Ranging and Pioneer

Thus spake Igor Khavkine
Oh No wrote:


What is measured is a shift in the wavefunction corresponding to an
eigenstate of acceleration. For a general motion in radial coordinates a
Newtonian acceleration toward the origin is given by -r^dotdot + r w^2,
where r is radial distance and w is angular velocity. In the case of
Pioneer the motion is principally radial and the first term dominates;
the result is an illusory radial acceleration. For a star in orbit the
motion is approximately circular, so the second term dominates. The
actual calculation is a little more complicated, but the net result for
a star in orbit is an apparent increase in orbital velocity, or rather a
shift in the wave function equivalent to such an increase.

Am I understanding correctly that you are saying the both the shapes of
galaxy rotation curves and the Pioneer blue shift are aspects of a
quantum phenomenon?

Yes.

Several questions beg in this case.

1. Which objects are you treating classically and which quantum
mechanically?

I treat the emission of a photon from a distant object and its detection
on Earth quantum mechanically. The distant object is a conglomeration of
quantum particles.

2. Can you rephrase all your references to "wave functions" in terms of
the language of an abstract Hilbert space of states and operators
observables?

Yes. In fact that is where I come in. I find that it is necessary to use
coordinates which are conformally flat in the time-radial plane in order
to do this, so that quantum mechanics is effectively formulated on a
Penrose diagram in the time-radial plane.

3. If you are proposing a quantum treatment of macroscopic objects like
stars or the Pioneer space craft, can you demonstrate with a
back-of-an-envelope estimate that said quantum effects would be
observable?

The quantum effects are observable when the accuracy of measurement of
position is less than the effective wavelength of the Doppler signal.
For Mars we have measurement accurate to about 10m, so the shift should
be present in optical frequencies in measurement of Mars, but at an
amplitude two orders of magnitude lower than can be detected by HIRES,
the high resolution echelle spectrometer in operation on the Keck
Telescope. For Pioneer the effective Doppler frequency is 1MHz,
equivalent to a wavelength of 300m. The effect is predicted to appear
when the accuracy of radar determinations of the position of Pioneer is
worse than 300m, which is basically when radar becomes unusable,
somewhere approaching the distance of Saturn. Potentially this can be
tested from the original Pioneer tapes, because cycle slip is a
prediction of the model (associated with collapse of the wave function).
If we downsample the signal to 10Hz, say, the effect should become
invisible. Currently cycle slip is treated as a "blunder point" and
eliminated from the data for analysis. I do not know if there are other
errors causing cycle slip which would make this test impossible.


Answers that are short and to the point would be best.

I hope these are short enough. I suspect they beg further questions, and
I look forward to answering them.



Regards

--
Charles Francis
substitute charles for NotI to email