Relational Blockworld: Towards a Discrete Graph Theoretic Foundation of Quantum Mechanics

TL;DR

This paper introduces a novel discrete graph-based path integral formalism for quantum mechanics within the Relational Blockworld interpretation, focusing on symmetry and avoiding singularities to better understand quantum phenomena like the twin-slit experiment.

Contribution

It develops a discrete graph-theoretic framework for quantum mechanics based on symmetry and the row space of the differential operator, offering a new perspective on quantum path integrals.

Findings

Derived a transition amplitude over a ladder graph with N vertices.

Interpreted the formalism in the context of the twin-slit experiment.

Proposed a method to avoid singularities in the path integral.

Abstract

We propose a discrete path integral formalism over graphs fundamental to quantum mechanics (QM) based on our interpretation of QM called Relational Blockworld (RBW). In our approach, the transition amplitude is not viewed as a sum over all field configurations, but is a mathematical machine for measuring the symmetry of the discrete differential operator and source vector of the discrete action. Therefore, we restrict the path integral to the row space of the discrete differential operator, which also contains the discrete source vector, in order to avoid singularities. In this fashion we obtain the two-source transition amplitude over a "ladder" graph with N vertices. We interpret this solution in the context of the twin-slit experiment.