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.

Time – as Understood in Extended Classical Mechanics (ECM)

July 25, 2025

Extended Classical Mechanics (ECM) asserts that time originates from energetic transitions and vibrational dynamics—not as a coordinate or dimension but as a physically emergent metric from real phenomena. This challenges relativistic interpretations that treat time as flexible and observer-dependent.

Why ECM Cannot Rely on the Relativistic Concept of Time

Relativity-based time dilation, governed by the Lorentz factor γ = 1/√(1 − v²/c²), has been critically challenged in ECM-related studies for the following reasons:

Critique Summary:

Neglect of acceleration: γ accounts only for relative velocity (v), not for the acceleration (a) that leads to that velocity.

Inapplicability in normal conditions: At low velocities (e.g. v = 100 m/s or even 1,000,000 m/s), γ ≈ 1, yielding negligible change. Thus, it’s non-functional in most real-world scenarios.

Lack of material response (k): The Lorentz formulation overlooks material stiffness or energetic resistance, a critical factor in energetic transitions.

Incompatibility with mass–energy transitions: ECM treats energy-mass transformation (Δm, ΔE) with direct application of phase-frequency dynamics, whereas γ fails to account for dynamic nuclear-scale interactions or stiffness-modulated deformation.

Conceptual deformation of classical structure: γ introduces a deformation of classical interpretations rather than an expansion or completion.

#Time #ECMTime

Extended Classical Mechanics (ECM) Challenges Quantum Claims of Negative Time and Probabilistic Photon Behaviour:

July 22, 2025

The analysed document, "Negative Time and Photon Behaviour: An ECM-Based Critique of Quantum Probabilistic Claims," primarily discusses the concept of "negative time" and the probabilistic behaviour of photons as claimed by some quantum theories. It then critiques these claims from the perspective of Extended Classical Mechanics (ECM). 

Here's a breakdown of the analysis:

1. The Claim of Negative Time:

Stuart Knaki references a discovery by Mohammad Qusir Rather and Aephraim Steinberg from the University of Toronto, who reportedly observed the "first evidence of negative time".

This observation suggests that photons exhibit a "peculiar curly or frizzy structure" and that their behaviour is governed by probabilistic principles, aligning with quantum mechanics where outcomes are subject to chance.

In the quantum mechanical context, negative time is interpreted as scenarios where time seems to move backward, challenging the conventional understanding of temporal flow.

Later, it's specified that these quantum-level claims, particularly from Aephraim Steinberg and his colleagues, involved photons interacting with ultracold rubidium atoms, where reemission appeared to occur before absorption, suggesting "negative dwell time". Popular science outlets have interpreted this as evidence challenging the unidirectional arrow of time.

2. Conventional Understanding of Time:

Conventionally, time is defined as "the indefinite continued progress of existence and events in the past, present, and future regarded as a whole".

A refined conventional definition describes time as "the indefinite continued progression of existence and events across past, present, and future, regarded collectively as a whole-advancing in an irreversible and uniform succession, and conceptualized as the fourth dimension beyond the three dimensions of space". This definition emphasizes its continuity, directionality, and role as a dimension underlying causality.

3. ECM's Perspective on Time:

ECM does not reject the uniform and unidirectional flow of time.

It treats all frequency displacements, phase transitions, and energetic reversions as events unfolding within the same irreversible temporal continuum. Time in ECM remains the backdrop for the evolution of energetic states, respecting its uniform unidirectionality.

ECM posits that at the universe's ultimate energetic threshold, a cyclic or reversible dynamic might emerge, not by violating the arrow of time, but through the reversion of energy states and frequency collapse at a cosmological limit. This suggests apparent reversals may manifest only at or beyond a critical energetic state, governed by ECM's mass-frequency interplay.

In ECM, time is not an independently flowing dimension but a derived consequence of phase displacement and frequency variation.

What is labelled "negative time" in quantum descriptions does not correspond to a literal reversal of temporal progression in ECM. Instead, it is understood as a localized inversion in phase behaviour or frequency collapse, especially under extreme energetic conditions.

