Rest Energy vs. Kinetic Energy in Extended Classical Mechanics (ECM): Beyond Classical and Relativistic Views.

Soumendra Nath Thakur                                                DOI
June, 01, 2025

The reinterpretation of the relativistic energy equation E = mc² within the Extended Classical Mechanics (ECM) framework offers deeper insight into the role of mass displacement during energy transitions. In ECM, the relativistic mass m is redefined as the displaced mass component, denoted ΔMᴍ. This effective mass Mᵉᶠᶠ includes not only the transition of ΔMᴍ from the original matter mass Mᴍ (i.e., a loss of −ΔMᴍ), but also encapsulates the interactional and energetic transformations that occur in high-energy phenomena such as nuclear reactions.

In standard relativistic physics, the rest mass m in E = mc² is often interpreted as being wholly converted into energy. However, in actual nuclear reactions, this is not entirely the case. The by-products of such reactions—alpha particles, beta particles, and residual nuclei—all retain a portion of the original rest mass. Hence, not all of the rest mass is converted into pure rest energy. Instead, a portion remains as bound rest mass ΔMᴍ, while the remainder is distributed into kinetic energy and radiative emission, particularly in the form of electromagnetic radiation.

Importantly, this emission includes particles traditionally considered massless—such as gamma rays and photons—which, in ECM, are interpreted as carrying apparent negative mass −ΔMᴍ, originating from internal energetic displacement rather than conventional rest mass.

Thus, in nuclear splitting:

Mᴍ_ɴᴜᴄᴇᴜꜱ = ΔMᴍ_ʀᴇꜱɪᴅᴜᴀʟ ɴᴜᴄᴇᴜꜱ + Mᴍ_ₐ,ᵦ + (−ΔMᴍ_ᵧ) + (−ΔMᴍ_ₚₕₒₜₒₙₛ)

This formulation reflects that both massive and massless reaction products arise from mass-energy redistribution, not from total annihilation or full rest-mass conversion. It also highlights that radiative products such as photons and gamma rays embody displaced energy with measurable effects, despite lacking rest mass in conventional terms.

In Classical Mechanics, energy is typically classified as either potential or kinetic. However, relativistic rest energy represents a more intricate form of transition—a fusion of potential-like binding effects and kinetic-like emissions—mediated through mass redistribution, emission of particles, and radiative losses. ECM captures this nuance by modelling rest energy release as a combination of physical mass displacement and interactional field effects, providing a coherent explanation for the emergence of both massive and massless products in high-energy processes.

Why is the speed of light what it is, and why not some other speed? - A repeat version.

Soumendra Nath Thakur 

June 01, 2025

This post addresses the question: “Why is the speed of light what it is, and why not some other speed?”

In contrast to relativistic theory, Extended Classical Mechanics (ECM) asserts that photons possess a negative apparent mass, which enables them to generate their own antigravitational force. This self-propelling mechanism allows photons to move freely through gravitational fields; gravity does not constrain their motion—instead, it contributes additional energy to photons when they traverse gravitational potentials.

Photons inherently tend toward unbounded velocities, theoretically approaching infinity. However, the limiting factor is not gravity, but rather a Planck-scale threshold, which sets the upper bound for meaningful physical quantities: a maximum possible frequency and a minimum meaningful wavelength. The ratio of these two (frequency to wavelength) defines the maximum meaningful speed, which is observed as the constant speed c. Thus, the speed limit of light is not imposed by spacetime curvature (as in relativity), but by dimensional and energetic constraints defined at the Planck scale, according to ECM.

Relativity maintains the constancy of c by enforcing a mutual compensation between a photon’s frequency and wavelength—this is mathematically consistent, but in ECM, it is viewed more as a convenient wave-based relation than a fundamental relativistic principle.

Accordingly, all electromagnetic waves propagate at the same speed because they are carried by photons, and the *photon itself is the mediator of the electromagnetic force. In ECM, it is the nature and energy constraints of the photon—not spacetime geometry—that determine and preserve this universal speed.

