Path integral and wave function collapse

TL;DR

This paper extends the Feynman path integral to include relativistic effects, deriving a wave-function-collapse equation and providing a new perspective on the quantum measurement problem by linking collapse to environmental noise and internal correlations.

Contribution

It introduces an extended path integral framework that derives a wave-function-collapse equation, offering a novel explanation for measurement and collapse within quantum mechanics.

Findings

Derivation of the Klein-Gordon equation from the extended path integral.

Introduction of a wave-function-collapse equation based on potential noise and internal correlations.

Reconciliation of wave-function collapse with quantum mechanics without contradiction.

Abstract

Quantum measurement problem is still unconsensus since it has existed many years and inspired a large of literature in physics and philosophy. We show it can be subsumed into the quantum theory if we extend the Feynman path integral by considering the relativistic effect of Feynman paths. According to this extended theory, we deduce not only the Klein-Gordon equation, but also the wave-function-collapse equation. It is showing that the stochastic and instantaneous collapse of the quantum measurement is due to the "potential noise" of the apparatus or environment and "inner correlation" of wave function respectively. Therefore, the definite-status of the macroscopic matter is due to itself and this does not disobey the quantum mechanics. This work will give a new recognition for the measurement problem.