ECM asserts that during all active stages of cosmic and quantum evolution, time retains its irreversible and uniform directionality, tied to the sequential unfolding of energetic events and apparent mass displacement.

The "negative time" observed in quantum optics experiments is interpreted within ECM not as a breakdown of temporal order, but as a manifestation of the extreme sensitivity of Δt to subtle fluctuations in frequency. Relations like 

Tdeg = x/360f = Δt or φ = 2nfΔt 

show that infinitesimal frequency changes can lead to dramatic shifts in Δt, "occasionally producing the illusion of a negative temporal interval". This is considered a deterministic outcome of phase-frequency structure, not a probabilistic anomaly.

ECM accommodates the interpretational appearance of negative time as a phase-based energetic anomaly while preserving the foundational integrity of cosmological temporal unidirectionality.

4. ECM's Critique of Photon Behaviour:

The claim that "photons exhibit a peculiar curly or frizzy structure, an appearance that is difficult to define clearly, often described as vague, indistinct, or hard to perceive" is seen by ECM as referring to interpretational challenges or observational limitations, not an intrinsic structure of photons. Such an appearance might result from entanglement, wave interference, or measurement distortions.

From ECM's standpoint, such ambiguity does not arise. ECM provides a well-defined and continuous description of photon behaviour across all relevant phases, from emission to its ultimate fate. ECM does not admit the notion of photons exhibiting a "curly" or "frizzy" nature, or any inherently unpredictable or ill-defined structure.

In ECM, photon dynamics, especially concerning negative apparent mass, are precisely described and governed by deterministic frequency-based principles. The idea of a photon possessing an inherently vague or chaotic structure is incompatible with the ECM framework.

The claim that "photon behaviour is based on or adapted to a theory of probability; subject to or involving chance variation" is also viewed by ECM as an interpretational challenge or observational limitation.

From ECM's perspective, photon behaviour is neither probabilistic nor indeterminate but is well-defined, coherent, and systematically governed by frequency and mass interactions across gravitational and anti-gravitational regimes. ECM offers a deterministic framework for understanding photon dynamics without resorting to probabilistic uncertainty.

5. Conclusion from ECM Perspective:

The observation of "negative time" at the quantum scale may reflect a temporal phenomenon specific to that scale, but it does not correspond to the irreversible, uniform time progression perceived at the cosmological scale, as clarified by ECM.

ECM suggests that apparent reversals in time may manifest only at or beyond a critical energetic fate.

ECM interprets the "negative time" observed in quantum optics experiments as a deterministic outcome of phase-frequency structure, not a probabilistic anomaly, where infinitesimal frequency changes can lead to dramatic shifts in Δt, creating an "illusion of a negative temporal interval".

ECM frames these behaviours within a causally coherent and structurally governed continuum, never implying retro causality or stochastic indeterminism.

For an interpretive analysis of recent quantum claims in light of this stance, refer to:

🔗 http://www.telitnetwork.itgo.com/ExtendedClassicalMechanics/NegativeTime/

Frequency and Energy in Extended Classical Mechanics (ECM):

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

Email: postmasterenator@gmail.com

Date: July 21, 2025

In Extended Classical Mechanics (ECM), the concepts of frequency and energy are reinterpreted with frequency (f) taking precedence as the most fundamental descriptor of a physical state. This framework positions frequency as more intrinsic to a system's dynamical evolution, independent of external reference frames, and dimensionally foundational for constructing observable quantities.

Frequency as the Primary Descriptor of Oscillation

In ECM, the argument for frequency's primacy is robust:

Synonymous with Vibration: Frequency isn't just a measure of vibration; it's considered synonymous with it. To talk about something vibrating or oscillating is, by definition, to imply a recurring event, and frequency quantifies that recurrence.

Mathematical Representation: ECM posits that frequency is the "only valid mathematical representation" of repetitive motion. Without a defined frequency, the concept of a regular, repeating vibration or oscillation becomes ill-defined. Consider a simple pendulum: its swing is described by its frequency (or period), not just its displacement.

