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Gravity speed (I know it's been beat to death, apologies in advance)

  1. May 10, 2012 #1
    I know the general premise is that the "speed of gravity" is equal to that of light speed, but something that doesn't quite make sense to me is this;

    Space itself can, and does expand faster than the speed of light right? By proxy it should be able to contract faster than the speed of light. Since a massive object causes gravity by warping space-time around it, that process of warping space-time should also be capable of moving faster than light. Therefor if you could magically disappear a star or magically make a star, the reach of the gravity and it's effect on distant objects should be able to travel as fast as the universe is expanding or as fast as the universe is capable of expanding. So the speed of gravity so to speak should be limited only by the maximum expansion rate the universe itself is capable of attaining.

    Now I know this is wrong. People much smarter than I have worked on it and come to the conclusion that the correct answer is C. I'm hoping some of those people much smarter than I who read these forums can explain why that is.

    Thanks in advance!
     
  2. jcsd
  3. May 10, 2012 #2

    PeterDonis

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    That is one way of describing in ordinary language what happens in certain spacetimes, yes. But you have to be careful because you can't draw all the implications you might think you can from that statement. See below.

    Again, this can happen in certain spacetimes (the time reverses of the ones in which the description of "space expanding faster than the speed of light" can apply). But you have to be careful drawing implications.

    This is one of those implications that you can't draw. The "process of warping spacetime" in the spacetime around a massive object, as you are thinking of it, is *not* the same, and can't be usefully compared to, the "expansion of space" in the spacetimes referred to above. In the latter spacetimes, whatever stress-energy is present is distributed uniformly throughout space, so there is no "process of warping"--nothing "travels" from one point in space to another while "space is expanding".

    Rather than take a "magical" example which is physically self-contradictory, let's take an example which actually could, in principle, be realized. Start with a perfectly spherical massive body, with other "test bodies" orbiting around it. Now create some kind of disturbance inside the massive body that breaks the spherical symmetry--say we start some kind of explosion inside it that ejects matter in opposite directions along a particular axis (so total momentum remains zero). The breaking of the spherical symmetry will have an effect on the orbits of the test bodies; but those effects will *not* be "felt" by the test bodies--their orbits will not change--until light has had time to travel from the event where the explosion begins. So if the explosion happens at time t = 0, and a test body is orbiting at 1 AU (the distance from Earth to Sun), then that test body's orbit won't change until 8 minutes after the explosion. That is the sense in which the "speed of gravity" is c.

    How does this differ from the universe as a whole expanding? The massive body with test bodies orbiting it is a bound system; space does not "expand" at all in this system. Put another way, there is no way to tell, from observations confined within the system (i.e., no observing of light or other signals coming in from outside), whether it is in an expanding universe, a contracting universe, or a universe whose size is constant. The only way to tell that is to observe signals coming in from outside the system, from the rest of the universe. We say that "the universe is expanding" because that model best explains the data coming in from outside. But it's not something we can observe locally.
     
  4. May 10, 2012 #3
    In one interpretation of cosmology, distant galaxies at rest with the Hubble flow are moving away from us at superluminal velocities. In this forum we do not like superluminal anything, but that is the preferred way of thinking of things in the Cosmology forums. However, we can live the cosmological interpretation as long as we are clear on the caveats. First, no distant galaxy is exceeding the speed of light relative to local objects at rest with the Hubble flow or for that matter relative to any local objects. Secondly, radiation from our Solar system can catch up with the distant superluminal galaxies, without ever exceeding the local speed of light along the way. That may seem a little paradoxical. How can light travelling at the speed of light (of course) catch up with a distant galaxy travelling at say seven times the speed of light? Well the paradoxical nature comes about because we are playing fast and loose with local and distant measurements. As the light from our galaxy approaches the distant galaxy travelling at 7c away from us, the light is actually moving at 8c relative to us, using consistent distant measurement methods. The outward moving light is effectively accelerated outward by the expanding space it travels through, but without ever exceeding c as measured locally. Anyway, the point as I am sure you have figured out by now, is that gravitational changes do not have to exceed the speed of light locally, in order to influence distant and apparently superluminal receding objects. No need for superluminal gravity.
     
  5. May 11, 2012 #4
    OK, so lemme see if I got this right. Given our current understanding of the universe is correct, a viewer outside our universe and looking at it as a whole as if it it were a balloon, gravity would appear to travel faster than light. From our relative position it would appear to travel no faster than light. It's the same principle that that distant galaxies will eventually appear to be traveling away from us faster than light even though they are not moving faster than light. Again working on the same premise of two guys playing catch on a train will appear to be throwing the ball faster than they really are.
     
  6. May 11, 2012 #5

    PeterDonis

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    No, from such a viewpoint gravity, as a "force", does not "travel" at all.

    I suppose you could say that gravitational radiation "appears to travel faster than light", just as light itself does from this viewpoint. More precisely: take two "comoving" observers in the expanding universe and have one send a light signal to the other. If we take the distance that the two observers are apart (in the "comoving" frame) when the second one receives the light, and divide that by the time it takes the light to travel (according to either observer, it doesn't matter which because all "comoving" observers share the same "flow of time", so to speak), we get an answer that is larger than c. The same would be true if one observer emitted gravitational radiation that was then received by the other.
     
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