Extended Classical mechanics' rebuttal to the Lorentz factor γ stands on nearly irrefutable physical and mathematical ground.

ResearchGate Link

Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803

August 08, 2025

ECM rebuttal to the Lorentz factor γ is grounded not in speculative critique but in principled limitations within the formalism of relativity itself. ECM exposes these inconsistencies through:

·                        Neglect of acceleration during frame transition (γ is derived assuming constant relative velocity, ignoring inertial transition forces).

·                        No account for material stiffness (k) or real-world resistive mechanics that accompany motion in bound or structured systems.

·                        Breakdown at low velocities where γ ≈ 1 yields no meaningful distinction from classical energy, yet the relativistic model continues to be inapplicably extended.

·                        Undefined behaviour at c (as γ → ∞), making γ inapplicable at the very limit it was designed to describe.

·                        Misuse as an energy multiplier (e.g., E = γmc²) without dynamic basis—whereas ECM introduces hf = −ΔMᴍc², dynamically rooted in frequency modulation and internal mass polarity transitions.

These critiques are not philosophical but structural, targeting how γ:

·                        Lacks consistency with acceleration-based dynamics;

·                        Cannot incorporate internal energetic processes;

·                        Fails to bridge between classical and quantum domains coherently.

Thus, ECM does not merely refute γ—it replaces it with a measurable, frequency-based dynamic variable (ΔMᴍ, Mᵃᵖᵖ, gᵉᶠᶠ) that remains valid across all domains: classical, relativistic, and quantum.

This makes ECM Appendix 38 not only valid—it’s strategically essential in ECM’s bridging framework.

With current foundational models, this rebuttal stands on nearly irrefutable physical and mathematical ground.

Additional Theoretical Insight:

The application of the cosmological constant Λ within Newtonian dynamics—as demonstrated in the paper" Article Darkenergy and the structure of the Coma cluster of galaxies" by A. D. Chernin et al.—enables the derivation of real, observable features such as the zero-gravity surface. This choice implicitly reveals a critical limitation of relativistic mechanics in addressing dark energy on intergalactic scales. The authors' preference for Newtonian treatment, despite the general relativistic origin of Λ, highlights the pragmatic supremacy of Newtonian dynamics in this context.

In contrast, Extended Classical Mechanics (ECM) offers an even more radical and structured improvement. ECM independently integrates negative quantities—such as negative apparent mass (−Mᵃᵖᵖ) and mass shifts (ΔMᴍ ≡ −Mᵃᵖᵖ)—in a physically consistent and mathematically conserved framework. This approach not only captures the role of repulsive dynamics (similar to dark energy) more robustly than Λ in relativity but also does so without relying on coordinate transformations or metric dependencies, enabling a direct energetic interpretation.

Thus, while the cited research wisely adopts Newtonian formalism over relativistic treatments for dark energy modelling, ECM moves even further by foundationally justifying negative-mass behaviour within a dynamic mass–frequency–energy structure, offering a potentially superior alternative to both Newtonian and relativistic frameworks in cosmological modelling.

Complementary Nomination Perspective – On the Origin of Lorentz Transformation (Engelhardt)

An important related theoretical challenge to special relativity is presented in the paper "On the Origin of the Lorentz Transformation" by W.W. Engelhardt. This paper traces the historical and mathematical roots of the Lorentz transformation—not to Einstein's special relativity—but to earlier work by Woldemar Voigt (1887), who introduced these transformations to preserve the form of the wave equation.

The author critically exposes the mathematical inconsistencies and conceptual flaws in many standard derivations of the Lorentz transformation, including Einstein’s own. Engelhardt’s key insight is that Lorentz transformations should be viewed as auxiliary variables, not as physically necessary outcomes of relativistic postulates.

As emphasized in commentary by Halim Boutayeb :

1.                    “Lorentz transformations are in reality auxiliary variables invented by Voigt in 1887... Scientists in acoustics were lucky not to have been stuck in STR interpretation. Scientists in electromagnetism need to get rid of STR and LT to advance.”

