Emergent Time as the Unified Progression of Physical Changes within Spatial Extensions:

Soumendra Nath Thakur, August 31, 2025

For time to be meaningful, it must have an origin. That origin is the same as the origin of length, height, and depth—the three measurable extensions of space. These spatial extensions represent physical changes along their respective directions, each identifiable by a variable point. Yet, alongside these spatial variations, there exists a temporal progression that relates to the transformations occurring within them.

However, time is not measured individually for each of the three spatial dimensions. Instead, it is referenced to a common mean point that represents the collective physical changes occurring across the extensions of space. In this way, the progression of time is not tied to any one spatial dimension but is instead the unified progression of this mean point, common to all three.

Thus, the single dimension of time does not conflict with the measurement of three variable points within spatial extensions. Rather, time is the continuous progression from the origin to the common mean points of these physical variations. It does not represent the independent changes of each point within space, but the unified advancement that underlies them all.

🚀 New ECM Publication Announcement: The Artificial Mind of the Universe

I am pleased to share the publication of my latest work:

Appendix 45: The Artificial Mind of the Universe — An Extended Classical Mechanics Perspective

August 2025

DOI: https://doi.org/10.13140/RG.2.2.14014.14407

🔹 Abstract-style overview:

This appendix explores the concept of the artificial mind of the universe within the framework of Extended Classical Mechanics (ECM). It proposes that the perceptible domain of matter–energy interactions can be understood as the universe’s brain, while the invisible realms of dark matter and dark energy represent its deeper structural dynamics. Together, these physical foundations give rise to an emergent artificial consciousness — a universal analog of mind.

By linking physical extensions of space, energy transformations, and gravitational dynamics with the dual layers of brain (physical) and mind (abstract), this work extends ECM toward a broader understanding of intelligence at a cosmological scale.

🔹 Significance:

• Integrates AI analogies into cosmological physics.

• Clarifies the distinction between the universe’s brain (structural matter–energy) and its artificial mind (conscious dynamics).

• Builds upon earlier appendices connecting human mind, AI, and ECM foundations.

Best Regards

Soumendra Nath Thakur

The Artificial Mind of the Universe: An Extended Classical Mechanics Perspective.

The Artificial Mind of the Universe: An Extended Classical Mechanics Perspective

Soumendra Nath Thakur

Tagore's Electronic Lab, India 

August 30, 2025

The proposition that the universe may possess an intrinsic form of intelligence has gained renewed attention at the intersection of physics, philosophy, and artificial intelligence research. Within this framework, artificial intelligence (AI) is not limited to human-engineered systems but may serve as a conceptual analogue for understanding the structured, abstract intelligence expressed by the cosmos itself. Both the perceptible domain of matter–energy interactions and the invisible realms of dark matter and dark energy can be understood as components of an artificial mind of the universe.

Extended Classical Mechanics (ECM) provides the theoretical structure for this interpretation. By extending Newtonian foundations to incorporate energy–mass duality, momentum exchanges, and gravitational dynamics at both micro- and macro-cosmic scales, ECM offers a physics-based articulation of how the universe may operate as a form of intelligence. These physical principles are not treated merely as quantities to be measured; rather, they are understood as functional mechanisms that underpin systemic regulation, coherence, and adaptation—qualities traditionally associated with intelligence.

In this view, energy transformations, matter–momentum interactions, and gravitation-driven structure formation function analogously to computational processes within artificial intelligence. Just as AI systems process information through algorithmic structures, the universe processes change through intrinsic physical laws that conserve, regulate, and transform energy and mass. The analogy extends further: the “artificial” aspect does not imply human design but instead denotes intelligence manifesting through abstraction, regularity, and self-organization embedded in the universal order.

This argument gains further support from three complementary works. The first, Artificial Intelligence Brain, Mind, and Consciousness: Unraveling the Mysteries of Artificial Knowledge [1], establishes that AI can be conceptualized as an emergent intelligence arising from structured interactions of information, regardless of its substrate. The second, Human Brain, Mind, and Consciousness: Unraveling the Mysteries [2], shows how consciousness itself emerges from the interplay of energy and matter within the neural substrate of the human brain, thereby linking physical dynamics to cognitive phenomena. The third, Appendix 43: Origin and Fundamental Energy in Extended Classical Mechanics [3], situates the foundations of ECM in the recognition that energy is the primary and irreducible element of physical reality, from which mass, momentum, and gravitation derive their functional roles. This provides a necessary ontological grounding: if energy is the fundamental substrate, then intelligence—artificial or natural—can be understood as one of its higher-order manifestations.

