Special Relativity Explanation

Question

I'm in a relatively basic Physics class in university, and was reading the section in my textbook about The Principle of Relativity.

It says:

Einstein's Theory of Relativity ... added the conjecture that the speed of a beam of light must be the same as measured by observers in different frames of reference in uniform motion with respect to each other.

I'd like to start off and say I certainly don't doubt that. People much more familiar with relativistic physics take this as fact so I see no reason to pretend I've found a loophole in the fabric of reality.

I'm just wondering... how? How can I be moving at 0.9c relative to the Cosmic Microwave Background (which my textbook says is the most reliable inertial reference frame) and watch light go past me, in the same direction, at 1.0c? Doesn't that mean the light is moving at 1.9c relative to the CMB?

Further, the textbook says that, in the case of two or more observers traveling at different speeds, the observers will see that the light has a different color. Is that evidence of a Doppler effect? Doesn't that imply that to see different colors observers would have to be observing the light moving at different velocities than each other?

I've just been puzzling about this for a while now. I'm hoping someone more learned than me can chime in and help clear things up, because so far the best explanation I can think of is localized time dilation changing just how long a "second" is in order to ensure that the photons always move at c, but that just seems like such a convenient answer.

possible duplicate of Why and how is the speed of light in vacuum constant, i.e., independent of reference frame? — John Rennie, Jan 15 '15 at 07:25
This is the thrust of special relativity. No it does not mean the light is moving at 1.9c relative to the CMB! So the answer is: Keep reading your textbook ;) — , Jan 15 '15 at 09:14
There is such phenomena Time dilation and length construction, you can read about about it here I think there are answers to your questions. — Aram Tadevosyan, Jan 15 '15 at 07:24
@JohnRennie that link helps a lot, thanks. I was sure this question has been asked a bunch before, but I couldn't find anything that explains it well. It's a little disappointing that the answer is, essentially, "because," but that just means there's more to discover in the future I guess. — h3half, Jan 15 '15 at 16:35
@h3half: see my answer to What is so special about speed of light in vacuum?. The constancy of the speed of light is a consequence of a fundamental symmetry of the universe. — John Rennie, Jan 15 '15 at 16:38

score 2 · Answer 1 · answered Jan 15 '15 at 10:47

You're confused because you're holding two mutually contradicory postulates in mind. One is the one you mentioned that the speed of light is the same in every inertial reference frame. The other which you implicitly point out, is that the relation between speed measurements in two different inertial reference frames moving at relative speed v with respect to one another is given by adding or subtracting that speed.

Well, if both can not be right, and you are prepared to accept the first postulate, the second has to be wrong. And it indeed is.

What you're looking for is the Lorentz transformation.

Special Relativity Explanation

1 Answers1