Black Holes, Singularities, Confusion

No, that does not work at all.Let's leave the quartz crystal alone, sitting in some suitable protective module. But you get on a space ship, and speed up to near c. Relative to you, the quartz is seen as moving at near c. You still observe the same slowdown. But we have left the quartz crystal alone. Nothing has changed in that system which could account for the change.

That would be the doppler effect time dilation.When you correct for the doppler effect, the relativistic time dilation remains. It is far easier to move the clock, than it is to move the observer. There isn't much doppler effect with GPS, because you are remaining at about the same distance from the GPS satellites. The time dilation is relativistic. There is an additional complication here. The GPS satellites are in a gravitational field, so one has to use GR, not just SR, to fully account for the effect. (Note, I'm far from an expert in GR).

As far as I know, most of the experimental data is with orbiting satelites. The situation is not symmetric, due to the different involvement of gravitation for the satellite and the ground based point. For a pure SR test, where there is symmetry, the two bodies rapidly move so far apart that measurement becomes difficult. The exception is in particle accelerators, where one can observe relativistic effects on the rapidly moving particles. But that's only possible for objects light enough to be accelerated to near c.I expect that cavediver knows more about what has actually been measured, and maybe it it will turn out that the kind of test you would like to see has been done.

Will you accept a mathematics explanation?"Curvature", as the term is used in relativity, is a mathematical term. It is defined in terms of the distance metric (as generalized to include time).To illustrate, consider a cylinder (the surface, not the solid). On the cylinder, we would measure distances as the shortest path along the cylinder. Mathematically, the cylinder is flat, so not at all curved. This corresponds to the fact that you cut cut down along the cylinder, and open it up so that it is flat, and you could do this without changing any distances (not counting those where the shortest path crosses the cut-line).Take out your atlas, and look at a Mercator projection map of the world. It is really an unwrapped cylinder. Think of it as a cylinder, with the left and right side taped together where they match. Now, let's suppose that we scrap our current way of measuring distance on earth. And, as a new distance metric, we use the old distance between the two places on the Mercator map. We could scale it, say one inch on the map = 100 miles on Earth. This will be a different distance metric than we ordinarily use. With this new metric, the north pole and the south pole will be an infinite distance away. With this new distance, the earth is flat.When physicists talk about curvature of space (or space-time), the metric they are using is based on light travel. The distance between two points is determined by the time it takes for light to travel between them. This was adopted as the standard for distance, following the Einstein conclusion that the velocity of light is the same for all observers.I hope that helps.

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