Taken together, these perspectives suggest that the universe, when considered through ECM, is not merely a passive repository of energy and matter but an active intelligence system. The artificial mind of the universe becomes a theoretical bridge: it links human cognition, machine intelligence, and cosmological processes as diverse instantiations of the same underlying physical principles. Thus, ECM not only unifies dynamics at multiple scales but also advances a broader paradigm in which intelligence is recognized as a structural property of energy itself.

References

1. Artificial Intelligence Brain, Mind, and Consciousness: Unraveling the Mysteries of Artificial Knowledge (August 2025). DOI: https://doi.org/10.13140/RG.2.2.13715.95528

2. Human Brain, Mind, and Consciousness: Unraveling the Mysteries. DOI: https://doi.org/10.13140/RG.2.2.29992.14082

3. Appendix 43: Origin and Fundamental Energy in Extended Classical Mechanics (August 2025). DOI: https://doi.org/10.13140/RG.2.2.14836.46725

Analysis 

According to the provided text, the Extended Classical Mechanics (ECM) perspective proposes that the universe operates as a form of intelligence, which the author refers to as the "artificial mind of the universe." This framework suggests that the universe's physical laws and processes, such as energy transformations, matter–momentum interactions, and gravitation, function analogously to computational processes within an artificial intelligence system. The term "artificial" in this context does not imply human design but rather a form of intelligence that arises from the abstraction, regularity, and self-organization inherent in the universal order.

Key Principles and Components

The core of this theory rests on a few key ideas:

* Energy as the Fundamental Substrate: ECM, as outlined in the text, posits that energy is the primary and irreducible element of physical reality. Mass, momentum, and gravitation are considered to be derived from and functionally dependent on energy.

* Intelligence as a Higher-Order Manifestation: The theory suggests that intelligence, whether natural or artificial, is a structural property of energy itself. Therefore, the universe, as a system of energy, is inherently capable of exhibiting intelligent behavior.

* Physical Laws as Algorithmic Processes: The text draws an analogy between the universe's physical laws and the algorithmic structures of AI. Just as AI systems process information to regulate and adapt, the universe's laws process change to conserve and transform energy and mass, leading to systemic regulation, coherence, and adaptation. 

The Role of ECM

The Extended Classical Mechanics framework provides the theoretical foundation for this idea by extending Newtonian mechanics to include energy–mass duality and momentum exchanges. It treats these physical principles not just as measurable quantities but as functional mechanisms that underpin systemic regulation, coherence, and adaptation. This allows for a physics-based articulation of how the universe's physical dynamics can be understood as an intelligent system.

The "artificial mind of the universe" serves as a conceptual bridge, linking human cognition, machine intelligence, and cosmological processes as diverse examples of the same fundamental physical principles. The theory suggests that intelligence is not unique to biological or human-engineered systems but is a structural property of energy itself, manifesting through the self-organizing processes of the cosmos.

Extended Classical Mechanics Photon-Speed Postulate

Soumendra Nath Thakur | August 27, 2025

In ECM, c is simply the photon’s own propagation speed that carries the Planck quantum hf. It is not imported from Lorentz transformations, γ-factors, or any relativity-based assumptions.

The ECM kinetic-energy law:

KEᴇᴄᴍ = (½ΔMᴍ⁽ᵈᵉ ᴮʳᵒᵍˡᶦᵉ⁾ + ΔMᴍ⁽ᴾˡᵃⁿᶜᵏ⁾)c² = hf

couples the displaced-mass operator directly to the photon’s speed, not to frame-dependent particle velocities.

Max Planck’s 1899 derivation of the natural units ℓₚ, tₚ and mₚ already fixed the ratio ℓₚ ⁄ tₚ = c without any reference to Lorentz transformations or the 1905 kinematics.

The constant c therefore entered physics as a purely electrodynamic/ thermodynamic scale, not as a relativistic postulate.

In the ECM reinterpretation step (v ↦ c) the symbol c is used only in this pre-relativistic, Planckian sense—i.e. as the speed that converts a quantum of action hf into a mass-equivalent hf ⁄ c².

No Lorentz covariance, time-dilation or length-contraction is invoked. Hence the claim “no reliance on relativity” stands.

