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The second postulate of Special Relativity says:

As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.

But isn't it also valid for sound waves? I mean, a jet flying above the speed of sound will not generate waves that travel at V+U (where V is the jet's velocity and U the speed of sound), but waves that travel at U. Provided that Maxwell's laws show that light is a wave, what's the point of this postulate?

Claudi
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3 Answers3

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Light doesn't travel at $c+V$ (where $V$ is the speed of the source), it travels at $c$.

What's the difference? It means that if you're flying towards someone at a speed $V$ and you shine a light at them, you measure the light to travel away from you at a speed $c$, but the other person measures it to fly past them also at a speed $c$ (i.e. not $V+c$).

In the case of sound, the source and observer may disagree on the relative speed. The source will measure the sound to propagate at a speed $U-V$, whereas the observer will measure it to propagate at $U$.

lemon
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The point is that the considered postulate states that the speed of light in the vacuum is $c$ with respect to each and every 'inertial' observer. It is independent of not only the source that is emitting the considered light quanta but also of the observer who is observing it as long as it is an inertial observer.

It is true that for a given observer, in a given medium, the speed of sound is independent of the source that emits the sound. But as 'lemon' has described, the speed of the sound does depend on upon the observer even if it is independent of its source - but the speed of light is independent of the both of them.

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The assumption that the speed of light is independent of the speed of the light source is false but sounds reasonable, the reasonableness due to the fact that the assumption is valid for all waves other than light. However, when combined with the principle of relativity, this assumption entails that the speed of light is independent of the speed of the observer as well, a conclusion which is almost obviously absurd. When the initially stationary observer starts moving towards the light source with speed v, the frequency he measures shifts from f=c/λ to f'=(c+v)/λ, which can only mean that the speed of the light relative to the observer has shifted from c to c'=c+v.

Pentcho Valev
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