Reevaluation of Relativistic Interpretations: Mechanical, Temporal, and Energetic Counterarguments under Extended Classical Mechanics (ECM)

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

November, 12, 2025

Abstract

This paper reevaluates the mainstream interpretation of relativistic phenomena through the framework of Extended Classical Mechanics (ECM), emphasizing the mechanical, temporal, and energetic origins of observed effects. It challenges the conventional attribution of GPS time corrections, time dilation, and spacetime curvature to relativistic causes, proposing instead that these arise from oscillator-based distortions and energetic variations consistent with classical mechanics.

In ECM, the behavior of timekeeping systems is governed by frequency stability rather than geometric deformation of spacetime. The analysis distinguishes between time dilation and time distortion, expressing the generalized temporal deviation as t′ = t ± Δt, where Δt represents either dilation or contraction depending on the oscillator’s energetic and mechanical state. This interpretation restores the concept of time as a fixed-scale phenomenon rooted in physical oscillation, not an elastic continuum.

The discussion further establishes that gravitational and velocity-dependent deviations in clock behavior stem from infinitesimal variations in oscillator energy (E = hf), negating the need for spacetime curvature to explain these effects. Through analytical reasoning and empirical parallels from electronic oscillator systems, ECM provides a consistent, frequency-governed alternative to relativistic constructs—preserving rational physical principles while unifying mechanics, energy, and time under a coherent classical framework.

Keywords: 

Extended Classical Mechanics (ECM), Time Distortion, Frequency Shift, Oscillator Deformation, GPS Time Correction, Relativity Reevaluation, Energy–Frequency Equivalence, Classical Dynamics

Argument 1: GPS Corrections vs. Time Dilation

The argument that GPS satellite corrections confirm “relativistic time dilation” is a misrepresentation. A clock—whether atomic or mechanical—is a physical device whose timekeeping depends on the stability of its oscillator. Any change in frequency results from mechanical or energetic deformation of that oscillator, not from abstract spacetime effects.

Relativistic correction implies adjustment for speed or gravitational potential. However, a GPS satellite cannot “correct” its orbital velocity or gravitational potential while in operation. To truly nullify such effects, it would have to be physically relocated to Earth’s surface under identical conditions—an obviously impossible situation.

In reality, the so-called relativistic corrections applied to GPS systems compensate for timekeeping errors caused by oscillator distortion arising from variations in velocity and gravitational potential. These corrections are thus mechanical and classical in nature, consistent with well-established principles of oscillator behavior under physical stress, rather than confirmations of relativistic time dilation.

Argument 2: Fixed vs. Relative Time Scale

It is a well-established fact that a clock’s oscillation frequency is predesigned and fixed within a definite physical range, maintaining a consistent scale of 360°. In practical mechanics and electronics, this frequency represents a stable temporal reference. Relativistic theory, however, departs from this fixed framework — proposing that the frequency of the same oscillator appears reduced under motion or in differing gravitational potentials, leading to what is termed time dilation.

In conventional representation, this is expressed as 

t′ = ∣t+Δt∣, where t′>t,

implying that the observed time always expands relative to the base time t. This unidirectional dilation — the stretching of the time scale — is regarded as an intrinsic outcome of relativistic conditions.

In Extended Classical Mechanics (ECM), however, time distortion is not confined to dilation alone. Instead, the deviation in time (Δt) may be positive or negative, depending on whether the oscillator’s frequency decreases or increases due to its energy, entropy, or mechanical conditions. Thus ECM generalizes the relation as

t′ = t ± Δt,

where Δt > 0 corresponds to slowed oscillation (dilation) and Δt < 0 corresponds to accelerated oscillation (contraction).

The essential point is that a clock does not experience “dilation of time” as a geometric stretching but a distortion of oscillation frequency caused by mechanical or energy variations. Therefore, the GPS satellite clock, whose oscillator undergoes deformation due to speed and gravitational potential, accumulates measurable error in time, not a change in the universal scale of time itself. The correction applied in GPS systems restores the oscillator’s frequency to its fixed, standard value — achieving stability, not “relativistic conformity.”

Argument 3. Oscillation Energy vs. Spacetime Geometry

ECM’s position that gravitational effects arise from tiny energy variations in oscillators is entirely consistent with physical principles. Every physical oscillator requires a constant energy input to maintain a constant frequency, as governed by E = hf. When frequency varies due to energetic or material influence, the effect is a direct mechanical or electromagnetic response, not the manifestation of curved spacetime.