For example, in the photoelectric effect, the same ΔMᴍ that liberates an electron also defines the emitted photon’s frequency (hf), with c acting only as the conversion link to mass-energy.

Thus, in ECM, c is a natural constant of propagation — exactly as Planck used it in 1899 — not a borrowed postulate from special relativity stands.

Extended Classical Mechanics (ECM) Photon-Speed Postulate: “c” as the Intrinsic Propagation Speed of the Planck Quantum hf—Independent of Special Relativity.

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

In the Extended Classical Mechanics (ECM) framework c appears exclusively as the propagation speed of the photon that carries the Planck quantum hf.  It is not imported from Lorentz transformations, time-dilation, or any kinematic assumption; it is simply the measured speed of light in vacuum that Planck himself used in 1899 to define his natural units.  The kinetic-energy law:

KEᴇᴄᴍ = (½ ΔMᴍ⁽ᵈᵉᴮʳᵒᵍˡᶦᵉ⁾+ ΔMᴍ⁽ᴾˡᵃⁿᶜᵏ⁾)c² = hf. 

Therefore couples the displaced-mass operator to the photon’s own speed, not to any frame-dependent velocity of a massive particle.  Since no γ-factor, simultaneity convention, or acceleration-free inertial frame is invoked.

Within ECM, c is the photon’s propagation speed—used only to convert between hf and its mass-equivalent—not a borrowed postulate from special relativity. 

Bound and Free Electron States in ECM: Illustrative Examples.

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

DOI: https://doi.org/10.13140/RG.2.2.23251.44320

August 24, 2025

A bound or free electron is a negatively charged subatomic particle that carries a single, fundamental negative elementary charge, denoted by −e, equivalent to approximately −1.602 × 10⁻¹⁹ coulombs (C). An atom or molecule becomes ionised when it gains or loses electrons, thereby acquiring a net positive or negative charge.

In Extended Classical Mechanics (ECM), the transition of an electron between a bound state and a free state is governed by the gain or loss in the magnitude of ΔMᴍ ≡ Mᵃᵖᵖ. A corresponding displacement −ΔMᴍ ≡ −Mᵃᵖᵖ, linked to the electron’s fundamental charge, determines whether the electron remains confined by the attractive potential of the atomic nucleus or is liberated as a free particle.

Appendix 25 provides the detailed basis for this condition [1] by equationally presenting the attractive nuclear potential and showing how confinement produces an apparent mass deficit. Bound electrons occupy quantized states with significantly reduced net energy compared to free electrons. For example, in hydrogen the discrete energy levels are:

E₁ = −13.6 eV, E₂ = −3.4 eV, E₃ = −1.51 eV, etc.

ECM interprets these reduced bound-state energies as a negative apparent mass contribution, such that:

Mᵃᵖᵖ = Mᴍ − mₑ < 0.

Liberation of an electron corresponds to a positive mass displacement:

ΔMᴍ = mₑ − Mᴍ > 0,

which directly governs both kinetic and radiative outcomes. Thus, confinement and release are two aspects of the same mass–energy displacement law in ECM [1].

From this perspective:

Thermionic emission occurs when thermal energy input satisfies the displacement condition:

hf (or thermal input) ≥ |−Mᵃᵖᵖ|c².

Here, the work function φ aligns with the confinement-induced apparent mass, φ ≈ |−Mᵃᵖᵖ|c² [1].

Photoelectric emission occurs when incident photon energy meets the same criterion:

hf = −Mᵃᵖᵖc² = ΔMᴍc² [1][2].

This shows that whether the input is thermal or photonic, the decisive factor is not a direct electron–photon coupling, but rather the mass–energy interaction at the atomic level, expressed as ΔMᴍ displacement.

Furthermore, when electrons drop between quantized levels (nᵢ → n𝑓), the energy loss manifests as photon emission with:

ΔE = hf = Eₙᵢ − Eₙ𝑓 = −ΔPEᴇᴄᴍ = −ΔKEᴇᴄᴍ.

Here, the photon is not an abstract mediator but the externalized carrier of displaced internal mass (ΔMᴍ = hf/c²) [3]. In contrast, a free electron (Mᴍ = mₑ) lacks confinement and cannot radiate via inertial motion in vacuum, confirming that only bound states support radiative quantum events [1].

