Principle of Relativity violation

[haroldholt]

This has been bugging me for a while and it may seem like a rather stupid question. I've been reading "Relativity" by Einstein and in section 7 of special relativity (the apparent incompatibility of the law of propagation of light with the principle of relativity) Einstein describes a thought experiment in which a ray of light is sent along a train track and a train is traveling in the same direction as the ray but obviously at a much slower velocity. He then goes on to say that we would expect the velocity of the ray of light relative to the train to come out to w = c - v. I understand it up to this point, but what I don't understand is why this is a violation of the principle or relativity.

As stupid as this may sound I would appreciate any help. I get the feeling that the answer is simple but for some reason I'm just missing it.

 

[anantchowdhary]

The speed of light is the same as measured in every frame.Therefore,if we measure the speed of light in a classical sense...It is a violation of relativity as you would expect the measured speeds to differ

 

[haroldholt]

But if we were to replace the ray of light with say a bird, then by adding velocities this would not violate the principle of relativity, would it?

 

[Doc Al]

He then goes on to say that we would expect the velocity of the ray of light relative to the train to come out to w = c - v. I understand it up to this point, but what I don't understand is why this is a violation of the principle or relativity.

I don't have that book handy to check the exact reference, but w = c - v is the expectation of Galilean relativity. But we know that the speed of light is independent of reference frame--a fact that contradicts this prediction of the (pre-Einstein) principle of relativity. Of course, the answer is to realize that Galilean relativity (and the Galilean addition of velocity formula) must be replaced with special relativity and its new way to add velocities.

 

[JesseM]

He then goes on to say that we would expect the velocity of the ray of light relative to the train to come out to w = c - v. I understand it up to this point, but what I don't understand is why this is a violation of the principle or relativity.

I think it's only a violation of the principle of relativity if you assume that Maxwell's laws of electromagnetism are valid in at least one frame, since Maxwell's laws predict that the speed of electromagnetic waves is always c regardless of the motion of the emitter. In the 19th century it was imagined that light waves were vibrations in a physical medium called the "aether", and that just as sound waves travel at a constant speed in the rest frame of the air, so light waves would travel at a constant speed in the rest frame of the aether. But if light waves traveled at different speeds in other frames (just as a person moving relative to the air measures sound waves moving at different speeds in different directions), this would be a violation of the principle of relativity, which says that the fundamental laws of physics should work the same way in every frame (assuming you consider Maxwell's laws to be fundamental rather than just local descriptions of how waves move in a particular physical substance like with sound waves).

 

[haroldholt]

So the principle of relativity assumes that for electromagnetic waves the velocity of light is invariant between reference frames? And that's why w = c - v is a violation of the principle of relativity?

 

[JesseM]

So the principle of relativity assumes that for electromagnetic waves the velocity of light is invariant between reference frames? And that's why w = c - v is a violation of the principle of relativity?

The principle of relativity just says that all the fundamental laws of physics should work the same way in every inertial frame. Maxwell's laws predict that electromagnetic waves always move at c, but like I said, before Einstein it was thought that Maxwell's laws only held exactly in the rest frame of the aether. But the principle of relativity suggests that if Maxwell's laws hold exactly in one inertial frame, they should hold exactly in every inertial frame, ruling out a violation of Maxwell's laws like electromagnetic waves moving at some speed other than c.

 

[haroldholt]

Which is basically what I said isn't it? That the principle of relativity takes into account Maxwell's equations and says that the velocity of light should be the speed c in all inertial frames? And that's why w = c - v violates the principle of relativity because it goes against Maxwell's equations and therefore the principle of relativity?

 

[JesseM]

Which is basically what I said isn't it?

Yeah, basically, I just wanted to make sure it was clear that the principle of relativity isn't specifically about Maxwell's laws, but rather about all fundamental laws of nature working the same in every inertial frame, with Maxwell's laws just being a special case.

 

[haroldholt]

Ok, thanks heaps for the help. It's really appreciated