Reinterpreting Liang and Caldwell’s Dark Matter Proposal via Extended Classical Mechanics

May 18, 2025

Soumendra Nath Thakur

Abstract

This paper presents a reinterpretation of Liang and Caldwell’s dark matter formation model (Cold Dark Matter Based on an Analogy with Superconductivity by Guanming Liang and Robert R. Caldwell) through the framework of Extended Classical Mechanics (ECM). Their original proposal suggests that cold dark matter (CDM) could originate from initially massless particles undergoing phase-like transitions into massive states via cosmic-scale deceleration. In ECM, this process corresponds to a reversible transformation between kinetic energy (expressed as negative apparent mass, −Mᵃᵖᵖ) and matter mass (Mᴍ), governed by effective acceleration (aᵉᶠᶠ). By treating mass not as an intrinsic attribute but as a dynamic energy state, ECM offers a classically grounded explanation for mass acquisition without invoking quantum symmetry breaking or exotic particles. The paper formalizes the dual-state energy mechanism behind kinetic-to-mass transitions, showing that dark matter may emerge naturally as the kinetic identity of particles fades through sustained deceleration. This reinterpretation expands the explanatory power of classical physics in cosmological contexts, offering a testable and coherent model for the origin of dark matter.

Clarifying the Misconception: No Circular Reasoning in the Definition of Planck Units:

May 17, 2025

The statement, "The speed of light from Lₚ / Tₚ (may) or may not be valid. Since Planck values for length and time were derived using light's speed (a circular reasoning?)", rests on an incomplete understanding of the origin and intent of Planck units. It is also not as an example of circular reasoning.

Planck introduced his natural unit system in 1899, well before Einstein’s special and general relativity theories were published (in 1905 and 1916, respectively). At that time, the speed of light (c) was not interpreted through a relativistic lens. Instead, Planck's goal was to construct a unit system derived entirely from fundamental constants of nature.

The Planck scale is defined using three constants:

• the speed of light c,
• the gravitational constant G, and
• the reduced Planck constant h-bar.

These constants were not chosen to define each other, but to provide universal units of length, time, mass, etc., that remain invariant across physical contexts. The expressions for Planck length Lp  and Planck time Tp use c, G and h-bar, but not in a way that implies circular logic. Rather, c is treated as a known constant—just as G and h-bar are—serving as part of a dimensional bridge between quantum mechanics and gravitation.

Thus, there is no logical fallacy involved. The Planck units are internally consistent and reflect natural scales set by the interplay of fundamental constants. Their construction is not dependent on any single one being derived from the others, and especially not on a derived dependence of c from Lp / Tp.

Therefore, no circular reasoning arises in this context, and the usage of c in defining Planck units is a matter of dimensional coherence, not definitional dependence.

Perspective on Conductivity and Charge Carriers in Extended Classical Mechanics (ECM)

May 16, 2025

From the perspective of Extended Classical Mechanics (ECM), electrical conduction in semiconductors involves more than just statistical movement of charge. Electrons are not merely particles responding to fields; they actively convert potential energy into kinetic motion, and in doing so, emit energy in the form of photons or field waves. The hole, traditionally understood as a vacancy, is reinterpreted in ECM as a virtual carrier of kinetic energy with negative apparent mass (−Mᵃᵖᵖ).

This dynamic symmetry—where the emergence of a hole represents a reactive, directional counterpart to the electron's movement—enriches our understanding of conduction. Particularly in doped semiconductors, holes are not simply the absence of electrons, but energy-transmitting entities generated by electron displacement and photon emission. This redefinition sets the stage for a new interpretation of charge separation, field interaction, and electromagnetic behaviour in solid state physics.

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