There is no necessity to invoke spacetime curvature to explain deviations in frequency or timing. The fundamental relationships E = hf and  f = 1/T = 1/λ remain valid without geometric reinterpretation. As an electronics engineer with direct experience handling such oscillatory systems, I affirm that these are empirically verified behaviors within the scope of classical mechanics and engineering practice, not relativistic phenomena.

Conclusion

Hence, all three mainstream arguments—relating to GPS corrections, relative time scales, and spacetime curvature—are misdirected. Each can be consistently and accurately interpreted within Extended Classical Mechanics (ECM) and classical oscillator physics without reliance on relativistic constructs.

References:

1. Relativistic effects on phaseshift in frequencies invalidate time dilation II. DOI: https://doi.org/10.36227/techrxiv.22492066.v2

2. Phase Shift and Infinitesimal Wave Energy Loss Equations. https://www.longdom.org/open-access/phase-shift-and-infinitesimal-wave-energy-loss-equations-104719.html

3. Reconsidering Time Dilation and Clock Mechanisms: Invalidating the Conventional Equation in Relativistic Context. https://doi.org/10.13140/RG.2.2.13972.68488

4. Perspective on Clocks, Frequencies, and the Illusion of Time Dilation. https://doi.org/10.13140/RG.2.2.20701.18403

5. Re-examining Time Dilation through the Lens of Entropy. https://doi.org/10.13140/RG.2.2.36407.70568

6. Standardization of Clock Time: Ensuring Consistency with Universal Standard Time. https://doi.org/10.13140/RG.2.2.18568.80640

7. Article: Exploring the Interplay of Clocks and Biological Time Perception. https://doi.org/10.13140/RG.2.2.23146.49601

8. Exploring Time Dilation via Frequency Shifts in Quantum Systems: A Theoretical Analysis. https://doi.org/10.13140/RG.2.2.23087.51361

9. Formulating Time's Hyperdimensionality across Disciplines. https://doi.org/10.13140/RG.2.2.30808.51209

10. Time Unveiled: A Journey through Hominin Evolution to the Nature of Time Perception. https://doi.org/10.13140/RG.2.2.31696.07680

ECM Phase Kernel Formalism: A Presentation of Gravity Beyond GR’s Spacetime Curvature

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

October 21, 2025

Extended Classical Mechanics (ECM) proposes that gravity is not a manifestation of spacetime curvature, as described by General Relativity (GR), but a force-based interaction emerging from a mass-binding condition between mass and energy. In this framework, gravitational attraction and cosmic expansion are both understood as consequences of this binding and its natural release — rather than as geometric effects of spacetime deformation. ECM introduces the concept of negative apparent mass (−Mᵃᵖᵖ) to represent the repulsive, energy-releasing phase of this interaction, thereby offering a physical explanation for phenomena attributed to dark energy and gravitational repulsion. [1, 2, 3]

Mathematical Derivation and Observational Basis:

A detailed mathematical derivation, supported by observational data, is presented here:

Gravity Beyond GR's Spacetime Curvature: ECM Mathematical Basis of the Phase Kernel Formalism

https://www.researchgate.net/publication/396617179_Gravity_Beyond_GR's_Spacetime_Curvature_Extended_Classical_Mechanics_ECM_Mathematical_Basis_of_the_Phase_Kernel_Formalism

1. Conceptual Framework

The ECM Phase Kernel Formalism reinterprets gravity as a phase modulation of waves caused by cumulative phase variations arising from mass-energy distributions. This wave-based approach reproduces the measurable predictions of GR in weak-field conditions — including Shapiro delay, gravitational lensing, and planetary perihelion precession— but attributes them to frequency and time distortions, not geometric curvature.

In ECM, gravitational influence acts as an effective refractive index that slows the phase velocity of waves and matter traversing a gravitational field. [9]

2. Gravity in ECM vs. General Relativity (GR)

General Relativity (GR):

● Interprets gravity as the curvature of spacetime produced by mass and energy. [4, 5, 6]

● Objects move along geodesics — the shortest paths — in this curved spacetime, which we perceive as gravitational motion. [7]

Extended Classical Mechanics (ECM):

● Describes gravity as a force-driven rather than geometry-driven effect. [2]

● Defines gravity as a mass-binding condition — a dynamic equilibrium that can bind or release mass-energy. [1]

● Explains cosmic expansion as the release of this bound state, independent of any spacetime expansion. [2, 8]

3. Key Concepts in ECM

• Mass-Binding Condition

Redefines gravity as a physical condition of mass-energy binding, providing a unified mechanism for subatomic, astrophysical, and cosmological phenomena. [1]

• Negative Apparent Mass (−Mᵃᵖᵖ)

Represents the repulsive or unbinding aspect of mass-energy interactions. This is not a “negative particle mass” but a derived gravitational term associated with kinetic energy, radiation, or field momentum. [2, 3]

This framework allows ECM to model cosmic acceleration and dark energy effects without invoking spacetime curvature.

