Research papers on Extended Classical Mechanics, which provide a reinterpretation of the Big Bang through pre-Planck phase transitions and the origin of the universe.

May 04, 2026

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

Based recent research (circa 2025–2026), 'Extended Classical Mechanics' (ECM) is a theoretical framework that reinterprets the 'Big Bang' not as a singular, explosive event, but rather as a continuous, frequency-driven phase transition occurring at the sub-Planckian level. This approach employs the principles of classical mechanics—expanded to incorporate the concepts of energy-frequency equivalence and "negative apparent mass"—to describe the birth of the universe; notably, it does not rely on spacetime singularities or inflationary fields. [1, 2, 3, 4, 5]

The key research papers and concepts regarding the reinterpretation of the Big Bang through the lens of ECM are outlined below:

Key Research Papers and Publications on ECM

• "Extended Classical Mechanics (ECM): A Sub-Planck Phase-Transition Framework for Cosmogenesis" (Thakur, S. N., February 2026): This paper establishes the foundational basis of the framework, proposing that the universe originates from a pre-geometric, zero-dimensional (0-dimensional) linear oscillation that subsequently transforms into a stable physical reality.

• "The Master Phase Transition in Extended Classical Mechanics: Physical Meaning and Empirical Basis" (February 2026): This work defines the process by which high-frequency potential energy (PE) transforms into kinetic energy (KE) and matter; in doing so, it regards the Planck scale not as a 'singularity,' but rather as a 'transition surface' (or a gradient relaxation process). 

• "Extended Classical Mechanics: Perspectives on Cosmological Models" (February 2026): This paper establishes a connection between ECM, [Penrose’s Conformal Cyclic Cosmology] (CCC), and [Sen’s Hypothesis]; it interprets the onset of a new cosmological epoch as a phase-driven manifestation emerging from a zero-dimensional potential reservoir.

• "Essence of Extended Classical Mechanics (ECM): A Foundational Framework Unifying the Three Branches of Physics" (October 2025): This provides a simplified summary explaining how the early universe's superluminal expansion was an orderly and regulated process, and how it was driven by 'Negative Apparent Mass' (NAM). [3, 6, 7, 8, 9, 10, 11]

Key Reinterpretations of the Early Universe

• The Big Bang as a Frequency Transition: ECM replaces the conventional "explosion" concept of the Big Bang with a frequency-driven transition (or an evolution of phase angles). • Pre-Planck Phase Transition: The universe originates from a pre-geometric, 0-dimensional potential energy reservoir. An imbalance in frequency arises within this latent energy, triggering a "phase shift" that leads to the emergence of physical time and spacetime.

• Sub-Planckian Dynamics: The pre-Planck epoch is defined as a "NAM-dominant" (Negative Apparent Mass) state, wherein potential energy converts into kinetic energy, thereby avoiding infinite density.

• Emergent Gravity and Spacetime: Rather than assuming gravity to be a geometric property, ECM proposes that gravity and mass are the result of a "mass-binding condition" that emerges during the transition into a stable (v=c) universe. 

• Unified Process: ECM employs a single mass-conversion formula to replace conventional Big Bang cosmology, proposing that the universe—rather than existing as a single, eternal physical entity—is "re-manifested." [1, 6, 7, 8, 9, 10, 12, 13]

Comparison with Conventional Models

• Vs. Standard Big Bang: Eliminates the initial singularity by replacing it with a 0-dimensional vibrational state.

• Vs. Inflation Theory: Explains rapid expansion as a result of the displacement of "negative apparent mass" (Mᵃᵖᵖ), rather than an inflation field. [7, 14, 15]

These papers point toward a paradigm shift wherein classical physics—when properly extended—proves sufficient to explain the primordial emergence of matter and space, thereby rendering a purely quantum-mechanical description of the origin unnecessary. [16, 17]

[1] https://www.researchgate.net/publication/394437141_Extended_Classical_Mechanics_ECM_A_Post-Relativistic_Interpretation_of_Early_Universe_Phenomena_and_Cosmic_Expansion

[2] https://www.researchgate.net/publication/394437141_Extended_Classical_Mechanics_ECM_A_Post-Relativistic_Interpretation_of_Early_Universe_Phenomena_and_Cosmic_Expansion

[3] https://www.linkedin.com/posts/telitnetwork_the-master-phase-transition-in-extended-classical-activity-7429205779750223872-FUM8

[4] https://www.researchgate.net/post/Extended_Classical_Mechanics_ECM_is_fundamentally_a_unified_theoretical_framework

[5] https://www.researchgate.net/publication/400360414_Frequency_Phase_Shift_Phase_Advance_and_Phase_Lag_in_Extended_Classical_Mechanics

[6] https://www.researchgate.net/profile/Soumendra-Thakur/publication/400748481_Extended_Classical_Mechanics_ECM_A_Sub-Planck_Phase-Transition_Framework_for_Cosmogenesis/links/698f0e2eca66ef6ab9926fd9/Extended-Classical-Mechanics-ECM-A-Sub-Planck-Phase-Transition-Framework-for-Cosmogenesis.pdf?origin=publication_list

[7] https://www.researchgate.net/publication/400748481_Extended_Classical_Mechanics_ECM_A_Sub-Planck_Phase-Transition_Framework_for_Cosmogenesis

[8] https://www.researchgate.net/publication/400615568_Extended_Classical_Mechanics_Perspectives_on_Cosmological_Models

[9] https://www.researchgate.net/publication/400830371_The_Master_Phase_Transition_in_Extended_Classical_Mechanics_Physical_Meaning_and_Empirical_Basis

[10] https://www.researchgate.net/publication/400615568_Extended_Classical_Mechanics_Perspectives_on_Cosmological_Models

