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serp777
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Since the most distant galaxies appear to be faster than the speed of light, due to the insertion of new space, does this mean that galaxies haven't actually gained any velocity as the universe accelerates?
Usually you want to calculate velocities locally. Calculating relative velocity of something which is half way across universe will not work like you'd expect, because velocity is a vector, which lives on a curved surface. If you want to compare velocities on two different points, you have to first move them to the same point (parallel transport, if you're familiar with the jargon), and if you do this in the case of expanding universe, you find that on average, the galaxies are not moving.
Of course, nothing stops you from talking about some sort of apparent velocity, where you forget about the curvature of the universe and just calculate what you see. You just cant' expect the apparent velocity to satisfy the usual rules, like v<c.
The apparent velocity is simply a logical conclusion: because of acceleration, at a certain point, the distance at which the the galaxy moves over a period of times is greater than light would travel normally. Since the two galaxies accelerate at the same rate, you can calculate every instantaneous position from a central reference point, and thus you know the two galaxies relative speed, which looks v>c.
So let's take a concrete example. Suppose you're an observer on the north pole of the earth, and a car is driving at a constant velocity southwards. Now, if the surface of the Earth were a manifold, the car would always move on a straight line in it's own reference frame. But viewed from north pole, it seems that it's motion is accelerating because it's moving on a curved surface. The apparent velocity of the car changes, while physical (local) velocity remains constant.
This makes sense, but doesn't this assume that the universe is in fact curved, and not infinite etc?
Since the most distant galaxies appear to be faster than the speed of light, due to the insertion of new space, does this mean that galaxies haven't actually gained any velocity as the universe accelerates?