Definitional Precedence: The idea is that vibration cannot be defined without frequency. This establishes frequency as the primary descriptor for any oscillatory system. It's the intrinsic characteristic that defines the very essence of its repetitive movement.

This perspective elevates frequency from being merely a derived quantity (like energy in the E = hf relation) to being the foundational property from which other related concepts emerge.

Reinterpreting the Planck Relation

The classical Planck relation, E = hf, is fundamentally reinterpreted in ECM. Here's how:

Energy as an Emergent Quantity: Unlike traditional physics where energy is a primary physical quantity, ECM views energy as an emergent concept. It's considered a secondary representation derived from a system's intrinsic frequency of phase transition or oscillation.

Conversion Constant: Instead of Planck's constant (h), ECM introduces its own conversion constant, for example, k = 5.558 × 10^−34 Js, which scales the system's intrinsic frequency to yield energy. This suggests that energy is a consequence of frequency, rather than frequency being a characteristic of energy.

Primacy of Frequency

ECM emphasizes the primacy of frequency over both energy and time (Δt) for several reasons:

Inherent to Dynamical State: Frequency is considered inherent to a system's dynamical state. It directly characterizes the ongoing evolution of a system without requiring an external timekeeper. This contrasts with energy, which depends on factors like system configuration (mass, motion, potential), and time, which is seen as relational and observer-dependent.

Fundamental for Oscillation: Frequency is deemed synonymous with vibration or oscillation and is presented as the only valid mathematical representation of such repetitive motion. It is argued that vibration cannot be defined without frequency, thus establishing frequency as the primary descriptor for oscillatory systems.

Cosmological Implications: In ECM cosmology, phenomena like redshift and energetic shifts are framed in terms of Δf (change in frequency) rather than time-based expansion. This perspective suggests that apparent energetic imbalances (ΔE) or mass variations (ΔM) over a duration (Δt) are governed by the fundamental phase-frequency evolution, not by the passage of time itself.

In essence, ECM proposes a shift from an energy-centric view to one where frequency is the foundational element driving physical processes and defining the nature of reality.

Comparative Analysis Report: Terry McMahon's Reformulations vs. Extended Classical Mechanics (ECM) Framework.

Prepared by: Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803
Date: July 21, 2025

Scholarly Cross-Comparison Now Live: Read on ResearchGate

Introduction

This report offers a focused, point-by-point comparative analysis between the reformulated physics approach proposed by Terry McMahon in his 2025 paper, Quantum gravity, special relativity & unification QGSM, and the Extended Classical Mechanics (ECM) framework developed independently. Both approaches challenge the foundations of relativity and quantum field theory, offering energy-centric alternatives to spacetime geometry and abstract force-carrying entities. Despite different terminologies, the two share foundational similarities as well as critical divergences.

Comparative Summary Table

Key Theme	Terry McMahon's View	ECM View	Commentary
Lorentz Factor & SR	Lorentz transformation introduces non-physical frame effects. Replaced with an index-based formulation.	SR time dilation is rejected; frequency governs Δt. Frame effects arise from energy-frequency shift, not geometry.	Both reject the Lorentz factor and spacetime-based time dilation. ECM emphasizes frequency displacement instead of dynamic index.
Photon Mass	Photons possess momentum → they must have mass. Mass evolves from bound (<c) to liberated (at c).	Photon/gamma ray emission represents displaced apparent mass (−Mapp), hence carries effective mass component.	Both assert non-zero mass association for free photons. ECM frames this via mass-displacement (ΔMM).
Planck Constant	Δf varies with energy scale. Not truly constant.	k = 5.558 x 10−34 Js derived in ECM as fundamental, linked to f0.	McMahon sees h as dynamic; ECM anchors a similar constant as derived from f0 via energetic continuity.
Gravity Mechanism	G is dimensionally flawed; gravity is energy density dependent, not geometric.	Gravity is mass-binding confinement of Meff; anti-gravity is liberated Mapp. No curved space required.	Both reject GR's geometry. ECM formalizes the binding/release mechanism through energy-mass structuring.
Gravitons & Fields	Gravitons unnecessary; field theory flawed.	No graviton; no field quantization. All transitions are real, observable mass shifts (ΔMM).	Total agreement on non-necessity of virtual field carriers.
Time & Causality	SR's time is geometrical fiction; proper time must emerge from energy-frequency behaviour.	Time is derived as f0; real dynamics follow frequency shift, not relativistic time.	McMahon calls for time redefinition; ECM implements it via f → Δt transformation.
Quantum Gravity	Must emerge from internal energy distributions, not curved spacetime.	ECM sees gravity and anti-gravity as reversible via ΔMM-mediated transitions.	Agreement in rejecting geometrisation in favour of physical transitions.
Unification of Forces	Energy-scaled parameters (running parameters) unify EM and gravity.	Mass-frequency correspondence allows unification without particle mediation.	Parallel strategies: dynamic parameters vs. frequency-mass equivalence.
Resistance from Academia	Journals resist anti-relativistic reformulations.	ECM development has been independent due to similar institutional resistance.	Shared experience of marginalization for paradigm-challenging frameworks.

