Single-Photon Double-Slit Interference in the 4+1 Formalism

Abstract

Unifying quantum theory with general relativity is challenging because of several problems related to time and to collapse in quantum measurements. In the double-slit experiment, the questions are how the momentum of the photon is transferred to a specific location on the screen and how the double slit recoils accordingly. This work investigates if these problems can be solved by adding a second time τ, which acts as an external evolution parameter, to standard four-dimensional spacetime. Within the resulting 4+1 formalism, a model for the single-photon double-slit experiment is developed. On the one hand, each spacetime associated to a value of τ relies on classical worldlines that obey local momentum conservation. On the other hand, these worldlines are allowed to readjust as a function of τ such that the quantum phenomenon of double-slit interference can be reproduced. The model explains how determinate outcomes are produced and how momentum transfer occurs in a way that satisfies the principles of relativity and local momentum conservation. As a result, the measurement problem and the problem of time evaporate, and an explanation for our experience of the present emerges. Since the presented model succeeds in explaining a key quantum phenomenon with essentially classical worldlines, this is relevant for the field of quantum gravity.