"Daryl McCullough" <stevendaryl3016@yahoo.com> wrote in message
news:d3kcjq0137h@drn.newsguy.com...
> In article <425d9028$0$39635$892e7fe2@authen.white.readfreenews.net>,
Aleksandar
>
> I think you are missing something here. The transformation
> equations
>
>     x' = Ax + Bt
>     t' = Cx + Dt
>
> are assumed to be valid for *all* values of x and t. That means
> that x' and t' are *functions* of x and t. Perhaps it would be
> clearer to write them explicitly as functions:
>
>     x' = f(x,t) = Ax + Bt
>     t' = g(x,t) = Cx + Dt
>


We are in complete agreement with above equations and your interpretation of
them. So let me start my comments from here:


> The constraints on x' and t' are the following
>
>     1. For *all* values of x and t: If x=ct, then x'=ct'.
>     2. For *all* values of x and t: If x=-ct, then x'=-ct'.
>     3. For *all* values of x and t: If x=vt, then x'=0.
>     4. For *all* values of x and t: If x=0, then x'=-vt'.
>

In (4) how can you say, for *all* values of x and t, when you specifically
say when x = 0? Please correct (4) into

For *only* value of x =0 , x' = -vt', where v = B/D.

Agree?


> Tell me how those 4 statements imply that x'=0. They *don't*.
> The constraints 1-4 are *conditionals*. They say *if* x and
> t have a certain relationship, *then* x' and t' have a
> corresponding relationship. *If* x=vt, *then* x'=0.
>

You do not use exactly the same approach, in my example (see Appendix A, I
assume you read it) we start with x' = 0 to get speed v = - B/A. But your
approach is correct too.

Those 4 statements do not imply that x = 0, only (4) implies that. If you
had used the same approach as I did in Appendix A, (4) would imply that x' =
0.

Agree?


> In terms of parameters A, B, C, and D, the 4 constraints above say:
>
>     1. forall t, Act + Bt = c(Cct + Dt)
>     2. forall t, -Act + Bt = -c(-Cct + Dt)
>     3. forall t, Avt + Bt = 0.
>     4. forall t, 0 + Bt = -v(0 + Dt).
>

The initial equation set actually describe motion, you don't have freedom to
use any t when x = 0. This would make (4) useless, but for the sake of
argument, I'll agree with you here. Let's proceed:


> These lead to the four equations:
>
>     1. Ac + B = Cc^2 + cD
>     2. -Ac + B = Cc^2 - cD
>     3. Av + B = 0
>     4. B = -vD
>

You have magically avoided to include your own conditional from previous
equation set "for all t, 0 + Bt = -v(0 + Dt)", or in other words
"if x = 0, then B = - vD". Please correct (3) and (4) into

   (3) Av + B = 0      ... if x = 0.
   (4) B = - vD        ... if x = 0.

Agree?

> which have the solutions:
>
>     B = -Av
>     C = -Av/c^2
>     D = A
>
> So the transformation equations simplify to
>
>     x' = A(x-vt)
>     t' = A(t-vx/c^2)
> 

I abolutely agree. The eqautions can have such form. Only one thing is
missing. Please include the conditional, the one which you magically dropped
out:

   x' = A(x-vt)       ...if x = 0
   t' = A(t-vx/c^2)   ....if x = 0

The derivation procedure is not valid in general case, only in case of x =0,
in your approach. This is exactly my point. I do not claim that Lorentz
transformation is not possible, I only claim that derivation procedures
which I have described in my article, and all others that I have ever seen,
and which I will describe in future updates, are mathematically invalid.


Aleksandar

 See also

http://www.masstheory.org
http://www.masstheory.org/lorentz.pdf