AFM: Apparent Wavelength, a non-QM hidden variable (3).

[Ned Latham]

[My apologies: I have bungled this article repeatedly. However, it's
now solid, and IMO, deserves consideration. This followup replaces
frequency and wavelength definitions echoing those of wave models with
definitions based purely on particulate properties.]

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 mentioning it, in my view.

Proceeding without that assumption however, is much more interesting.
A considered emission theory must define frequency and wavelength on
particulate properties:

Frequency : spin rate; ie, the number of revolutions per unit time;
Wavelength: linear distance travelled during one revolution

but those definitions clearly imply constancy. Neither changes as a
result of relative motion betweem source and observer, but the observer
experiences change: a considered emission theory must account for that.

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
a quantity which as far as I can tell has never been mooted before:

Apparent Wavelength[1]: the quotient of the speed and the frequency.

Given v[1] = v[0] * (c + v) / c, that gives

lambda[1] = (v[0] * (c + v) / c) / f[0]
= v[0] / f[0] * (c + v) / c
= 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 change. 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] the predicted wavelength measurement

[Ned Latham]

Ned Latham wrote:
>
> [My apologies: I have bungled this article repeatedly. However, it's
> now solid, and IMO, deserves consideration. This followup replaces
> frequency and wavelength definitions echoing those of wave models with
> definitions based purely on particulate properties.]

I must apologise again. The definition of apparent wavelength below
is, IMO, unsatisfactory (so much for solid). In fact a considered
ballistic/emission theory must redefine both frequency and wavelength
(I should also make it clear that with "emission theory" I mean
particulate emission, not wave emission); I now define four coexistent
quantities:

Arrival frequency of a stream of particles:
the rate at which the stream's particles reach the observer;

Phase frequency of a particle:
its spin rate; ie, the number of revolutions it makes per unit
time;

Objective wavelength:
the distance a particle travels relative to the source while
revolving once;

Apparent wavelength[*]:
the distance a particle travels relative to the observer while
revolving once.

That last is ballistically equivalent to the definition below, but
stated in physical terms rather than mathematical.

Note that the definition of arrival frequency defines a measurable
quantity proportionate to brightness.

> 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 mentioning it, in my view.
>
> Proceeding without that assumption however, is much more interesting.
> A considered emission theory must define frequency and wavelength on
> particulate properties:
>
> Frequency : spin rate; ie, the number of revolutions per unit time;
> Wavelength: linear distance travelled during one revolution
>
> but those definitions clearly imply constancy. Neither changes as a
> result of relative motion betweem source and observer, but the observer
> experiences change: a considered emission theory must account for that.
>
> 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
> a quantity which as far as I can tell has never been mooted before:
>

> Apparent Wavelength[*]: the quotient of the speed and the frequency.

>
> Given v[1] = v[0] * (c + v) / c, that gives
>
> lambda[1] = (v[0] * (c + v) / c) / f[0]
> = v[0] / f[0] * (c + v) / c
> = 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 change. 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.
>
> ========

> [*] the predicted wavelength measurement