# Question on Einstein's Simple derivation of Lorentz Transformation.

In appendix 1 of Einstein's "Relativity, The Special and General Theory", a book intended for the general public, he gives a derivation of the Lorentz transformation.

The math involved is pretty straightforward, but I wonder if anybody can clarify his reasoning for his equation 3 (below)

He has two frames, with motion along x and x’ coordinates. The path of light shined along the positive direction of these axis is described by:

\begin{align*} x -ct = 0 & \ \ \ (1) \end{align*}

\begin{align*} x' -ct' = 0 & \ \ \ (2) \end{align*}

He states:

“Those space-time points (events) which satisfy (1) must also satisfy (2). Obviously this will be the case when the relation “

$$(x' -ct') = \lambda(x -ct)$$

is fulfilled in general, where $\lambda$ indicates a constant; for, according to (3), the disappearance of (x – ct) involves the disappearance of (x' – ct')”

His “Obviously” isn’t so obvious to me. Given what he described I don’t see how the concurrent disappearance implies that these are linearly related by a constant. This step isn't terribly suprising given that the whole point of the appendix is to find the linear transformation between these (ie: the Lorentz tx.).

If I pretend that I didn't know that such a linear relationship was being looked for, I don't follow is argument of why to expect these should be linearly related. Is this obvious to anybody else?

--
ps. For reference I found an online version of this appendix here:

http://www.bartleby.com/173/a1.html

(I didn’t look to see if the whole book is there … I’ve got a copy from the public library).

Fredrik
Staff Emeritus