• Force-Based Explanation

By maintaining a force-centric interpretation, ECM aims for a physically grounded and empirically measurable understanding of gravitational and cosmological effects. [2]

4. Implications of the ECM Model

Cosmic Expansion:

The acceleration of the universe arises from the evolving relationships among mass-energy terms — not from an expansion of spacetime. [8]

Dark Energy:

The effects attributed to dark energy emerge from the negative apparent mass (−Mᵃᵖᵖ) component inherent in radiation and kinetic energy fields. [3]

Reexplanation to GR:

ECM provides a consistent, classical-mechanical reexplanation that reproduces GR-like results under weak-field limits, while extending applicability to quantum and cosmological domains. [2]

5. Core Principles of the ECM Phase Kernel Formalism

• Gravity as Phase Modulation

Gravity manifests as a cumulative phase shift affecting all oscillatory systems — matter waves, photons, and fields — due to the presence of mass-energy.

• Time Dilation and Shapiro Delay

Gravitational time dilation corresponds to a progressive slowing of an internal beat frequency or oscillation rate as a system approaches higher gravitational potential — mathematically equivalent to the Shapiro delay observed in GR. [9]

• Unified Lensing Model

Combines geometric and Shapiro-type delays within a single phase-based framework, treating lensing as a coherent phase-variation process rather than geometric bending.

• Perihelion Precession

Interprets orbital precession as an angular phase perturbation, not as motion along a curved spacetime path.

• Testable Predictions

The model’s predictions can be verified by fitting phase-shift coefficients to precision datasets — e.g., Cassini spacecraft tracking, VLBI, and pulsar timing — to identify possible deviations from GR. [9]

References

[1] Definition of Gravity in Extended Classical Mechanics (ECM) https://www.researchgate.net/post/Definition_of_Gravity_in_Extended_Classical_Mechanics_ECM

[2] Gravitating Mass as an Emergent Polarity-Governed Quantity in ECM https://www.researchgate.net/post/Gravitating_Mass_as_an_Emergent_Polarity-Governed_Quantity_in_ECM

[3] ECM-Based Rebuttal on the Gravitational Nature and Weight of Massless Waves https://www.researchgate.net/post/ECM-Based_Rebuttal_on_the_Gravitational_Nature_and_Weight_of_Massless_Waves

[4] Einstein’s General Theory of Relativity Explained – space.com https://www.space.com/17661-theory-general-relativity.html

[5] Understanding GR: Educational Video Reference https://www.youtube.com/watch?v=c2Gv3Th6UM8

[6] Recent Study on Spacetime Curvature Dynamics – ScienceDirect https://www.sciencedirect.com/science/article/abs/pii/S0960077924012591

[7] Einstein’s Curved Spacetime Visualization https://www.youtube.com/watch?v=P4kDyWs_IuI

[8] Application of Extended Classical Mechanics (ECM) – In Brief 2 https://www.researchgate.net/post/Application_of_Extended_Classical_Mechanics_ECM-In_Brief2

[9] ECM Phase Kernel Formalism – Mathematical Framework http://www.telitnetwork.itgo.com/ExtendedClassicalMechanics/ECMPhaseKernel/

Extended Classical Mechanics: The Phase Kernel Formalism — Rethinking Gravity Beyond Spacetime Curvature

This presentation introduces Extended Classical Mechanics (ECM) through the Phase Kernel Formalism, a wave-based reformulation of gravity that replaces spacetime curvature with cumulative phase variation.

Speakers A and B explain:

The phase-algebra derivation of Shapiro delay, matching GR through phase shift interpretation.

A unified gravitational lensing model merging geometric and Shapiro-type delays.

Perihelion precession reinterpreted as angular phase perturbation rather than curved motion.

Extraction of phase-shift coefficients from precision data (Cassini, VLBI, pulsar timing) to test ECM predictions against GR.

Key Idea: ECM reproduces GR’s measurable results in weak fields but redefines gravity as phase modulation instead of spacetime geometry — opening a new lens on gravitational physics.

Short Caption

“Gravity as Phase — ECM’s Alternative to Spacetime Curvature”

Essence of Extended Classical Mechanics (ECM): A Foundational Framework Unifying the Three Branches of Physics

Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803 | Date: October 09, 2025

Extended Classical Mechanics (ECM) is the unifying foundation capable of guiding the three prevailing branches of physics:

1. Newtonian Classical Mechanics — governed by macroscopic mass–motion relations (F = Ma), where mass (M) and time (t) are treated as constants.