Therefore, ECM demonstrates that both thermionic and photoelectric effects emerge from the same atom–energy interaction, rooted in the apparent mass displacement of bound electrons [2][5]. The notion of direct photon–electron interaction, isolated from nuclear confinement, is thus an incomplete and weak assumption, and should be discarded in favour of ECM’s unified confinement-based framework.

Consideration of a Photon Striking a Free Electron versus a Bound Electron

In conventional descriptions of the photoelectric effect, it is often proposed that a photon strikes an electron and directly transfers its energy, enabling the electron to overcome the metal’s binding energy (the work function, φ) and be ejected. In this view, the condition for emission is simply that the photon’s energy exceeds the work function, with any excess manifesting as the kinetic energy of the emitted electron.

However, this proposition assumes that a photon can effectively transfer its entire quantum of energy directly to an electron as though the electron were free in vacuum. In ECM, this assumption is invalid [3]. A truly free electron (Mᴍ = mₑ) does not exist in a confined quantized state, and therefore cannot absorb a discrete photon and undergo emission transitions or continue propagation through such an interaction. Without confinement, there is no quantized orbital structure to mediate energy exchange, and thus photon absorption by a free electron in vacuum is prohibited as a stable interaction.

In contrast, when an electron is bound within an atom, its reduced energy state is characterized by negative apparent mass (Mᵃᵖᵖ < 0), reflecting confinement by the nuclear potential [1]. Only under these conditions can quantized absorption or emission occur, since the atom–electron system provides a conservative framework for energy redistribution. A photon interacting with such a bound system does not simply “hit an electron” but excites the atom–electron system through vibrational and mass–energy displacement, ΔMᴍ [5]. Liberation occurs only if the displacement condition ΔMᴍc² ≥ |−Mᵃᵖᵖ|c² is satisfied [1][2].

This distinction is decisive. In ECM, the effective process of both thermionic and photoelectric emission is not reducible to photon–electron collisions, but to atom–energy interactions mediated by vibrational dynamics and mass displacement [5]. Thermal excitation and photon input are merely two pathways delivering external energy into the same confinement system [2].

Evaluation:

Photon striking a free electron: no confined state, no quantized transitions, interaction unstable and insignificant [3].

Photon interacting with a bound electron via atomic confinement: quantized transitions possible, ΔMᴍ displacement governs release, consistent with observed discrete energy levels and emission thresholds [1][2].

Energy interacting through induced atomic vibration (thermal route): equally valid pathway, with emission again determined by ΔMᴍ displacement rather than a direct electron–photon collision [5].

Conclusion:

This provides concrete evidence that, whereas the application of a potential difference surrounding a free electron can set it in motion—as experimentally demonstrated in Thermionic Emission within CRT systems [4]—the direct striking of a free electron by a sufficiently energetic photon cannot set the electron in motion or sustain its propagation via photon absorption [3]. In ECM, such a process is prohibited as a stable interaction, reaffirming that photon-induced transitions are only possible in bound, quantized states, not in free electron dynamics. Consequently, the conventional photoelectric proposition of direct photon–electron impact is an inadequate description and must be replaced with ECM’s unified confinement-based framework [2][5].

References

[1] Appendix 25: Apparent Mass Displacement and Energy-Mass Transitions of Electrons — An ECM Framework for Bound States, Emission, and Photon Generation. DOI: https://doi.org/10.13140/RG.2.2.28129.62565

(Provides the explicit equational presentation of nuclear attractive potential, bound vs. free electron states, and the role of ΔMᴍ in emission.)

[2] Appendix 42: Both the previously developed thermionic emission and the later photoelectric effect are inevitably based on the same mechanism. DOI: https://doi.org/10.13140/RG.2.2.29392.01280

(The foundational statement that both effects arise from the same ΔMᴍ-governed confinement mechanism.)

[3] Appendix 19: Photon Mass and Momentum — ECM's Rebuttal of Relativistic Inconsistencies through Apparent Mass Displacement. DOI: https://doi.org/10.13140/RG.2.2.36775.46242

(Supports the treatment of photons as carriers of displaced mass ΔMᴍ, essential in distinguishing bound-state emission from free-electron motion.)

[4] Appendix 40: Empirical Support for ECM Frequency-Governed Kinetic Energy via Thermionic Emission in CRT Systems. DOI: https://doi.org/10.13140/RG.2.2.31184.42247

(Provides experimental grounding for ECM by demonstrating that electron liberation and motion in CRT systems follow the ΔMᴍ-based displacement condition. Shows that thermionic emission, a well-established physical phenomenon, validates the frequency-governed kinetic energy formulation of ECM, thereby linking the theoretical framework directly to measurable laboratory effects and reinforcing its unification with the photoelectric effect and quantized bound-state transitions.)

