Here is why the Relativistic Spacetime does not exist:

Soumendra Nath Thakur 

April 26, 2026

Emerging foundational analyses increasingly indicate that quantum-level physics does not support the ontological existence of relativistic spacetime. What has long been treated as a physically real continuum in the framework developed by Albert Einstein is more accurately understood as a mathematical construct—effective within limited regimes, but not fundamental to reality itself.

In parallel, my work in *Extended Classical Mechanics (ECM)*, developed since 2022, has consistently advanced this position: spacetime is not a primary entity, but a derived representation arising from deeper physical processes governing mass–energy manifestation and transformation.

Accordingly, it is no longer tenable for physics to regard Einsteinian spacetime as an unquestioned foundation. Its continued treatment as physically real risks imposing artificial constraints on theoretical development. A necessary shift is underway—from accepting spacetime as fundamental, to recognizing it as an emergent or model-dependent abstraction.

Ref. https://iai.tv/articles/spacetime-does-not-exist-auid-3555

এক্সটেন্ডেড ক্লাসিক্যাল মেকানিক্স (ECM) - বর্ধিত চিরায়ত বলবিদ্যা

সংক্ষিপ্ত পরিচিতি:
ECM একটি তাত্ত্বিক কাঠামো যা চিরায়ত বলবিদ্যা, মহাকর্ষ এবং কোয়ান্টাম বলবিদ্যাকে একটি সমন্বিত রূপে ব্যাখ্যা করার প্রচেষ্টা।

প্রবর্তক ও লেখক

'এক্সটেন্ডেড ক্লাসিক্যাল মেকানিক্স' (Extended Classical Mechanics - ECM)-এর প্রধান প্রবর্তক এবং লেখক হলেন সৌমেন্দ্র নাথ ঠাকুর (Soumendra Nath Thakur) [১.২.৫, ১.৩.৪, ১.৪.১]।

এই তাত্ত্বিক কাঠামোটি মূলত তাঁর দ্বারা উদ্ভাবিত এবং তিনি ভারতের অধিবাসী [১.২.৫, ১.৩.৫]।

সংস্থা

সংস্থার নাম: Tagore's Electronic Lab (ভারত) [১.২.৫, ১.৪.১]।

ECM-এর মূল ধারণা

এটি চিরায়ত বলবিদ্যা (Classical Mechanics), মহাকর্ষ এবং কোয়ান্টাম বলবিদ্যার একটি সমন্বিত রূপ, যেখানে ভরের ডাইনামিক রিডিস্ট্রিবিউশন (Dynamic mass redistribution) বা গতিশীল ভর পুনর্বণ্টনের মাধ্যমে মহাকর্ষ ও শক্তি ব্যাখ্যা করা হয় [১.২.৫, ১.৪.৬]।

ভরের পুনর্বিন্যাস: ECM-এর দৃষ্টিভঙ্গি

ঐতিহ্যগতভাবে, ক্লাসিক্যাল মেকানিক্স-এ ভরকে স্থির কিছু হিসাবে বিবেচনা করা হয় — একটি অন্তর্নির্মিত প্রতিরোধ যা পরিবর্তন হয় না, আপনি যেভাবেই বস্তুটিকে ধাক্কা দিন বা সরান না কেন।

কিন্তু এক্সটেন্ডেড ক্লাসিক্যাল মেকানিক্স (ECM) আরও ঘনিষ্ঠভাবে পর্যবেক্ষণ করে যে, যখন কোনও বল বাস্তবে প্রয়োগ করা হয়, তখন ভরের কী ঘটে।

ECM এই ধারণাটিকে চ্যালেঞ্জ করে এবং ভরকে কেবল শক্তির আধার হিসেবে নয়, বরং শক্তির প্রকাশ ও প্রচারে একটি সক্রিয় কাঠামোগত অংশগ্রহণকারী হিসেবে পুনর্বিন্যাস করে।

এটি প্রচলিত E = mc² ভিত্তিক ভর-ত্রুটির ব্যাখ্যাকে পুনর্বিবেচনা করে, এবং প্রস্তাব করে যে ভর কখনও ধ্বংস হয় না; বরং এটি গতিশীলভাবে স্থানচ্যুত (redistributed) হয়।

গবেষণা ও প্রকাশনা

এই বিষয়ের ওপর বেশ কিছু গবেষণাপত্র — যেমন পিয়ার-রিভিউকৃত প্রকাশিত গবেষণাপত্র এবং প্রিপ্রিন্ট গবেষণা নিবন্ধ — ২০২২-২৩ থেকে ২০২৬ সাল পর্যন্ত বিভিন্ন জার্নাল ও রিসার্চগেটে উপলব্ধ [১.৩.৪, ১.৪.৮]।

© Extended Classical Mechanics (ECM) Portal

The Pre-Planck Scales A Forbidden Zone: The Question of Physical and Mathematical Significance of Sub-Planckian Scales.

