Quantum mechanics in a discrete model of classical physics

Hans-Thomas Elze

We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete states is introduced, which presently is still treated as decoupled from the system. This is motivated by the recent discussion of ``timeless'' reparametrization invariant models, where discrete physical time has been constructed based on quasi-local observables. Employing the path-integral formulation of classical mechanics developed by Gozzi et al., we show that these deterministic classical systems can be naturally described as unitary quantum mechanical models. We derive the emergent quantum Hamiltonian in terms of the underlying classical one. Such Hamiltonians typically need a regularization - here performed by discretization - in order to arrive at models with a stable groundstate in the continuum limit. This is demonstrated in several examples, recovering and generalizing a model advanced by 't Hooft.

Pavel Šťovíček, J. Tolar

Marin van Heel

For creating a measurable Physics, we must first revisit its theoretical foundations. Deterministic Physics cannot be measured and therefore cannot be proven experimentally since an infinite amount of energy is required to confirm a Law of Physics to infinite precision. This “measurement problem” existed ever since Physics – centuries ago – slowly separated from its deterministic theological roots. Given the experimental successes of deterministic Newtonian Mechanics, deterministic Physics nevertheless became the law-of-the-land. The introduction of Quantum Mechanics in the 1920s threw a spanner in the works and re-emphasised the importance of that underlying measurement problem. Rather than removing Classical Physics' deterministic inheritance, however, the science community reacted by introducing deterministic postulates to make Quantum Mechanics “fit” the prevailing classical framework. Unphysical postulates like the existence of a wavefunction, assumed to be a “complete” description of a physical system, and its square was assumed to be “measurable”, created a series of problems at the core of Physics, which remained unresolved for more than a century. This (part-4) paper promotes a discrete uncertainty principle as the foundation of a Discrete Physics. Symmetric-sampling incorporates this discrete uncertainty principle from the onset and provides comprehensive rules for handling measurements and discrete computer representations of signals and functions. This principle applies to all of Physics, including classical Quantum Mechanics and General Relativity. The red line of this paper is to complete the original “X-ray-microscope” model experiment proposed by Heisenberg in 1927. Retracing Heisenberg’s original “Gedanken” experiment helps us pinpoint the deterministic flaws at the core of Classical Physics and Quantum Mechanics, while assessing a fresh comprehensive Discrete Physics.

Lester C. Welch

Miguel Lorente

Joseph H. C. Wong

This paper introduces the Advanced Observer Model (AOM), a novel framework that integrates classical mechanics, quantum mechanics, and relativity through the observer’s role in constructing reality. Central to the AOM is the Static Configuration/Dynamic Configuration (SC/DC) conjugate, which examines physical systems through the interaction between static spatial configurations and dynamic quantum states. The model introduces a Constant Frame Rate (CFR) to quantize time perception, providing a discrete model for time evolution in quantum systems. By modifying the Schrödinger equation with CFR, the AOM bridges quantum and classical physics, offering a unified interpretation where classical determinism and quantum uncertainty coexist. A key feature of the AOM is its energy scaling model, where energy grows exponentially with spatial dimensionality, following the relationship E∝ ( π ) n . This dimensional scaling connects the discrete time perception of the observer with both quantum and classical energy distributions, providing insights into the nature of higher-dimensional spaces. Additionally, the AOM posits that spacetime curvature arises from quantum interactions, shaped by the observer’s discrete time perception. The model emphasizes the observer’s consciousness as a co-creator of reality, offering new approaches to understanding the quantum-classical transition. While speculative, the AOM opens new avenues for addressing foundational questions in quantum mechanics, relativity, dimensionality, and the nature of reality.