Reconciling Gravitational Radiation, Dark Sector Phenomena, and Extended Classical Mechanics (ECM): Toward a Unified Framework

Soumendra Nath Thakur

Tagore’s Electronic Lab, India, 

postmasterenator@gmail.com postmasterenator@telitnetwork.in

May 29, 2025

 

Abstract

This section explores the conceptual integration of gravitational radiation and dark sector phenomena within the framework of Extended Classical Mechanics (ECM). ECM extends Newtonian principles by introducing dynamic mass concepts, such as displaced mass and apparent mass, while strictly preserving dimensional consistency. Gravitational radiation is reinterpreted not as the curvature of spacetime but as a consequence of real mass-energy displacement within energetic systems. Similarly, ECM provides alternative explanations for dark matter and dark energy, modelling them as emergent effects of gravitational mass redistribution rather than as independent fields or exotic particles. The framework also offers reinterpretations of relativistic phenomena, such as gravitational lensing and time dilation, through the lens of internal energy restructuring. By offering a consistent, matter-based alternative to both relativistic gravity and particle-based cosmology, ECM has the potential to unify gravitational and antigravitational interactions under a common mechanical paradigm.

Introduction

Reconciling gravitational radiation, dark sector effects, and ECM principles involves integrating Extended Classical Mechanics (ECM) with established cosmological models and observations of dark matter and dark energy. ECM, which extends Newtonian mechanics to incorporate dynamic mass components and reinterprets relativistic behaviour, can offer a framework for understanding these phenomena. 

Gravitational Radiation and ECM:

·         ECM can offer a reinterpretation of gravitational radiation, viewing it not as a field interaction, but as a consequence of mass displacement and energy shifts within a system.

·         ECM's focus on potential energy as a central regulatory mechanism in mass systems can be applied to understanding how energy is transferred and radiated during gravitational events.

·         ECM's strict adherence to dimensional consistency in mass and radiation expressions is crucial for ensuring a self-consistent framework. 

Dark Sector Effects and ECM:

·         ECM can provide a framework for understanding dark matter and dark energy, viewing them as emergent gravitational phenomena rather than exotic particles or fields. 

·         ECM's introduction of dynamic mass components, including negative apparent mass and effective mass can help model the gravitational and inertial interactions of dark matter and dark energy. 

·         ECM's reinterpretation of relativistic behaviour, particularly time dilation and gravitational lensing, can offer alternative explanations for cosmological observations involving dark energy and the expansion of the universe. 

·         ECM can potentially offer a unified treatment of gravitational and antigravitational interactions, aligning with cosmological observations of dark energy and cosmic expansion. 

Displaced mass, gravitational field strength, and energy release in extreme stellar systems under Extended Classical Mechanics (ECM):

Soumendra Nath Thakur
May 27, 2025

This section explores how neutron stars, under the framework of Extended Classical Mechanics (ECM), express extreme gravitational behaviour through mass displacement and energetic transformation—independently of relativistic mechanics. The ECM model reinterprets gravitational field strength gᴇᴄᴍ as a function of mass displacement per unit time, specifically as the rate of negative apparent mass generation d(−ΔMᴍ)/dt. In such dense astrophysical bodies, the immense matter mass Mᴍ gives rise to both rest energy (ΔMᴍC²) and kinetic energy (ΔMᴍ as KE via radiated gamma or photon particles), without requiring relativistic gamma correction. The photon-induced kinetic energy component emerges as negative apparent mass −Mᵃᵖᵖ, linking light-like particle emission to mechanical displacement within the gravitational structure. The ECM framework establishes calculable energy output in these systems, with clear partitioning between rest energy and displaced kinetic energy, and redefines gravitational interaction not through spacetime curvature, but via dynamic internal restructuring and mass redistribution. This interpretation is suitable for both theoretical modelling and experimental validation in high-energy astrophysics.

