Explaining Retrocausality Phenomena in Quantum Mechanics using a Modified Variational Principle

Abstract

A modified lagrangian with causal and retrocausal momenta was used to derive a first causal wave equation and a second retrocausal wave equation using the principle of least action. The retrocausal wave function obtained through this method was found to be equivalent to the complex conjugate of the causal wave function, thus leading to the conclusion that a retrocausal effect is already implicit in quantum mechanics through the means of complex conjugation of the wave function when computing the probability density for a particle. Lastly, the same variational principle was employed with a fractionary langriangian, (that is, containing fractional Riemann derivatives) to obtain a pair of modified wave equations, one causal and other retrocausal, both of which correspond to the differential equation of a damped oscillator in the free particle (potential energy V=0) case. The solutions of this damped wave equations remain to be explored.