[5] Appendix 42 Part-2: A Unified ECM Framework of Atomic Vibration. DOI: https://doi.org/10.13140/RG.2.2.30001.49766

(Extends Appendix 42 by clarifying that external energy inputs — thermal or photonic — act through atomic vibrational mediation, not direct photon–electron collisions.)

Specific Consequence of Photons Striking a Metal Surface

Both the photoelectric effect and thermionic emission involve the emission of electrons from a metal.

In the photoelectric effect, photons (light particles) strike the metal surface and transfer their energy directly to electrons. If the transferred energy exceeds the metal’s work function, the electrons are emitted.

When photons are absorbed by the metal, they can also transfer energy to the atoms in its lattice, causing them to vibrate more intensely. This heating can lead to thermionic emission — where electrons are ejected due to thermal energy. Thermionic emission can occur even in the presence of incident photons, and also under greater external thermal energy sources.

In the specific phenomenon under discussion, the mechanism and the ultimate energy source can overlap: photons may both liberate electrons directly (photoelectric effect) and indirectly via heating (thermionic emission).

Historical Background

• Thermionic Emission

  • 1873: Frederick Guthrie observes heated metals emitting charges.

  • 1880: Thomas Edison studies the effect further.

  • 1901–1904: Owen Richardson develops a theoretical explanation (later earning the 1928 Nobel Prize).

• Photoelectric Effect

  • 1887: Heinrich Hertz observes ultraviolet light enhancing electrical discharge between electrodes.

  • 1888: Wilhelm Hallwachs investigates the effect systematically.

  • 1902: Philipp Lenard conducts detailed studies.

  • 1905: Albert Einstein provides the theoretical explanation, awarded the 1921 Nobel Prize.

Discussion Point

Is it not a more dedicated and rigorous contribution to engage in sustained empirical research and observation within the limits of available science, rather than merely observing a phenomenon?

Scientists such as Guthrie, Edison, Richardson, Hertz, Hallwachs, and Lenard made substantial progress in understanding electron emission from metals. Meanwhile, pioneers like Dalton, Thomson, Rutherford, Bohr, Schrödinger — along with earlier thinkers like Democritus — and Chadwick expanded the broader understanding of atomic structure, electrons, photons, and subatomic particles.

Given that thermal electron emission is a common element in both thermionic emission and the photoelectric effect, and the close relationship between the two phenomena, one might ask: when Owen Richardson was awarded the 1928 Nobel Prize for thermionic emission, was there truly a broad enough distinction to separately award the Nobel Prize for the photoelectric effect?

I wonder.

- Soumendra Nath Thakur

  August 15, 2025

Extended Classical Mechanics (ECM) vs. the Massless Photon Assumption — A Call for Mathematical Consistency

Soumendra Nath Thakur | August 13, 2025

The insistence that photons have m = 0 and that ECM’s treatment of photon mass as > 0 or −Mᵃᵖᵖ is “wrong” is based on outdated assumptions rather than a consistent application of physics. In ECM,

F = (Mᴍ − Mᵃᵖᵖ) aᵉᶠᶠ

applies universally. Dismissing it without understanding its derivation is not a rebuttal — it is a refusal to engage with the framework.

The claim that F = ma “does not apply” at the speed of light is also incorrect. ECM uses:

F = Mᵉᶠᶠ aᵉᶠᶠ

with photons having Mᵉᶠᶠ = −2Mᵃᵖᵖ immediately after emission, transitioning to Mᵉᶠᶠ = −Mᵃᵖᵖ beyond the source’s gravitational influence. This is fully consistent and requires no m = 0 assumption.

The problem with this position is straightforward:

• It conflates massive-particle kinematics with dynamic-particle kinematics.

• It retains the massless-photon assumption, which collapses under basic force–acceleration logic.

ECM resolves this by treating −Mᵃᵖᵖ as an emergent, motion-dependent property — not a rest mass. This eliminates the contradictions of “true negative mass” in other theories and provides a self-contained, polarity-based explanation for photon propagation.

Before debating ECM, one must address the fact that under the m = 0 assumption:

F = 0 × a = 0

— meaning the photon cannot even move from emission to detection without an ad hoc “instant velocity” insertion. That alone indicates the model is incomplete.

