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There in fact is a large project underway to determine precisely this, as a test of Einstein's theory of relativity. It is called Gravity Probe B, and is an earth-orbiting satellite designed to remain in polar orbit over the Pacific Northwest for two years or so. It will use four extremely precise gyroscopes to measure space-time and changes in it, and whether the Earth 'drags' changes in space-time around with it as it orbits. One of the prime questions it aims to answer is whether or not gravity propagates instantaneously or at the speed of light.

It is possible for gravity to propagate instantaneously without violating any of the laws of relativity (or other physical laws) as long as it isn't possible to transmit information using this phenomenon. This would likely mean that gravity is not a wave or particle; if it were, then it would be subject to manipulation that could be used to transmit information faster than light. If, however, gravity is a 'bending' of space-time, then it would require other violations of 'law' to use it to transmit information - for example, in order to have a gravitic signal one would need to be able to create energy and/or matter, or to destroy the same such that it suddenly stopped bending space by its presence. Since energy cannot be created or destroyed, it would not be possible to send information using this effect.

http://einstein.stanford.edu/index.html

...it is a NASA mission planned for launch from Vandenberg AFB on a Delta-II rocket, sometime in fall 2002.

The following in response to a vanished writeup:

Energy does, in fact, 'have' gravity. Matter is condensed energy, as exemplified by E = mc2. Enough energy in one place bends space, just like matter. Although you can change matter into energy, absolutely right, that doesn't change anything! The 'center of mass' of this wave of matter and energy doesn't move faster than light. In a perfectly spherical explosion, it doesn't move at all. Ergo, such a conversion wouldn't tell us anything about gravity's travels.

We don't, in fact, know if gravitons exist. If they do, then yup, we have a problem with gravity moving FTL. However, if it isn't composed of gravitons but is rather a field distortion, then sure it could.

If a distortion, then (as we saw above) we can't transmit information FTL, since the only way to do that would be to create or destroy energy/matter so as to cause 'pulses' in the field. Since we're pretty sure we can't do that, we're still in the clear. If we could in fact drop mass into, say, hyperspace, so that it no longer affected our spacetime, then that would be the perfect experiment on the subject of gravity's speed.

Note: Okay, tdent has backed me to a wall. If gravity is FTL, you should be able to transmit information by semaphore, or by wagging a mass back and forth. tdent points out that in such a case, the vector of its gravitational field should change instantly, so that while it might require really really sensitive instrumentation to detect at long distances, there's no theoretical reason the change couldn't transmit information. Hm. Back to the metaphor drawing board.

One way of thinking of this is to consider what would happen if the sun were to suddenly wink out of existence.

As far as I understand it, one of the big differences between Newton's and Einstein's theories of gravity is in their treatment of this question.

Under Newton's theory, the earth changes path immediately and heads off in a straight line, tangent to its previous orbit (modulo the slight effects of other planetary bodies.)

Einstein, however, thought that the earth's path would not diverge for about 8 minutes (or whatever time it takes light to reach the earth from the sun.) This was (if my memory is correct) actually one of the considerations that led him to formulate his theory of relativity.

At any rate, the standard formulation of general relativity assumes this is true, and that gravitational effects propagate at the speed of light.

(update: 8/9/2002)

Although GR is one of the most well tested scientific theories, and it has passed every test so far, this aspect of the theory has not yet been tested - but it is due to be tested today (Sept 8, 2002). Physicists hope, by measuring the effect of the gravity of Jupiter on light from quasar QSO J0842+1835 (a very distant object), which will pass within about 3.7 arc seconds' angular distance from it, to resolve the question once and for all.

The perturbation of the light will be measured using "Very Long Baseline Interferometry" (VLBI) as proposed by Sergei Kopeikin in his letter Testing the propagation of gravity by very long baseline interferometry in Astrophysical Journal, 556 (1): L1-L5 Part 2, Jul 20 2001, where he says:

we emphasize that there are two relativistic parameters to be measured in the VLBI experiment in order to test the validity of general relativity -- the PPN parameter gamma and the gravity propagation parameter delta [...] The primary goal of the new experimental test of general relativity proposed in the present Letter is to set direct observational limits on the parameter delta that will measure the effect of retardation in the propagation of gravity by the moving Jupiter. According to the Einstein theory of relativity, one must expect that the numerical value of the parameter delta must be equal to zero.

Got that?

Me either. I guess what it means is that the exact timing of the wobble in the quasar's light caused by Jupiter's gravity, as Jupiter moves towards and past the quasar's position in the heavens, can be used to determine whether Jupiter's gravity is propagating as predicted by the theory.

Kopeikin himself has indicated he expects delta will be measured at zero, and most physicists will surely be very surprised if general relativity fails this test where it has passed so many others - the expectation is likely to be along the lines of "Ok, Einstein was right again. Back to work, everyone."

However, if the result diverges from the predictions of GR, and can be confirmed, physics will take a big step into uncharted territory. A theory will be required that makes all the predictions made by general relativity, except the predictions about frame dragging, which is where the propagation speed of gravity enters into the theory. Such theories are currently either very obscure or nonexistent. Additionally, the fortunes of gravitons - the so-far undetected particles which are hypothesised by particle physicists to transmit the gravitic force, as photons transmit the electromagnetic one, as indicated below, will surely take a severe turn for the worse.

Info about Kopeikin's proposal from the usenet newsgroup sci.physics.research, in the thread "Speed of gravity" -- A final resolution and, in particular articles <ajl94l\$c2n\$1@glue.ucr.edu> by John Baez and <Pine.GSO.4.42.0206160810080.27740-100000@clyde> by Stephen Speicher.

To the best of my knowledge (and I could be wrong), energy also has gravity, and is affected by it (see gravitational lensing). Because of this, it makes no difference that matter can be converted into energy; the energy still exerts the same gravitational influence.

I personally do not believe gravity can be transmitted instantaneously. The main reason for this is that, if you apply your Lorentz transformation to something moving at an infinite speed, you get some fairly ridiculous answers. Imaginary numbers coming out your ears. Some of them infinite. If you can explain to me how a graviton experiences imaginary time (in infinite quantities) I'll accept it.

Well, actually I probably won't. Rewrite quantum mechanics and come back to me.

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