Emergence I (Extended Edition with Full Derivations): A Unified Field Theory from Wave Intersections on a Pre-Geometric Canvas
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| Format: | Recurso digital |
| Language: | English |
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2026
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| _version_ | 1866901931871436800 |
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| author | Ong, Edwin |
| author_facet | Ong, Edwin |
| contents | <p>This paper presents a complete, mathematically rigorous unified field theory in which spacetime, quantum mechanics, gauge forces, and gravity emerge from a single mechanism: wave intersections on a pre-geometric canvas.</p> <p>The theory is built from first principles. The fundamental entities are mathematical oscillators (pulsating points) with intrinsic frequency: one time point and three space points. Their analog oscillations generate continuous space waves and time waves. When a space wave and a time wave intersect above threshold, a closed wave — a spacetime particle — forms. These particles collectively form a discrete voxel lattice, which is physical spacetime. Gravity arises from compression of this lattice.</p> <p>From these postulates, this paper derives step by step:</p> <p>· The Einstein field equations (via Regge calculus with a complete convergence proof)<br>· Maxwell's equations (U(1) gauge theory)<br>· Yang-Mills equations (SU(2) and SU(3) gauge theories)<br>· The Schrödinger equation (from slowly varying envelope approximation)<br>· The Born rule (from scale separation and time-averaged intensity)<br>· The Klein-Gordon and Dirac equations<br>· The Standard Model gauge group SU(3)×SU(2)×U(1) (from spatial charge)<br>· The spin-statistics connection (from loop twist topology)</p> <p>The paper is presented in two parts:</p> <p>· Part I preserves the original 2D formulation with 36 postulates and five core equations, capturing the essential physical picture with simplicity and clarity.<br>· Part II generalizes to 3+1 dimensions, introduces the sixth core equation (spatial charge and gauge symmetry), and provides complete derivations.</p> <p>A postulate reduction table demonstrates that the 36 original postulates condense to 7 fundamental postulates, with the remainder becoming derived theorems. The model resolves the measurement problem (threshold collapse), black hole singularities (minimum lattice spacing ℓ_P), and the information paradox (closed wave phases). Open problems are acknowledged honestly.</p> <p>What this paper is: A complete, self-contained derivation of the fundamental equations of physics from a small set of pre-geometric postulates.</p> <p>What this paper is not: A compatibility study. (Compatibility with 50+ phenomena across all of physics is demonstrated in companion Papers II–VIII.)</p> <p>Keywords: unified field theory, canvas model, emergence, pre-geometric, wave intersections, discrete spacetime, lattice gravity, quantum gravity, Einstein equations, Maxwell equations, Yang-Mills, Schrödinger equation, Born rule, spin-statistics, dark matter, black hole remnants</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19940261 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Emergence I (Extended Edition with Full Derivations): A Unified Field Theory from Wave Intersections on a Pre-Geometric Canvas Ong, Edwin <p>This paper presents a complete, mathematically rigorous unified field theory in which spacetime, quantum mechanics, gauge forces, and gravity emerge from a single mechanism: wave intersections on a pre-geometric canvas.</p> <p>The theory is built from first principles. The fundamental entities are mathematical oscillators (pulsating points) with intrinsic frequency: one time point and three space points. Their analog oscillations generate continuous space waves and time waves. When a space wave and a time wave intersect above threshold, a closed wave — a spacetime particle — forms. These particles collectively form a discrete voxel lattice, which is physical spacetime. Gravity arises from compression of this lattice.</p> <p>From these postulates, this paper derives step by step:</p> <p>· The Einstein field equations (via Regge calculus with a complete convergence proof)<br>· Maxwell's equations (U(1) gauge theory)<br>· Yang-Mills equations (SU(2) and SU(3) gauge theories)<br>· The Schrödinger equation (from slowly varying envelope approximation)<br>· The Born rule (from scale separation and time-averaged intensity)<br>· The Klein-Gordon and Dirac equations<br>· The Standard Model gauge group SU(3)×SU(2)×U(1) (from spatial charge)<br>· The spin-statistics connection (from loop twist topology)</p> <p>The paper is presented in two parts:</p> <p>· Part I preserves the original 2D formulation with 36 postulates and five core equations, capturing the essential physical picture with simplicity and clarity.<br>· Part II generalizes to 3+1 dimensions, introduces the sixth core equation (spatial charge and gauge symmetry), and provides complete derivations.</p> <p>A postulate reduction table demonstrates that the 36 original postulates condense to 7 fundamental postulates, with the remainder becoming derived theorems. The model resolves the measurement problem (threshold collapse), black hole singularities (minimum lattice spacing ℓ_P), and the information paradox (closed wave phases). Open problems are acknowledged honestly.</p> <p>What this paper is: A complete, self-contained derivation of the fundamental equations of physics from a small set of pre-geometric postulates.</p> <p>What this paper is not: A compatibility study. (Compatibility with 50+ phenomena across all of physics is demonstrated in companion Papers II–VIII.)</p> <p>Keywords: unified field theory, canvas model, emergence, pre-geometric, wave intersections, discrete spacetime, lattice gravity, quantum gravity, Einstein equations, Maxwell equations, Yang-Mills, Schrödinger equation, Born rule, spin-statistics, dark matter, black hole remnants</p> |
| title | Emergence I (Extended Edition with Full Derivations): A Unified Field Theory from Wave Intersections on a Pre-Geometric Canvas |
| url | https://doi.org/10.5281/zenodo.19940261 |