[11] https://www.researchgate.net/post/Essence_of_Extended_Classical_Mechanics_ECM_A_Foundational_Framework_Unifying_the_Three_Branches_of_Physics

[12] https://papers.ssrn.com/sol3/Delivery.cfm/6221099.pdf?abstractid=6221099&mirid=1

[13] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6281778

[14] https://www.researchgate.net/post/How_Extended_Classical_Mechanics_ECM_Shows_That_the_Universes_Formation_Evolution_and_Structure_Follow_Naturally_from_Physical_Laws

[15] https://arxiv.org/pdf/1208.0801

[16] https://www.researchgate.net/profile/Soumendra-Thakur/publication/400761065_Extended_Classical_Mechanics_ECM_Principle-Based_Pre-Planck_Dynamics/links/698f59af7247bc6473e06bdc/Extended-Classical-Mechanics-ECM-Principle-Based-Pre-Planck-Dynamics.pdf

[17] https://www.facebook.com/fromquarktoquasars/posts/the-universe-didnt-form-from-just-one-big-bang-but-also-from-a-series-of-rapid-f/1257105712694025/

Ontological Neutrality of Temporal Variables in Extended Classical Mechanics (ECM).

Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
postmasterenator@gmail.com / postmasterenator@telitnetwork.in
May 03, 2026

Introduction

Special relativity robbed time of its independence by destroying the Newtonian notion of an absolute, universal "tick" and redefined time in a manner contrary to classical notions of absolute temporal ordering; this change creates a conceptual tension with the broader classical framework of physics and the abstract framework of mathematics.

Physics and mathematics operate within distinct but deeply interconnected domains. Physics is concerned with empirically grounded descriptions of physical systems, while mathematics provides the formal language and structural framework used to represent such descriptions. Each discipline answers questions that are well-posed within its own domain of validity.

Within this context, the question of whether “time exists” is not a strictly physical question unless time is first defined operationally.

"Time is defined as the indefinite and continuous progression of existence and events—encompassing past, present, and future as a unified whole—and is characterized by its irreversible nature."

The above definition is understood as a standard lexical and conceptual definition of time in natural language, capturing its intuitive and conventional meaning as used in general discourse. Physics, however, employs a distinct operational framework in which temporal quantities are defined through measurement procedures and expressed as quantifiable parameters derived from reproducible physical processes.

In physical theory, time is introduced through such measurement procedures—most fundamentally as what is read by clocks and inferred through consistent physical correlations. Within this framework, time is not treated as a fundamental postulate but as an operationally defined construct associated with the ordering and quantification of physical change.

Accordingly, within physics, time is not regarded as a self-subsisting entity but as a measurable parameter inferred from the evolution of physical systems. Outside this operational domain, time functions as a mathematical structure used to encode ordering, change, and phase relations. In such representations, temporal variables act as relational coordinates mapping transformations of physical states into a consistent formal structure.

Consequently, attributing absolute ontological status to time lies outside the direct adjudicative scope of physics, while simultaneously remaining embedded within the formal representational scope of mathematics. Physics does not adjudicate the metaphysical primacy of time, but rather establishes the conditions under which temporal ordering is operationally defined and experimentally validated.

This distinction motivates the following formal principle in Extended Classical Mechanics (ECM), which treats temporal variables as structurally indispensable yet ontologically non-primitive mapping constructs within physical theory.

ECM Domain Separation Principle

In Extended Classical Mechanics (ECM), physical description and mathematical structure occupy distinct but interdependent domains:

• Physics governs operationally measurable transformations of existence, expressed through observables, energy exchange, and state transitions.

• Mathematics governs abstract structural representation, providing the symbolic and geometric framework within which physical relations are encoded.

These domains are non-equivalent but coupled, such that no mathematical construct is physically meaningful unless it admits operational correspondence, and no physical law is expressible without mathematical structure.

Ontological Neutrality of Time

Within ECM, temporal variables do not constitute ontologically primary entities. Instead, they function as emergent relational mappings derived from frequency–phase structure and measurable transition rates. This is captured in the generalized phase-time correspondence:

Tₓ° = x°/360°fꜱᴏᴜʀᴄᴇ = Δt 

This relation expresses time not as a fundamental background parameter, but as a phase-normalized projection of cyclic dynamics. Accordingly, temporal quantities are interpreted as transformations of underlying frequency structure into measurable intervals of change.

From this perspective:

•  Time is not an independently existing physical substance.

•  Time is not a purely free-standing mathematical abstraction disconnected from physics.

•  Time is a derived mapping variable, defined only through the correspondence between physical state evolution and mathematical representation.

Domain Non-Transgression Criterion

A strict separation must be maintained between ontological claims and representational structures:

•  Physics does not adjudicate the absolute ontological status of mathematical constructs.

•  Mathematics does not determine physical existence, but encodes relational consistency.

•  Any attempt to classify time as “purely real” or “purely abstract” independent of operational context constitutes a category error.

Thus, physics is not tasked with resolving metaphysical abstraction, and mathematics is not an ontology-generating framework for physical existence.

ECM Interpretation of Temporal Variables

In ECM, temporal variables are best understood as:

• Derived relational coordinates, not primitives.

• Phase-encoded measures of transformation, not background substrates.

• Operational mappings between frequency structure and observed change, rather than intrinsic entities.

This interpretation preserves consistency across physical modeling while avoiding unnecessary ontological commitments.

Conclusion

Time, within ECM, is ontologically neutral: it is neither asserted as a fundamental entity nor dismissed as a purely abstract construct. Instead, it is treated as a structurally necessary mapping between measurable physical transformation and its mathematical representation. This neutrality ensures that temporal variables remain fully operational within physical theory while remaining free from unwarranted metaphysical inflation.

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.