DOI: https://doi.org/10.13140/RG.2.2.20913.44643

Extended Classical Mechanics (ECM) is a theoretical framework proposed by Soumendra Nath Thakur, offering a post-relativistic cosmological model that reinterprets fundamental physical concepts such as mass, energy, force, and gravitational interaction.

A New View of Mass and Gravity:

Unlike traditional frameworks, which treat mass as a constant and unchanging quantity, ECM proposes that mass is a frequency-dependent, energy-related property—one that is redistributable, transformable, and field-dependent. According to ECM, gravitational effects are not governed by spacetime curvature or an external force but arise from an interplay between apparent mass and effective mass. The effective mass (Mᵉᶠᶠ) is described as the net gravitational mass resulting from the displacement of a negative apparent mass (−Mᵃᵖᵖ) from the total matter mass (Mᴍ), expressed as:

Mᵉᶠᶠ = Mɢ = Mᴍ − Mᵃᵖᵖ

In this view, gravity is redefined not as a force or geometric distortion but as a mass-binding condition, where the interaction between positive and negative mass components determines gravitational behaviour.

ECM introduces a three-phase model of cosmic evolution, governed by the progressive redistribution of mass-energy rather than relying on speculative inflationary fields or assumptions like spacetime curvature.

Variable Matter Mass:

The concept of variable matter mass (Mᴍ) is central to ECM’s theoretical structure. Matter mass evolves dynamically through interactions, oscillations, and energy exchange processes influenced by frequency–time distortions—how energy oscillations alter time perception—and energy density structures (ρᴇ), or how energy is distributed in space.

A key feature of ECM is Bidirectional Mass Transformation, where:

Primordial energy condenses into matter, forming particles and structures.

Matter, in turn, dissipates back into energy, particularly under the influence of dark energy.

This transformation is governed by the interplay between apparent and effective mass components. As dark energy’s negative effective mass (−Mᵃᵖᵖ) increases, it can reduce or invert matter mass, driving processes such as cosmic expansion and anti-gravitational effects.

This approach offers an alternative explanation for cosmic phenomena like dark matter, dark energy, and accelerating expansion without invoking hypothetical particles or unknown forces.

Relation to Other Theories:

Newtonian and Einsteinian Physics:

ECM challenges the assumption that mass is static and that inertial and gravitational mass are inherently equivalent. While Newtonian and Einsteinian frameworks treat mass as invariant except in relativistic contexts, ECM proposes that mass varies intrinsically through frequency-governed oscillations and energy interactions, extending classical ideas into a dynamic domain.

Conformal Cyclic Cosmology (CCC):

The theory of CCC, proposed by Roger Penrose, suggests the universe undergoes infinite cycles where the end of one “aeon” transitions into the beginning of another. For this to occur, all massive particles must lose their mass or decay over time.

ECM explicitly aligns with CCC by offering concrete energetic mechanisms for how mass transitions occur between massless and matter-dominated states. According to ECM, as matter mass dissipates back into energy—through frequency-driven oscillations—it mirrors the transition from the end of one cosmic phase to the birth of the next. This physical explanation strengthens CCC’s requirement for massless states at cosmic endpoints and provides a mechanism consistent with observations of large-scale cosmic anomalies.

Mathematical Foundations and Observational Relevance

ECM’s mathematical formulation for effective mass, kinetic energy, and mass oscillations demonstrates how variations in mass-energy relationships arise naturally from fundamental energetic processes. For example:

For photons and massless particles, kinetic energy is fully explained by frequency-dependent mass-energy relations.

Eᴇᴄᴍ = ∆Mᴍc² = Mᴍc²

For massive particles, matter mass is expressed as contributions from de Broglie frequency oscillations (∆Mᴍᵈᴮ) and Planck-scale energy interactions (∆Mᴍᴾ):

Mᴍ = ∆Mᴍᵈᴮ + ∆Mᴍᴾ, f = fᵈᴮ + fᴾ

KEᴇᴄᴍ=(∆Mᴍᵈᴮ + ∆Mᴍᴾ) c²

These formulations integrate micro-level quantum behaviours with macro-level cosmic phenomena, offering a unified framework.

Observational studies on dark energy’s influence on galaxy clusters, along with anomalies in cosmic microwave background radiation, provide empirical support for ECM’s predictions.

Applications and Broader Implications:

ECM’s variable matter mass framework connects with earlier works such as:

Appendix 30: Post-latent energetic dynamics and dual-state evolution of the universe.

Appendix 32: Energy density structures underlying frequency-dependent mass.

Appendix 43: Reinterpreting the origin of mass as a transformation of primordial energy.

Together, these applications reinforce ECM’s unified approach, bridging theoretical constructs with real-world observations and offering fresh insights into the evolution of the universe.

Conclusion

Extended Classical Mechanics (ECM) presents a transformative reinterpretation of mass, gravity, and cosmic evolution. By redefining mass as a frequency-dependent, emergent property influenced by energy oscillations and distortions, ECM challenges long-standing assumptions in classical and relativistic physics.

The framework’s explanation of dark energy’s role in reducing or inverting mass, its alignment with cyclic cosmology theories, and its grounding in observable phenomena provide a comprehensive model that integrates particle kinetics with large-scale cosmic dynamics.

ECM’s approach deepens our understanding of how energy and matter interact across scales, offering profound implications for both theoretical physics

and cosmology.