p. 2: "The standard model does not have the property of scale invariance. Many of our particles have definite nonzero masses. But there could be a sector of the theory, as yet unseen, that is exactly scale invariant and very weakly interacting with the rest of the standard model. In such an interacting scale invariant sector in four space-time dimensions, there are no particles because there can be no particle states with a definite nonzero mass.

"Scale invariant stuff, if it exists, is made of unparticles.

"But what does this mean? It is clear what scale invariance is in the quantum field theory. Fields can scale with fractional dimensions. Indeed, much beautiful theory is devoted working out the structure of these theories.4 But what would scale invariant unparticle stuff actually look like in the laboratory? In spite of all we know about the correlation functions of conformal fields in Euclidean space, it is a little hard to even talk about the physics of something so different from our familiar particle theories. It
does not seem a priori very likely that such different stuff should exist and have remained hidden.

"But this is no reason to assume that it is impossible. We should determine experimentally whether such unparticle stuff actually exists. But how will we know if it we see it? That is one of the questions I address in this note.
...
p. 3, footnote 6: "Infinite extra dimensions, however, can have unparticle-like behavior. See [6]."

Subject: The "boundary points" of asymptotically flat spacetime, Sec. 2.3
Date: Mon, 17 Sep 2007 22:50:18 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: J Frauendiener <j.t.frauendiener@cma.uio.no>,
joerg.frauendiener@uni-tuebingen.de
Cc: "Szabados,L." <lbszab@rmki.kfki.hu>,
M Kunze <markus.kunze@uni-due.de>,
Simone Calogero <calogero@mct.uminho.pt>,
Alan D Rendall <rendall@aei-potsdam.mpg.de>,
Steven G Harris <harrissg@slu.edu>

Dear Dr. Frauendiener,

I quoted from your lrr-2004-1 at
http://www.god-does-not-play-dice.net/Trautman.html#K1

I wonder if you can define GWs on asymptotically flat spacetime,

http://www.god-does-not-play-dice.net/Trautman.html#dipole

http://www.god-does-not-play-dice.net/Trautman.html#LSC

Since you can "attach boundary points to all null-geodesics", such that "these points together form a three-dimensional manifold that is smoothly embedded into a larger extended space-time", I believe you should be able to solve the problems with GWs at the links above, as well as the generic problem of "conformal embedding" of [something] into [something else] at

http://www.god-does-not-play-dice.net/Straumann.html#Eric_note

http://www.god-does-not-play-dice.net/Straumann.html#refs

I wonder if your colleagues can do it, too.

Kindest regards,

Dimi Chakalov

On 9/10/07, Szabados,L. <lbszab@rmki.kfki.hu> wrote:
[snip]
> For a very nice, readable and really pedagogical introduction of
> all these notions see the Livrev paper by Joerg Frauendiener in
> 2004. You will find the references to all the classical, original
> papers there.
[snip]
------

Note: Jörg Frauendiener explained above the "boundary points" of asymptotically flat spacetime as follows: he can attach boundary points to all null-geodesics, although the general recipe for making a geodesic is far from being understood; see the geodesic hypothesis in Alan Rendall's review above.

More importantly, he stated, "these points together form a three-dimensional manifold that is smoothly embedded into a larger extended space-time."

Imagine those "boundary points" as absolute zero "temperature": it has a finite value, but cannot be reached by any physical system. Further on the analogy breaks down, because all "points" on the numerical axis that go down to the absolute zero "temperature" are indistinguishable: if you happen to live in an asymptotically flat spacetime, any point from it will be as "close" to the "boundary points" as any other one. Check out the Cosmological Principle above.

I believe the idea due to Aristotle -- the First Cause -- can be explored for understanding the "boundary points": if you travel with the "speed" of light, your proper time will be frozen, and you will enter the global mode of spacetime in which the whole universe is ONE. It seems to me that this is the most natural way to fix a 'numerically finite but physically unattainable boundary' at which the whole universe is ONE. It cannot be physically reached from the teleological local mode of spacetime, hence it seems as being placed "at infinity".

But what is 'global mode of spacetime'? If you live in an asymptotically flat spacetime, it will be both "at infinity" and "inside the singularity", hence you will never reach it. See again the white area in Fig. 3.1 here.

As Alan Rendall put it, "the study of these matters is still in a state of flux."

Subject: What precisely do we mean by a singularity anyway?
Date: Sat, 8 Sep 2007 16:51:27 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: Don Marolf <marolf@physics.ucsb.edu>
Cc: <schmekel@berkeley.edu>,
<garfinkl@oakland.edu>,
<comergl@slu.edu>,
<matt.visser@mcs.vuw.ac.nz>,
<giddings@physics.ucsb.edu>,
<banks@scipp.ucsc.edu>,
<hartle@physics.ucsb.edu>,
<pullin@lsu.edu>,
<jpereira@ift.unesp.br>,
Joshua Goldberg <goldberg@physics.syr.edu>

Don Marolf, MOG No. 30, Fall 2007 (arXiv:0709.0942v2), p. 26: "On the other hand, suppose that current expectations are wrong, and that all approaches eventually agree on at least the qualitative character of their predictions. Such a result would require an approach-independent explanation. As an optimistic theorist, I would expect its discovery to reveal some new and deep truth about the fundamental nature of quantum gravity."

Dear Dr. Marolf:

I believe an approach-independent explanation can be elaborated by resolving the issue of quasi-local energy,

http://www.god-does-not-play-dice.net/Trautman.html#dipole

This task was raised by Tullio Levi-Civita in 1917. Notice that I haven't yet received your reply to my email from Tue, 12 Sep 2006 19:32:04 +0300,

http://www.god-does-not-play-dice.net/arXiv.html#Marolf

I still don't know the reason why my paper on GWs was deleted by the moderators of physics.GR (or by you).

NB: If you wish to defend your beliefs, as stated in your email from Wed, 21 Sep 2005 15:06:31 -0700, please follow the first link above and find 1 (one) error.

I extend this offer to all recipients of this email. The task is on the table since 1917, again.

Looking forward to hearing from you,

Dimi Chakalov
--

Note: Take, for example, Steve Giddings' lecture "Observables in Quantum Gravity" (The Quantum Nature of Spacetime Singularities, KITP, January 8-26, 2007), Slide 3:

In QFT (all physics except gravity), there is the Measurement Problem inherited from QM, which Steve Giddings failed to mention, as well as the long standing puzzle with the vacuum energy, as stressed by Richard Feynman. Not surprisingly, S. Giddings encountered the severe problem mentioned at the end of his slide. As he and his colleagues acknowledged in "Observables in effective gravity", hep-th/0512200 v4:

"Moreover, locality is only recovered in an approximation, and is in general spoiled by both quantum and gravitational effects. Thus locality is both relative and approximate."

On September 13, 2006, I suggested to Giddings, Marolf, and Hartle to elaborate on the implications from their ‘pseudo-local’ observables for "GR astronomy", but I am seriously doubtful they have the guts to do it.

To show that locality can be both relative and exact, I will try to elaborate on the expression "the metric is treated as a field which not only affects, but also is affected by, the other fields present" (see above).