The assertion that sub-Planckian scales lack physical significance within the current measurable framework is increasingly open to scrutiny, as it does not constitute a logically robust or conceptually complete position. Even if one were to argue that the sub-Planckian domain is beyond direct physical interpretation, it does not follow that it must be stripped of mathematical relevance. On the contrary, mathematical structures routinely extend far beyond empirical reach, and their legitimacy is not contingent upon current observability.

For instance, frameworks such as 10- or 11-dimensional String Theory are widely regarded as mathematically meaningful despite their lack of direct experimental confirmation. In this context, it becomes difficult to justify a selective restriction that excludes domains of even smaller magnitude—such as sub-Planckian regimes—on the basis of scale alone. Any such selective exclusion risks narrowing the conceptual scope of mathematical physics and, in doing so, may hinder deeper structural understanding rather than clarify it.

It is also essential to recognize that even the Planck length lies far beyond present observational and experimental capability. The highest experimentally probed frequency scales to date are of the order of ~10³⁰ Hz, which remains significantly below the Planck frequency (~10⁴³ Hz). This gap raises a fundamental methodological question: if theoretical physics is already willing to extend mathematical reasoning well beyond directly observable regimes (for example, into frequency domains exceeding current experimental limits), then on what consistent basis is the exploration of pre-Planckian scales excluded? Whether this exclusion is methodological caution or an implicit epistemic limitation remains an open question.

This issue becomes even more significant when considering that Planck-scale quantities—such as tₚ, ℓₚ, fₚ, Eₚ, and Mₚ—are not independent entities in isolation, but emerge through interrelated differential constructions. From this perspective, relationships such as t₀ − tₚ ≤ tₚ and ℓ₀ − ℓₚ ≤ ℓₚ, or conversely f₀ − fₚ ≥ fₚ, E₀ − Eₚ ≥ Eₚ, and M₀ − Mₚ ≥ Mₚ, suggest that these quantities are embedded within a broader relational structure rather than existing as absolute foundational constants. Their interpretation therefore depends critically on the underlying mathematical framework used to define their emergence.

Consequently, excluding the notion of pre-Planckian scales raises a deeper conceptual issue: it risks rendering Planck-scale entities themselves without an explicit generative basis, leaving them as effectively ungrounded reference points derived only from higher-scale observational constraints. Without a consistent microscopic or pre-Planckian formulation, their origin remains theoretically incomplete.

From this standpoint, the absence of a widely accepted mathematical description of the pre-Planckian domain does not imply its nonexistence or irrelevance. Rather, it highlights a gap in current theoretical frameworks. Within this context, approaches such as Extended Classical Mechanics (ECM) attempt to address precisely this gap by treating sub-Planckian regimes not as forbidden zones, but as domains requiring deeper structural formulation beyond conventional interpretive boundaries.

Frequency as the Ontological Primitive and Time as an Emergent Consequence: Extended Classical Mechanics (ECM)

https://doi.org/10.5281/zenodo.19683405

Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
Tagore's Electronic Lab, India
postmasterenator@gmail.com / postmasterenator@telitnetwork.in
April 21, 2026

Abstract

This work presents a structured formulation of Extended Classical Mechanics (ECM) in which frequency (f) is established as the fundamental ontological parameter governing physical reality, while time (t) is treated as an emergent consequence of phase evolution rather than a pre-existing coordinate.

The framework departs from the conventional interpretation f = 1/T by asserting that frequency is intrinsic and time is derived. Within this perspective, the relation E = hf is reinterpreted as a physical identity indicating that energy itself is a manifestation of frequency-governed phase dynamics. Consequently, temporal intervals arise from the accumulation of phase, expressed through t ∝ ϕ/f, making time a measurable outcome of underlying dynamical processes.

The formulation further provides a coherent reinterpretation of established physical phenomena. Effects traditionally attributed to spacetime structure—such as time dilation—are described in ECM as consequences of frequency variation in physical systems, rather than geometric deformation. Similarly, cosmological observations such as redshift are interpreted as frequency shifts (Δf), offering an alternative description of cosmic evolution.