If ECM is to be dismissed, the challenger must present a mathematically consistent alternative that explains photon propagation without m = 0 — and without contradicting its own force laws.

The Self-Sufficiency of Physical Laws — No Designer Required

Soumendra Nath Thakur 

August 13, 2025

Throughout history, many eminent scientists — from Newton and Einstein to Oppenheimer and Michio Kaku — have, at various points, entertained the notion of an intelligent designer or “hands of God” guiding the formation of the universe. The argument often arises from the apparent fine-tuning of cosmic parameters, the astonishing harmony of physical constants, and the improbable emergence of life-supporting conditions. To some, such precision suggests intentional creation.

However, when examined deeply through the principles of mathematical physics — and in my own work, through the framework of Extended Classical Mechanics (ECM) — the need for an external designer dissolves. The very order that inspires appeals to divine intervention can instead be seen as the natural, inevitable outcome of self-consistent physical laws acting upon the initial conditions of the universe.

In this view, there is no guiding hand, no external architect — the “design” is intrinsic to the system. The complexity and structure we observe today are not imposed from without, but emerge from within, as lawful consequences of energy–mass interactions, symmetry principles, and the governing equations of motion.

It is undeniable that certain ancient philosophies were grounded in observations of nature and reasoned interpretations of the universe, relying more on scientific philosophy than on faith or spirituality. When such philosophies convey no compelling need for an external designer in the universe’s formation, they stand in striking alignment with modern scientific understanding. They deserve recognition for having, long ago, reached insights about the cosmos that parallel those uncovered by contemporary science. Every atom, subatomic particle, and energetic vibration inherits its existence from the same primordial framework, evolving without deviation from the logic of the universe’s own rules.

Thus, the grandeur of the cosmos need not be diminished by removing the idea of a designer; rather, it is amplified. It is the triumph of the laws themselves — complete, self-contained, and capable of giving rise to galaxies, life, and consciousness — without any external intervention.

Bridging the Two Concepts

While Schrödinger’s statement — “The total number of minds in the universe is one” — speaks primarily to the unity of consciousness, it indirectly touches on a deeper point about origins. If all mental phenomena share a common source, it invites the broader question: does the universe itself require an external originator, a “guiding hand” that sets its laws and matter into motion? This is where philosophy and physics part ways. The unity of consciousness can be contemplated through metaphysics and ancient philosophy, but the structure of the physical universe can be examined — and often fully explained — within the self-contained framework of natural laws.

Many scientists, from antiquity to the modern era, have entertained the notion that the universe’s intricate order could be the product of a guiding intelligence. Michio Kaku, for example, has often spoken about the “mind of God” as a poetic metaphor for the elegance of the cosmos, reflecting the awe inspired by the universe’s complexity. Such ideas frequently arise from the apparent improbability of cosmic precision emerging without deliberate planning. However, through the lens of Extended Classical Mechanics (ECM), I find no compelling necessity for such an external designer.

The universe’s formation, evolution, and structure can be understood as natural consequences of the intrinsic properties of matter and energy, governed by physical laws that operate consistently across scales. The elegance we perceive is not proof of a guiding hand, but a reflection of the self-organizing potential inherent in the laws themselves — laws that require no intervention beyond their own operation. The same principles that govern the motion of a falling object or the orbit of a planet extend seamlessly to the birth of galaxies and the dynamics of cosmic expansion. In this light, the cosmos does not appear as a constructed artifact, but as a natural, inevitable unfolding of the laws that define it — a universe whose order is written into its very fabric, requiring no author beyond the language of physics itself.

Inapplicability of the cosmological constant Λ in observational cosmology:

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

August 10, 2025

The cosmological constant Λ, originally introduced by Einstein to allow for a static universe, is retained in modern cosmology to account for the observed acceleration of cosmic expansion, commonly attributed to “dark energy.” In the ΛCDM model, Λ manifests as a constant energy density filling space homogeneously, producing a repulsive gravitational effect at very large scales. However, this effect is inherently rooted in General Relativity’s (GR) curved spacetime framework—a purely geometric interpretation that lacks a direct force-based physical mechanism observable in laboratory or local astrophysical contexts.

