Re: Derivation of Lorentz Transformation (ctd. from sci.physics.research)

Daryl McCullough wrote:
> Thomas Smid says...
>
> >Writing arguments to variables is only justified as an aid in order
> >to keep track of things when doing mathematical operations like
> >differentiation or integration for instance.
>
> Yes, the point of making the variables explicit is to point
> out and correct simple mistakes of reasoning. That's exactly
> the reason that I wanted to make the variables explicit: to
> point out and correct simple mistakes of your reasoning.
>
> >In this case, the functional dependences are all fully
> >written out in the equations and there is no point in
> >indicating them separately again as an
> >argument,
>
> The point is that you are getting the functional
> dependencies *wrong*. Writing out the dependencies
> explicitly shows exactly *where* you are wrong.
>
> Refusing to write out the functional dependencies
> shows that you are both wrong and *dishonest*. You
> are unwilling to address your own mistakes.
>
> >and it definitely can not make a difference for the
> >algebra.
>
> It can't make any difference in the algebra if the
> algebra is done correctly, as Einstein did. But it
> makes a big difference if the algebra is done
> *incorrectly*, which is your case. Spelling out
> the details shows where your mistakes are.
>
> >So I am afraid that if you can't make your point here
> >without writing the arguments, it only indicates that
> >your maths is incorrect.
>
> Uh, you've got that exactly backwards. If you can't make your
> point even *when* you make the arguments explicit, then that's
> an indication that your mathematics is incorrect.
>
> That's the case that we are in, Thomas. You have an argument
> against Einstein's derivation. When we make all the steps
> explicit, your argument disappears. That shows that there is
> something wrong with *your* argument. A correct argument cannot
> be made incorrect by adding more details, but an incorrect argument
> can be made to *seem* correct by leaving out details.

You have probably not properly read my opening post in this thread.
What you are doing is to use the assumption that the coefficient B in
x'=Ax+Bt is different from zero in order to re-interprete the original
contraints in a way that makes the latter consistent with the
transformation equation, but you don't realize that the constraints are
now not compatible with the invariance of c anymore (and using the
arguments on the variables doesn't change anything about it).
The invariance of c clearly implies that in the unprimed frame, after a
given time t, two light signals will be at a point x=ct in the positive
direction and a point x=-ct in the negative direction. Similarly, in
the primed frame, after a given time t', two light signals will be at a
point x'=ct' in the positive direction and a point x'=-ct' in the
negative direction. These are the *constraints* that you have to impose
on the transformation equations and they tell you that B in x'=Ax+Bt
must be zero. You are not entitled to reversely enforce functional
dependences of the transformation equations (as postulated by you) on
the constraints. The latter are fully defined the way I gave it above
and there is nothing that could change this. Otherwise you would be
merely perverting the principle of the invariance of the speed of
light.

Thomas

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