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The two different formulas are based on different assumptions. The time dilation formula assumes that there are two events in spacetime and that the two events are in the same position in one reference frame. The length contraction formula assumes that there are two worldlines in spacetime and that the two worldlines are at rest in one reference frame. For ...


7

Light itself moves only through space, so it doesn't move at all in time. I think this is where your misunderstanding lies. In relativity, elapsed time depends on the reference frame in which it is measured. It is true that the proper time along a path followed by a light ray in vacuum is constant. So, relative to its own reference frame no time elapses for ...


4

From this and your previous question, I suspect your confusion stems from the interpretation of $L$ in the length contraction formula. In fact this is something that confused me a lot when I was starting out. Consider two observers attached to frames $S$ and $S^\prime$, with $S^\prime$ moving at speed $v$ relative to $S$ in the $x$-direction. Let their ...


2

Curvature represents tidal effects, and the equivalence principle is by definition only applicable to regions of spacetime where tidal effects are too small to notice. So the equivalence principle on its own cannot tell you about curvature. However, if you couple the equivalence principle with some basic observations then you can infer that curvature is ...


2

The choice of Riemannian metric $h_{\mu \nu}$ is itself arbitrary, since there are multiple inequivalent rank-2 non-degenerate tensors on an arbitrary space; and different choices of $h_{\mu \nu}$ will lead to different "preferred time directions." For example, consider the following two rank-2 tensors on Minkowski space with coordinates $t$, $x$, ...


2

This might just be vocabulary, but you do not have absolute time even in special relativity. In classical mechanics, absolute time means that if you synchronizes everybody's clocks, they stay synchronized. It doesn't matter which frame of reference you use, everybody agrees on what time it is. You are getting at a similar idea by choosing one frame of ...


1

A point to bear in mind is that motion can only be defined relatively. The concept of absolute rest is meaningless- it is directly comparable to the concept of absolute height: there always has to be a datum point from which a height is measured. To extend the analogy, the concept of objective simultaneity is no more meaningful than the concept of level. If ...


1

It may help to look at a case where both length contraction and time dilation are relevant in analyzing the motion of light, and how the formulas are consistent when correctly applied. Consider a "light clock", a channel in which a light pulse reflects back and forth. In its rest frame, the channel has length $0.5$ and so light takes time $1$ to ...


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