Appendix 23_Part-2: Frequency as More Fundamental than Mass in Extended Classical Mechanics

Abstract

Extended Classical Mechanics (ECM) posits that frequency-induced energy is more fundamental than mass. This appendix elaborates on the derivation of effective mass (M^eff) and kinetic energy (KE_ECM) from primary frequency components, incorporating both de Broglie and Planck contributions. The framework demonstrates that mass is a secondary manifestation of underlying energy cycles, providing a unified understanding of photon energy, dynamic mass, and potential energy, independent of relativistic mass–energy postulates.

Keywords

Frequency, Planck frequency, de Broglie frequency, effective mass, KE_ECM, photon energy, dynamic mass, Extended Classical Mechanics, potential energy, energy–mass relation

Introduction

Extended Classical Mechanics (ECM) considers the primordial energetic state of the universe, wherein potential energy transforms into kinetic energy prior to the formation of mass. ECM asserts the primacy of frequency in energy manifestations, challenging the conventional notion that mass is the fundamental physical entity.

Frequency as the Fundamental Quantity in ECM

This appendix continues from Appendix 23, emphasizing that the total effective frequency — comprising de Broglie (f^dB) and Planck (f^P) components — governs the emergence of matter mass (M_M) and kinetic energy (KE_ECM). ECM’s formulation treats mass as a frequency-induced phenomenon rather than a fundamental constant.

Mathematical Formulation

1. Planck Relation:
   E = hf
2. ECM Kinetic Energy (photon velocity v = c):
   KE_ECM = ½ M^eff c²
3. Effective Mass from Photon Energy:
   M^eff = hf / c²
4. Unified ECM Kinetic Energy (de Broglie + Planck contributions):
   KE_ECM = (½ ΔM_M^dB + ΔM_M^P) c² = hf

   where f = f^dB + f^P

Rebuttal

ECM’s frequency-based formulation bypasses inconsistencies associated with relativistic mass–energy equivalence, particularly in photon and sub-light particle dynamics (see Appendix 38 forthcoming). Traditional interpretations relying on invariant mass are replaced by frequency-derived effective mass and dynamic mass principles.

Applications across Previous Appendices

• Appendix 7 – Photon sourcing and emission pathways: ECM frequency framework explains photon inheritance.
• Appendix 15 – Photon-based energy redistribution and electron dynamics: linked to frequency contributions to kinetic energy.
• Appendix 20 – Frequency scaling in ECM: foundational for understanding dynamic mass generation.
• Appendix 23 – Frequency-origin of energy, photon kinetics, and mass displacement: provides the primary theoretical basis.
• Appendix 31 – Frequency and energy relations in ECM: reinforces photon–mass–frequency linkage.

Conclusion

Frequency is the primary physical quantity in ECM, with mass as a derived manifestation of energy cycles. The Planck and de Broglie components together define dynamic mass and kinetic energy. This appendix complements Appendix 23 by emphasizing the direct derivation of effective mass from frequency, providing a self-consistent framework for photon energy, potential energy, and mass emergence in ECM.

Alphabetical List of Mathematical Terms (ECM Context)

References

• Appendix 23: Frequency-Origin of Energy, Photon Kinetics, and Mass Displacement in ECM
• Appendix 7; Appendix 15; Appendix 20; Appendix 31; Appendix 38 (forthcoming)