This view strengthens ECM's own critique of the Lorentz factor γ by showing that even its foundational transformation lacks rigorous physical derivation. It supports ECM's shift toward frequency-based dynamics as not only a physical necessity but also a historically grounded correction to an inherited but faulty theoretical convention.

Entanglement as Ancestral Encoding — A Causal Resolution in Extended Classical Mechanics (ECM)

Soumendra Nath Thakur

July 30, 2025

ResearchGate Discussion link

Entangled subatomic particles may be more accurately understood not as entities physically connected across space, but as offspring of a common energetic source—each inheriting observable characteristics through initial energetic constraints imposed at Δt = 0, the moment of joint origin. Whether in atomic, subatomic, or nuclear contexts, their correlated behaviours reflect ancestrally encoded features rather than real-time interaction.

For instance, a liberated photon inherits its frequency f, directionality, and polarization directly from the electron undergoing a quantum transition. In turn, free electrons carry forward their internal kinetic configuration and apparent mass Mᵃᵖᵖ, shaped by their prior bound state within a parent atom. Similarly, in nuclear processes, α (alpha), β (beta), and γ (gamma) emissions inherit their physical traits—such as effective phase states, wave energy, and directionality—from their respective parent nuclei.

This framework, within Extended Classical Mechanics (ECM), offers a causal and quantifiable explanation for why emitted or separated particles exhibit twin-like or entangled behaviour. According to ECM, the kinetic energy KEᴇᴄᴍ of such particles is defined as (see: Appendix 31: Frequency and Energy in ECM):

  KEᴇᴄᴍ = ½Mᵉᶠᶠv²

where v is the particle’s velocity, and Mᵉᶠᶠ is the effective mass inclusive of inherited structural symmetry.

• For massive particles (e.g., electrons, α/β particles), v < c

• For massless or radiative particles (e.g., photons, γ-rays), v = c, and energy is entirely frequency-driven

This foundational relation is further enhanced in ECM to reflect the frequency-origin of kinetic energy, incorporating dual mass displacement mechanisms (Appendix 31, Appendix 35):

  KEᴇᴄᴍ = (ΔMᴍ⁽ᵈᴮ⁾ + ΔMᴍ⁽ᴾ⁾)c² = hf

Where:

• ΔMᴍ⁽ᵈᴮ⁾ = hf𝑑ʙ/c², mass displacement due to inherited de Broglie frequency

• ΔMᴍ⁽ᴾ⁾ = hfᴘ/c², mass displacement due to Planck-frequency-induced energy

• Total inherited frequency: f = f𝑑ʙ + fᴘ

This shows that the kinetic behaviour of a liberated or entangled particle arises from a superposition of wave-mechanical and quantum-emission frequencies inherited from its parent system. The observed energy is not the result of post-separation interaction, but a direct outcome of ancestral encoding.

In ECM, frequency f is not just a measurable trait—it is a core inherited identity. The corresponding effective gravitational acceleration gᵉᶠᶠ, representing the particle’s energetic-gravitational coupling and internal symmetry state, also evolves continuously from its origin at Δt = 0, unless perturbed. Thus, identical or complementary values of gᵉᶠᶠ, Mᵃᵖᵖ, or oscillator phase shift x° between particle pairs indicate not ongoing physical linkage, but co-originated symmetry.

From this perspective, particles once bound in a shared parent system retain synchronized traits because their wave structures, phase origins, and energetic embeddings were simultaneously defined under the same initial boundary conditions. In ECM terms, persistence of identical gᵉᶠᶠ trajectories or conserved energy per phase Eₜₒₜₐₗ/ϕ expresses structural coherence, not instantaneous communication.

Conclusion:

Entanglement Is Not Physical Connection Across Space, But Ancestral Encoding Across Time

Popular interpretations often suggest that entangled particles remain “physically connected regardless of distance.” However, such claims imply a nonlocal spatial mechanism that lacks both theoretical grounding and empirical necessity.

