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

Discussion on internal mass-energy compensation, dimensional regulation, and gravitational embedding principles:

Soumendra Nath Thakur 

May 27, 2025

1. Internal Potential Energy Restructuring

In the reply:

 “...refers to the 'stored energy resulting from the spatial configuration of mass within a gravitational or kinetic system'... ECM posits that this restructuring is not abstract but reflects real shifts in the potential binding energy...”

In the section:

 “...a rest mass generates a negative energy well (gravitational potential U)... reflects the energetic imbalance in surrounding space (mass displacement)...”

Alignment with ECM: Strong. Both present gravitational potential energy as an internal, real mass-energy restructuring, not abstract curvature or external field effect. The section’s view of gravitational potential as a real deformation of surrounding space is entirely supported by the quoted reply.

2. Mass Displacement and Apparent Mass

In the reply:

“Mass displacement refers to a temporary energetic shift in matter mass, denoted as ∆Mm... resulting in observable effects like apparent mass reduction (in gravity) or gain (in KE)...”

In the section:

“Negative apparent mass of photon dynamically reacts by generating positive kinetic energy... positive KE allows it to climb out of the gravitational well...”

Alignment with ECM: Precise. Both describe ∆Mm (displaced mass) as a real energetic shift—whether as suppressed (gravitational) or active (kinetic). The photon’s escape via positive KE (from -M^app) is just a mirror of this principle in motion-dominated context.

3. Dimensional Regulation (1/m and k)**

In the reply:

 “...ECM resolves this by introducing a scaling constant k... such that terms like k/mc^2 yield mass-equivalent corrections that are dimensionally valid...”

in the section:

 “...expressions involving deformation or restoration due to kinetic energy (KE) are understood as real physical redistributions of mass-energy...”

Alignment with ECM: Fully consistent. Though the section doesn’t overtly show 1/m forms, it relies on dimensionally regulated forms of KE, implicitly governed by the standard ECM scaling principle.

4. Antigravitational Interpretation Without External Field

In the reply:

“...what appears as a negative gravitational field is a manifestation of real apparent mass reduction under potential energy constraints... Compensation occurs within the system via mass-energy reconfiguration...

In the section:

“Antigravity is not a cause but an effect... gravitational and antigravitational fields are complementary reactions under different mass conditions (real vs. apparent)...”

Alignment with ECM: Excellent. Both emphasize that ECM treats gravitational and antigravitational effects as intrinsic mass-energy reconfigurations, without invoking any external or homogeneous cosmic field. Instead, everything is resolved internally through ∆Mm and dynamic equilibrium.

5. Final Philosophical Outlook

In the reply:

“...avoiding the ontological and energetic ambiguities often introduced by postulated cosmic fields.”

In the section:

“...trajectory is dictated by the equilibrium between negative potential energy and its internally modulated kinetic displacement.”

Alignment with ECM: Strong philosophical coherence. Both stand on ECM’s non-reliance on external symmetries or abstract field theories, choosing to interpret all gravitational and kinetic behaviour within the energy dynamics of real matter systems.

Conclusion

The quoted reply is not only consistent with the section but reinforces it perfectly as a foundational theoretical statement. 

For a detailed discussion on internal mass-energy compensation, dimensional regulation, and gravitational embedding principles referenced in this section, see also:

1. Thakur, S. N. (2025). Response to Wolfgang Konle on gravitational embedding and mass displacement [Comment on the post Reconciling gravitational radiation and dark sector effects with ECM principles]. ResearchGate. https://www.researchgate.net/post/Reconciling_gravitational_radiation_and_dark_sector_effects_with_ecm_principles/1

Layman Summary Chapter: Gravitational Strength and the Dynamic Redistribution of Kinetic and Apparent Mass in ECM:

Soumendra Nath Thakur 

May 27, 2925

In simple terms, this chapter explains how gravity really works from the perspective of Extended Classical Mechanics (ECM)—a new way of thinking about physics that treats motion, mass, and energy more physically than in traditional science.

First, it introduces a new idea: gravitational strength isn’t just about pulling objects downward—it’s about how much gravity reshapes the internal energy and mass of a system. ECM gives it a new name: gᴇᴄᴍ and it measures how much a system’s mass gets pushed around or deformed due to gravity.

Then, it explains kinetic energy (the energy something has when it moves) in a whole new way. Normally, we think kinetic energy is just something objects have when they move. But in ECM, kinetic energy is actually a temporary shift in real mass—some of the object’s matter is “borrowed” and turned into energy when it speeds up, and “given back” when it slows down or stops. This mass shift is shown as:

◉ (Original mass – shifted mass) + shifted mass = moving object with kinetic energy

◉ When slowing down: (Original mass + returned mass) – kinetic energy = rest

This leads to an even cooler insight about light and photons—particles that normally don’t have mass. ECM says they do have a kind of "negative mass" when they're moving. And when photons are near very strong gravity (like near a black hole), this negative mass becomes even more negative, making them more energetic. But they never turn into real mass—just more intense forms of energy in motion.

In short: gravity doesn’t just pull things—it reshapes the energy and mass inside things. Movement isn’t just about speed—it’s about a real, physical shift in matter. And light is deeply affected by strong gravity, changing its energy without ever needing a normal kind of mass.

This chapter lays the groundwork for rethinking gravity, motion, and energy from an entirely physical and measurable viewpoint—one that makes ECM a powerful tool for explaining nature in both ordinary and extreme situations.