By grounding physical description in operationally definable quantities—frequency, phase, and energy—this approach establishes a unified framework in which:

• Phase evolution governs dynamics,
• Energy expresses frequency,
• Time emerges from measurable phase progression.

This perspective aims to address foundational inconsistencies by removing the assumption of time as an independent background parameter and instead treating it as a derived, system-dependent observable rooted in frequency dynamics.

Keywords

Extended Classical Mechanics (ECM), Frequency Ontology, Emergent Time, Phase Evolution, Energy–Frequency Relation, E = hf Interpretation, Time Deviation, Frequency-Governed Dynamics, Apparent Mass (Mᵃᵖᵖ), Mass Redistribution (ΔMᴍ), Thermionic Emission (ECM), Non-Relativistic Time Interpretation, Frequency Shift (Δf), Cosmological Redshift Alternative, Phase-Based Time, Deterministic Energy Transformation, ECM Time Theory, Frequency-Based Physics, Unified Physical Framework, Ontological Frequency Model,

---

Extended Classical Mechanics (ECM) establishes frequency (f) as a fundamental, time-independent ontological entity that characterizes the intrinsic dynamical state of a system. In this framework, frequency is not defined as events per unit time; rather, it exists prior to and independent of time. Consequently, time (t) is not a foundational coordinate but an emergent quantity arising from phase progression (ϕ) and energy transformation governed by E = hf.

Core Conceptual Foundations

Primacy of Frequency over Time

ECM departs from the conventional definition f = 1/T by asserting that frequency is inherently fundamental, while time is a derived construct. Frequency represents the intrinsic rate of phase evolution, whereas time reflects a relative measure constructed from this progression. Thus, f is absolute in the physical sense, while t is emergent and system-dependent.

Energy as a Manifestation of Frequency

Within ECM, the relation E = hf is not merely a proportionality but a physical identity: energy is understood as the direct manifestation of frequency-governed phase dynamics. Energy does not “possess” frequency; rather, it is expressed through it.

Emergence of Time from Phase Dynamics

Time is defined through the accumulation of phase:

t ∝ ϕ / f

This establishes time as a derived measure of phase evolution, not an independent dimension. Observable temporal intervals correspond to structured phase transitions driven by underlying frequency.

Physical Reinterpretations

Reframing Relativistic Effects

Phenomena traditionally attributed to spacetime structure—such as time dilation and the twin paradox—are reinterpreted in ECM as consequences of physical variations in system frequency due to velocity, energy redistribution, or environmental influence. Thus, clock deviation reflects frequency modulation, not geometric deformation of time.

Cosmological Perspective via Frequency Shifts

At the cosmological scale, observed changes such as redshift are interpreted as frequency shifts (Δf) rather than expansion of time or spacetime itself. This provides an alternative framework in which cosmic evolution is described through transformations in frequency structure.

Unifying Perspective

By treating frequency as the fundamental “clock” of reality, ECM offers a unified interpretive basis in which:

• Phase evolution governs dynamics,
• Energy expresses frequency,
• Time emerges from measurable phase progression.

This approach aims to reconcile foundational inconsistencies by removing the assumption of time as a pre-existing backdrop and instead grounding physical description in frequency-governed, operationally definable quantities.

Conclusion

Extended Classical Mechanics (ECM) provides a coherent reformulation of physical description by establishing frequency (f) as the fundamental ontological quantity and treating time (t) as an emergent consequence of phase evolution. This shift removes the need to assume time as a pre-existing background parameter and instead grounds it in measurable, physically operative processes.

Through the relations E = hf and t ∝ ϕ/f, ECM unifies energy, phase, and temporal behaviour within a single framework of frequency-governed dynamics. In this formulation, physical phenomena—including thermal processes, mechanical interactions, and cosmological observations—are consistently described as manifestations of frequency variation and mass-energy redistribution.

By reinterpreting time deviation as a consequence of changes in system frequency, ECM offers an alternative to spacetime-based explanations while remaining anchored in observable quantities. This enables a deterministic and operationally defined pathway from mass redistribution (ΔMᴍ) to frequency (f) and ultimately to time deviation (Δt).

Overall, ECM advances a unified and physically grounded perspective in which:

• frequency governs dynamical evolution,
• energy expresses frequency structure,
• and time emerges as a measurable consequence of phase progression.

This framework not only clarifies the physical origin of time but also provides a consistent basis for re-examining foundational assumptions across classical, quantum, and cosmological domains.