In ECM, these interpretations are replaced with a more causally consistent alternative: entanglement arises from the ancestral encoding of frequency, energy, and phase symmetry at the moment of common origin (Δt = 0). The correlations observed in Bell-type experiments emerge from embedded identity parameters—such as gᵉᶠᶠ, Mᵃᵖᵖ, and x°—inherited from their mutual parent system.

Thus, entangled particles “share the same fate” not through present-time physical linkage, but because their energetic identities were synchronously encoded. This preserves both realism and causality, offering a coherent ECM-based explanation of quantum correlation—without invoking paradoxes of spacelike nonlocality.

—Soumendra Nath Thakur (ORCiD: 0000-0003-1871-7803)

Tagore’s Electronic Lab, India

See related appendices: Appendix 31, Appendix 35, and Appendix 29 (on redshift-phase-frequency relationships)

#Entanglement #QuantumFoundations #ExtendedClassicalMechanics #Causality #PhaseSymmetry #deBroglie #QuantumInterpretation #ECM

Analysis of Appendix 32 (v2.1): Energy Density Structures in Extended Classical Mechanics (ECM) Authored by Soumendra Nath Thakur.

July 29, 2025

This appendix advances the ECM framework by rigorously redefining energy density in dynamic, massless systems, particularly photons, through the formalism of frequency-governed apparent mass displacement. It rejects the conventional assumption that the photon's mechanical mass is zero, and instead adopts the ECM-consistent identity that the photon's mechanical mass (Mᴍ) is equivalent to the negative of its apparent mass (−Mᵃᵖᵖ). This reframing permits the photon's effective mass (Mᵉᶠᶠ) to be modelled as a dual displacement: one inherited from its source field and another gained or withheld depending on the gravitational context of the detector. 

The appendix introduces a gravitational-frame-dependent model where energy density (ρ) differs based on whether the photon regains energy via gravitational blueshift during approach. In gravitational wells like Earth, the photon’s full effective displacement is recovered, yielding ρ = 2Mᵃᵖᵖ/V. In field-neutral zones (e.g., Lagrange points), the second displacement is absent, resulting in ρ = Mᵃᵖᵖ/V. This asymmetry is then linked to redshift interpretation: ECM concludes that redshift measured within gravitational wells is gravitationally distorted due to blueshift-induced modulation and cannot be considered intrinsic.

Further, the appendix introduces a composite kinetic energy framework for both dynamic and inertial systems using a unified frequency model. Here, total energy is governed by the sum of de Broglie (f𝒹ʙ) and Planck (fᴘ) frequencies. The derived ECM-compatible kinetic energy equation relates energy displacement to these two frequency components through additive mass displacement terms, unifying descriptions of electrons, photons, and other energy-bearing particles within a single pressure-energy-density formalism.

Finally, the appendix derives pressure from volumetric energy displacement under gravitational and non-gravitational conditions, solidifying ECM’s interpretation of pressure as a direct consequence of frequency-based mass redistribution. These findings reinforce ECM’s broader thesis that frequency—not rest mass—forms the primary determinant of energy, motion, and pressure, and that all such observables are inherently relational to the gravitational environment in which they are measured.

Summary of Appendix 32 (v2.1): 

This appendix advances the ECM framework by rigorously redefining energy density in dynamic, massless systems, particularly photons, through the formalism of frequency-governed apparent mass displacement. It rejects the conventional assumption that the photon's mechanical mass is zero, and instead adopts the ECM-consistent identity that the photon's mechanical mass (Mᴍ) is equivalent to the negative of its apparent mass (−Mᵃᵖᵖ). This reframing permits the photon's effective mass (Mᵉᶠᶠ) to be modelled as a dual displacement: one inherited from its source field and another gained or withheld depending on the gravitational context of the detector. 

