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Years ago, my brother and I had an argument where I was trying to convince him that nothing could travel faster than the speed of light. I was pursuing this in the context of Special Relativity. My main thought was to contrast the behaviour of light to the behaviour of baseballs thrown from train-cars, say. To me, this is an interesting and surprising feature, and I thought he'd be interested.

Instead, he turned the argument into "you don't really know that nothing can go faster than light". Over the years, we've gone back and forth where he'll claim that some new result proves that I was wrong. I've mostly been dismissive, since the cites are mostly pop-sci or will say something like there might be some 1 part in 10^17 discrepancy, or something.

So, recently, I sent him the Wikipedia article on Metric Expansion, and he shot back with "see, matter is traveling faster than the speed of light."

Is this an accurate statement, or does it hinge on interpreting "traveling"? I.e. one can make a distinction between traveling through space, and space itself expanding.

Was I wrong to say (again, according to GR not SR) "nothing can travel faster than the speed of light" (ignoring tiny fluctuations, and according to currently known physics)?

Qmechanic
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Jabavu Adams
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    You won't be wrong. But working with non flat spaces, you have to add "locally". You can always choose locally flat coordinate frame in which nothing can move faster than "c". I guess you have encountered an analogy with an inflating balloon. Two points there are not really traveling, they move relative to each other simply because there is constantly appearing new "space" between the two points – Kosm Feb 12 '16 at 03:26
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    I'll specify what "locally" means. Imagine a photon traveling through a warped space from A to B. Then imagine some other particle traveling through exactly the same warped space, again, from A to B. Then the particle cannot come to the point B faster that the photon. But if the photon traveled through an expanding space, and the particle - through the static, then it may come in less time. – Kosm Feb 12 '16 at 03:45
  • @Kosm when you write "it may come in less time", does "it" refer to the photon or to the particle? – Jabavu Adams Feb 12 '16 at 09:35
  • to the particle. It can "outrun" the photon, but the photon will have covered longer distance (points A and B are the same!), since it moved through an expanding space, so its not quite fair to say "outrun". – Kosm Feb 12 '16 at 13:35
  • Possible duplicates: http://physics.stackexchange.com/q/26549/2451 and links therein. – Qmechanic Feb 17 '16 at 17:38
  • Just a quick comment to @Kosm above: Such is not the case when there is curvature, you CANNOT construct a Minkowski coordinate system in an open nhd of a general point in a curved spacetime, since there may be cross-terms that do not vanish. A prime example is the Kerr metric, where you simply CANNOT construct Minkowski coordinates in the nhd of a point, for the simple reason that the cross-term (say in t and phi) cannot be transformed away. Of course you can introduce Minkowski coordinates in the TANGENT space, because it is by definition flat. – Dr. Ikjyot Singh Kohli Feb 17 '16 at 17:45
  • @Dr.IkjyotSinghKohli so, the Christeffel symbols cannot be set to zero? – Kosm Feb 18 '16 at 03:19
  • @Kosm Ahh. But, to achieve true "flatness", it is not enough to simply set the Christoffel symbols to zero, but their derivatives as well! :) – Dr. Ikjyot Singh Kohli Feb 18 '16 at 04:18
  • Oh, i see you mentioned open neighborhood of a point. But doesn't locally flat mean a possibility of a flat metric at a given point? – Kosm Feb 18 '16 at 04:36

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