Quantum Wavespace Theory

A Simplified Physical Foundation

Quantum Wavespace Theory (QWST) explores whether the familiar structure of relativistic quantum physics emerges from a single, constrained standing-wave substrate rather than from a collection of independent postulates. The theory assumes only Lorentz invariance, a universal propagation speed, and a maximum sustainable energy density, from which stable eigenmodes naturally arise. Within this framework, particles are not fundamental objects but persistent wave configurations; electric charge, gauge invariance, and spin reflect phase-closure and boundary geometry; and gravitational behavior emerges from slow boundary leakage. QWST does not replace established theories such as the Dirac equation or quantum electrodynamics, but seeks to clarify their geometric and dynamical origin within a deeper wave-based foundation.

Figure 1-4. Evolution of a one-dimensional spherical nucleon mode as energy is increased. The wave saturates at a finite central density, forming a steep-gradient boundary that reflects excess energy outward until a stable standing-wave configuration is reached.

A Simplified Physical Foundation
https://zenodo.org/records/17822703

Quantum Wavespace Eigensystem, Part I
https://zenodo.org/records/17617160

Quantum Wavespace Eigensystem, Part II
https://zenodo.org/records/17617465

Quantum Wavespace Eigensystem, Part III
https://zenodo.org/records/17944948

Quantum Wavespace Theory
https://zenodo.org/records/17094408

The latest publications are available here: https://zenodo.org/communities/qwst/

Figure 5. Models of Nucleon, Electron, Photon, and Quarks.

Core Concepts of Quantum Wavespace Theory (QWST)

Wavespace Substrate
The universe is modeled as a continuous, Lorentz-invariant standing-wave substrate governed by two constraints: a universal propagation speed and a maximum stable energy density. This substrate is not an added medium, but the global boundary condition required for consistent wave dynamics.

Particles as Stable Eigenmodes
Elementary particles arise as long-lived standing-wave eigenmodes of the substrate. Only two stable families exist: spherical modes that store energy (nucleons) and cylindrical modes that redirect energy (leptons).

Saturation and Boundary Formation
When wave amplitude reaches the maximum sustainable energy density, a steep gradient forms that acts as a natural boundary. This replaces ad hoc confinement mechanisms and explains particle stability.

Emergent Charge, Spin, and Gauge Structure
Electric charge, spin-1/2 behavior, and U(1) gauge invariance arise from phase circulation and boundary-phase redundancy of cylindrical eigenmodes, rather than being postulated as fundamental symmetries.

Geometric Origin of Physical Constants
Constants such as the fine-structure constant ( $\alpha$ α), electron mass, magnetic anomaly, and gravitational coupling emerge as geometric overlap invariants of admissible eigenmodes, rather than free parameters.

What Quantum Wavespace Theory Is Not

QWST is not an alternative to the Standard Model, quantum mechanics, special relativity, or general relativity.
QWST does not compete with established physical theories—it explains why they work. QWST provides a deeper, more primitive foundation from which these theories emerge as effective limits. Their mathematical form and empirical success are preserved, while their origin is traced to underlying wave and boundary dynamics.

QWST does not introduce complexity – it is a closed system defined by C and P0.
QWST does not introduce hidden variables, additional dimensions, new forces, or speculative particles. It does not modify the Dirac equation, Maxwell’s equations, or Einstein’s field equations within their established domains of validity.

QWST is not packaging existing physics in a new mathematical language.
QWST is not an interpretation layered on top of existing formalisms, nor a reformulation of quantum mechanics in different mathematical language. It does not posit an ether, preferred reference frame, or violation of Lorentz invariance.

QWST is not numerology.
Its relationships were not obtained by fitting constants to data, but arise from a physical model constrained by energy saturation and wave stability. The agreement with measured constants was discovered after the framework was established, not imposed beforehand.

QWST is not an ether or a recycled wave theory.
It introduces a new ingredient—a Lorentz-invariant, saturation-limited wavespace that supports only specific stable eigenmodes—rather than revisiting earlier mechanical or geometric models of space.

How QWST Differs from Standard Quantum Theory

No Fundamental Particles or Fields
QWST does not assume particles, fields, or gauge symmetries as primitives. These emerge from wave geometry and saturation constraints.

Wave–Particle Duality Resolved
Wave and particle behavior are unified: localized particles are standing waves whose coherence and boundary structure determine observable behavior.

Gravity as Boundary Leakage
Weak gravitational effects arise from slow energy leakage through saturated boundaries, producing an effective refractive structure consistent with general relativity in the weak-field limit.

Unified Geometric Framework
Quantum mechanics, electromagnetism, and gravity emerge from a single constrained wave substrate, without quantization rules or renormalization as fundamental inputs.

Predictions & Potential Tests

Reproduces the fine-structure constant and electron magnetic anomaly without perturbative renormalization.
Predicts specific saturation-driven particle structures and boundary geometries.
Suggests experimentally testable deviations when wave saturation or boundary closure fails at high excitation.

Status

Quantum Wavespace Theory is a mathematically explicit, wave-based framework that reproduces key empirical results of quantum electrodynamics and gravitation while offering a deeper geometric explanation of their origin. It is an active research program developed across multiple peer-reviewed preprints and companion analyses.

QUANTUM WAVESPACE THEORY 2024 – DETAILED DOCUMENT(QWST)

The full 110-page PDF is available below. It includes extended derivations of the electron magnetic anomaly, FFT analyses of empirical elastic and fusion data showing the shell-spacing fingerprint, and 3D visualizations of the nucleon, electron, and photon generated directly from the eigenfunctions.

