Quantum theory is classical mechanics with non-local existence

TL;DR

This paper introduces a novel approach linking classical and quantum mechanics through a generalized variational principle, suggesting non-local particle existence in phase space and offering insights into quantum measurement paradoxes.

Contribution

It derives the quantum propagator from a modified Hamilton's principle allowing non-local paths, bridging classical and quantum theories with a unified framework.

Findings

Derivation of quantum propagator from a generalized variational principle

Introduction of non-local particle trajectories in phase space

Natural emergence of the transactional interpretation

Abstract

I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized to allow many paths due to the non-local existence of particles in phase space. This principle allows a physical system to evolve non-locally in phase space while still allowing a representation that uses many classical paths. Whereas a point in phase space represents a classical system's state, I represent the state of a non-local system by a mixed trajectory. This formulation naturally leads to the transactional interpretation for resolving the paradoxes of the measurement problem. This principle also suggests a more flexible framework for formulating theories based on invariant actions and provides a single conceptual framework for discussing many areas of science.