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Physics
Special and General Relativity
Thought Exp: Gen Relativity & Time Dilation
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[QUOTE="PeroK, post: 6428265, member: 493650"] Time dilation is not relevant here. First, we have an object (A, say) that emits two pulses of light in opposite directions. In A's reference frame both pulses move at speed ##c##, of course. Now, we have a frame of reference in which A is moving at nearly the speed of light. In this frame of reference, both light pulses will move at ##c## and A will move at ##v = 0.99c##, or whatever. There is not the same symmetry in this frame. The key to understanding this is [I]relativistic velocity addition[/I]. The formula for this is: $$u'= \frac{u + v}{1 + uv/c^2}$$ This is different from Newtonian velocity addition, which is simply ##u' = u + v##. Here ##u## is the velocity of a particle in one frame and ##v## is the relative velocity of that frame to a second frame; and ##u'## is the velocity of the particle in the second frame. A key point of this formula is that it keeps the speed of light [I]invariant [/I](this means the same in all reference frame - note that [I]conserved[/I] means it stays the same over time). I.e. if we put ##u = c##, then: $$u' = \frac{c + v}{1 + cv/c^2} = c \frac{1 + v/c}{1+ v/c} = c$$ And we see that indeed ##u' = c## and light has the same speed in all reference frames (independent of ##v##). If we apply it in your scenario, we see that the speed of both light pulses is ##c## in both frames. [/QUOTE]
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Special and General Relativity
Thought Exp: Gen Relativity & Time Dilation
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