Related Works and Supporting Publications

Hierarchical Knowledge Architecture of ECM Publications

This section organizes ECM-related works into a structured hierarchical architecture, ranging from foundational ontological postulates to derived applications and interpretative extensions. The hierarchy reflects the progression from fundamental physical assumptions to system-specific formulations and comparative analyses.

1. Layer 1 — Ontological Foundation: Frequency as a Physical Primitive
   
   Frequency as a Time-Independent Physical Quantity: Extended Classical Mechanics Interpretation
   Foundational formulation establishing frequency as an ontological primitive independent of time in ECM.
   DOI: https://doi.org/10.5281/zenodo.19660483
2. Layer 2 — Conceptual Framework and System Definition
   
   Extended Classical Mechanics (ECM) Conceptual Principles
   Provides a conceptual exposition of the foundational principles of ECM, bridging the interpretative framework between core theoretical formulation and derived applications.
   URL: https://www.researchgate.net/post/Extended_Classical_Mechanics_ECM_Conceptual_Principles
3. Extended Classical Mechanics (ECM): Consistent Fundamental Energy Principle – Planck-Scale Frequency Origins
   Establishes Planck-scale frequency origins and unified energy–frequency–mass framework in ECM.
   SSRN DOI: http://dx.doi.org/10.2139/ssrn.6221099
   Zenodo: https://zenodo.org/records/19375374
4. Layer 3 — Internal Theoretical Development and Derivations
   
   Appendix 24: The Physical Primacy of Frequency over Time – Time Dilation as Phase-Induced Time Distortion in ECM
   Develops time dilation interpretation through phase-based frequency distortion mechanisms.
   DOI: https://doi.org/10.13140/RG.2.2.30764.17288
5. Appendix 31: Frequency and Energy in Extended Classical Mechanics (ECM)
   Establishes frequency as the fundamental descriptor of physical system identity and energy manifestation.
   DOI: https://doi.org/10.13140/RG.2.2.30435.67369
6. ECM Interpretation of Time Dynamics
   Defines time as an emergent outcome of frequency-governed mass–energy evolution.
   URL: https://www.researchgate.net/publication/396713981_ECM_Interpretation_of_Time_Dynamics
7. Layer 4 — Derived Applications and Physical Implementations
   
   ECM Derivation of Frequency-Based Time Dilation
   Derives time dilation effects from frequency variation rather than spacetime curvature.
   ResearchGate URL:
   https://www.researchgate.net/post/ECM_Derivation_of_Frequency-Based_Time_Dilation
   Blogspot URL:
   https://soumendranaththakur.blogspot.com/2026/04/ecm-derivation-of-frequency-based-time_7.html
8. A Comparative Framework for Extended Classical Mechanics' Frequency-Governed Kinetic Energy
   Provides comparative formulation of kinetic energy under frequency-governed ECM interpretation.
   DOI: https://doi.org/10.20944/preprints202508.1031.v1
9. A Nuanced Interpretation of Thermionic Emission in the Framework of Extended Classical Mechanics (ECM)
   Describes thermionic emission as deterministic mass–frequency redistribution within ECM.
   DOI: https://doi.org/10.13140/RG.2.2.12597.59369
10. Layer 5 — Physical Reinterpretations and Experimental Consequences
    
    Time Deviation in ECM Due to Thermal and Mechanical Influences
    Explains time deviation as frequency modulation caused by thermal and mechanical energy input.
    Available at:
    https://www.researchgate.net/post/Time_Deviation_in_ECM_Due_to_Thermal_and_Mechanical_Influences
11. Relativistic effects on phase shift in frequencies invalidate time dilation II
    Challenges relativistic time dilation interpretation through frequency-phase analysis.
    TechRxiv DOI:
    https://doi.org/10.36227/techrxiv.22492066.v2
12. Effect of Wavelength Dilation in Time – About Time and Wavelength Dilation
    Discusses wavelength–time coupling and its implications for temporal interpretation.
    Preprint URL:
    https://easychair.org/publications/preprint/ZJpB

© 2026 Soumendra Nath Thakur

Licensed under Creative Commons Attribution 4.0 International (CC BY 4.0)

Frequency as a Time-Independent Physical Quantity: Extended Classical Mechanics (ECM) Interpretation

Author: Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
Tagore's Electronic Lab, India
postmasterenator@gmail.com or postmasterenator@telitnetwork.in
April 20, 2026

Abstract

This work establishes frequency as a fundamentally physical and time-independent quantity, whose primary correlate is energy, expressed through the relation E = hf. It challenges the conventional elevation of the period (T) as a primary entity and demonstrates that time is not fundamental but emerges as a derived measure of phase transformation. By introducing the concept of a primordial frequency (f₀) and its first phase transition, the framework defines the emergence of time as a consequence of the first event. This formulation provides a physically grounded reinterpretation of time as a secondary construct arising from energetic phase dynamics.