Harry W. Schmitz derived the limiting pressure of a nucleon core in the 1970s as a direct consequence of his theoretical standing-wave framework:

P₀ = 5.15851475432 × 10³⁵ Pa

Nearly forty years later, the first experimental extraction of the proton’s internal pressure distribution by Burkert, Elouadrhiri, and Girod (2018) reported a central pressure of order 10³⁵ Pa, the highest known in the universe. Before publication in 2018, no experimental value was available.

Their analysis also located a zero-pressure node defining the proton’s effective radius, distinct from earlier RMS charge-radius estimates. They reported the internal pressure changes sign from repulsive to binding at approximately 0.6 fm, matching the zero-pressure node r₀ predicted by H. W. Schmitz.

r₀ = 6.60724060118 × 10⁻¹⁶ m

Both the central pressure and the node radius coincide with the values calculated by H. W. Schmitz in the 1970s. This constitutes a rare case where a quantitative prediction, made decades before experiment, was later confirmed at the same scale. The precision of these predictions provides a benchmark for future measurements: as empirical constraints on pressure distributions and spatial scales improve, they will further test the theory’s predictive framework. The agreement underscores the predictive and falsifiable nature of the QWST postulates.

Quantum_Wavespace_Theory_2025 (2)Download

An analysis of
The Physical and Philosophical Nature of the Universe
By H. W. Schmitz and H. A. Schmitz
Published in 1982 by Harry Arthur Schmitz
Copyright 1982 by Harry A. Schmitz
Library of Congress catalog card number: 83 – 70164

PREFACE

This series introduces the scientific community to an obscure yet remarkable treatise written in the 1970s by my father, Harry Walter Schmitz. His original work, The Physical and Philosophical Nature of the Universe, presents a unified field hypothesis with conceptual and mathematical rigor. Despite the strength of its foundational premise, the theory has remained largely unknown within mainstream physics.

We—the current authors—are engineers rather than physicists. Leveraging recent advancements in artificial intelligence, we undertook a comprehensive review and analysis of H. W. Schmitz’s original manuscript. Our analysis confirmed that Quantum Wavespace Theory is internally consistent, mathematically rigorous, and logically well-founded. Most notably, we successfully validated the theory’s capability to derive fundamental physical constants—including the Rydberg constant, Planck’s constant, and the fine-structure constant—from the first principles defined within the theory. These results stand as compelling evidence that QWST may offer a deeper foundational understanding of quantum mechanics and wave interactions.

Our primary aim is to spark interest and inspire further investigation by the physics community. Modern high-performance computational methods and advanced simulations could further validate, refine, and potentially extend the original theory. We believe this work holds tremendous potential for new insights into the physical underpinnings of quantum theory, and will provide a robust framework for innovative research—particularly in fusion energy and quantum-scale phenomena.

We humbly invite researchers, physicists, and computational scientists to rigorously test and explore the implications of Quantum Wavespace Theory.

Quantum Wavespace Theory (QWST)
In the articles that follow, we focus on the idea that our universe emerged from a fundamental wave framework, which we call “quantum wavespace.” This core hypothesis provides a direct, mathematical bridge to the observed quantization in atomic and subatomic physics. Where standard quantum mechanics offers precise predictions but limited insight into why nature is so quantized, Quantum Wavespace Theory proposes that stable wave resonance patterns within a universal wave continuum are the underlying cause. By specifying boundary conditions—such as the speed of light , the fundamental frequency of wavespace, and the maximum stable energy density—we are able to derive fundamental physical constants used in contemporary physics.

QWST builds on a striking premise: that all material phenomena emerge from stable wave modes within a universal, dynamic wavespace. The theory sets forth a rigorous—though still evolving—mathematical structure first conceived in the 1970s and now poised for expansion using today’s more powerful computational capabilities. We invite readers to examine the mathematical arguments presented here, assess the derivations of constants, and consider how modern numerical modeling could further illuminate QWST’s predictions.

The Physical and Philosophical Nature of the Universe (PPNU)
While Harry Walter Schmitz’s original writings also discuss cosmological and philosophical perspectives, these aspects, though fascinating, are beyond the scope of this edition. Here, our objective is more targeted: to show how a wave-only paradigm can replicate (and potentially refine) the core successes of quantum theory, and to invite critical examination of these derivations by experts in physics and mathematics. We may explore the broader cosmological framework of the treatise in the future, but this text remains focused on the atomic-nuclear scale.

The complete contents of Harry Walter Schmitz’ treatise are available in the original 1982 Edition, The Physical and Philosophical Nature of the Universe by H. W. Schmitz and H. A. Schmitz. Special thanks to my brother, Harry Arthur Schmitz, for publishing our father’s final transcript of his treatise, after his unexpected passing in 1979. This edition, titled Quantum Wavespace Theory, focuses on structures and interactions at the atomic-nuclear level. It includes a focused analysis of the original chapters 5 through 12 of The Physical and Philosophical Nature of the Universe. Given the extreme density of the material, the chapters covering cosmological concepts, including the analysis of the evolution of wavespace, are best left for review in a separate edition that focuses on cosmology. H. A. Schmitz has published a number of papers exploring these aspects in his work exploring the Fractal Cosmos.

This edition was developed in hopes of bringing these concepts into the public forum. After the departure of our father, my brother and I were faced with the challenge of presenting his work, despite lacking his profound insight and extensive interdisciplinary knowledge. My brother and I have Mechanical Engineering Degrees, with my brother having a PhD in Material Science—qualifications that only begin to represent the breadth of understanding our father possessed.

We ask, with humility, that those in the science community—who are far more qualified than we are—review these concepts. We hope this edition, with its focus on atomic-nuclear interactions, will serve as a foundation for applying QWST to experimental physics, and will support the goal of refining and testing its principles for practical applications.

Here are direct links to the PDF articles: