Soumendra Nath Thakur
Tagore's Electronic Lab, WB, India
Abstract
In classical physics, the relationship W=F⋅s defines work as force acting through space, and quantum theory introduces the Planck constant h as the fundamental quantum of action. However, both frameworks become inadequate at frequencies approaching the Planck limit fᴘₗₐₙₖ ≈ 1.855 × 10⁴³ Hz. Extended Classical Mechanics (ECM) introduces a refined energetic domain where spacetime, mass, and classical action cease to function as defining constructs. This appendix presents a critical re-examination of action, frequency, and energy interactions beyond the Planck threshold. It describes the transition into a regime of super-Planckian energetic oscillations, where particle identity is lost, potential energy is instantly rendered kinetic, and only energetic wave behaviour remains. Importantly, this framework preserves energy conservation, albeit through abstract, non-quantized means, proposing a new proportionality constant k where h fails. Connections to published ECM materials and quantum-gravitational unification are included to support this conceptual and mathematical extension of physical theory.
1. Classical and Quantum Action Breakdown
In standard mechanics, physical work is defined as:
W = F⋅sAnd in quantum mechanics, action is characterized by:
h ∼ E⋅t or h ∼ p⋅xHowever, these frameworks both fail to accurately describe energy interaction at or beyond the Planck frequency threshold. At this scale, ECM shows that space and time are no longer stable constructs and classical action loses physical applicability. Instead, energy transforms instantly into a purely kinetic vibrational field, and conventional particulate carriers of momentum or mass cease to exist.
2. Energetic Environment Beyond Planck Scale
At the Planck boundary:
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Rest mass collapses; no material particle structure persists.
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Spacetime decomposes into non-local vibratory states.
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Potential energy cannot remain latent; it converts directly into immediate kinetic manifestation.
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Conservation of energy persists but not via classical measurable action.
This corresponds to a regime defined by:
Δf = f₀− fᴘₗₐₙₖ during t₀− tᴘₗₐₙₖHere, Planck's constant h can no longer serve as a useful quantum of action. Instead, ECM postulates a separate constant k, governing super-Planckian transitions, which are described by pure oscillatory existence.
3. Unified Gravitational Field and Pre-Spacetime Oscillation
In this state:
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Energetic density approaches infinity.
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Gravitational influence becomes unbounded and self-unified.
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No classical force or rest mass structure exists.
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All known physical laws break down—except the principle of energy persistence.
ECM redefines this realm as a zero-dimensional oscillatory continuum, where:
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Time exists only as cyclical recurrence.
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Frequency becomes the sole parameter of physical distinction.
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Propagation trends toward superluminal oscillation—not via signal transmission, but via pure geometric vibration.
4. Physical Meaning of Super-Planckian Frequencies
Planck frequency fᴘₗₐₙₖ = 1/tᴘₗₐₙₖ does not mark the upper bound of energetic phenomena but rather signifies a dimensional transition zone. Observable high-frequency radiation such as:
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Ultra-high-energy gamma rays (e.g.,
lies far below this threshold.
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Beyond this, hyper frequencies may exist within a non-local, pre-physical substratum—functionally invisible under classical spacetime observation.
5. ECM Position: Beyond h, Beyond Mass, Beyond Force
ECM maintains:
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Conservation of energy continues beyond Planck boundaries.
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New constants must replace h in describing such energetic domains.
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Planck’s constant is a threshold, not a finality.
ECM thereby unifies gravitational, quantum, and energetic phenomena through oscillatory logic, not particulate behaviour.
List of ECM Appendices and Annexures
• Appendix A – Standard Mass Definitions in ECM
• Appendix 3 – Fundamental Total Energy in ECM
• Appendix 4 – Negative Apparent Mass and Mass Continuity in ECM
• Appendix 5 – Temporal Modulation vs Temporal Scale Variation in ECM
• Appendix 6 – Angular-Time Correspondence in ECM
• Supplement A – Interpretive Basis and Conclusion to Appendix 6
• Supplement A2 – External Commentary on Supplement A
• Appendix 7 – ECM-Specific Framework for Photon Sourcing and Emission Pathways
• Appendix 8 – Energetic Structures Beyond Planck Threshold and the Breakdown of Classical Action
Primary References (from Appendix 8 content)
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Thakur, S. N. (2025). Appendix 3: Fundamental Total Energy in ECM. https://doi.org/10.13140/RG.2.2.21532.19841
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Thakur, S. N. (2025). Mass-Energy Transformations in ECM. https://doi.org/10.13140/RG.2.2.24863.27040
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Thakur, S. N. (2025). Periodicity and Phase Shift Dynamics between the Big Bang and Planck Time. https://doi.org/10.13140/RG.2.2.29274.25285
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Thakur, S. N. (2024). Description of Planck Equation and Energy-Frequency Relationship. https://www.researchgate.net/publication/375416343
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Thakur, S. N. (2024). Unified Quantum Cosmology: Exploring Beyond the Planck Limit with Universal Gravitational Constants. https://doi.org/10.32388/26u31c
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Thakur, S. N. (2024). Why is 1° time interval (T) the smallest meaningful mathematical expression of the Planck frequency? https://doi.org/10.13140/RG.2.2.32358.40001
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Thakur, S. N. (2023). Quantum Scale Oscillations and Zero-Dimensional Energy Dynamics. https://doi.org/10.13140/RG.2.2.36320.05124
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Thakur, S. N. (2023). Energy Persistence Beyond Planck Scale. https://www.researchgate.net/publication/375488896
Additional References
• Thakur, S. N. (2025). Supplement A to Appendix 6 – Interpretive Basis and Conclusion.
• Thakur, S. N. (2025). Supplement A2 – Commentary on Supplement A.
• Additional references to standard photon physics, emission spectra, and synchrotron mechanisms as discussed in astrophysics literature (NASA, CERN reports, etc.)
