Relativistic Effects on Phase Shift in Frequencies Invalidate Time Dilation II

The Preface

The paper challenges the concept of time dilation in special relativity, maintaining that it is actually a misinterpretation of wavelength dilation caused by relativistic effects. The authors suggest that the equation for time dilation,

t′ = t / √(1 - v²/c²),

is incorrect and fails to explain the cause of time distortion. They propose that time is an abstract and conceptual dimension, not influenced by relativistic effects such as speed or gravity, and it is the wave properties and corresponding wavelength distortions that lead to time distortions.

Experimental results using piezoelectric crystal oscillators demonstrate that phase shifts in frequencies correspond to time shifts due to relativistic effects.

The authors emphasize that time is an emergent concept related to events and should not be considered an entity affected by relativistic effects.

They conclude that the concept of time dilation is a misconception and that the observed effects are actually the dilation of wavelengths in clock oscillations, resulting in errors in clock readings.

Phase shift in relative frequencies due to wavelength enlargement results in errors in clock readings, misinterpreted as time dilation.

Relativistic Effects on Phase Shift in Frequencies Invalidate Time Dilation II

About Time and Wavelength Dilation – Version 2.2

DOI: 10.36227/techrxiv.22492066.v2

Soumendra Nath Thakur¹⁺   Priyanka Samal²   Deep Bhattacharjee³

¹ Tagore's Electronic Lab., India
² Berhampur University, India
³ INS Research, Department of Geometry & Topology, India
³ Electro Gravitational Space Propulsion Laboratory, India
³ Actual Intelligence Division, CXAI Technologies Ltd, Cyprus

May 2023

Reference – 20 Titles

Abstract

Relative time emerges from relative frequencies. It is the phase shift in relative frequencies due to infinitesimal loss in wave energy and corresponding enlargement in the wavelengths of oscillations, which occur in any clock between relative locations due to relativistic effects or differences in gravitational potential, that result in error in the reading of clock time — wrongly presented as time dilation.

Keywords: phase shift, relativistic effects, wavelength dilation, piezoelectric crystal oscillator

⁺ Corresponding Author:
¹ postmasterenator@gmail.com
² priyankasamal9437@gmail.com
³ itsdeep@live.com
¹ ² ³ The authors have no conflict of interests related to this paper.

Introduction

The Theory of Relativity adopts Minkowski spacetime that combines three-dimensional Euclidean space and fourth dimensional time into a four-dimensional manifold, wherein time is robbed of its independence, rather considered 'natural'.
The Theory of Relativity also conveys that the proper time is dependent on relativistic effects and expressed as t < t′, where t′ is time dilation.

The equation of time dilation is:

t′ = t / √(1 - v²/c²)

where t′ is dilated time, t is proper time, v is relative speed, and c is the speed of light in free space.

The points in consideration here are –

• 'Proper time' including 'relative time' is not natural or the event itself but an emerging concept, mathematical in character.
• 'Space' is not natural or eventual itself but a three-dimensional extent as a mathematical concept.
• Whether 'spacetime,' which combines three-dimensional Euclidean space and fourth-dimensional time into a four-dimensional manifold, is not natural, nor eventual itself, nor dependent on relativistic effects but a four-dimensional extent as a mathematical concept.
• Whether time is not distorted due to relativistic effects.

The conjectural equation of time dilation was based on Doppler's formula, which failed to identify any cause of time distortion. Whereas the wave equation; in the properties of a wave, in combination with the Planck equation has been able to successfully identify the distorted frequencies due to the relativistic effect that has the influence factor. The distorted frequencies in the equation yield a relative value of time for the corresponding wavelength dilation, which is erroneously known as time dilation.

This expression for time in time dilation contradicts the expression t = t′ as in classical mechanics, where time is absolute. Stephen Hawking upheld the concept of imaginary time in his book "The Universe in a Nutshell". Time is defined as the indefinite continued progression of events in the past, present and future existences and considered as a whole, succeeding in irreversible and uniformed succession, which is referred to in the fourth dimension above the three spatial dimensions. Therefore, events invoke time but not vice versa. What special relativity represents in time dilation is not time, and time dilation does not have time. It is rather error in the clock oscillation.

Counter-examples such as experiments made on piezoelectric crystal oscillators show that wave distortions correspond to time distortions due to relativistic effects, thus disproving the conjectural equation of time dilation; and invalidates time dilation altogether.
The time dilation equation t՚ = t/√(1 − v²/c²) is wrong.