Conclusion

Terry McMahon's reformulations and the ECM framework arrive independently at converging conclusions: spacetime curvature is not fundamental, time is emergent from energy behaviour, and photons are not massless. Where McMahon uses "running parameters," ECM formalizes transitions using mass-displacement (ΔM_M), effective and apparent mass (M^eff, M^app), and frequency (f) as foundational. This comparative insight opens the door to potential synthesis or mutual reinforcement of both models under a shared principle of energy-centric realism.

Intellectual debate fosters a deeper and more accurate understanding for everything.

July 21, 2025

This statement underscores the transformative power of engaging with diverse perspectives through reasoned discourse. When individuals with differing viewpoints engage in intellectual debate, it's not merely about winning an argument, but about a collaborative process of inquiry.

Through this process, assumptions are challenged, logical inconsistencies are exposed, and ideas are rigorously tested against alternative interpretations and evidence. Participants are compelled to articulate their positions with greater clarity, to consider counter-arguments, and to integrate new information that might refine or even alter their original understanding. This dynamic exchange moves beyond superficial comprehension, leading to a more nuanced, comprehensive, and ultimately, more accurate grasp of the subject matter, whatever it may be. It's a continuous cycle of questioning, defending, learning, and evolving one's understanding.

- Soumendra Nath Thakur

Fundamental Role of Frequency in Physical Description: A Dimensional and Conceptual Justification

Author: Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803  Email: postmasterenator@gmail.com

Date: July 20, 2025

Scientific Statement:

In Extended Classical Mechanics (ECM), frequency is posited as the most fundamental descriptor of physical state, more primary than both energy (E) and time (Δt), based on its direct association with intrinsic dynamical evolution, independence from external reference systems, and dimensional precedence in the construction of observable quantities.

Description:

In the classical Planck relation E = hf, energy appears as the product of a constant h and frequency f, suggesting an equivalence. However, ECM reinterprets this relation: energy is not a primary physical quantity, but rather an emergent one - a secondary representation of the system's intrinsic frequency of phase transition or oscillation, scaled by a conversion constant (e.g., ECMs k = 5.558 x 10⁻34 Js).

Unlike energy, which depends on system configuration (mass, motion, potential), and time Δt, which is relational and observer-dependent, frequency is inherent to the systems dynamical state. Whether referring to the oscillation of a field, the cycling of a phase, or the emission profile of a particle, frequency directly characterizes the ongoing evolution of the system without requiring an external timekeeper.

This primacy is reinforced by the role of frequency in ECM cosmology, where redshift and energetic shifts are framed in terms of Δf rather than time-based expansion. The apparent energetic imbalance ΔE or mass variation ΔM over a duration Δt is governed by the fundamental phase-frequency evolution, not by the passage of time itself.

