Eliminating the Wavefunction from Quantum Dynamics: The Bi-Hamilton–Jacobi Theory, Trajectories and Time Reversal

We observe that the Schrodinger equation may be written as two real coupled Hamilton-Jacobi (HJ)-like equations, each involving a quantum potential. Developing our established programme of representing state through exact free-standing deterministic trajectory models, it is shown how evolution treated autonomous propagation congruences. The wavefunction at point derived from action functions, generated by single trajectory. model shows conservation expressed continuity not necessary component theory state. Probability determined difference in congruence densities. also illustrates time-reversal symmetry implemented collective behaviour elements individually disobey conventional transformation (T) displacement (scalar) and velocity (reversal). prove an integral curve linear superposition vectors can algebraically curves one constituent labelled associated with other constituent. A corollary establishes relations between functions diverse including where obey different transformations. This illustrated showing (T-obeying) de Broglie-Bohm sequence points on (non-T) HJ trajectories, vice versa.