garys_2k said:
Gravity is the equivalent of acceleration, according to SR. No test can tell the difference.
Back up a second here. First off, special relativity does not (and in fact cannot) address gravity. Special relativity can tell us nothing about gravity. It is explicitly a description of space WITHOUT gravity.
But more critically, you're actually getting the comparison slightly wrong, and the distinction DOES matter. An accelerating frame is equivalent to a stationary frame in a uniform gravitational field. That requirement for a uniform field is an ABSOLUTELY critical part. That's why we cannot use special relativity to describe gravity, because gravity is NOT uniform. To get slightly technical, the acceleration picture of gravity is only a local picture, and describes the tangent space at the point you're interested in, but it is NOT sufficient to describe the complete effects of non-uniform gravitational fields. It is precisely because gravity is NOT uniform that a whole new description of its effects is needed, which is where GR comes from.
Gravity has been shown, in accordance with GR, to cause time dialation. GPS clocks are set to accommodate for the fact that they're not as far down in earth's "gravity well." Clocks run faster out in space due to less gravity in that environment compared with clocks on the earth's surface.
Not quite. When comparing clock rates at different locations, it's really the gravitational potential that matters, not simply the gravitational field. And the distinction is important. If you put a clock at the center of the earth, there would be ZERO gravity there (ignoring the sun, etc. for simplicity), but it would run SLOWER than a clock at the surface of the earth, because it would still be at a lower gravitational potential.
So, does acceleration cause (by GR) time dialation? I can find no references that this has ever been tested. Have there been tests of acceleration (either linear or centripital) causing time changes?
Sort of, but in the case of acceleration (not gravity), it only applies when the observer is accelerating. For example, if you take two obervers with clocks, put one of them, say, 1 km in front of the other, and then accelerate both of them at the same rate, after a while the observer in the back will start to say that the clock of the observer in front is running faster than his. But he will ALSO start to say that the distance between them is increasing. An observer who was stationary in their starting rest frame (the only reference frame where they start accelerating at the same time), however, will NOT agree with this, and will state that their clocks are running at the same speed, and they remain separated by the same distance. The accelerating oberver conflicts with this because in the moving reference frame, they did NOT both start accelerating at the same time.
In short, yes, you can replicate some of this. But in the absence of gravity, you NEVER need to treat acceleration as anything distinct. There are NO effects arrising from acceleration itself that cannot be understood as simply changing reference frames.
I guess the bottom line question: Would a clock in a centrifuge run at a different time than one sitting on the table next to it? I think it should (via gravity = acceleration EP), but can find nothing to back up that assumption.
Yes, a clock running in a centrifuge would run slower than one sitting on the table next to it. But actually, you missed the important question, because this is really just a velocity time dilation problem, and here's how you can tell the difference. Take two centrifuges, one with a radius of 1 meter, one with a radius of 2 meters. Now put clocks in them spin them up such that they both have the SAME tangential velocity. The clock in the 1-meter centrifuge will experience twice the acceleration of the 2-meter centrifuge. So they have the same instantaneous speed with respect to the table-bound clock, but different accelerations. Special relativity tells us that BOTH centrifuge clocks will run at the SAME rate, and both will run slower than the table-bound clock. Acceleration, per se, isn't what's slowing them down.
For a more mathematical explanation, in special relativity, the space-time metric (the length between points in spacetime) looks like:
s^2 = x^2 + y^2 + z^2 - (ct)^2
where s^2 is negative for time-like separations. To find out the length of time experienced by a clock, you basically just integrate this equation (using ds, dx, dy, dz, and dt instead) along the trajectory the clock takes through space-time, and the time is given by |s|/c. Velocity matters, since that gives you the relationship dx/dt, etc, and so you can use velocity to convert your integral into an integral over dt only. But acceleration, which is (d^2)x/(dt)^2, doesn't come into this calculation directly, it only matters in that the velocity you use isn't constant any longer. In the case of a centrifuge, however, it simplifies because while velocity changes, the magnitude doesn't, and so you can basically ignore acceleration completely.
