Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803 | postmasterenator@gmail.com | June 28, 2025
Abstract:
Extended Classical Mechanics (ECM) offers a foundational reinterpretation of motion and gravity, shifting the focus from externally imposed forces to the internal transformation of mass-energy into dynamically effective quantities. Within this rigorously defined framework, ECM reconstructs the origin of the Big Bang as a self-triggered physical event—emerging through the spontaneous and mathematically expressible conversion of a non-positive gravitational potential (−∆PEᴇᴄᴍ) into universal-scale kinetic energy (KEᴇᴄᴍ,ᴜₙᵢᵥ). This formulation provides a concrete, testable foundation that unifies cosmological expansion, force emergence, and mass-energy redistribution under the principle of internal energetic causality.
1. Foundations of Effective Dynamics in ECM
In ECM, the nature of motion and gravitational interaction departs fundamentally from classical interpretations. Instead of being driven solely by externally applied forces, these dynamics emerge from internal transformations of mass-energy and the resulting effective quantities: effective force (Fᴇᴄᴍ), effective mass (Mᵉᶠᶠ), and effective acceleration (aᵉᶠᶠ).
The effective force in motion, Fᴇᴄᴍ, is defined as:
Fᴇᴄᴍ = Mᵉᶠᶠaᵉᶠᶠ = (Mᴍ − ∆Mᴍ) aᵉᶠᶠ
Similarly, the gravitational force Fɢ in ECM becomes:
Fɢ = Mᵉᶠᶠgᵉᶠᶠ ⋅ h = (Mᴍ − ∆Mᴍ)gᵉᶠᶠ ⋅ h
Here, internal energy displacement drives the transformation of potential energy (PEᴇᴄᴍ) into kinetic energy (KEᴇᴄᴍ), mediated by the emergence of apparent negative mass (−Mᵃᵖᵖ), equivalent to −∆Mᴍ.
2. Internal and External Force Roles in ECM
In classical systems governed by matter mass (Mᴍ), forces act externally in a Newtonian sense. But when the mass involved is −Mᵃᵖᵖ, ECM shows that the force emerges internally as a direct result of energy redistribution:
−∆PEᴇᴄᴍ → KEᴇᴄᴍ = −Mᵃᵖᵖc²
Beyond Planck threshold, this equation becomes:
−∆PEᴇᴄᴍ → KEᴇᴄᴍ = −Mᵃᵖᵖv², where v > c, as beyond Planck threshold: >ℓₚ/\<tₚ results → v > c
This shift defines force not merely as an applied interaction but as an emergent property of internal energetic imbalance.
3. Dual Force Action and Energetic Mass Dynamics
Effective force in ECM has a dual character:
• On Mᴍ: leads to a decrease in matter mass, converted to energy.
• On −Mᵃᵖᵖ: acts directly, enabling self-sustained growth of kinetic energy.
The system transitions from classical mass structure to a mass-energy dynamic where −Mᵃᵖᵖ not only arises from transformation but actively sustains force.
4. Gravitational Polarity and Threshold Effects
The gravitational polarity of an ECM system depends on the ratio of Mᴍ to |∆Mᴍ|:
• Mᴍ > |∆Mᴍ| ⇒ Positive gravitational polarity (attractive)
• |∆Mᴍ| > Mᴍ ⇒ Negative gravitational polarity (repulsive)
This polarity threshold determines whether systems gravitate or expand internally, a foundation for radiation-induced motion, inflation, and dark energy.
5. Mathematical Formulations
• Motion: Fᴇᴄᴍ = Mᵉᶠᶠaᵉᶠᶠ, Eₜₒₜₐₗ = PEᴇᴄᴍ + KEᴇᴄᴍ
• KE from displacement: KEᴇᴄᴍ = −∆PEᴇᴄᴍ = ∆Mᴍc²
• Gravitational field: gᵉᶠᶠ(h) = G(Mᵉᶠᶠ/r²) or gᵉᶠᶠ ∝ 1/hf where hf = E is the Planck equation
These expressions ground ECM in testable, internally consistent mathematics.
6. Big Bang as an Internally Generated Event
According to ECM, the Big Bang does not require external causation. Instead, it is explained as the spontaneous transformation:
−∆PEᴇᴄᴍ → KEᴇᴄᴍ,ᴜₙᵢᵥ
• The dominance of −Mᵃᵖᵖ leads to internal force generation
• Repulsive gravitational polarity initiates expansion
• No spacetime preconditions are required
This aligns with Appendix 10 on pre-universal energy fields and deep potential collapse without thermodynamic or inertial structure.
7. Connection to Dark Energy
Dark energy in ECM is the observable consequence of ongoing internal conversions of −∆PEᴇᴄᴍ into KEᴇᴄᴍ:
• Persistent repulsive pressure
• No need for exotic fields or λ-constants
• Arises from displacement of −Mᵃᵖᵖ across cosmic gravitational gradients
Thus, dark energy and the Big Bang share the same causal mechanism in ECM: internally mediated mass-energy polarity.
8. Unified Synthesis
ECM offers a self-contained model for force, mass, and motion. The Big Bang is reinterpreted not as a singularity requiring external input, but as an energetic inevitability arising from mass-energy disequilibrium:
• −Mᵃᵖᵖ dominance
• Polarity inversion
• Self-generated expansion
This energetic structure continues to power cosmic acceleration today.
Conclusion:
The ECM framework, through its effective quantities and internally emergent forces, reconstructs the Big Bang as a self-triggered outcome of gravitational potential collapse. It provides a unified explanation for both cosmological birth and present-day acceleration, grounded in mathematically defined internal mass-energy dynamics.
The Big Bang, in ECM, is not the beginning of time imposed from outside, but the consequence of a fundamental energetic instability within a non-positive gravitational potential field—a self-unfolding event that continues to define the universe.
References:
1. Thakur, S. N. (2025). Foundational Formulation of Extended Classical Mechanics. https://doi.org/10.20944/preprints202504.1501/v1
2. Thakur, S. N. (2024). Extended Classical Mechanics: Vol-1. https://doi.org/10.20944/preprints202409.1190.v3
3. Thakur, S. N. (2024). A Nuanced Perspective on Dark Energy: ECM. https://doi.org/10.20944/preprints202411.2325.v1
4. Thakur, S. N. (2024). Unified Study on Gravitational Dynamics: ECM Vol-2. https://www.researchgate.net/publication/384501200
5. Appendix 17: Internal Force Generation and Non-Decelerative Dynamics in ECM under Negative Apparent Mass Displacement. DOI: https://doi.org/10.13140/RG.2.2.26584.61446
