Ontological Foundations of the Variational Principles and the Path Integral Formalism

TL;DR

This paper explores the ontological connections between variational principles and the path integral formalism in quantum physics, proposing that all possible histories contribute to the observed phenomena.

Contribution

It introduces an ontological framework linking variational principles and path integrals, emphasizing the summation of all possible histories at the quantum level.

Findings

Quantum systems explore all possible histories simultaneously.

The actual history results from summing all alternative histories.

Macroscopic trajectories emerge from the collective influence of all possible paths.

Abstract

In this paper, I consider the issue of how two mathematical models of modern physics, the variational principles and the quantum path integral formalism, relate to reality. I assume that the observed phenomena are consistent with the calculations because both of these models have some common ontological foundations. According to the hypothesis of the summation of coexisting alternative possibilities, at the quantum level, the system at once moves along all histories that possible in given boundary conditions. The actual history is a mere result of the summation of all these alternative possible histories. This resultant history differs from others with the minimal action and maximal probability. I observe this history as a macroscopic trajectory of the system.