Surrealistic Bohmian trajectories do not occur with macroscopic pointers

TL;DR

This paper demonstrates that surrealistic Bohmian trajectories are artifacts of small pointers and do not occur with macroscopic pointers, emphasizing the importance of including many particles in the analysis of quantum measurements.

Contribution

It shows that surrealistic trajectories only appear with small pointers and vanish for macroscopic pointers when many particles are considered, clarifying the interpretation of Bohmian mechanics.

Findings

Surrealistic trajectories occur only with small pointers.

Macroscopic pointers do not exhibit surrealistic trajectories.

Proper interpretation of all trajectories reveals no surrealism.

Abstract

We discuss whether position measurements in quantum mechanics can be contradictory with Bohmian trajectories, leading to what has been called \textquotedblleft surrealistic trajectories\textquotedblright\ in the literature. Previous work has considered that a single Bohmian position can be ascribed to the pointer. Nevertheless, a correct treatment of a macroscopic pointer requires that many particle positions should be included in the dynamics of the system, and that statistical averages should be made over their random initial values. Using numerical as well as analytical calculations, we show that these surrealistic trajectories exist only if the pointer contains a small number of particles; they completely disappear with macroscopic pointers. With microscopic pointers, non-local effects of quantum entanglement can indeed take place and introduce unexpected trajectories, as in Bell experiments; moreover, the initial values of the Bohmian positions associated with the measurement apparatus may influence the trajectory of the test particle, and determine the result of measurement. Nevertheless, a detailed observation of the trajectories of the particles of the pointer can still reveal the nature of the trajectory of the test particle; nothing looks surrealistic if all trajectories are properly interpreted.