Dual Manifestations of Electron Displacement in ECM: Holes and Photons

May 16, 2025

In the framework of Extended Classical Mechanics (ECM), photons and holes are proposed as dual manifestations of electron displacement, unifying kinetic energy exchange and apparent mass dynamics. When an electron moves, it not only generates a propagating photon (carrying kinetic energy with negative apparent mass) but also leaves behind a localized "hole," a deficit of mass-energy equilibrium, also exhibiting negative apparent mass. This framework interprets kinetic energy as a directional quantity embedded within mass relations, rather than an abstract scalar. 

DOI: https://doi.org/10.13140/RG.2.2.20536.87041

Clarifying the Nature of Michaud’s Contribution and Addressing Oversimplification

Vaibhav Sunder’s comment, while poetic in tone, appears to misinterpret the core intent of Mr. André Michaud’s clarification. It is important to emphasize that Michaud’s contribution was not merely a linguistic clarification, but a reassertion of Einstein’s original physical and theoretical intent in the 1905 paper. His distinction reveals how modern retellings of Einstein’s postulates have abstracted away from their original scope and meaning—especially by shifting from emission-based descriptions of light to observer-invariant formulations devoid of mechanical grounding.

This has significant consequences for how relativity has been developed and interpreted since. Michaud’s effort encourages a theoretical return to physical principles that Einstein himself aligned with, rather than the more geometric and axiomatic structures that later dominated relativistic interpretation. In this light, Michaud’s work is not about semantics but about theoretical clarity, with direct implications for ongoing frameworks like ECM or synchronized kinematic-electromagnetic mechanics.

Furthermore, Vaibhav's statement that physics cannot be translated into intuitive, everyday language unless embedded in the "rhythms" of mathematics oversimplifies the relationship between formalism and understanding. While mathematics is undeniably the precise language of physics, its purpose is to model, not mystify. To suggest that physics can only be understood or expressed through mathematical rhythm risks reinforcing an elitist view that equates intellectual depth solely with mathematical articulation.

This tendency often leans into intellectual supremacy, which, if left unchecked, can shade into intellectual dishonesty—where genuine clarity and accessibility are sacrificed for technical intimidation. Intuition and language, when grounded in physical understanding, play a crucial role in both communicating and developing physical insight. History shows us that the greatest physicists—Einstein included—valued physical reasoning as much as mathematical formulation.

Let us not forget: equations alone do not yield understanding. It is the synthesis of meaning and mathematics that advances science.

Soumendra Nath Thakur

May 16, 2025

ECM-Based Response to the Question: Is the Speed of Light the Speed of Universal Expansion?

May 16, 2025

Dear Joseph Tommasi,

Thank you for your question—it's a valuable one that touches the heart of cosmological interpretation.

To answer it clearly: No, the speed of light is not the speed at which the universe is expanding. These are distinct physical concepts. The speed of light, c ≈ 299,792,458 m/s, is a universal physical limit derived from electromagnetic wave propagation and constrained by quantum Planck scales—not by the universe’s expansion rate.

In standard cosmology, based on general relativity, the expansion of the universe is interpreted as the stretching of spacetime itself, and superluminal recession of distant galaxies is described as a metric phenomenon. However, Extended Classical Mechanics (ECM) offers a different perspective—recession is not due to spacetime stretching, but rather due to a physical separation driven by the interaction between gravitational and antigravitational forces.

This reinterpretation aligns with observational research such as A. D. Chernin et al.'s work on the Coma Cluster, which highlights the role of dark energy as a repulsive force in shaping large-scale cosmic structures. In the ECM framework, dark energy is modelled as a real physical component with negative apparent mass (−Mᵃᵖᵖ). It exerts an antigravitational force, causing matter-dominated galaxies to accelerate away from one another—not passively drift apart due to expanding coordinates.

In this view, Hubble’s Law:

    v = H₀ × d

is interpreted not as a kinematic rule emerging from an expanding metric, but as a dynamic expression of net force-driven recession, where gravitational attraction becomes increasingly overpowered by the repulsive dynamics of dark-energy-dominated space. When galaxies are distant enough, the antigravitational effect dominates, leading to recession velocities exceeding the speed of light.

This superluminal motion is not paradoxical in ECM, because it does not involve particles exceeding c through space. Instead, it represents a physical divergence caused by a growing imbalance between attractive and repulsive mass-energy components.

Additionally, ECM holds that while mathematical models may permit divergence of speed due to ever-increasing frequency and negative apparent mass, physical reality remains constrained by quantum mechanical bounds—notably the Planck length (Lₚ) and Planck time (Tₚ)—yielding the natural speed limit:

    c = Lₚ / Tₚ

Thus, the speed of light remains the upper bound for any real signal or interaction, even in a universe with force-driven superluminal recession.

In conclusion, under ECM, the speed of light and the rate of universal expansion arise from distinct causes. Light speed is a quantum boundary of propagation, while galactic recession reflects real, force-induced acceleration arising from the interplay of gravitational and antigravitational components across cosmic distances.

