Re: The fallacy of affirming the consequent

[Pentcho Valev <pvalev@BAS.BG>]

This additional linearity premise does not belong to the original axioms does it?
Can Lorentz equations be validly deduced from Einstein's two initial axioms, in
the absence of additional ad hoc premises?

Pentcho Valev

Ken Caviness wrote:

> Pentcho Valev wrote:
>
> > However Einstein needs something different:
> >
> > B -> A, A, therefore B                                      /4/
> >
> > He proceeds in accordance with /4/ - builds Lorentz equations on B and
> > so creates the sequence (A therefore B therefore Lorentz equations) -
> > the illusion is that
> > Lorentz equations ultimately stem from A. In fact, A CAN be a corollary
> > of B or Lorentz equations, in accordance with /3/, but Lorentz equations
> > can BY NO MEANS be
> > deduced from A.
>
> I vividly remember an assignment in my freshman year Engineering Physics class
> where we were asked to _derive_ the Lorentz transformation equations from
> Einstein's postulates that the laws of physics and the speed of light are the
> same for all inertial observers.  I have since used this in my classes or as a
> homework assignment.  The only additional assumption needed is that the
> transformations be linear in all the variables (x,y,z,t,x',y',z',t').  That
> was handled by the statement that we would _first_ seek a set of
> transformation equations which was linear, but if necessary we could back off
> from that requirement.
>
> Briefly, if you let
>
> x = A x' + B y' + C z' + D t', y = E x' + ..., etc., the unknown constants can
> be identified by symmetry arguments and the requirement that the speed of
> light be measured by both primed and unprimed observers as c.  The Lorentz
> transformation falls out in your lap, i.e., the Lorentz equations can indeed
> "be deduced from A" + the additional requirement that the dependence be
> linear.
>
> For what it's worth,
>
> Ken Caviness
> Physics Department
> Southern Adventist University
> http://physics.southern.edu/