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I am wondering whether or not literally anything can travel faster than the speed of light. For example, if gravity from a star immediately ceases to have an effect if it suddenly and magically vanishes, then this is an example of information traveling faster than the speed of light.

However, if a star's gravity is still present when it disappears, then we have the curious case of things being attracted towards stuff that doesn't exist!

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The continuation of gravitational effects after the star has dissappeared is no different than the continuation of light from the same star. When we witness supernovae, we can deduce that the light that we had previously seen from that star had been emitted from a star that "no longer exists" without requiring any magic. – AdamRedwine Aug 20 '12 at 20:41
No material object that may transmit genuine information may travel faster than light; mirages such as shadows are not constrained in this way, however. Also, the equations of general relativity imply that a star can't just disappear. Einstein's equations (for the field caused by mass distributions) says that the Einstein tensor is proportional to the stress-energy tensor, and because the Einstein tensor has a vanishing divergence (an identity requiring no assumptions), the stress-energy tensor (i.e. energy-mass and momentum) has to be (covariantly) conserved, too. – Luboš Motl Aug 20 '12 at 20:54
Thanks for the responses. Can you clarify what is meant by a "shadow"? – Nicholas Hill Aug 20 '12 at 20:58

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The speed of gravitational waves is finite and very likely the speed of light. If a star (for instance the Sun) suddenly disappeared, we would not immediately feel anything. Assuming the speed of gravitational waves is the speed of light, during more or less eight minutes (in the case of the Sun), we would see the Sun and feel its gravitational field.

As long as Special Relativity and causality be exact concepts, nothing able to carry information can travel faster than light.

However, shadows and other things can travel faster than light. You can compute the speed of the spot of a laser that has been aimed at the surface of the Moon and you will realize that can be faster than light, but this spot cannot carry information.

Let me add that thanks to this effect (the finiteness of signal speed propagation), we can study the remote past of the universe (close to its origin) by means of looking at very distant objects.

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This is not a good answer--- you can't make mass suddenly disappear in GR, it makes the equations inconsistent. – Ron Maimon Aug 21 '12 at 3:24
I know that GR does not allow things to just disappear. I though —and I think— that the spirit of the question was about the finiteness of gravity waves speed. The answer is correct, although surely there are more complete answers. Note the conditional "if a star ...." in my answer and try to understand what the OP is asking. – drake Aug 21 '12 at 3:41
I agree, but one should go the extra mile to make the answers completely correct, so that they serve a good pedagogical purpose. The problem can be asked in Coulomb gauge in electromagnetism--- if you suddenly made the electron lose its charge, will the electrostatic field suddenly vanish? The answer is yes in Coulomb gauge, and this is why you need conservation of charge in EM. – Ron Maimon Aug 21 '12 at 3:44
OK, I'll try to do that, I know you often go the extra mile and I've learnt from you a lot during the last month. – drake Aug 21 '12 at 5:09
Your statement about electrodynamics is a little misleading because you need gauge freedom to fix a gauge and you need charge conservation to have gauge freedom and if you have gauge freedom then physical effects are independent of the particular gauge chosen (although I know what you have in mind is that in Coulomb gauge you have a Poisson equation which is "static"). But I agree that if charge is not conserved (and then one needs to modify Maxwell equations, deleting the current-displacement for example) then one has action at distance effects like the one you say. – drake Aug 21 '12 at 5:09
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Using the term "gravity" as though it were a material substance that can be given and taken away is conceptually incorrect. All matter has the property of "gravitational attraction" by which it is attracted to all other matter. This property cannot be switched off, so it's not realistic to imagine that it can be. If you're asking whether or not a star's gravitational attraction exists whether or not the star is luminous enough to be visible, the answer is certainly yes.

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You can't make the sun disappear. The equations of General Relativity guarantee that the local divergence of the stress tensor is zero. What you can do is convert all the atoms in the sun to gravitons, which rush out at the speed of light. In this case, the gravity is unchanged until the graviton wave hits you.

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There is comment with the same content of this answer, Ron. By the way, do you think it is necessary to mention the hypothetical quanta of the gravitational field to answer this question? Classical gravity is enough and you know that. – drake Aug 21 '12 at 3:45
@drake: You are right, I was just saying this to give the closest thing to vanishing I could think of. Just say something along the lines of this answer in yours, and I'll delete it. – Ron Maimon Aug 21 '12 at 3:50
I don't want you to delate your answer. The content is in two comments but sometimes I see comments deleted so it is better if it is in n answer. And I think the content is relevant and important. – drake Aug 21 '12 at 5:12

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