Electrons and Holes in Solid-State Systems: An ECM Interpretation of Dynamic Mass.

May 16, 2025

This work explores the dynamic interplay of electrons and holes in solid-state systems through the framework of Extended Classical Mechanics (ECM), which introduces the concept of negative apparent mass (−Mᵃᵖᵖ) as a counterpart to active motion. Within semiconductors, electrons serve as mobile negative charge carriers, while holes represent the absence of electrons and behave as positively charged quasi-particles. ECM reinterprets this duality by modelling the hole as a virtual kinetic-energy carrier with −Mᵃᵖᵖ, emerging from the motion of electrons. The analogy mₑ − mₑ = −mₕ illustrates this dynamic symmetry: the motion of an electron (mass mₑ) implies a reciprocal emergence of a hole (−mₕ), not as nothingness but as a reactive, directional mass component. This perspective extends naturally to charge flow in piezoelectric systems, where surface-bound electrons and emergent holes interact dynamically with lattice stress and field-induced polarization. Further, the shared characteristics between holes and photons—both arising from electron transitions and both exhibiting negative apparent mass—are examined, suggesting a unified interpretation of energy, charge, and mass duality under ECM. These insights pave the way for a redefinition of current, charge separation, and electromagnetic emission in both classical and quantum regimes.

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.