A Scientific Misconception in Time Dilation

Events invoke time. The defect in the equation:

t՚ = t/√(1 − v²/c²)

is that relativistic effects, such as speed or gravity of the real events, can never interact with the proper time (t) referred to in the fourth dimension. This means, the {1/√(1 − v²/c²)} part of the equation (Lorentz factor) cannot influence or interact with the proper time (t) to enlarge it and get the time dilation (t′) as in the equation. The piezoelectric crystal oscillators show that the error in wave corresponds to time shift due to relativistic effects.

The observations made on the effect of dark energy do not show anti-gravity, caused by dark energy, affects time in any manner, except causing enlargement in the wavelength due to expansion of space. It is naturally unauthorized and disprovable to enlarge the scale of proper time, instead of distortion in the wavelength of clock oscillation.

Even very small changes in the gravitational forces (G-force) cause internal particles of matter to interact with each other, which is known to cause stresses and associated deformations in the internal matter.

Wavelength distortions, due to the phase shift in relative frequencies, correspond exactly to time distortion; through the relationship

λ ∝ T

where λ denotes the wavelength and T denotes the period of oscillation of the wave. So that relativistic effects, such as speed or gravitational potential differences, affect the clock mechanism because of phase shifts in the frequencies and corresponding increase in the wavelength of the clock oscillation, resulting errors in reading of the clock time, but incorrectly perceived as time dilation.

Real events in space never reach the fourth direction of time, either through interactions or relativistic effects such as motion or gravity. Events within space will not have a natural reach toward the dimension of proper time, so that eventual effects can never affect proper time beyond its ideal succession, to obtain time dilation. A clock reading should always follow the order of time sequence; otherwise, the external distortion will cause incorrect readings in the clock mechanism. The dimension of time is considered abstract rather, conceptual.

It would be wrong to try to change proper time like in the conjectural equation of time dilation. Relativistic effects cannot interact with proper time to get time dilation. Apart from this, the concept of time dilation defies the conventional scientific definition of time involving existence and events. Proper time should never be stripped of its independence and retained as 'natural' even in the four-dimensional continuum of spacetime. There is no time dilation anywhere; instead, the dilation of the wavelength of the clock oscillation causing errors in the clock time. Wavelength distortions mathematically correspond exactly to time distortions; as in λ ∝ T.

General Foundations

| Time is called T, the period of oscillation, so that T = 2π/ω. The reciprocal of the period, or the frequency f, in oscillations per second, is given by the expression:

f = 1/T = ω/2π = E/h = v/λ.

Where h is Planck constant, f, v, λ, T and E respectively represent frequency, velocity, wavelength, time period and Energy of the wave.

| Doppler shift is the change in frequency of a wave in relation to an observer who is moving relative to the wave source.

| Time distortion always originates from wavelength distortion but the time dilation of special relativity is not understood from wavelength distortion and so it does not follow the general rules.

| Special relativity does not escape the fundamental equivalence between wavelengths and time, which is much more general than special relativity.

| Distortions of wavelengths exactly correspond to time distortions λ ∝ T.

| Time is the indefinite continued progress of existence and events in the past, present, and future regarded as a whole, succeeding in irreversible and uniformed succession, referred to in the fourth dimension above three spatial dimensions. Therefore, time is not what special relativity presents as in time dilation and there is no time in time dilation. It is rather error the in wave.

| Time is an imperceptible fourth dimensional concept so protected from relativistic effects like speed or gravity, nor it subject to real interference or influence or interaction with the cosmic events. The events rather invoke time.

| The term cosmic time signifies a relationship between the time since the Big Bang and the events within the Universe. The distortion in proper time always originates from wavelength distortion, including in special relativity, and therefore proper time subject to synchronization with ideal time in near approximation, as done with the atomic clocks.

Experimental Results

Experiments made in electronic laboratories on piezoelectric crystal oscillators show that the wave corresponds to time shift due to relativistic effects.

We get the wavelength λ of a wave is directly proportional to the time period T of the wave, that is λ ∝ T, derived from the wave equation:

f = 1/T = v/λ = E/h.

where h is Planck constant and f, v, λ, T and E represent frequency, velocity, wavelength, time period and Energy of the wave respectively.

