Underlying Determinism, Stationary Phase and Quantum Mechnics

TL;DR

This paper introduces a new time scale where particles are point-like and fluctuate without dynamics, deriving quantum mechanics from underlying determinism and stationary phase principles.

Contribution

It proposes a novel time scale and a framework linking determinism, stationary phase, and quantum measurement, offering a new perspective on quantum foundations.

Findings

Wave function defined by averaging the square root of density

Stationary phase determines observable peaks in macrovariables

Underlying determinism selects a single measurement branch

Abstract

In a newly introduced time scale $\tau$, much smaller than the usual $t$, any object is assumed to be a point-like particle, having a definite position. It fluctuates without dynamics and the wave function $\Psi$ is defined by averaging the square root of the density. In $t$-scale, the Schr$\ddot{\rm o}$dinger equation holds and for a macrovariable just a classical path is picked up as a peak of $\Psi$ by the stationary phase, which is the observable signal. In the measuring process, the stationary phase branches into many but one branch is selected by underlying determinism, leading to the correct detection probability.