Footnote: Frequency as Fundamental

Frequency is more fundamental than energy. It is synonymous with vibration or oscillation, since frequency is the only valid way to mathematically represent such repetitive motion. Vibration cannot be defined without frequency; hence, frequency precedes energy as the primary descriptor of oscillatory systems.

Dimensional Analysis:

Quantity	Symbol	Dimensional Form
Frequency	f	[T⁻1]
Time	Δt	[T]
Energy	E	[ML2T⁻2]
Planck constant or ECM constant	h or k	[ML 2 T⁻1]

From the relation E = hf ⇒ [E] = [h][f]
Substituting dimensions: [ML2T⁻2] = [ML2T⁻1] x [T⁻1]

This confirms frequency is the more elementary term: both energy and Planck's constant depend dimensionally on it. Furthermore, frequency derives solely from inverse time, while energy couples mass, length, and squared inverse time.

Importantly, frequency does not depend on energy, but energy cannot be defined without frequency, if one accepts E = hf as fundamental. Similarly, Δt is just the inverse of frequency, and thus frequency subsumes the role of time as well:

f = 1 / Δt      ⇒      Δt = 1 / f

Therefore, both E and Δt are derived quantities, contingent upon f.

External Validation of Frequency s Primacy in Physical Definition

The ECM position-that frequency is more fundamental than both energy and time-finds clear support in both experimental standards and foundational quantum theory.

1. Time Defined via Frequency in SI Units
   The International System of Units defines the second via the fixed frequency of radiation from cesium-133 atoms:
   

   The second is defined by taking the fixed numerical value of the caesium frequency ∆ν(Cs) to be 9,192,631,770 when expressed in the unit Hz (s⁻¹). - NIST

   This makes time a derived quantity from frequency, not vice versa.
2. Quantum Energy as Frequency of Phase Evolution
   In quantum mechanics, energy is expressed through phase evolution:
   ψ(t) ∝ e−iEt/ħ = e−2πift
   Energy (E) is interpreted as the product of frequency (f) and Planck's constant. This supports the ECM position that frequency governs state evolution.
3. Dimensional Coherence Reinforced
   From E = hf:
   [E] = [h][f] = [ML2T⁻1] x [T⁻1] = [ML2T⁻2]
   Again showing energy is a frequency-scaled quantity.
4. Experimental Clocks Rely on Frequency
   All modern atomic clocks define time intervals by counting cycles of atomic transitions-i.e., frequency. This operational priority supports the ECM claim that time Δt is secondary to frequency.
5. Uncertainty Principle Prioritizes Frequency's Accuracy
   In the energy-time uncertainty relation, a precise energy value requires a long-duration observation of a stable frequency. Thus, frequency accuracy is logically prior to energy definition.

Conclusion:
These empirical and theoretical pillars collectively reinforce the ECM stance:

Frequency is not merely a useful parameter but the ontological basis of time, energy, and mass relations.

Post-Latent Energetic Dynamics and the Dual-State Evolution of the Universe in ECM

Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803 | Tagore's Electronic Lab, India | postmasterenator@gmail.com

July 18, 2025

Abstract

In Extended Classical Mechanics (ECM), the origin and evolution of the universe are fundamentally reinterpreted through a frequency-based cosmological framework that eliminates the need for an initial mass singularity or explosive Big Bang. Instead, ECM posits that the universe begins from a quiescent field of latent potential energy defined purely by frequency, void of mass, motion, or classical energy. The transition from this latent state into observable dynamism occurs via a frequency displacement—a post-latent transition—initiating the reversible emergence of apparent mass and kinetic energy. This leads to a primordial energetic imbalance where the magnitude of negative apparent mass exceeds gravitational mass, generating a repulsive dynamic that drives early cosmic expansion.

In ECM, mass is not intrinsic but emerges through the reversible extraction of potential energy. The early universe evolves in two distinct energetic states: an unobservable pre-Planckian regime where negative apparent mass manifests as dark energy, and an observable regime where parts of that energy settle into dark matter or stabilize into visible matter. The equivalence ΔMᴍ ≡ −Mᵃᵖᵖ governs these transformations, highlighting the cyclic and reversible energetic rhythm of the cosmos. ECM thus proposes a non-singular, wave-governed universe, where frequency, phase, and time govern mass emergence and cosmic structure through reversible energetic displacement rather than irreversible mass-based collapse or inflation.

