Parametric separation of variables and the complete propagation law
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);
- discovery of Green's function wave solutions with intrinsic phase acceleration and expansion (Section 3);
- first explanation of the range data lags in the flyby anomalies (Sections 4, 5 and Appendix C);
- elegant proof of redundancy of quantization postulate (improving over arXiv:1602.04136, Appendix D); and
- possible redundancy of speed of light postulate over variable measuring rods and clocks (Section 7 conclusion).
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). Experimental verification is being planned, to be performed in a proposed prototype of an acceleration spectrum receiver under funding review.