Abstract
Solving partial differential equations by separation of variables is
historically thought to require equating the parts to a constant. Shown,
with robust observational support, is that equating to a function of
time yields a dimension of novel solutions to the wave equation. They
transform known solutions in time, represent Doppler with acceleration,
and correct wave idealizations that wrongly constrained fundamental
physics, as well as communication and spectrum use.
This is a draft version meant to time-stamp & share for comments mainly
the following:
-
discovery of incompleteness of Fourier’s method and the full
separation of variables for the wave equation (Section 2, Appendices
A, B);
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discovery of Green’s function wave solutions with intrinsic phase
acceleration and expansion (Section 3);
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first explanation of the range data lags in the flyby anomalies
(Sections 4, 5 and Appendix C);
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elegant proof of redundancy of quantization postulate (improving over
arXiv:1602.04136, Appendix D); and
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possible redundancy of speed of light postulate over variable
measuring rods and clocks (Section 7 conclusion).
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An equivalence principle between true acceleration in Doppler and uplink
transmitter frequency ramp appears already implied by the similarity of
the anomalies with ramping (NEAR) and without (Rosetta 2005).
This revision corrects the volume of tracking data that was involved in
the NASA/ESA trajectory analyses (pp 10,11).
