If one is on a spaceship traveling through a 'very' curved section of space-time, are there experiments one could perform on the ship that would reveal measurable differences between the very curved space and the 'usual flat' space one experiences 'around' the Earth? Note, any straight ruler on the ship would still seem straight relative to a person on the ship. Would laser beams be distorted?
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$\begingroup$ Is one following a geodesic? $\endgroup$– JimCommented May 8, 2015 at 16:37
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$\begingroup$ I'm not sure? Would any discernible distortions be greater perpendicular to a geodesic? $\endgroup$– 201044Commented May 8, 2015 at 16:40
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$\begingroup$ Well, the equivalence principle should still hold, but beyond that, yes. Not being on a geodesic could feel very different from normal flat space. $\endgroup$– JimCommented May 8, 2015 at 16:43
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$\begingroup$ When you say distortions, that makes me worried. Curved space due to gravity does not mean space is actually curving around such that a ruler would look bent and warped. $\endgroup$– JimCommented May 8, 2015 at 16:44
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$\begingroup$ if the curvature was great enough would there not be a measurable acceleration? $\endgroup$– JaywalkerCommented May 8, 2015 at 16:46
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Assuming that the elements of a ruler are following geodesics, the distortion is governed by the Raychauduri equation (http://en.wikipedia.org/wiki/Raychaudhuri_equation).
If the space is highly curved the result is stresses due to the expansion or contraction of the different parts of the ruler following slightly different geodesics.
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$\begingroup$ So distortions to a ruler would be noticeable in the ship. But if the ship is traveling with uniform speed would this violate the principle of equivalence? $\endgroup$– 201044Commented May 8, 2015 at 17:02