Warm regards,

Soumendra Nath Thakur

A Reflection on Human Purpose, Intellect, and the Role of Suffering — In Response to the Interpretation of Existential Progress

@Jared Pelkey

May 16, 2025

Yes, my Lordship,

I am honoured to share my reflections on the text in question, which indeed resonates with profound philosophical depth. At its heart, the post asserts that human existence is not intended for suffering, but for a nobler journey—to explore, understand, and respect the universe and its intricate interplay as a unified whole. I find this vision compelling and aligned with the essential purpose of conscious life.

Human consciousness, in my humble view, does more than merely assign meaning to reality; it is uniquely capable of probing the abstractness behind observable phenomena. Our intellect grants us not only the tools for questioning and discovery, but also for constructing valid mathematical abstractions to bridge the gap between the perceptible and the imperceptible—a necessary act when confronting the vastness and subtlety of the cosmos.

The post’s rejection of suffering as a necessity for growth strikes me as both historically and ethically accurate. Freedom, stability, and open-minded, evidence-based inquiry—not preconceptions—are the real catalysts for progress. Liberal democracies have proven this in practice, yet I believe it is not democracy alone, but the understanding of universal science and our rightful place within it, that truly elevates human potential.

I particularly appreciated the emphasis on peace, self-improvement, and harmony as innate human drives. However, it is important to distinguish pleasurable hardship—such as dedication, perseverance, and disciplined rigor—from suffering in its negative, dehumanizing sense. Growth does not require anguish; rather, it calls for responsible freedom, where individuals pursue truth and contribute meaningfully, not for selfish gain but in recognition of the greater good.

Lastly, while freedom, reason, and creativity are indeed philosophical ideals, I respectfully submit that philosophical reflection must ultimately be grounded in mathematically valid abstraction—for without grounding, philosophy can drift into speculation. Thus, our noblest inquiries are those that align intellect with reality, freedom with responsibility, and creativity with truth.

With deep respect,

I remain faithfully yours in shared pursuit of wisdom.

Restoring Dynamic Mass in Classical Mechanics - The Foundation of Extended Classical Mechanics (ECM)

Chapter: 

DOI: http://doi.org/10.13140/RG.2.2.35190.72009

Soumendra Nath Thakur

• ORCiD: 0000-0003-1871-7803
• Tagore's Electronic Lab, WB, India; postmasterenator@gmail.com or postmasterenator@telitnetwork.in

May 13, 2025

Abstract

This chapter establishes the foundation of Extended Classical Mechanics (ECM) by addressing a fundamental oversight in classical mechanics: the failure to recognize the dynamic mass component inherent in kinetic energy. While classical mechanics accepts the inverse mass relationship a ∝ 1/m in Newton's second law; it never assigns physical meaning to the inverse-mass term. ECM resolves this by interpreting 1/m as a representation of negative apparent mass −Δm, revealing that kinetic energy is carried by a real but negative dynamic mass component.

Building on this insight, ECM reformulates the force equation as:

Fᴇᴄᴍ = (M + (−Mᵃᵖᵖ))⋅aᵉᶠᶠ  = Mᵉᶠᶠ⋅aᵉᶠᶠ

And for systems consisting purely of dynamic energy (like photons), as:

Fᴇᴄᴍ = (−2Mᵃᵖᵖ))⋅aᵉᶠᶠ

This generalized formulation accounts for both static matter and massless energy carriers by incorporating gravitational modulation of dynamic mass. The chapter demonstrates how this correction not only completes and extends classical mechanics, but also offers a consistent mechanical explanation for photon behaviour, repulsive gravitational effects (as in dark energy), and the cosmological gravitating mass Mɢ ​. ECM thus provides a unified framework linking classical force laws with modern and cosmological physics by restoring the missing dynamic mass component to the mechanics of energy.

1. Classical Mechanics and the Hidden Mass of Kinetic Energy

In classical mechanics, the force equation F=ma implies that acceleration is inversely proportional to mass:

a ∝ 1/m

This inverse dependence is mathematically consistent, but its physical meaning is overlooked. If we reinterpret:

1/m = −Δm

We treat the inverse-mass effect as a negative mass component −Δm, linked to the dynamic aspect of energy. Though not recognized classically, this idea introduces a mass contribution originating not from rest matter, but from motions itself—the dynamic mass of kinetic energy.

In the classical energy equation:

Eₜₒₜₐₗ = PE + KE = mgh + ½mv²

We now reinterpret:

• m −Δm as the effective mass for potential energy,

• −Δm as the effective energetic mass contributing to kinetic energy.

Corrected expressions become:

PE = (m − Δm)gh, KE = ½(m−Δm)v² ⇒ −Δm = dynamic energy carrier.

2. The ECM Force Equation and the Role of Negative Apparent Mass

This insight leads directly to the ECM force equation, which accounts for both matter mass Mᴍ​ and negative apparent mass −Mᵃᵖᵖ​:

Fᴇᴄᴍ = (M + (−Mᵃᵖᵖ))⋅aᵉᶠᶠ = Mᵉᶠᶠ⋅aᵉᶠᶠ ​

Where:

• Mᵉᶠᶠ​ is the total effective mass participating in the force interaction,

• aᵉᶠᶠ is the effective acceleration derived from dynamic energy behaviour.