Whereas the time interval T(𝑑𝑒𝑔) for 1° of phase is inversely proportional to the frequency (f). We get a wave corresponding to the time shift.

For example, 1° phase shift on a 5 MHz wave corresponds to a time shift of 555 picoseconds (ps).

We know, 1° phase shift = T/360. As T = 1/f,

1° phase shift = T/360 = (1/f)/360

For a wave of frequency f = 5 MHz, we get the phase shift (in degree°)

= (1/5000000)/360
= 5.55 × 10⁻¹º
= 555 ps.

Therefore, for 1° phase shift for a wave having a frequency f = 5 MHz, and so wavelength λ = 59.95 m, the time shift (time delay) Δt = 555 ps. (approx).

Moreover, for 360° phase shift or, 1 complete cycle for a wave having frequency 1Hz (of a 9192631770 Hz wave); the time shift (time delay) Δt = 0.0000001087827757077666 ms (approx).

Time shift of the caesium-133 atomic clock in the GPS satellite: The GPS satellites orbit at an altitude of about 20,000 km. with a time delay of about 38 microseconds per day.

For 1455.50003025° phase shift or, 4.043055639583333 cycles of a 9192631770 Hz wave; time shifts (time delays) Δt = 0.0000004398148148148148 ms. (approx) or, 38 microsecond time is taken per day.

Conclusion

The phase shifts of frequency due to gravitational potential differences or relativistic effects correspond to dilation of wavelengths of the clock oscillation, which show errors in the clock reading and are misrepresented as time dilation. Time dilation is actually wavelength dilation.

Comment

Phase shifts in frequency due to relativistic effects cause dilation in the wavelengths of clock oscillations. The resulting errors in clock readings have been misinterpreted as time dilation. True time remains an abstract, conceptual dimension; observed effects are wavelength dilation, not temporal distortion.

Piezoelectric crystal oscillator experiments confirm that wave distortions lead to measurable time shifts. For example, a 1° phase shift on a 5 MHz wave corresponds to 555 ps. GPS satellite clocks show cumulative daily delays (~38 μs) consistent with phase shift calculations.

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Core Phase-Shift Relation for ECM Time Distortion

Introduction.
The identity
x° phase shift = Tx° / 360 = (x° / f) / 360
directly converts a measured phase displacement into an equivalent time offset. In ECM this identity is fundamental and model-independent: a measured phase shift encodes a corresponding time distortion without requiring the source mass, its velocity, or gravitational potential.

A2.1 Core formula

Let f0 be the reference frequency, and let x°per sec be the observed phase shift in degrees per second. One cycle equals 360°, and T = 1 / f0. Then:

Δtper second = x°per sec / (360 · f0)
(A2.1)

A2.1.1 Fundamental Phase → Frequency → Time Relations

From the definition of phase drift:

x°/s = 360 · (f0 − fobs) = 360 · Δf

Thus,

Δf = x°/s ÷ 360

Using the definition of fractional frequency deviation:

Δtper second = Δf / f0

This yields the compact ECM identity:

Δtper second = Δf / f0

(phase drift → Δf → Δt, fully algebraic and model-independent)

A2.2 Daily conversion

To convert to a daily quantity:

Δtper day = 86,400 · x°per sec / (360 · f0)
(A2.2)

A2.3 GPS numeric example

Using standard GPS values:

x°per sec = 1455.50003025 °/s
f0 (Cs hyperfine) = 9,192,631,770 Hz

Applying (A2.1) gives:


Δtper second ≈ 4.398148148 × 10⁻¹⁰ s/s
Using (A2.2):
Δtper day ≈ 38 μs/day

A2.4 Interpretation & usage

Model independence. The phase-shift identity requires only the observed phase drift and the reference frequency. No velocity, gravitational potential, or mass calculation is needed.

Link to κ (optional). If converting Δt into a mass-equivalent: use ΔE = h Δf and ΔM = ΔE / c². Then κ = Δt / ΔM. This is optional, as phase → Δt conversion is self-contained.

References & Notes: The phase→time identity is fully algebraic. The GPS data reproduces the standard GNSS net offset. In ECM, this empirical Δt is used to extract the corresponding effective-mass scaling constant κ.

ECM Interpretation of Phase Shift, Redshift, and Phase Kernel Relation

This section explores the Extended Classical Mechanics (ECM) interpretation of phase shift and redshift through the concept of the Phase Kernel Relation, linking motion-induced frequency variation with effective-mass transitions and cosmic-time distortion.

