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If you are in a flat space(time), i.e. without any source of gravitation, in a spaceship, and you emit a ray of light across the spaceship, both the spaceship and the light will be in the same frame of reference. The frame will be inertial - not accelerated - and therefore the light will follow a straight path. Yet if a boost is applied to the spaceship, it ...


This is how you do the calculation. The elapsed time on an observer's clock is called the proper time, $\tau$, and it is calculated by integrating the metric: $$ c^2d\tau^2 = \left(1-\frac{2GM}{c^2r}\right)c^2dt^2 - \frac{dr^2}{1-\frac{2GM}{c^2r}} - r^2d\theta^2 - r^2\sin^2\theta d\phi^2 $$ In this case we'll assume all motion is radial so $d\theta = ...


The fact that the clock near the earth would run continually slower - i.e. the difference between the two would grow the more time they are seperated - is enough to be equivalent to different rates of acceleration. It is not like it runs more slowly for at bit and then runs at the same rate as the other one, but slightly behind.


Your experiment looks ok to me. There is no resolution of the paradox, so it's one way to look at the root of the 'quantize gravity problem'. Another experiment with the same detector: If the detector is in on a shelf, when it drops off the shelf, it is supposed to mysteriously stop seeing gravitons, even though the 'flux' has not changed. Note that the ...

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