# Einstein's Derivation, why is light velocity c-v and c+v?

1. Aug 20, 2005

### Perspicacious

Why is light velocity c-v and c+v in Einstein's derivation, On the Electrodynamics of Moving Bodies (Annalen der Physik vol XVII 1905 p 891-921)?

2. Aug 20, 2005

### robphy

If you are referring to
§ 2. On the Relativity of Lengths and Times
$$t_B - t_A = \displaystyle \frac{r_{AB}}{c-v}$$ and $$t'_A - t_B = \displaystyle \frac{r_{AB}}{c+v}$$
(see http://www.fourmilab.ch/etexts/einstein/specrel/www/ ),
light velocity is c.
$$t_B - t_A = \displaystyle \frac{r_{AB}}{c-v}$$ comes from $$c(t_B - t_A) = r_{AB} + v(t_B - t_A)$$,
where $$c(t_B - t_A)$$ is the distance that light travelled, and $$v(t_B - t_A)$$ is the distance that the moving-observer (the rod) travelled.
Note that all of these variables are measured in the "stationary system".

3. Aug 20, 2005

### Perspicacious

Thanks. I got that. Now what's the meaning to the expression, "If we place x'=x-vt, it is clear that a point at rest in the system k must have a system of values x', y, z, independent of time" and the sentences that come next? What is being set up for the big equation that follows? What is $$\tau$$? I can't get past Einstein's tortured explanation.

4. Aug 22, 2005

### JesseM

A while ago on this usenet thread I posted my own attempt to follow Einstein's derivation of the Lorentz transform in his original 1905 paper. Here it is:

5. Mar 11, 2008

### rbj

are you Daryl McCullough? or no, what is a different post in that thread? i thought this post from Daryl was interesting (answering essentially why it's $8 \pi$ instead of $4 \pi$, where that extra factor of 2 comes from). i just thought it would be cool to point that out to Daryl if you're the same.

6. Mar 11, 2008