In physics, the speed of a wave is defined independently from the speed of its source.
Then why did Einstein say that the speed of lightwaves is independent of their source – why not claim that the speed of any wave is independent of its source?
The speed of sound in air is approximately 330 meters per second, while the speed of a wave in an ideal gas is given by $\sqrt{\gamma \frac{RT}{M}}$ (where $R$ is the general gas-constant, $T$ is the temperature of the gas, $M$ its molar mass, and $\gamma$ a property of the gas itself).
Why are lightwaves special?
To answer this question, let’s compare what happens to the sound of a car when it:
- is standing still relative to us, and
- is driving toward us at a speed of 30 meters per second (108 km per hour).
Rotating parts inside a car engine move much faster than the car itself — often comparable to, or even faster than, the average molecular speed in air (about 500 meters per second). The effect of the car’s own speed is negligibly small. Even so, both the speed of the car and the speed of the car’s internal components have a very small influence on the sound vibrations that are transmitted to the medium (air): the speed of the wave will be slightly higher than the usual speed of sound in air very near the car.
Conclusion: the speed of a sound wave is indeed dependent on the speed of the source of the wave, but in everyday life this is not noticeable.
Everywhere in physics (including in Einstein’s theory), the speed of a wave is determined by the medium through which that wave propagates. What is special about light is that it is a wave that does not need a medium – that is why the speed of light in a vacuum is a constant.
Read this blogpost to learn what the mathematical consequenses are of the assumption that the speed of light is independent of the speed of its source – it is the same in all reference frames.
Mathematical details of special relativity:
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