AFM: Apparent Wavelength, a non-QM hidden variable.

[Ned Latham]

There are numerous experimental tests that purport to confirm Special
Relativity theory and/or refute what the testers and their reviewers
call emission theory, but those examining doppler shift all seem to
depend on the assumption that emission theory predicts wavelength
constancy even when source and observer are in relative motion.

That assumption is pretty thin. Any theory predicting so is falsified
by the very existence of doppler shift in light. There's no ground for
denying that; therefore no such theory is viable, and there's no reason
to bother with disproving it. Or even mentoning it, in my view.

The opposite assumption however, that emission theory predicts variable
wavelength when source and observer are in relative motion, is much more
interesting; the accepted definitions of frequency and wavelength wrt
streams of particles are intuitiuvely correct and are clearly congruent
with their waveform equivalents[1], but unlike SR with its FoR magic,
a potentially viable emission theory must account for the effect of
relative motion between the source and the observer explicitly. The
frequency definition does that, but the wavelength definition does not.

What the observer experiences is not the objective wavelength, it is
instead the change in distance between source and observer while one
wavelength passes; in other words, the wavelength experienced is the
objective wavelength changed inversely as the speed. It is given by
a quantity which as far as I can tell has never been mooted before:

Apparent Wavelength[2]:
the quotient of the emission speed and the measured frequency.

Given f = f[0] * (c + v) / c, that gives
lambda = c / (f[0] * (c + v) / c)
= c * (c / (f[0] * (c + v))
= c / f[0] * (c / (c + v))
= lambda[0] * c / (c + v)

In other words, a considered emission theory must necessarily define a
wavelength doppler shift factor of c / (c + v), which is the inverse of
the speed shift and the frequency shift. The conventional assumption
turns out to be false.

Doppler shift tests that purport to falsify emission theory are therefore
invalidly and incorrectly interpreted. Their results should be reexamined,
specifically to determine whether within the bounds of experimental error
they are actually consistent with the predictions of just one of SR and
emission theory.

As well, the teaching should be amended, and the hidden variable revealed.

========
[1] Frequency : the rate at which particles reach a given point in space;
: the rate at which wave peaks reach a given point in space;
Wavelength: the distance between particles in the direction of movement,
: the radial distance between wave peaks.

[2] The predicted wavelength measurement. It too has a waveform equivalent:
the quotient of the propagation speed and the measured frequency.

[Ned Latham]

[This followup replaces a poorly worded fourth paragraph in the
original. My apologies for the bungle.]

There are numerous experimental tests that purport to confirm Special
Relativity theory and/or refute what the testers and their reviewers
call emission theory, but those examining doppler shift all seem to
depend on the assumption that emission theory predicts wavelength
constancy even when source and observer are in relative motion.

That assumption is pretty thin. Any theory predicting so is falsified
by the very existence of doppler shift in light. There's no ground for
denying that; therefore no such theory is viable, and there's no reason
to bother with disproving it. Or even mentoning it, in my view.

The opposite assumption however, that emission theory predicts variable
wavelength when source and observer are in relative motion, is much more
interesting; the accepted definitions of frequency and wavelength wrt
streams of particles are intuitiuvely correct and are clearly congruent
with their waveform equivalents[1], but unlike SR with its FoR magic,
a potentially viable emission theory must account for the effect of
relative motion between the source and the observer explicitly. The
frequency definition does that, but the wavelength definition does not.

What the observer experiences is the objective wavelength altered by

the change in distance between source and observer while one wavelength

passes; in other words, changed inversely as the speed. It is given by