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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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    The difference is that sound travels through a medium, whereas there's no luminiferous aether. – lemon Jul 05 '16 at 08:15
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    The point you are trying to make is not clear. Yes, the speed of sound is constant relative to the medium, not the source nor the observer. So what? Are you asking a question about sound or about the postulates of SR? – sammy gerbil Jul 05 '16 at 08:17
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    @lemon So, the key point of the postulate is not that the speed of light is independent of the frame of reference (which could be assumed as "normal" provided that light is a wave) but that it actually propagates at constant speed without the need of a medium. – Claudi Jul 05 '16 at 08:19
  • @sammygerbil I'm asking about what's the important point of the second postulate: that light propagates without a medium or that it does at constant speed. But it's fine now: the key is that light propagates without the need of a medium or aether, but it does at constant speed like a "usual" wave that actually propagates through a medium. – Claudi Jul 05 '16 at 08:22
  • @sammygerbil I just gave more importance to the fact that the speed of light was independent of the reference frame. – Claudi Jul 05 '16 at 08:23
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    Just to set the physical record straight: Maxwell's equations don't say anything about light. One has to come up with experimental validation that light behaves according to Maxwell's equations, which isn't completely trivial, since one can't actually measure E and B-field components on light directly. Sound waves, on the other hand, do not behave according to these equations. They behave according to the equations of thermodynamics and fluid mechanics. – CuriousOne Jul 05 '16 at 08:27
  • The "empty space" part makes it not apply to sound. – Devsman Jul 05 '16 at 13:26
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    @Claudix, i have asked the same basic question about the 2nd postulate. . and that was a repeat of another question. i am still unsatisfied with the answers. seems to me that if *all* of the physics is the same for the two inertial observers (that are in motion relative to each other), that means that both have to experience the same $\mu_0$ and the same $\epsilon_0$. – robert bristow-johnson Jul 06 '16 at 01:06

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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  • I see... So actually sound waves do not travel at the same speed when measured from the source and an observer? – Claudi Jul 05 '16 at 08:27
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    @Claudix That's correct. – lemon Jul 05 '16 at 08:32
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    Imagine two people conversing within a super-sonic Concorde. All of the air within inside the plane will be traveling at supersonic speed relative to air outside the plane, but will be essentially stationary relative to the passengers. Consequently, the propagation of sound within the plane will be unaffected by the speed at which it is traveling. – supercat Jul 05 '16 at 18:48
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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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  • EM radiation does not undergo doppler shifts with respect to observers and sources in relative motion. Michelson and Morley's experiment in 1887 demonstrated this pretty conclusively. You say that light waves undergo such a frequency shift -- have you actually seen this? I bet not... – Zorawar Jul 05 '16 at 16:11
  • "EM radiation does not undergo doppler shifts with respect to observers" – Pentcho Valev Jul 05 '16 at 16:38
  • "EM radiation does not undergo doppler shifts with respect to observers". Not true. See this: http://physics.bu.edu/~redner/211-sp06/class19/class19_doppler.html "Let's say you, the observer, now move toward the source with velocity vO. You encounter more waves per unit time than you did before. Relative to you, the waves travel at a higher speed: v'=v+vO. The frequency of the waves you detect is higher, and is given by: f'=v'/λ=(v+vO)/λ." – Pentcho Valev Jul 05 '16 at 16:48
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    The speed of light does not change - it is the wavelength that changes. This is a critical distinction. – J... Jul 05 '16 at 18:49
  • "The speed of light does not change - it is the wavelength that changes." The observer starts moving towards the source, and the wavelength of the light he is going to meet miraculously changes so that the speed of the light relative to the observer can remain unchanged? Isn't that too absurd? See the quotation above: "Let's say you, the observer, now move toward the source with velocity vO. You encounter more waves per unit time than you did before. Relative to you, the waves travel at a higher speed: v'=v+vO." – Pentcho Valev Jul 05 '16 at 19:38
  • It certainly seemed absurd when Einstein asserted this cornerstone of the Special Theory of Relativity in 1905. – Don Branson Jul 05 '16 at 20:15
  • @PentchoValev "You encounter more waves per unit time than you did before. Relative to you, the waves travel at a higher speed" - no, they have a higher frequency. They still travel at the same speed. – J... Jul 05 '16 at 21:07
  • @PentchoValev: Yes, sorry, for some reason I was completely mixed up and made a huge error: it does indeed undergo a doppler effect. The point that I should have originally said is that the result is not the classical one for waves but rather the relativistic result, which is not what you have above. – Zorawar Jul 05 '16 at 21:14
  • @PentchoValev: "The observer starts moving towards the source, and the wavelength of the light he is going to meet miraculously changes so that the speed of the light relative to the observer can remain unchanged? Isn't that too absurd?" Who's to judge what nature chooses to do? Lorentz contraction and time dilation effects occur and the effect is that the speed of light is constant. (Or, you can view it the other way round and take the speed of light to be constant as the fundamental principle and everything else is just an effect.) – Zorawar Jul 05 '16 at 21:20
  • " ... the assumption ... that the speed of light is independent of the speed of the light source is false ... is valid for all waves other than light. " There's a lotta double negatives in that. Might make it hard to parse your meaning. So @PentchoValev, is " ... the assumption ... valid... that the speed of [gravitational waves] is independent of the speed of the [gravity wave] source is false." ?? – robert bristow-johnson Jul 06 '16 at 00:50
  • so putting it another way without all of the double negatives, @PentchoValev, is it true or false that the speed of propagation of a light beam depends on the speed of the source of the light beam?? and is it is it true or false that the speed of propagation of a gravity wave depends on the speed of the source of the gravity wave?? please answer "Yes, the wave speed depends on the source of the wave." or "No, the wave speed does not depend on the source of the wave." and please answer for 1. light waves, 2. sound waves, 3. gravity waves. – robert bristow-johnson Jul 06 '16 at 00:58
  • Why do you use the phrase "almost obviously absurd" to describe a proposition that almost every serious physicist in the world believes, and which is supported by tons and tons of empirical evidence? – Dawood ibn Kareem Aug 01 '16 at 03:06