Keywords:

Extended Classical Mechanics, latent frequency field, apparent mass, post-latent transition, dark energy, dark matter, frequency displacement, energetic asymmetry, cyclic cosmology, reversible dynamics, gravitational stabilization, mass-energy transformation, Planck threshold, kinetic extraction,

In the framework of Extended Classical Mechanics (ECM), the universe does not begin with a massive explosion or singularity, as is commonly depicted in traditional cosmological models. Instead, it emerges from a quiet, uneventful field of latent potential energy, a primordial state defined entirely by frequency. This field carries no mass, no motion, and no classical energy in the conventional sense—it is a state of pure potential, not yet disrupted by asymmetry or displacement.

This latent frequency condition represents the pre-dynamical phase, prior to any observable transformation. Once a displacement occurs within this field—triggered by frequency change over time or phase—dynamism begins. This moment is referred to in ECM as the post-latent transition. It marks the point where a portion of the potential energy field is reversibly extracted, leading to the manifestation of mass-equivalent dynamics.

Emergence of Apparent Mass and the Initial Energetic Imbalance:

According to ECM, the universe’s earliest energetic condition is defined by an imbalance between two forms of mass: gravitational mass and apparent mass. Gravitational mass corresponds to the familiar attractive force that shapes structure in the cosmos. In contrast, apparent mass—particularly in its negative form—acts as a repulsive kinetic driver, emerging from displaced potential energy and carrying the dynamical role of expansion.

At the origin, ECM proposes that gravitational mass is less than the magnitude of negative apparent mass. This asymmetry is critical, as it leads to a powerful phase of repulsive expansion that temporarily overwhelms gravitational attraction. In ECM interpretation, this is the true beginning of observable cosmic evolution—driven not by mass but by the displacement of frequency-defined energy into kinetic form.

From Frequency Displacement to Cosmic Expansion:

Once the latent field undergoes displacement, the frequency shift results in the appearance of mass-like behaviour, most notably in the form of negative apparent mass. This mass is not permanent but rather a transient energetic state, fuelled by the kinetic extraction of energy from the original potential. It serves as the key agent behind the initial high-velocity expansion of the universe—effectively functioning as the ECM analogue to inflation.

As this expansion proceeds, frequency gradually decays, and the kinetic energy associated with the apparent mass begins to transform again. Gravitational mass slowly increases, or the magnitude of apparent mass decreases, leading eventually to a phase of gravitational stabilization. This transition represents a cyclic energetic rhythm, as the universe oscillates between potential and kinetic dominance, between displacement and restoration.

Two Distinct States in ECM Cosmology:

ECM cosmology defines two distinct energetic states of the universe:

1. The Unobservable State:

This state exists prior to or beyond the Planck threshold. It is characterized by a frequency regime that lies outside the limits of measurement or observation. During this phase, frequency displacement initiates the emergence of mass-equivalent forms. A portion of the resulting apparent mass maintains sufficient dynamism to remain in motion, manifesting as what ECM identifies as dark energy—a kinetic component exhibiting anti-gravitational behaviour. Some of this dark energy continues into the observable state and may later partially transform into ordinary mass, associating itself with what is recognized as dark matter.

2. The Observable State:

This state occurs within the Planck threshold, where frequency values fall into measurable and interpretable domains. In this phase, the same dynamic principle continues. Portions of the earlier apparent mass, now with reduced dynamism, behave as dark matter—retaining some of the anti-gravitational characteristics of dark energy but with diminished motion. Simultaneously, other portions stabilize further and contribute to the formation of observable matter, such as massive particles and atomic structures.

Cyclic Energetic Interpretation:

Central to ECM is the idea that apparent mass is reversible. It arises from the subtraction of potential energy and can, under the right conditions, revert to its original form. This reversibility is not just a theoretical curiosity—it forms the backbone of a cyclical universe model where energy constantly oscillates between latent potential, kinetic dynamism, and gravitational structure.

