Can a particle moves zigzag in time?

TL;DR

This paper investigates quantum transitions involving time zigzags within standard quantum mechanics, showing that while wave functions are singular at zigzag points, such paths are not suppressed but contribute zero to the amplitude.

Contribution

It demonstrates that time zigzags are not suppressed in quantum mechanics and analyzes their effects without introducing new postulates.

Findings

Wave function singular at time zigzags.

Time zigzags contribute zero to the quantum amplitude.

Results apply to single particles and scalar fields.

Abstract

Amplitudes of quantum transitions containing time zigzags are considered. The discussion is carried out in the framework of the Minkowski metric and standard quantum mechanics without adding new postulates. It is shown that the wave function is singular at the instant of the time zigzag. Nevertheless, we argue that time zigzags are not suppressed at the quantum level, but their contribution to the amplitude is zero. The result is valid for a single particle and a non-interacting scalar field.