➤ Read Full Article

Author's Comment on SR's Misapplication of Clock Time Measurement Error vs. Cosmic Time Distortion in the Lorentz Factor

Author: Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803
Correspondence: postmasterenator@gmail.com
November, 21, 2025

Abstract

This comment challenges the conventional interpretation of relativistic time dilation by maintaining that Δt′ > Δt reflects a measurement deviation in clock time rather than a genuine physical dilation of time. Any claim of time dilation presupposes the use of a standard clock, and without such a device, the notion cannot be empirically defined. The Lorentz factor (γ), although mathematically consistent, is misapplied in Special Relativity when interpreted as altering the rate of physical clocks, which are inherently susceptible to external distortions.

In contrast, when treated purely as a mathematical transformation, γ more appropriately describes distortions in cosmic time—a timescale shaped by entropy-driven evolution rather than mechanical clock behaviour. Extended Classical Mechanics (ECM) formalizes this distinction by deriving cosmic time variability from entropic changes (ΔS), effective-mass transitions (ΔMapp), and frequency–mass equivalence, yielding a dynamic temporal framework that parallels Penrose’s Conformal Cyclic Cosmology (CCC).

The analysis emphasizes a fundamental structural divide: SR concerns clock-based time measurement, whereas ECM and CCC describe cosmic time conditioned by entropy and mass–frequency transitions. This distinction clarifies that “relativistic time dilation” is better understood as a measurement error imposed by misinterpreting the Lorentz factor, rather than as a legitimate physical phenomenon.

Time dilation (Δt′) is commonly described as an enlargement of an observed time interval relative to the proper time interval (Δt), such that Δt′ > Δt. However, discussing any claimed dilation of time requires explicit reference to a standard clock, because without a physical device that actually measures time, the very concept of time dilation cannot be empirically defined or verified. The assumption that Δt represents a literal physical dilation of time measured by such a clock is therefore challenged.

Instead, the deviation represented by Δt′ is better interpreted as an error in the measurement of the standard or proper time Δt. Under this interpretation, the term “relativistic time dilation” becomes an untenable misnomer for what is, in essence, a measurable timing deviation. This alleged error arises from applying the Lorentz factor (γ) directly to clock time, even though γ remains mathematically consistent only when not tied to SR’s flawed physical interpretation.

Special Relativity’s formulation of time dilation is inherently physical and relies on clocks, which are themselves susceptible to distortions from external influences. By contrast, the Lorentz transformation—treated purely as a mathematical structure—does not redefine the scale of clock-measured time. Instead, the Lorentz factor (γ) more naturally corresponds to distortions in cosmic time, not clock time, consistent with the entropy-driven evolution presented in Extended Classical Mechanics (ECM): A Unified Framework for Frequency-Mass Equivalence, Entropic Time Distortion, and Cosmological Self-Regulation .

ECM explicitly derives distortable cosmic time from entropic increases (ΔS), effective-mass transitions (ΔMapp), and frequency-mass equivalence, establishing a variable cosmic timescale that stretches or compresses according to the universe’s entropic state. Such ECM-based entropic time distortion closely parallels the conformal rescaling of time in Roger Penrose’s Conformal Cyclic Cosmology (CCC), where each aeon demands a smoothed, entropy-conditioned cosmic temporal framework.

Thus, the distinction is structural and essential: SR addresses clock time—measured by physical devices—whereas ECM (and, by resemblance, CCC) addresses cosmic time shaped by entropy and mass-frequency transitions. Recognizing this difference is crucial for avoiding the misapplication of the Lorentz factor to clock time, which generates the erroneous interpretation known as relativistic time dilation.

Conclusion:
Time dilation, as presented by SR, is maintained to be a measurement error in clock time rather than a genuine physical effect, whereas the Lorentz factor (γ) properly applies to cosmic time distortion driven by entropic evolution.

Appendix A1 — Mathematical Derivation of Cosmic Time Distortion (Δt) from Effective-Mass Transitions

The distinction between clock time and cosmic time is central to ECM’s treatment of temporal evolution and directly addresses the conceptual error in associating the Lorentz factor (γ) with physical clock dilation. While Special Relativity ties Δt′ to distortions allegedly imposed on mechanical clocks, ECM demonstrates that temporal variation arises strictly from changes in a system’s effective mass—a quantity shaped by entropy (ΔS), apparent-mass transitions (ΔMapp), and the frequency–mass equivalence relation.

