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Pentcho Valev wrote:
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.
In his "Relativity: The special and general theory" Einstein does not postulate
linearity but almost explicitly introduces a third axiom:
1. Principle of special relativity
2. Postulate of the constancy of the speed of light: If and only if the speed of
light in the first inertial frame is c >> v, then in another inertial frame having
a speed v with respect to the first it is c as well.
3. Postulate of the variability of the speed of light: If and only if the speed of
light in the first inertial frame is as low as v (x = vt), then it is zero in the
other inertial frame (x' = 0).
Physically, the third axiom sounds silly but mathematically it is equipollent to
the second - it is indispensable for the determination of initially unknown
parameters.
Wild. But couldn't 3 be rephrased as:
3. If and only if in a reference frame S the speed v of a reference frame S'
(x = vt) is equal to the speed of light, then the speed of light is zero in S'
(x' = 0).