| _version_ | 1866901876561149952 |
|---|---|
| author | Thakur, Soumendra Nath |
| author_facet | Thakur, Soumendra Nath |
| contents | <p>This preprint presents the <strong>ECM Master Equation</strong>, a foundational axiom of Extended Classical Mechanics (ECM), establishing a unified transformation framework linking potential energy, mass variation, frequency, and kinetic energy.</p> <p>In ECM, physical reality is not composed of independent entities such as mass, energy, or force. Instead, all physical evolution is governed by a <strong>continuous frequency-driven manifestation process</strong>, expressed through the transformation chain:</p> <p><strong>ΔPEᴇᴄᴍ ↔ ΔMᴍ ↔ f ↔ ΔKEᴇᴄᴍ</strong></p> <p>Within this structure:</p> <ul> <li><strong>Potential energy (ΔPEᴇᴄᴍ)</strong> represents latent configurational imbalance,</li> <li><strong>Mass variation (ΔMᴍ)</strong> represents redistribution of that imbalance,</li> <li><strong>Frequency (f)</strong> encodes the rate of transformation,</li> <li><strong>Kinetic energy (ΔKEᴇᴄᴍ)</strong> emerges as the observable manifestation.</li> </ul> <p>The governing constraint of the framework is:</p> <p><strong>ΔKEᴇᴄᴍ = ΔMᴍ c² = h f</strong></p> <p>This relation is interpreted not as rest-energy equivalence, but as a <strong>dynamic manifestation identity</strong>, where energy arises from frequency-governed mass redistribution.</p> <p>A key contribution of this work is the introduction of a <strong>Planck-normalized frequency–mass mapping</strong>, defined through:</p> <ul> <li><strong>f₀ = fᴘ + Δf₀</strong> (layered frequency structure)</li> <li><strong>ΔMᴍ = k f</strong> (pre-Planck regime)</li> <li><strong>ΔMᴍ = h f</strong> (Planck regime)</li> <li><strong>ΔMᴍ / Mᴘ = f / fᴘ</strong> (normalized scaling relation)</li> </ul> <p>This formulation unifies emergent and fundamental regimes under a single scalable framework.</p> <p>The model further develops:</p> <ul> <li><strong>Hierarchical frequency decomposition</strong> (source, Planck, and observed components),</li> <li><strong>Composite mass structure</strong> (wave and Planck contributions),</li> <li><strong>Quantum transition interpretation</strong> as discrete frequency reconfiguration events:<br><strong>ΔE = -ΔPEᴇᴄᴍ = -ΔKEᴇᴄᴍ = h f</strong></li> </ul> <p>This implies that quantum emission is not a purely particle-level event but a <strong>restructuring of the underlying mass–potential–frequency field</strong>.</p> <h3><span><strong>Significance</strong></span></h3> <p>The ECM Master Equation provides a <strong>single unifying axiom</strong> for:</p> <ul> <li>Mass–energy transformation</li> <li>Quantum transitions</li> <li>Frequency-based dynamics</li> <li>Planck-scale normalization</li> <li>Emergence of observable physical phenomena</li> </ul> <p>It reframes physical laws as projections of a deeper <strong>frequency-governed transformation process</strong>, offering a coherent alternative foundation for classical and quantum descriptions within a unified formalism.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19560139 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | ECM Master Equation: Unified Frequency–Mass–Energy–Potential Axiom Thakur, Soumendra Nath Extended Classical Mechanics Frequency–Mass Relation Planck Normalization Kinetic Energy Emergence Potential Energy Transformation Quantum Transitions Unified Physical Axiom Phase-Based Dynamics <p>This preprint presents the <strong>ECM Master Equation</strong>, a foundational axiom of Extended Classical Mechanics (ECM), establishing a unified transformation framework linking potential energy, mass variation, frequency, and kinetic energy.</p> <p>In ECM, physical reality is not composed of independent entities such as mass, energy, or force. Instead, all physical evolution is governed by a <strong>continuous frequency-driven manifestation process</strong>, expressed through the transformation chain:</p> <p><strong>ΔPEᴇᴄᴍ ↔ ΔMᴍ ↔ f ↔ ΔKEᴇᴄᴍ</strong></p> <p>Within this structure:</p> <ul> <li><strong>Potential energy (ΔPEᴇᴄᴍ)</strong> represents latent configurational imbalance,</li> <li><strong>Mass variation (ΔMᴍ)</strong> represents redistribution of that imbalance,</li> <li><strong>Frequency (f)</strong> encodes the rate of transformation,</li> <li><strong>Kinetic energy (ΔKEᴇᴄᴍ)</strong> emerges as the observable manifestation.</li> </ul> <p>The governing constraint of the framework is:</p> <p><strong>ΔKEᴇᴄᴍ = ΔMᴍ c² = h f</strong></p> <p>This relation is interpreted not as rest-energy equivalence, but as a <strong>dynamic manifestation identity</strong>, where energy arises from frequency-governed mass redistribution.</p> <p>A key contribution of this work is the introduction of a <strong>Planck-normalized frequency–mass mapping</strong>, defined through:</p> <ul> <li><strong>f₀ = fᴘ + Δf₀</strong> (layered frequency structure)</li> <li><strong>ΔMᴍ = k f</strong> (pre-Planck regime)</li> <li><strong>ΔMᴍ = h f</strong> (Planck regime)</li> <li><strong>ΔMᴍ / Mᴘ = f / fᴘ</strong> (normalized scaling relation)</li> </ul> <p>This formulation unifies emergent and fundamental regimes under a single scalable framework.</p> <p>The model further develops:</p> <ul> <li><strong>Hierarchical frequency decomposition</strong> (source, Planck, and observed components),</li> <li><strong>Composite mass structure</strong> (wave and Planck contributions),</li> <li><strong>Quantum transition interpretation</strong> as discrete frequency reconfiguration events:<br><strong>ΔE = -ΔPEᴇᴄᴍ = -ΔKEᴇᴄᴍ = h f</strong></li> </ul> <p>This implies that quantum emission is not a purely particle-level event but a <strong>restructuring of the underlying mass–potential–frequency field</strong>.</p> <h3><span><strong>Significance</strong></span></h3> <p>The ECM Master Equation provides a <strong>single unifying axiom</strong> for:</p> <ul> <li>Mass–energy transformation</li> <li>Quantum transitions</li> <li>Frequency-based dynamics</li> <li>Planck-scale normalization</li> <li>Emergence of observable physical phenomena</li> </ul> <p>It reframes physical laws as projections of a deeper <strong>frequency-governed transformation process</strong>, offering a coherent alternative foundation for classical and quantum descriptions within a unified formalism.</p> |
| title | ECM Master Equation: Unified Frequency–Mass–Energy–Potential Axiom |
| topic | Extended Classical Mechanics Frequency–Mass Relation Planck Normalization Kinetic Energy Emergence Potential Energy Transformation Quantum Transitions Unified Physical Axiom Phase-Based Dynamics |
| url | https://doi.org/10.5281/zenodo.19560139 |