What does the constancy of speed of light mean?

[Ibix]

Thus generally the "speed of light" is that relative to and measured by the observer, but the "speed of sound" is that relative to the medium.

If you want a unique "speed of sound", yes, you have to define it that way.

There's nothing wrong with defining the speed of a sound wave as its speed relative to some observer, but then there isn't a particular value. It's more useful for everyone to know the speed of sound relative to the medium; then if you know your speed relative to the medium then you can figure out the speed relative to you.

This is a different behaviour to light, where the speed relative to you is always $c$. It's worth noting that the constant $c$ emerges from the maths of relativity whether light travels at that speed or not.

 

[thaiqi]

Thanks.

 

[bhobba]

The speed of light is both invariant and constant.

Of course true. But again I, for the OP's benefit, want to emphasize that purely from the symmetries of an inertial frame, having nothing to do with light, you get the Lorentz Transformations where the C in those equations is a speed that is the same for all observers. It could be infinity, in which case you get the Galilean Transformations - the usual transformations found in Newtonian Physics. The question is, is the C in the equations finite or infinite. If its finite then it really can be any value because you can change it by simply changing the units used.

Its relation to light is, interestingly, you can derive Maxwell's equations from Coulomb's Law and Relativity::
http://www.cse.secs.oakland.edu/haskell/Special Relativity and Maxwells Equations.pdf

Now we see that C must be finite otherwise many phenomena we know to be true would not happen eg you would not have magnetism or even the existence of light. So we see it is not the constancy of the speed of light that 'really' determines relativity. The very existence of light itself, magnetism and other EM phenomena, all described by Maxwell's equations, implies the C in relativity is finite, the speed of light, and is the same speed in all inertial frames.

So while it is not wrong to derive relativity as Einstein did from the axiom of the constancy of the speed of light, a deeper analysis shows that the very existence of EM phenomena, including light, tells us the C in the Lorentz Transformations is finite which implies its speed is the same in all inertial frames - and all the other EM phenomena.

Again, interestingly, if you read the first chapter of Schwinger's book on EM, you will see a derivation of Maxwell's equation from Coulomb's law and the existence of EM radiation. So the very existence of EM radiation, along with relativity, implies its speed is constant, and the C in the Lorentz Transformations is the speed of light.

Just as an aside most seem to have Jackson as their reference for Electromagnetism, but IMHO Schwinger is better and is my EM reference
https://www.amazon.com/dp/0738200565/?tag=pfamazon01-20

Because its so widely used Jackson it still worthwhile to also get. But he has some views I am not particularly happy with, such as his view derivations of Maxwell's equations are silly - at least in discussing it with someone they mentioned it to me. I hope the above shows that's not quite the case. I personally don't have a copy but am thinking of getting one.

Thanks
Bill