1. Conceptual Clarification

There is no problem here—certainly no “fundamental” one. If any issue arises, it does not concern the time-independence of frequency; rather, it originates from a preconception that elevates the relation f = 1/T into a physically primary description, thereby reifying the period T as an intrinsic entity. This interpretation is conceptually misplaced.

The relation E = hf expresses a direct physical correspondence between energy and frequency. By contrast, f = 1/T is a representational identity that expresses periodicity in terms of a chosen parameter T, corresponding to one full cycle (360°) of phase. Thus, while both relations are mathematically valid, they do not carry equal ontological weight: E = hf reflects a physical equivalence, whereas T functions as a derived measure of cyclic completion.

2. Frequency as a Time-Independent Physical Quantity

Frequency, in its physical sense, is not defined by time but by intrinsic phase structure. Its measurable manifestation is energy, as given by E = hf. Although one may write f = 1/T, this does not imply that frequency is ontologically dependent on time; rather, it shows that time-based intervals can be constructed from an already existing frequency.

The expression h(1/T) does not independently yield energy unless 1/T is first recognized as frequency. Thus, it is not T that gives rise to energy, but frequency that provides physical meaning to such representations. In this sense, T is an abstract parameterization, while f is the physically operative quantity.

3. Time as a Derived Measure of Phase Transformation

Given that T = 1/f, a phase increment of x° corresponds to a derived interval:

T(x°) = x° / (360f)

In particular, for a 1° phase shift:

Δt = 1° / (360f)

This formulation makes explicit that time intervals are not fundamental entities but arise as measures of phase progression. Frequency, through its energetic basis, is primary; time is a constructed mapping of phase change.

4. Emergence of Time from the First Event

Time has no meaning in the absence of events. In the primordial condition—denoted as f₀—no phase transformation occurs; this state is therefore unmanifested and eventless, and consequently devoid of time.

Time emerges only when a phase transformation takes place, expressed as Δf₀(x°). The very first such transformation—corresponding to a 1° phase shift of the primordial frequency f₀—constitutes the First Event. In this transition, f₀, initially present as potential energy, undergoes transformation into kinetic expression through Δf₀.

It is precisely through this first phase transformation that time arises, quantified as:

Δt = 1° / (360f)

Conclusion

Frequency, grounded in its energetic manifestation, is the primary physical quantity. Time, by contrast, is not fundamental; it emerges as a derived measure of phase transformation associated with energetic change. Thus, time is not an intrinsic constituent of reality but a consequence of the first and subsequent events within a dynamically transforming energetic framework.

References

1. Appendix 24: The Physical Primacy of Frequency over Time – Time Dilation as Phase-Induced Time Distortion in ECM (July 2025).
   Argues that frequency is the primary quantity while time is a secondary construct, with measurable time offsets arising from phase shifts at a given frequency.
   DOI: https://doi.org/10.13140/RG.2.2.30764.17288


2. Appendix 31: Frequency and Energy in Extended Classical Mechanics (ECM) (July 2025).
   Establishes frequency as the fundamental descriptor of a physical system’s identity, rather than a derivative measurement of energy.


3. Extended Classical Mechanics (ECM): Consistent Fundamental Energy Principle – Planck-Scale Frequency Origins (February–March 2026).
   Establishes that intrinsic pre-Planck frequency governs all energetic manifestations, and that time emerges from cumulative phase imbalance relative to stabilized Planck-scale manifestation.
   SSRN DOI: http://dx.doi.org/10.2139/ssrn.6221099
   Zenodo: https://zenodo.org/records/19375374


4. ECM Derivation of Frequency-Based Time Dilation (April 2026).
   Proposes that cosmic time is absolute and unaffected by gravity, while measurable clock time is distorted due to frequency shifts rather than spacetime curvature.


5. ECM Interpretation of Time Dynamics (October 2025).
   States that time is not an independent variable in ECM but a measurable outcome of frequency-governed energy–mass evolution.


6. Time Deviation in ECM Due to Thermal and Mechanical Influences.
   Available at: https://www.researchgate.net/post/Time_Deviation_in_ECM_Due_to_Thermal_and_Mechanical_Influences

© 2026 Soumendra Nath Thakur

Licensed under Creative Commons Attribution 4.0 International (CC BY 4.0)