Superposition and time delay are incompatible between them

TL;DR

This paper demonstrates that wave functions depending on two different time-position vectors cannot simultaneously possess superposition and separation of variables properties, revealing fundamental incompatibilities in quantum wave function structures.

Contribution

It provides a rigorous proof showing the incompatibility between multi-time wave functions and key quantum principles like superposition and separation of variables.

Findings

Wave functions with two different time entries cannot have superposition.

Separation of variables is incompatible with multi-time wave functions.

The result clarifies fundamental limitations in quantum wave function formulations.

Abstract

We analyse the properties of wave functions $\psi(x,t;y,s)$ that depend at once on two time-position vectors $(x,t)$ and $(y,s)$ with different time entries $t\neq{s}$. In particular, we prove that the existence of such wave functions is indeed incompatible with the superposition property and the technique of separation of variables.