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Imagine that we are in a rocket accelerating with some magnitude $a_1 = dx^2/d^2t$, also imagine that we have a stationary rocket ship in close proximity to ours, stationary relative to our reference frame, we will notice the stationary ship to measure time. (If we have a clock on board that ship which is visible to ours) at some time $t_0$.

Now the question leads to this, the time measured on our ship will be moving relative to the stationary ship, but the equivalence principle tells us that if we accelerate at some magnitude we can't tell it apart from gravity, but gravity bends spacetime in such a manner that time will be slowed relative to some reference frame, but if we compare the two clocks on these ships, ours and the stationary one, will our measurement account for the bending of spacetime due to the acceleration?

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  • $\begingroup$ I don't think this is the place for debate questions either... $\endgroup$ – gt6989b Aug 6 '15 at 20:27
  • $\begingroup$ @gt6989b Indeed. I forgot to mention that in my comment above. $\endgroup$ – wltrup Aug 6 '15 at 20:28
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"a stationary rocket ship in close proximity to ours, stationary relative to our reference frame"

If the two ships are stationary with respect to one another, then their clocks will run identically (in fact, all physics will be identical in both ships) unless there are actual sources of gravity with non-negligible tidal forces across the distance separating the ships, in which case any differences in the physics within the ships (beyond non-inertial effects) will be due to those tidal forces and not to any relative acceleration between the ships.

"will our measurement account for the bending of spacetime due to the acceleration?"

Acceleration doesn't bend space-time. Matter-energy distributions do.

You're misinterpreting the Equivalence Principle. The EP states that a uniform gravitation field is physically indistinguishable from a uniform acceleration. It does not say, nor imply, that a uniform acceleration is a source of gravity. Actual sources of gravity are not uniform since, for them to be uniform they would have to exist over an infinitely large domain.

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