Re: Teaching logic is urgent (the only reasonable transformatio

[Ken Caviness <caviness@SOUTHERN.EDU>]

At 12:21 PM 06.06.03 +0200, pvalev wrote (quoting me, KC):

> > Moreover, as Pentcho himself points out, they are incompatible
> > with the postulate of the constancy of the speed of light.  This
> > principle has been repeatedly tested and found reliable, from the
> > Michelson-Morley experiments on to more modern tests.  In itself,
> > this eliminates any transformation that does not agree with the
> > constancy of the speed of light (at least within the limits of
> > experimental error).
>
> Let me make a seemingly pompous statement here. Although I have not
> read enough about performed experiments, I am sure the principle, in
> its claim that the speed of light is independent of the speed of the
> observer, has NEVER been tested. My conviction involves the
> understanding that, essentially, the respective experiment is unique.
> The light source must be outside the (moving) system of the observer,
> and the observer must record the times the light enters and then
> leaves his/her system. If such an experiment had ever been done,
> textbooks would have mentioned it. I don't believe the
> conclusion "speed of light does not depend / depends on the speed of
> the observer" could be extracted from different experiments,
> Michelson-Morley included.
>
> Pentcho

The Michelson-Morley and later interferometry experiments show that the
movement of the earth is irrelevant to the measured speed of light.  I'm
sure everyone here understands the concept of an interferometer: a light
beam is split (say by a half-silvered mirror) and the two beams continue at
right angles, are reflected along their individual paths and
recombined.  If the path-lengths are equal and if the speed of light is the
same for each beam (travelling in the two perpendicular directions), then
there will be constructive interference of the two beams.  In practice it
would be very hard to guarantee equal path lengths if using monochromatic
light, but for white light it's fairly clear, and even for laser light, if
one path is slowly adjusted (say with a vernier-calibrated knob that
slightly displaces one of the reflecting mirrors or stretches the base,
etc.) the alternation between constructive and destructive interference is
striking and easily verifiable.  Now we rotate the interferometer, or we
wait until the earth is headed in a different direction in its orbit around
the sun.  The old idea of simply adding or subtracting relative velocities
(here subtracting the velocity of the earth [or better, that spot on the
surface of the earth] with respect to the ether from the velocity of light
with respect to the ether to get the velocity of light with respect to the
earth) would lead us to believe that the speed of light should depend on
the direction with respect to "the actual velocity" of that point on
earth.  Of course we all know the punchline, no such dependence was found,
the constructive interference, once found, never changes to destructive
interference.  So whether we're moving toward or away from or transverse
with respect to the source of light, or indeed at any angle and speed
whatever, we measure the speed of light to be the same, c.  (Or the path
length is sneakily changing automagically to match the changed speed of
light -- see below.)

This is a fantastic realization.  Mention has already been made of Hendrik
Lorentz' attempt to explain the "null-result" of the MM experiment by a
theory of the electron leading to a Lorentz-Fitzgerald compression of the
arm of the interferometer oriented in the direction of the earth's
motion.  This works fine, but note that it reduces to exactly the same
Lorentz transformation which is found in special relativity.  In this
sense, Einstein's taking the constancy of the speed of light as an axiom
doesn't change anything:  we get the same equations for transforming
between reference frames.  But deriving it from a more limited and
comprehensible set of suppositions is a much more "elegant" approach.  I
appeal to Occam's Razor.  In any case, we may consider the constancy of the
speed of light an axiom or a result, but it's still "true".  (In the sense
that using this model gives more accurate predictions than the previously
used Galilean and Newtonian model.  Yes, we also know that SR has in its
turn been superceded by GR, quantum relativistic models, and now a
generation of attempts at grand unified theories, super grand unified
theories, string theory, brane models, etc, etc.  But that's not what we're
talking about here.  We're comparing to Pentcho's "only reasonable
transformation", and at this level, SR provides a weird but logically
self-consistent model, and the right answers.  Other linear
transformations, such as Pentcho's, do not give the right answers (such as
explaining the results of the MM experiment, of cosmic-ray generated muon
decay, relativistic momentum increase in linear accelerators, cyclotrons &
synchrotrons, and E = m c^2, the explanation of fission and fusion and
basically all of nuclear physics).

I think probably I've said all that I can on this thread.  Sorry if I've
sounded too dogmatic, but I'll have to agree with Bob Sciamanda's
assessment that the supposed inconsistencies of the Lorentz transformation
which Pentcho refers to are miscalculations or misinterpretations.  Yes,
and I've done my share of those, too!  But as I've said before, what I find
so fascinating about relativity is that the apparent paradoxes keep melting
away, it really is mathematically self-consistent.

Enjoy!

Ken