The appendix introduces a gravitational-frame-dependent model where energy density (ρ) differs based on whether the photon regains energy via gravitational blueshift during approach. In gravitational wells like Earth, the photon’s full effective displacement is recovered, yielding ρ = 2Mᵃᵖᵖ/V. In field-neutral zones (e.g., Lagrange points), the second displacement is absent, resulting in ρ = Mᵃᵖᵖ/V. This asymmetry is then linked to redshift interpretation: ECM concludes that redshift measured within gravitational wells is gravitationally distorted due to blueshift-induced modulation and cannot be considered intrinsic.

Further, the appendix introduces a composite kinetic energy framework for both dynamic and inertial systems using a unified frequency model. Here, total energy is governed by the sum of de Broglie (f𝒹ʙ) and Planck (fᴘ) frequencies. The derived ECM-compatible kinetic energy equation relates energy displacement to these two frequency components through additive mass displacement terms, unifying descriptions of electrons, photons, and other energy-bearing particles within a single pressure-energy-density formalism.

Finally, the appendix derives pressure from volumetric energy displacement under gravitational and non-gravitational conditions, solidifying ECM’s interpretation of pressure as a direct consequence of frequency-based mass redistribution. These findings reinforce ECM’s broader thesis that frequency—not rest mass—forms the primary determinant of energy, motion, and pressure, and that all such observables are inherently relational to the gravitational environment in which they are measured.

#ECM #UnifiedFrequencyModel #GravitationalFrameDependent #EnergyDensity #FrequencyGoverned #ApparentMassDisplacement #EffectiveDisplacement #deBroglie #Planck #ECMcompatible #KineticEnergy #VolumetricEnergyPressure 

New ECM Appendix Published! - Energy Density Structures in Extended Classical Mechanics

July 27, 2025

📘 Appendix 32: Energy Density Structures in Extended Classical Mechanics (ECM)
🔗 https://doi.org/10.13140/RG.2.2.22849.88168

This latest addition to the ECM series redefines energy density as a frequency-driven scalar quantity, arising from the dynamic decomposition of mass into mechanical and apparent components. It presents a frame-dependent structure where even massless systems—like photons—possess well-defined energy density grounded in oscillatory behaviour.

The appendix also draws astrophysical parallels with the Coma cluster, showing how ECM’s scalar mass logic mirrors the interplay of matter and dark energy observed in large-scale cosmic systems.

If you're interested in:
✅ Non-curvature-based gravitational modelling
✅ Energy density from frequency principles
✅ Frame-specific scalar mass interpretation
✅ Bridging mechanics with astrophysics

…this work may offer the clarity and consistency you’ve been looking for.

#ExtendedClassicalMechanics #EnergyDensity #PhotonMass #ScalarMass #DarkEnergy #Astrophysics #ScientificPublication #Gravitation

Implications of Negative Gravitational Mass (−Mɢ) and Frequency-Based Total Energy in ECM:

Total Energy Interpretation in ECM

Total Energy at emission:

Eₜₒₜₐₗ = PEᴇᴄᴍ + KEᴇᴄᴍ → (−Mᵃᵖᵖ) + (−Mᵃᵖᵖ) = −2Mᵃᵖᵖ

Since v = c, then

Eₜₒₜₐₗ = ½(−2Mᵃᵖᵖ)c² = −Mᵃᵖᵖc² → ΔMᴍc²

Thus,

Eₜₒₜₐₗ = ΔMᴍc² = hf/c²

Where −Mᵃᵖᵖc² corresponds to ΔMᴍc²

This formulation tightly binds frequency (f), mass shift (ΔMᴍ), and apparent mass (Mᵃᵖᵖ), emphasizing the frequency-origin of energetic processes.

·         Photon Trajectories: Deflection in gravitational fields occurs due to the effective curvature induced by differential Mᵉᶠᶠ values, where Mᵉᶠᶠ = Mᴍ - Mᵃᵖᵖ:.

·         Dark Energy Behaviour: Negative Mɢ explains the repulsive force contributing to the Universe’s accelerated expansion.

·         Gravitational Redshift: Arises not from spacetime distortion but from variations in Mᵃᵖᵖ and ΔMᴍ.