In this view:

• Dark energy represents the active phase of apparent mass, driving accelerated expansion.

• Dark matter marks the residual, decelerated phase, still unobservable but less dynamic.

• Ordinary matter emerges as the stabilized result of kinetic energy transformations entering gravitational equilibrium.

ECM thus presents a cosmological model that is wave-based rather than mass-based, governed by transformations of frequency, phase, and time—not by initial mass concentration or singularities. The universe is born from energy displacement and evolves through reversible energetic phases, offering a fundamentally different lens through which to understand its origin, structure, and fate.

Energetic Imbalance at the Origin: The Role of Apparent Mass and Frequency Displacement in ECM

In Extended Classical Mechanics (ECM), the foundational relations among frequency f, phase φ, and time Δt—including f₀, f₁, and Δf—adhere to classical wave principles across all scales. Crucially, the quantum constants such as Planck’s constant h and quantized energy E = hf are not applicable at the universal origin, since these constants are defined only within or below the Planck threshold and lack physical meaning when extrapolated to pre-Planckian regimes. (See: Relevant Appendix/ces on ECM constants and Planck limitations.)

At the heart of the universe’s origin, ECM proposes a fundamental mass-energy asymmetry:

Mɢ < |−Mᵃᵖᵖ|

This inequality suggests that the negative apparent mass dominates over gravitational mass during the universe's earliest phase. The implications of this asymmetry are central to ECM cosmology:

• High-velocity expansion is initiated by −ΔMᴍ-mediated kinetic energy,

• A net repulsive dynamic temporarily overcomes gravitational attraction,

• Gravitational stability only emerges later, as Mɢ increases or |−Mᵃᵖᵖ| decreases.

In earlier ECM discussions, it was shown that the universe originates not from a singular mass event but from an uneventful field of latent potential energy, defined solely by frequency. This latent energy undergoes frequency displacement, initiating the appearance of kinetic mass-like phenomena, particularly negative apparent mass −Mᵃᵖᵖ, which acts as a dynamical driver of cosmic inflation and initial acceleration.

This energetic cycle gradually evolves: as frequency decays, gravitational mass Mɢ vanishes, and the system reverts to a frequency-defined potential state—restoring the pre-inflationary conditions in a rhythmic manner. This formulation provides a mathematically coherent connection between cosmological redshift, apparent mass displacement, and energetic reversion, highlighting a cyclic rhythm of expansion and contraction rooted in frequency dynamics rather than mass-based singularities.

The central equivalence governing this transformation is:

ΔMᴍ ≡ −Mᵃᵖᵖ

Here, −Mᵃᵖᵖ serves as the kinetic driver, translating reversible frequency changes into observable energetic behaviour. (See: Appendices on Energetic Reversion, Mass Displacement, and Cosmological Frequency Cycles for derivations and further discussion.)

Latent Frequency Field and the Dual-State Emergence of the Universe in ECM:

Post-Latent Transition:

In Extended Classical Mechanics (ECM), the universe does not originate from a singular mass-based event, but rather from an uneventful field of latent potential energy, defined solely by frequency. The governing energetic expression for this primordial state is:

PEᴇᴄᴍ,ᵤₙᵢᵥ = (PEᴇᴄᴍ,ᵤₙᵢᵥ − ΔPEᴇᴄᴍ,ᵤₙᵢᵥ) + ΔPEᴇᴄᴍ,ᵤₙᵢᵥ

Where:

• −ΔPEᴇᴄᴍ,ᵤₙᵢᵥ → −Mᵃᵖᵖ

• −ΔPEᴇᴄᴍ,ᵤₙᵢᵥ → −ΔMᴍ

This reflects that the observable energetic portion of the universe arises from a reversible extraction of potential energy, transforming into kinetic mass-equivalent dynamics.

Two Fundamental States of the Universe in ECM:

ECM distinguishes between two primary energetic states of the universe:

Condition 1: Unobservable State (Beyond the Planck Scale, Pre-Origin):

• Defined by f₀ → f₁, where frequency displacement initiates energetic asymmetry.

