Double Slit Experiment in the Heisenberg Picture of Quantum Mechanics

TL;DR

This paper revisits the double slit experiment within the Heisenberg picture, arguing that interference can be explained without non-locality and emphasizing the importance of defining observables as functions of space and time.

Contribution

It clarifies the role of locality in the double slit experiment and compares measurement frameworks in the Heisenberg picture, challenging some existing claims.

Findings

Interference fringes do not require non-local explanations.

Position and momentum observables should depend on both space and time.

Comparison between projective measurements and the 'Church of the Larger Hilbert Space'.

Abstract

We present the standard double slit experiment with non-relativistic particles in the Heisenberg Picture of quantum mechanics. Our motivation is threefold. First and foremost, and contrary to some claims in the literature, we show that there is no need to talk about non-locality when explaining the interference fringes. Secondly, we emphasise the fact that even in the non-relativistic regime, and in order to preserve locality, we should define the position and momentum observables of a particle as functions of both space and time (and not just time). Thirdly, our presentation compares the projective measurements in the Heisenberg picture with the "Church of the Larger Hilbert Space", the latter of which is seldom discussed in the Heisenberg picture of quantum mechanics.