“Test of relativistic gravity for propulsion at the Large Hadron Collider”

Up first is Franklin Felber’s “Test of relativistic gravity for propulsion at the Large Hadron Collider” (available online: http://arxiv.org/abs/0910.1084)

My problem with this paper starts right with the second sentence of the introduction with this statement: “Within the weak-field approximation of general relativity, exact solutions have been derived for the gravitational field of a mass moving with arbitrary velocity and acceleration (Felber, 2005a).”

There are several points that should stick out in the mind of the reader. First, “weak-field approximation” and “exact solution” should not go in the same sentence. Perhaps, within the approximation it is exact, but it is not an exact solution (else it wouldn’t be an approximation). Second, “a mass moving with arbitrary velocity” is a pretty dangerous statement, because it suggests possibly ignoring the speed of light constraint.

Confusingly, when one follows the reference to the paper he is citing, “Weak ‘antigravity’ fields in general relativity”, we get another version of our initial point: “We recently derived and analyzed exact time-dependent field solutions of Einstein’s gravitational field equation for a spherical mass moving with arbitrarily high constant velocity”, where the ‘recent derivation’ in 2005 takes you to a paper from 2008 called, “Exact ‘antigravity-field’ solutions of Einstein’s equation”.

But back to the initial paper we are considering, and onto the third sentence: “The solutions indicated that a mass having a constant velocity greater than 3^-½ times the speed of light c gravitationally repels other masses at rest within a narrow cone.”

Totally ignoring the derivation of this result for the time being (which is not present in his paper or any of the initial citations), we will continue to analyze the language used here. The phrase “masses at rest” should stand out as odd to a relativist. Rest in terms of what, I wonder? Our arbitrarily fast, accelerating, mass? In what frame could the author possibly mean? “At rest” is a warning sign in any paper that claims to be written about relativity, because even basic students of special relativity should have the notion of ‘no absolute, well-defined state of rest’ drilled into them.

Fourth sentence: “At high Lorentz factors (γ >> 1), the force of repulsion in the forward direction is about -8γ⁵ times the Newtonian force.”

Again, simply looking at the language here, the phrase “Newtonian force” should jump out at you. What force are we talking about? In the Newtonian view of physics, we do refer to objects moving under the force of gravity, but in general relativity, we really should not. Gravity is simply a manifestation of the geometry of spacetime. An object moving along the curved spacetime manifold isn’t ‘moving under a force’, but rather, it is in inertial motion along a curved manifold. There is no force pushing objects out of straight paths, objects are still following the straightest path; gravity corresponds to the changes in the spacetime geometry along that path. Relativists should be careful not to ascribe a particle’s action to a ‘gravitational force’. While this is a pet peeve of mine, and a bad habit, good and respectable physicists do use the term “gravitational force”, partly out of habit, and partly because, in the Newtonian limit, it’s not so offensive.

Another quote to consider from the fourth sentence is, “in the forward direction”. Now our *Galilean* relativity should be telling us to be more precise with a statement like, but one can give the author the benefit of the doubt to assume he meant “forward” as along the path of our mass.

The second paragraph continually mentions this “exact-solution” to the Einstein equations, which is of course, just as dubious a claim as it was the first time the author made it. For those who aren’t familiar with the Einstein equations, they are non-linear PDEs that are quite difficult to solve exactly, which is why very few exact solutions exist (and they are all a big deal), and why most modern exact solutions are found numerically these days.

In the second paragraph, we have: “These exact ‘antigravity-field’ solutions were calculated from an exact metric first derived, but not analyzed, by (Hartle, Thorne and Price, 1986).”

Now, I am somewhat familiar with the reference he cites: “Black holes: The membrane paradigm”, edited by Thorne, Price, and MacDonald, but I am not familiar enough with the particular paper he citing, “Gravitational Interaction of a Black Hole with Distant Bodies” (by Hartle, Thorne, and Price) to know which “exact metric” he is referring to. Nevertheless, I do know that that particular paper was treating the “The long-term, secular evolution of a black hole weakly perturbed by gravitational forces of objects far from the event horizon is examined using the 3+1 formalism of the membrane paradigm”, which makes it fairly hard to guess what he would be referencing there.

It’s a little surprising that if Felber was actually working within the Membrane paradigm, that the word “membrane” doesn’t appear anywhere in the text of his paper, or “black hole”, or “event horizon”, for that matter. While often consequences derived from the study of event horizons are applicable in many other settings, it’s hard to see the connection the author is making in this case.

In Hartle, Thorne, and Price, an “exact analytical solution is found for the lapse, shift and spatial metric of a moving, nonrotating black hole” which leads Felber to claim, “The exact results confirm that a large mass moving faster than 3^-½c could serve as a driver to accelerate a much smaller payload from rest to a good fraction of the speed of light.” While I know I said I was just going to address the language here, I must point out that this claim/inference Felber is making seems quite without merit. He also doesn’t bother to assert how he has come to such a conclusion.

Onto the opening sentence of the third paragraph of the introduction: “The exact results are consistent with the repulsion of relativistic particles by a static Schwarzschild field, discovered
by (Hilbert, 1924).” Interestingly, his first attempt to back his claims up, outside of referencing himself or the strange appeal to Hartle, Thorne, and Price, comes in the form of a scan of section of Hilbert’s German version of his memoir, Die Grundlagen der Physik. Now, my German is pretty rusty, but Felber does cite a recent, English account of Hilbert’s curious result here: http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.1578v1.pdf.

Instead of going over the whole debate on gravitation repulsion, I’ll direct any curious reader to the paper that I believe should be the current authority on the topic. It is “Gravitational repulsion in the Schwarzschild field”, by McGruder (Phys. Rev. D 25, 3191 - 3194 (1982)). Very nicely, he goes over the historical background of the initial results of gravitational repulsion and the great number of papers that followed them. A small point to mention, Hilbert’s results, found independently by Bauer, were for particles near the Schwarzschild radius. Later, McVittie and Jaffe and Shapiro showed that repulsion could occur anywhere in the Schwarzschild field, so long as the total particle velocity was greater than 2^-½c, not 3^-½c, like Felber is using.

Anyway, McGruder concludes an important result, which shouldn’t be a surprise these days to people who are familiar with similar solutions, that “gravitational repulsion can occur in the Schwarzschild field; but, it can only be detected by an observer whose meter sticks and clocks are not affected by gravity”. The important final line of his conclusion is, “that gravitational repulsion is not a function of the total particle velocity or energy; rather, its occurrence depends on the relationship between the transverse and radial velocity.” Unfortunately, it seems as if Felber is not familar with this work (ie. didn't do a google search of "repulsive gravity").

Now back to Felber: Nowhere near finished with the introduction, we have come to some fairly major issues. He is using a metric (although I see no evidence of him actually ‘using’ it anywhere), taken from the Membrane paradigm (not for a Schwarzschild field), using out of date results that only apply to near the Schwarzschild radius, and a very faulty interpretation of how these results can be interpreted/observed.

The ‘meat’ of the paper is his outline for an experiment to test his notion of gravitational repulsion at the LHC… so it can be assessed for the “potential of relativistic ‘antigravity’ for propulsion of payloads in the distant future.” Now, this claim seems so fanciful on it's own, that many readers wouldn't have bothered to give Felber a chance. Ruling something out, purely because it doesn't fit with conventional knowledge is bad science. However, sloppy mathematics, ignoring current research, poor foundations, and leavings things as undefined as possible is also bad science.

-S.C. Kavassalis