• Governing equivalence:

ΔPEᴇᴄᴍ,ᵤₙᵢᵥ ≡ KEᴇᴄᴍ,ᵤₙᵢᵥ → ΔMᴍ ≡ −ΔMᴍ

• In this pre-Planckian regime, a portion of ΔMᴍ sustains cosmic dynamism as KEᴇᴄᴍ,ᵤₙᵢᵥ and manifests as dark energy (DE) — exhibiting anti-gravitational behaviour.

• Some of this dark energy persists into Condition 2, partially converting into observable mass Mᴍ, binding with dark matter (DM).

Condition 2: Observable State (Within the Planck Scale):

• Transition defined by fᴘ → fᴏᵦₛₑᵣᵥₐᵦₗₑ, where the frequency enters the detectable domain.

• The same kinetic-potential equivalence applies:

KEᴇᴄᴍ,ᵤₙᵢᵥ → ΔMᴍ ≡ −ΔMᴍ

• A portion of ΔMᴍ that loses dynamism (↓KEᴇᴄᴍ,ᵤₙᵢᵥ) or regains gravitational coupling becomes dark matter (DM) — still exhibiting anti-gravitational behaviour but with reduced kinetic drive.

Energetic Interpretation in ECM

• The equivalence ΔMᴍ ≡ −ΔMᴍ expresses the reversible nature of energetic transformation: apparent mass emerges from the subtraction of potential energy and may later revert.

• Dark energy corresponds to the active kinetic component of apparent mass that fuels expansion.

• Dark matter emerges as the residual, decelerated kinetic component, gravitationally reactive but still non-luminous.

This dynamic view frames the entire evolution of the universe as an oscillatory frequency-driven transformation, where latent frequency displaces into mass-equivalent motion, then reverts through decay. Mass is thus not fundamental but a transient expression of energetic displacement across phase and time.

Alphabetical List of Terms in ECM (with Descriptions, Units, and Appendix References)

Term	Description	Unit	Relevant Appendix
Δf	Change in frequency; describes the shift during frequency displacement, central to redshift dynamics.	Hz	Appendix 6, Appendix 29
ΔMᴍ	Change in mass-equivalent dynamics, interpreted as reversible kinetic transformation of apparent mass.	kg	Appendix 6, Appendix 29, Appendix 30
ΔPEᴇᴄᴍ	Change in potential energy in ECM framework; represents extracted energy from a latent frequency field.	J	Appendix 6, Appendix 29
f₀, f₁	Initial and displaced frequencies before and after cosmic energetic transition.	Hz	Appendix 6, Appendix 29
fᴘ	Planck threshold frequency—defines boundary between unobservable and observable cosmological regimes.	Hz	Appendix 30
fₒᵦₛₑᵣᵥₐᵦₗₑ	Frequency range within measurable and gravitationally interactive state-space.	Hz	Appendix 6, Appendix 29
G (Gravitational Mass, Mɢ)	Mass component contributing to gravitational attraction. In ECM, G <	−Mᵃᵖᵖ	at origin.
KEᴇᴄᴍ	Kinetic energy in ECM, equivalent to extracted potential energy; initiates mass-like motion.	J	Appendix 6, Appendix 29
Mᵃᵖᵖ (Apparent Mass)	Emergent, reversible, often negative mass associated with frequency displacement; not intrinsic but dynamic.	kg	Appendix 6, Appendix 29, Appendix 30
Mᴍ	Observable mass formed through transformation and stabilization of ΔMᴍ.	kg	Appendix 29
PEᴇᴄᴍ	Potential energy defined in ECM by the frequency field prior to displacement.	J	Appendix 6, Appendix 29
φ (Phase)	Angular phase variable used in wave dynamics to interpret phase-time transformations.	radians	Appendix 6
t, Δt	Time and time interval associated with phase or frequency shift; crucial for dynamism in ECM.	s	Appendix 6, Appendix 29

 

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