Why does light travel at the speed of light?

[elfmotat]

And my replies to some of them contained phrases as "No. I have just said the contrary." Other of those posters wrote (about the same link that you are using now to defend your point): "Baez doesn't make a lot of sense to me"... I explained to another poster that that speed is the norm of the velocity, and that velocity is a three-vector not a four-vector.

 

And so on. Therefore, I am not going to accept your argument by evident reasons.

 

 

 

In my above demonstration of that the speed of light is globally c, I only forgot to say that I am using the standard four-velocity. Therefore v is the standard velocity and |v| the standard speed. I am so accustomed to use standards that I do not always emphasize it in my writings.

 

I ignored "the most important part" of your last post by reasons explained in the last part of my #67.

 

You're exceptionally good at dodging questions; have you considered politics?

 

This is what I want you to answer:

 

-What is "the standard four-velocity?" I've never heard of this before. How does this get around the fact that the four-velocity of a photon is undefined?

-What do you mean by "the relation between and ?" What relation exists between a general affine parameter and dt?

-What do you mean by "symmetries of the Schwarzschild metric," and why would symmetry in a particular vacuum solution imply constant speed in general?

-What does the following mean (please expand it out, or show it using more conventional notation):

-How do said the said relation between and and symmetries in the Schwarzschild solution imply the following:

-How does ds²=0 imply the following:

- (Most importantly) do you agree that, in my example, the person on the platform would measure the speed of light to differ from c? If so, how do you reconcile this with your belief that the speed of light in a vacuum is always c? If not, please point out the error(s) in my logic/calculation.

A discussion of equations of motion, clocks, etc. in general relativity is given in the section "The physical interpretation of the equations of point mechanics. Standard equations of motion. Standard simultaneity" found in Möller's classic textbook. Also relevant is the section "Propagation of light signals. Fermat's principle".

 

In both sections Möller computes the standard velocity and speed of a light particle. He uses another notation but his equation [math]\hat{w} = |\hat{\mathbf{w}}| = c[/math] is the equivalent of my last equation, |v| = c, in the demonstration #67.

 

Of course, Möller says the same in words:

 

we find that the standard speed of light is c in all directions and everywhere.

 

This result was waited in pure physical terms because v, the standard velocity, is a gauge-invariant three-vector.

 

I can't find either of those sections, nor that quote. Please provide page or section numbers.

Edited June 4, 2012 by elfmotat