In ECM, cosmic time is not a geometric artefact nor a kinematically induced contraction or dilation. Rather, it is the physical timescale generated by a system’s intrinsic oscillation frequency, which is governed by the effective mass state (Meff). An increase in effective mass elongates local temporal intervals, while a decrease shortens them. Thus, time distortion is a physical consequence of mass–frequency evolution, independent of motion relative to an observer.

Formally, ECM defines the intrinsic temporal interval as tcos = 1 / f(Meff). For the monotonic relationship f ∝ 1 / Meff, the change in cosmic time is Δtcos = κ ΔMeff, with κ a proportionality constant reflecting the mass–frequency scaling. This demonstrates that a change in effective mass corresponds directly to a change in cosmic time.

Clock time, by contrast, is a measurement standard. Deviations in Δt′ reflect measurement error when interpreted as literal temporal change. Mechanical clocks do not encode the entropic or effective-mass state of the system, and thus SR’s application of γ to clocks conflates measurement deviation with physical temporal evolution.

A spatial gradient in effective mass similarly produces a gradient in cosmic time, and ECM’s redshift relation follows directly: z ≈ ΔMeff / Meff ≈ Δtcos / tcos. Redshift thus becomes a physical expression of cosmic time distortion rather than a function of relative velocity or spacetime curvature. This interpretation aligns with Penrose’s Conformal Cyclic Cosmology, in which cosmic time is entropy-conditioned and smoothed across aeons.

The Lorentz factor (γ) is therefore interpreted as a mathematical scaling of cosmic time rather than a clock dilation mechanism. ECM establishes a rigorous, mass-frequency-driven basis for cosmic time distortion, distinguishing physical cosmic time from clock time, replacing geometric dilation with entropic–mass evolution, and providing a consistent alternative to the relativistic reading of Δt′ > Δt.

A Courtroom-Style Scientific Rebuttal to the Defendant’s Statement on Relativistic Time Dilation, Frequency Shift, and Phase-Shift Interpretations

Abstract

This rebuttal addresses the defendant’s claims regarding the nature of relativistic time dilation and its relationship to frequency and wavelength distortions. While the defendant asserts that phase-shift–induced distortions in oscillatory systems provide a superior explanation of observed temporal differences, the argument is shown to be scientifically inconsistent, internally contradictory, and based on selective and opportunistic framing of physical principles. Using a courtroom-style structure—while maintaining the full rigor of scientific reasoning—this paper identifies the conceptual errors, logical reversals, and methodological misrepresentations present in the defendant’s statement, and reasserts the correct causal structure of relativistic phenomena as established in modern physics.

1. Induction: Statement of the Case

The defendant makes several interconnected claims:

  1. That relativistic effects—specifically relative velocity and gravitational potential—cause phase shifts, wave-energy loss, and wavelength enlargement in oscillatory clocks.

  2. That these distortions lead to clock error, which is then “wrongly presented” as time dilation in mainstream relativity.

  3. That the standard relativistic time dilation formula is incorrect because relativistic effects are asserted to act on the measurement apparatus rather than on time itself.

  4. That experimental evidence involving oscillatory systems, such as piezoelectric crystal clocks, supports this alternative interpretation.

Simultaneously, however, the defendant asserts:

This dual posture—treating wavelength shifts as both a cause and a confirming effect of time dilation—constitutes a central contradiction.

The task of this rebuttal is to demonstrate, with scientific precision, that the defendant’s claims suffer from:

2. Charges of Scientific Inconsistency

Charge 1 — Causal Reversal

Relativity asserts:
time dilation → frequency shift.
The defendant reverses this causation without physical justification, implying:
frequency shift → time dilation.

Charge 2 — Category Error

Velocity and gravitational potential are physical causes.
Frequency and wavelength are descriptive properties of oscillatory systems, not causal agents.

Charge 3 — Opportunistic Redefinition

The defendant alternately classifies frequency shifts as “relativistic effects” and “instrument distortions,” depending on argumentative convenience.

Charge 4 — Misrepresentation of Relativity

The defendant frames relativity as if it deduces time dilation from wavelength changes, which is categorically false. Relativity deduces time dilation from spacetime geometry.

