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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 |
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