Explaining Retrocausality Phenomena in Quantum Mechanics using a Modified Variational Principle

TL;DR

This paper introduces a modified variational principle incorporating causal and retrocausal momenta to derive wave equations, revealing retrocausality as implicit in quantum mechanics and extending to fractional derivatives with damped oscillator equations.

Contribution

It develops a novel variational framework that derives both causal and retrocausal wave equations, linking retrocausality to complex conjugation in quantum mechanics and incorporating fractional derivatives.

Findings

Retrocausal wave function is equivalent to the complex conjugate of the causal wave function.

Derived fractional wave equations resemble damped oscillators.

Retrocausality is implicit in quantum probability calculations.

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.