This figure visually summarises the core ECM interpretation presented in this Technical Findings. 

Figure Description:

This figure visually showing a neutron star under ECM interpretation, with arrows and annotations indicating:

Left Panel: Traditional Interpretation:

• Mass density (ρ) → spacetime curvature (GR)
• Gravitational field strength ↔ geometric deformation
• No mass-displacement term

Right Panel: ECM Interpretation

• Core Matter Mass (Mᴍ) labelled
• Arrows → showing mass displacement:

  • Outward kinetic deformation (ΔMᴍ) for photon/gamma emission
  • Inward structural strain (−ΔMᴍ) as apparent mass

Gravitational strength gᴇᴄᴍ shown as:

       gᴇᴄᴍ = d(−ΔMᴍ) ÷ Mᴍ

  (Field strength as deformation rate per matter mass)

• Labels on:

  • Rest energy release: ΔMᴍ·c²
  • Kinetic energy via photon emission: ΔMᴍ ⇒ −Mᵃᵖᵖ

Citation for the Research:

1. Thakur, S. N. (2025, May 27). Displaced mass, gravitational field strength, and energy release in extreme stellar systems under Extended Classical Mechanics (ECM). ResearchGate. https://doi.org/10.13140/RG.2.2.29304.76807

2. Thakur, S. N. (2025), Appendix A – Standard Mass Definitions in Extended Classical Mechanics (ECM), ResearchGate, DOI: https://doi.org/10.13140/rg.2.2.31762.36800

3. Thakur, S. N. (2025). Explanation in the usage of matter mass (Mᴍ) within solar or terrestrial regimes: Dark matter in Extended Classical Mechanics (ECM). ResearchGate. https://doi.org/10.13140/RG.2.2.30117.41441

How Force, Mass, and Energy Interact in Extended Classical Mechanics (ECM): A Layman Explanation Without Relativity:

Soumendra Nath Thakur 
May 27, 2025

Extended Classical Mechanics (ECM) supports classical mass-energy equivalence but without relying on relativity. The main question it explores is: how does matter behave internally when a force is applied to it?

In ordinary materials, this internal response isn't always visible — we just see the object move, fall, or accelerate. But in materials like piezoelectrics, the internal effect is quite obvious: when mechanical or gravitational force is applied, these materials generate electrical energy. This is a clear example of force being converted into energy.

But how does this conversion happen? It happens because the force causes the material to deform — its internal atomic or molecular structure shifts. This rearrangement releases energy, and in doing so, the material loses a small amount of its rest mass. This is written as:

          (Mm − ∆Mm)

where Mm is the original mass of matter and ∆Mm is the portion lost due to this internal shift, converted into kinetic energy (KE).

In ECM, this lost mass appears as a temporary apparent mass, denoted −M^app, derived from the internal matter itself. So, the effective mass of the object under motion or deformation becomes:

          M^eff = (Mm − M^app)

This process reverses when the force is removed — the material returns to its rest state, regaining its mass and structure.

The kinetic energy is expressed classically as:

          KE = (1/2)M^eff v² = ∆Mm

So, ECM interprets kinetic energy as an expression of mass loss — i.e., mass-energy equivalence in classical terms.

For particles like photons (which are massless in conventional physics but treated differently in ECM), the equation adjusts because they carry negative apparent mass. For example, a pair of such particles would have:

          −M^app + (−M^app) = −2M^app

And since photons move at the speed of light v = c, the energy equation becomes:

          KE = (1/2)(−2M^app)c² = M^eff c²

This matches the energy-frequency relation:

          E = KE = M^eff c² = hf

So the famous Planck relation E = hf emerges here without using relativity.

In ECM, this means that moving mass loses energy in the form of internal mass displacement, and adding or removing energy changes its internal mass configuration.

Hence, a strong gravitational field can affect the mass of objects within its range — not because of spacetime curvature (as in relativity), but because it displaces the internal mass structure of the object through interaction