The past of a quantum particle

TL;DR

This paper proposes a method to analyze the past of a quantum particle based on the weak trace it leaves, challenging the classical notion of a single trajectory and emphasizing the role of forward and backward evolving states.

Contribution

It introduces a novel approach using weak measurements to determine the quantum particle's past, incorporating both forward and backward quantum states for a more accurate description.

Findings

Weak trace measurement can reveal the particle's past.

Contradictions to classical trajectory assumptions are demonstrated.

The method provides a more complete quantum past description.

Abstract

Although there is no consensus regarding the "reality" of the past of a quantum particle, in situations where there is only one trajectory with nonvanishing quantum wave of the particle between its emission and detection points, it seems "safe" to associate the past of the particle with this trajectory. A method for analyzing the past of a quantum particle according to the weak trace it leaves is proposed. Such a trace can be observed via measurements performed on an ensemble of identically pre- and post-selected particles. Examples, in which this method contradicts the above common sense description of the past of the particle are presented. It is argued that it is possible to describe the past of a quantum particle, but the naive approach has to be replaced by both forward and backward evolving quantum states.