Microscopic theory of quantum physics

TL;DR

The work addresses deriving quantum phenomena from a microscopic, axiom-minimal framework based on deterministic particle interactions governed by Newton's law. It introduces a conservative interaction potential $V_{ ext{int}}$ (mediated by unobservable dark particles) that yields a quantum potential $V_{ ext{quant}}$ in the continuum limit, leading to the Schrödinger equation for $\psi = R e^{i S/\hbar}$. Key results include (i) quantized energy spectra in a particle-in-a-box, (ii) interference patterns in a double-slit setup from deterministic trajectories, and (iii) a formal derivation of $i\hbar \partial_t \psi = -\frac{\hbar^2}{2m} \partial_{xx}^2 \psi + V \psi$ from microscopic dynamics. The approach positions QM as an emergent description of underlying deterministic interactions, with potential extensions to relativistic and field-theoretic contexts and prospects for new experimental predictions.

Abstract

I present a microscopic framework in which quantum phenomena emerge from particle-particle interactions governed by Newton's second law of motion. Within this approach, stationary states and quantized energy spectra arise naturally for the particle in a box. The same dynamics reproduces interference fringes in the double-slit experiment. Finally, I derive the Schrödinger equation from the underlying principles.

Figures (3)

• Figure 1: Trajectories of particles in a one-dimensional box of length $L=100\,\mathrm{nm}$, corresponding to (a) the first, (b) the second, and (c) the third quantum mechanical energy state. In each subfigure, the left panel displays the quantum mechanical probability density, while the right panel shows particle trajectories evolving under the microscopic interaction potential \ref{['eq:potential']}. The trajectories form standing-wave-like distributions whose periodicities, indicated in the figures, are directly related to the quantized energies shown in figure \ref{['fig:box_energies']}.
• Figure 2: Comparison of the microscopic energy levels $E_{\mathrm{micro},n}$ with the quantum mechanical prediction $E_{\mathrm{box},n}$ for a particle in a one-dimensional box of length $L=100\,\mathrm{nm}$. The periods $T_n$ used to compute $E_{\mathrm{micro},n}$ are extracted directly from figure \ref{['fig:box_trajs']}. The agreement demonstrates that the discrete energy spectrum emerges naturally from the microscopic interaction dynamics.
• Figure 3: Simulated trajectories in the double-slit setup with slit separation $2X=100\,\mathrm{nm}$ and slit width $\sigma=10\,\mathrm{nm}$. Shown on the left is the quantum mechanical probability density at $t=0\,\mathrm{ps}$, represented by the sum of two Gaussian wave packets corresponding to the two slits. Deterministic particle trajectories evolving under the microscopic interaction potential \ref{['eq:potential']} are displayed in the central panel. On the right, the quantum mechanical probability density at $t=20\,\mathrm{ps}$ reveals the interference pattern on the detection screen. The trajectory ensemble reproduces this pattern, illustrating how quantum-like interference emerges naturally from the microscopic dynamics.