Re: Mathematical Inconsistencies in Einstein's Derivation of the Lorentz Transformation

Thomas Smid says...

>I am sorry, but you still misinterprete the variables as specific
>coordinates. x1 and x2 are *not* coordinates but scalar variables for
>the two directions representing the vector variable x. Fully written it
>would be x1(t)=ct, x2(t)=-ct etc. I merely left out the argument (t) in
>my equations.

That doesn't change my objections to your derivation. You wrote

(3c) x1'+c t' = (A+B)(x1+ct)
(4b) x2'-c t' = (A-B)(x2-ct)

The point is that x' and t' are *functions* of x and t. Since x2(t)
is unequal to x1(t), the corresponding value of t' in (4b)
is *not* equal to the corresponding value of t' in (3c).

Let's put in all the functional dependence explicitly. The
transformation equations are these

x'(x,t) + c t'(x,t) = (A+B) (x + ct)
x'(x,t) - c t'(x,t) = (A-B) (x - ct)

Now, you want to specialize to the case x1(t) = ct in
the first equation, and specialize to the case x2(t) = -ct
in the second equation. Fine. That gives us:

x'(ct,t) + c t'(ct,t) = (A+B) (2ct)
x'(-ct,t) - c t'(-ct,t) = (A-B) (-2ct)

Now, we use the fact that x' = ct' in the top
equation, and x' = -ct' in the bottome equation to get:


2 c t'(ct,t) = (A+B) (2ct)
-2 c t'(-ct,t) = (A-B) (-2ct)

Your mistake was assuming that t'(ct,t) = t'(-ct,t).

--
Daryl McCullough
Ithaca, NY

.