A Non Relativistic Argument Against Continuous Trajectories of Particles

TL;DR

This paper presents a thought experiment demonstrating that assuming particles follow continuous trajectories leads to contradictions with quantum predictions, suggesting such trajectories cannot exist if quantum mechanics is correct.

Contribution

It provides a non-relativistic argument against the existence of continuous particle trajectories based on quantum predictions and thought experiments.

Findings

Continuous trajectories imply particles land on two detectors simultaneously.

Quantum formalism predicts specific detection probabilities.

Contradiction arises if particles are assumed to follow continuous paths.

Abstract

A thought experiment is described and the probability of a particular type of results is predicted according to the quantum formalism. Then, the assumption is made that there exists a particle that travels from the source to one of the detectors, along a continuous trajectory. A contradiction appears: for agreeing with the quantum prediction, the particle has to land at once on two space separated detectors. Therefore, the trajectory of the particle, if it exists, cannot be continuous.