Charge 5 — Mischaracterization of the Alternative Model

The defendant’s description simultaneously claims to replace time dilation and to support it through the same phenomenon, producing irreconcilable conceptual conflict.

3. Prosecution of the Defendant’s Claims (C1–C4)

C1 — “Phase shift and wavelength distortion explain observations better than time dilation.”

This claim confuses measurement distortion with temporal transformation.
Empirically:

all exhibit the same relativistic temporal transformation independent of electromagnetic oscillation.

If wavelength distortion alone were the cause, these systems would produce divergent results. They do not.

Therefore, C1 contradicts empirical reality.

C2 — “Observed differences are time error, not time dilation.”

This claim implies that clocks malfunction under relativistic conditions.
But relativistic time dilation is consistently verified in systems that:

Muon lifetime extension alone refutes C2 universally.
Thus, C2 is experimentally invalid.

C3 — “The standard formula is incorrect because effects interact with the clock, not with time.”

This is a misrepresentation.

Relativity does not claim that “effects interact with time.”
It states that the metric structure of spacetime determines how proper time accumulates along worldlines.

The defendant attacks a claim that relativity does not make—
constituting a scientific straw-man.

C4 — “Evidence from wave distortions disproves the time dilation formula.”

Wave distortions illustrate how a specific clock responds, not how time itself transforms.
All physical processes—from atomic to subatomic to macroscopic—slow by the same Lorentz factor under identical conditions.

Thus, C4 is not simply unsupported; it is contradicted by overwhelming cross-disciplinary evidence.

4. Exposure of Internal Contradictions (E1–E5)

E1 — Wavelength treated as both cause and effect

The defendant alternately describes frequency shift as:

This is logically incompatible.

E2 — Implicit denial of universality of relativistic transformations

If wavelength distortion were the mechanism, non-oscillatory processes would deviate. They do not.

E3 — Opportunistic use of gravitational redshift

The defendant cites gravitational redshift as supporting time dilation,
while simultaneously claiming frequency shifts replace time dilation.

This contradiction invalidates the argument.

E4 — Causal structure inversion

Relativity: metric curvature → time dilation → frequency shift.
Defendant: frequency shift → clock error → pseudo–time dilation.

This reversal lacks physical, mathematical, and empirical justification.

E5 — Misuse of experimental evidence

The defendant presents wave-based clock results as universal disproof, ignoring non-wave-based confirmations of time dilation.

Such selective evidence handling is scientifically unacceptable.

5. Scientific Verdict

After systematic examination, the defendant’s argument is found to be:

The correct causal structure, upheld by both theoretical foundations and experimental confirmations, is:

Relativistic velocity and gravitational potential differences alter the accumulation of proper time.

This change in proper time then causes corresponding shifts in frequency and wavelength.

Thus:

The defendant’s statement is therefore rejected in full due to scientific, logical, and evidential failure.

ECM-Based Concluding Remark

While the preceding analysis demonstrates the logical, physical, and evidential failure of interpreting phase-shifted waveforms as a universal explanation for relativistic timing, an Extended Classical Mechanics (ECM) perspective supplies an even deeper structural resolution. ECM distinguishes clock time, measured by device-bound oscillatory processes, from cosmic time, which emerges from entropic evolution, effective-mass transitions (ΔMᵉᶠᶠ), and frequency–mass equivalence (hf = ΔMᴍc²).

In this framework, distortions observed in clocks—whether atomic, optical, mechanical, or electromagnetic—reflect deviations in the device’s response, not intrinsic changes in time itself. Conversely, the Lorentz factor (γ), when interpreted independently of Special Relativity’s physical assumptions, naturally aligns with ECM’s treatment of entropy-conditioned cosmic time distortion, rather than with literal physical dilation of clock time.

The failure of phase-shift arguments to explain relativistic effects across all physical systems highlights precisely why ECM separates device-level distortions from cosmic-scale temporal evolution. This distinction restores internal consistency and situates observed timing deviations within a broader entropic and mass–frequency dynamical context, while avoiding the contradictions embedded in SR’s traditional treatment of time dilation.

In summary: ECM provides a coherent, entropy-driven, mass–frequency–regulated account of temporal distortion, in which the Lorentz factor applies to cosmic time structure rather than to clock-based time measurement—thereby resolving ambiguities that neither SR nor phase-shift interpretations can fully address.