For systems made entirely of dynamic energy (e.g., photons or unbound electromagnetic energy), the ECM force law becomes:

Fᴇᴄᴍ = (−2Mᵃᵖᵖ))⋅aᵉᶠᶠ  

The factor −2 arises from:

• the intrinsic apparent mass −Mᵃᵖᵖ​,

• an additional gravitational modulation analogous to the gravitational energy contribution in massive systems.

3. Extension to Modern and Cosmological Physics

Photon Dynamics

Photons, though massless in conventional models, carry energy and momentum. ECM reconciles this by assigning photons a total negative dynamic mass of −Mᵃᵖᵖ, leading to the photon-specific force law:

Fᴇᴄᴍ = (−2Mᵃᵖᵖ))⋅aᵉᶠᶠ  

This resolves the paradox of force and inertia in light: energy can exert force through effective dynamic mass even in the absence of rest mass.

Dark Energy Analogy

ECM identifies dark energy as a large-scale manifestation of photon dynamic energy characterized by a single negative apparent mass −Mᵃᵖᵖ, not −2Mᵃᵖᵖ. This value represents the inherent energy of a photon after escaping gravitational influence and expending the corresponding potential energy. The remaining −Mᵃᵖᵖ​​ persists in zero-gravity spheres and dark-energy-dominated space and is permanently expended as the photon undergoes cosmic redshift.

Thus, the repulsive cosmological effect attributed to dark energy corresponds to:

Fᴇᴄᴍ = (−Mᵃᵖᵖ))⋅aᵉᶠᶠ

This formulation reveals that the accelerated expansion of the universe is a mechanical consequence of effective force acting on residual dynamic mass in low-gravity space.

Cosmological Models

In cosmology, the gravitating mass Mɢ governs cosmic expansion. ECM reformulates it as:

            Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ) = Mɢ

This corresponds directly to the framework in Chernin et al. (2013), where:

• Mᴍ​: matter mass (ordinary + dark matter),

• −Mᵃᵖᵖ: ECM’s analogue of the cosmological dark energy term.

Thus, ECM reinterprets cosmological gravitating mass Mɢ as a special case of its generalized effective mass framework.

4. Conclusion

The classical failure to recognize the negative dynamic mass of kinetic energy created a critical theoretical gap. ECM closes this by:

• assigning real mass to dynamic energy,

• completing classical force and energy laws,

• Providing a consistent mechanical foundation for photons, dark energy, and cosmic expansion.

ECM not only redefines classical mechanics but also establishes a coherent and unified view of modern and cosmological phenomena through the physical reality of dynamic mass.

Appendix: Denotations (Alphabetical List)

Symbol	Description
aᵉᶠᶠ	Effective acceleration
Eₜₒₜₐₗ	Total mechanical energy
F	Classical force
Fᴇᴄᴍ​	Effective force in ECM
g	Gravitational field strength
h	Height in potential energy
KE	Kinetic energy
Mᵃᵖᵖ	Apparent (negative) mass in ECM
​Mᵉᶠᶠ	Effective mass = Mᴍ + (−Mᵃᵖᵖ)
Mɢ​	Gravitating mass in cosmology
​Mᴍ	Matter mass (includes ordinary and dark matter)
PE	Potential energy
v	Velocity
Δm	Equivalent negative dynamic mass from 1/m relationship

Funding

• No specific funding was received for this work.

Conflicts of Interest

• No potential competing interests to declare.

5. References

1. Thakur S.N. (2025). A Nuanced Perspective on Dark Energy: Extended Classical Mechanics. Int. J. Astron. Mod. Phys., 01(01), 2025;01(1):001. https://magnivelinternational.com/journal/articledetails/28

2. Thakur, S. N. (2025). Foundational Formulation of Extended Classical Mechanics: From Classical Force Laws to Relativistic Dynamics. Preprints. https://doi.org/10.20944/preprints202504.1501.v1

3. Thakur, S. N., & Bhattacharjee, D. (2023b, October 30). Phase Shift and Infinitesimal Wave Energy Loss Equations. Longdom. https://www.longdom.org/open-access/phase-shift-and-infinitesimal-wave-energy-loss-equations-104719.html

4. Thakur, S. N. (2024). Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. Preprints. https://doi.org/10.20944/preprints202409.1190.v3

5. Thakur, S. N. & Tagore’s Electronic Lab. (2025). Rotational phase shift and time distortion in a rapidly rotating piezoelectric system. In Tagore’s Electronic Lab [Journal-article]. https://doi.org/10.13140/RG.2.2.24780.32640

6. Thakur, S. N. (2025). Mathematical Derivation of Frequency Shift and Phase Transition in Extended Classical Mechanics (ECM). ResearchGate, 390208822. https://doi.org/10.13140/RG.2.2.36663.02721.