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| Format: | Recurso digital |
| Language: | English |
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2019
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| Online Access: | https://doi.org/10.5281/zenodo.17759726 |
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| _version_ | 1866902233869713408 |
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| author | Hanamura, Satoshi |
| author_facet | Hanamura, Satoshi |
| contents | <p>[5 Application] This paper presents the first systematic application of the geometric framework introduced in <em>A Model of an Electron Including Two Perfect Black Bodies</em> (DOI: <a href="https://zenodo.org/records/16759284" target="_blank" rel="noopener">10.5281/zenodo.16759284</a>). It marks a conceptual step toward linking the 0-Sphere electron model with stochastic processes in quantum mechanics.</p> <p>The analysis builds on the closed geometric equation<br><em>E₀ = E₀ ( cos⁴(θ/2) + sin⁴(θ/2) + 1/2 sin²(θ) )</em>,<br>assigning it a quantum-mechanical interpretation. This allows the two-kernel model to account algebraically for random walk and Brownian motion phenomena.</p> <p>A key insight comes from the temporal phase dynamics between kernels <em>A</em> and <em>B</em>. During inter-kernel transitions, the photon sphere oscillates harmonically. At the π time phase, all electron energy transfers to kernel <em>B</em>, giving sin⁴(θ/2) = 1. At this instant, the photon sphere’s energy drops to zero, creating a unique geometric state in which motion becomes differentiable across all temporal domains. The next kernel is then chosen probabilistically, forming the stochastic basis of the model.</p> <p>The study advances from one-dimensional random walks (drunkard’s walk) to two-dimensional lattice configurations. This dimensional progression shows how instantaneous velocity nullification enables the coexistence of continuous motion with genuine randomness, requiring probabilistic landing points to maintain mathematical continuity.</p> <p>As the first exploration of stochastic applications within the internal-structure model, this work establishes groundwork for explaining how deterministic geometric equations can produce apparently random quantum behaviors, opening a new research direction in the 0-Sphere theoretical program.</p> <p><strong>Relation to Previous Works:</strong></p> <ol> <li> <p>0-Sphere Model — DOI: <a href="https://zenodo.org/records/16759284" target="_blank" rel="noopener">10.5281/zenodo.16759284</a></p> </li> <li> <p>Coexistence of Dirac Positive/Negative States — DOI: <a href="https://zenodo.org/records/16817190" target="_blank" rel="noopener">10.5281/zenodo.16817190</a></p> </li> <li> <p>Anomalous Magnetic Moment via Lorentz Contraction — DOI: <a href="https://zenodo.org/records/16871305" target="_blank" rel="noopener">10.5281/zenodo.16871305</a></p> </li> </ol> <p>Community: <a href="https://zenodo.org/communities/satoshi-hanamura-papers/" target="_blank" rel="noopener">Satoshi-Hanamura-Papers</a></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17759726 |
| institution | Zenodo |
| language | eng |
| publishDate | 2019 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Transition Theory of An Electron Traveling from Uncertain to Causal Basis Hanamura, Satoshi 0-Sphere model <p>[5 Application] This paper presents the first systematic application of the geometric framework introduced in <em>A Model of an Electron Including Two Perfect Black Bodies</em> (DOI: <a href="https://zenodo.org/records/16759284" target="_blank" rel="noopener">10.5281/zenodo.16759284</a>). It marks a conceptual step toward linking the 0-Sphere electron model with stochastic processes in quantum mechanics.</p> <p>The analysis builds on the closed geometric equation<br><em>E₀ = E₀ ( cos⁴(θ/2) + sin⁴(θ/2) + 1/2 sin²(θ) )</em>,<br>assigning it a quantum-mechanical interpretation. This allows the two-kernel model to account algebraically for random walk and Brownian motion phenomena.</p> <p>A key insight comes from the temporal phase dynamics between kernels <em>A</em> and <em>B</em>. During inter-kernel transitions, the photon sphere oscillates harmonically. At the π time phase, all electron energy transfers to kernel <em>B</em>, giving sin⁴(θ/2) = 1. At this instant, the photon sphere’s energy drops to zero, creating a unique geometric state in which motion becomes differentiable across all temporal domains. The next kernel is then chosen probabilistically, forming the stochastic basis of the model.</p> <p>The study advances from one-dimensional random walks (drunkard’s walk) to two-dimensional lattice configurations. This dimensional progression shows how instantaneous velocity nullification enables the coexistence of continuous motion with genuine randomness, requiring probabilistic landing points to maintain mathematical continuity.</p> <p>As the first exploration of stochastic applications within the internal-structure model, this work establishes groundwork for explaining how deterministic geometric equations can produce apparently random quantum behaviors, opening a new research direction in the 0-Sphere theoretical program.</p> <p><strong>Relation to Previous Works:</strong></p> <ol> <li> <p>0-Sphere Model — DOI: <a href="https://zenodo.org/records/16759284" target="_blank" rel="noopener">10.5281/zenodo.16759284</a></p> </li> <li> <p>Coexistence of Dirac Positive/Negative States — DOI: <a href="https://zenodo.org/records/16817190" target="_blank" rel="noopener">10.5281/zenodo.16817190</a></p> </li> <li> <p>Anomalous Magnetic Moment via Lorentz Contraction — DOI: <a href="https://zenodo.org/records/16871305" target="_blank" rel="noopener">10.5281/zenodo.16871305</a></p> </li> </ol> <p>Community: <a href="https://zenodo.org/communities/satoshi-hanamura-papers/" target="_blank" rel="noopener">Satoshi-Hanamura-Papers</a></p> |
| title | Transition Theory of An Electron Traveling from Uncertain to Causal Basis |
| topic | 0-Sphere model |
| url | https://doi.org/10.5281/zenodo.17759726 |