2. Einsteinian Relativistic Mechanics — governed by the Lorentz factor (γ = 1/√(1 − v²/c²)), which introduces velocity-dependent variations in mass, time, and length, giving relativity its mechanical character beyond mere geometric representation [1].

3. Quantum Mechanics — governed by frequency-dependent energy quantization (E = hf) and probabilistic microstates.

ECM not only extends these frameworks through mass-differential formalism — employing effective mass (Mᵉᶠᶠ), apparent mass (Mᵃᵖᵖ), and mass differentials (ΔMᴍ) — to link the macroscopic, relativistic, and quantum regimes under a single principle, but also integrates gravitational and antigravitational effects within the same formalism [2].

In ECM, these dual aspects are interpreted as complementary manifestations of energy redistribution through mass differentials:

KEᴇᴄᴍ = (ΔMᴍᵈᵉᴮʳᵒᵍˡᶦᵉ + ΔMᴍᴾˡᵃⁿᶜᵏ)c² = ΔMᴍc² = hf

— establishing ECM as the frequency–mass–energy bridge unifying mechanical, relativistic, quantum, gravitational, and antigravitational domains.

In short, Extended Classical Mechanics (ECM) provides a unified framework integrating Newtonian, Einsteinian, and Quantum Mechanics through a mass-differential formalism that includes Mᵉᶠᶠ (effective mass), Mᵃᵖᵖ (apparent mass), and ΔMᴍ (mass differentials). ECM naturally incorporates gravitational and antigravitational effects as complementary energy redistribution phenomena. Relativistic behaviors emerge from frequency-dependent phase distortions rather than spacetime geometry, and quantum energy quantization is seamlessly integrated, establishing ECM as a frequency–mass–energy bridge across scales.

Footnotes:

[1] In Extended Classical Mechanics, the Lorentz factor (γ) is not treated as an external relativistic correction but as an emergent consequence of the variation of effective mass (Mᵉᶠᶠ) with motion-induced frequency distortion. Thus, γ represents mass–frequency coupling, not spacetime geometry:

γ = 1/√(1 - v²/c²) ⇒ Mᵉᶠᶠ = γMᴍ

Accordingly, phenomena such as relativistic mass increase, time dilation, and length contraction emerge as frequency-dependent phase distortions within the mass-energy continuum, rather than as geometric curvature of spacetime [3].

[2] In ECM, antigravitational effects correspond to transitions involving negative apparent mass (−Mᵃᵖᵖ). These transitions represent the outward or energy-release phase of the mass-differential field, complementing the inward (gravitational) phase associated with positive Mᵃᵖᵖ. Together, these form a balanced mass–energy duality driving both attraction and expansion phenomena across physical scales [4].

References:

1. Einstein, A. Zur Elektrodynamik bewegter Körper, Annalen der Physik, 1905.

2. Planck, M. Über die Begründung des Gesetzes der Energieverteilung im Normalspektrum, Annalen der Physik, 1900.

3. Appendix 21: Effective and Apparent Mass Dynamics in Extended Classical Mechanics (ECM). DOI: https://doi.org/10.13140/RG.2.2.25261.38882

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

Extended Classical Mechanics (ECM) -Adopted Definition of Space and Time:

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

October 07, 2025

ECM adopts three-dimensional Euclidian space and a hyperdimensional temporal extension to form a unified existential manifold, wherein space and time emerge interdependently from the evolution of physical existence.

In this framework, space represents the measurable extensions of existence—length, width, and depth—while time arises as a relational descriptor of sequential change, not as an independent dimension. The emergence of time began with the first existential event—the Big Bang—when both space and time originated as mutually dependent extensions describing the transformation of mass–energy within the universe.

Time in ECM is thus conceptual and derivative, representing the ordered progression of existential events within space rather than a standalone coordinate. The hyperdimensional extension of time expresses the meta-evolution of events governing all spatial changes, distinguishing cosmic evolution from localized temporal measurement.

Accordingly, standard clock time in ECM serves only as a reference of fixed oscillatory frequency, subject to distortion (Δt) under external conditions such as gravitational, energetic, or cosmological influences. Cosmic time, in contrast, expresses the cumulative distortion of existential order—the measurable degree of transformation from the universe’s initial ordered state toward increasing disorder.

Hence, ECM redefines the spacetime manifold not as a geometric continuum but as an existential framework where space quantifies physical extension and time quantifies the ordered change of existence within that extension.