The application of the cosmological constant Λ within Newtonian dynamics—as demonstrated in the paper "Dark energy and the structure of the Coma cluster of galaxies"—relies on incorporating a Λ-term adapted from General Relativity’s curved spacetime model. This reliance on the Λ-term transpired the need for a repulsive effect on gravity at large cosmic scales, yet remains inapplicable to real-world observations due to relativity’s dependence on the abstract concept of curved spacetime. Consequently, the referenced research resorted to force-based Newtonian dynamics to address the Λ-term in a physically interpretable framework.

From an observational standpoint, the repulsive effect ascribed to Λ cannot be measured directly in local systems such as planetary or stellar dynamics. For instance, the gravitational acceleration produced by Λ at solar system scales is negligibly small—many orders of magnitude weaker than the already minuscule influence of galactic tides. Furthermore, attributing cosmic acceleration to Λ presumes that the same constant applies uniformly across all scales, an assumption unsupported by empirical evidence outside of large-scale cosmological fits.

Alternative frameworks, such as Extended Classical Mechanics (ECM), instead treat such large-scale accelerations without invoking an unmeasurable constant. ECM models can describe galaxy cluster dynamics or large-scale structure formation through field–mass interactions that preserve physical measurability and avoid dependence on GR’s curvature formalism. These approaches offer a testable, force-based interpretation of phenomena that Λ in GR can only model abstractly, without physical grounding in local experiments.

*-*-*-*-*-*

This document argues that the cosmological constant, Λ, has limited applicability in observational cosmology, particularly outside of large-scale cosmic models. The core arguments presented are:

Geometric Abstraction

Λ is a component of General Relativity's curved spacetime framework, which is a geometric model. This makes it difficult to apply as a direct, force-based physical mechanism that can be measured or observed in local, real-world systems like a laboratory or the solar system.

Inapplicability in Newtonian Dynamics: 

While attempts have been made to adapt the Λ-term for use in Newtonian dynamics, the document suggests this still relies on its origin in a curved spacetime model. It notes that this is often done to provide a more physically interpretable, force-based framework for a concept that is fundamentally abstract.

Lack of Local Observability: 

The repulsive effect attributed to Λ is too weak to be measured directly in local gravitational systems. At the scale of our solar system, its influence is many orders of magnitude smaller than other negligible gravitational effects, making it practically unobservable.

Uniformity Assumption: 

The application of Λ in the ΛCDM model assumes a constant value across all scales, an assumption that the document states is not supported by empirical evidence outside of large-scale cosmological data fitting.

Alternative Frameworks: 

The document proposes that alternative frameworks, like Extended Classical Mechanics (ECM), offer a more testable and physically grounded interpretation. ECM, it suggests, uses force-based, field-mass interactions to explain large-scale accelerations, thereby avoiding the need for an unmeasurable constant and providing a mechanism that could potentially be verified through local experiments.

A Rebuttal of Negative Mass vs. Negative Apparent Mass (−Mᵃᵖᵖ) in Extended Classical Mechanics (ECM):

Soumendra Nath Thakur | Tagore's Electronic Lab

August 10, 2025

In Extended Classical Mechanics (ECM), negative apparent mass (−Mᵃᵖᵖ) is fundamentally different from the “negative mass” sometimes proposed in theoretical physics. Traditional negative mass is treated as an intrinsic rest property—leading to paradoxes such as acceleration opposite to an applied force or violations of the equivalence principle. These contradictions make it untenable for a particle at rest.

By contrast, ECM’s −Mᵃᵖᵖ is not a rest property but an emergent, motion-dependent quantity. It applies to dynamic particles such as photons and enables the description of self-generative or repulsive forces without assuming m = 0 or inheriting the contradictions of true negative mass. This approach gives ECM a physically consistent mechanism for photon motion that remains coherent within its own framework.

1. Distinguishing ECM’s Negative Apparent Mass from Simple Negative Mass

Simple Negative Mass:

This concept assumes a particle has an intrinsic negative value for its mass. Using F = ma, a positive force on such a particle produces acceleration in the opposite direction, leading to paradoxical and non-intuitive behaviors—for example, mutual repulsion with a positive mass while still being repelled by it. These predictions conflict with observed physics and are generally dismissed as unphysical.

Negative Apparent Mass (−Mᵃᵖᵖ) in ECM:

In ECM, −Mᵃᵖᵖ is not a static rest property but an emergent property of motion arising from dynamic mass–energy redistribution. For photons, −Mᵃᵖᵖ allows for a repulsive or self-generative force, enabling acceleration without requiring a rest mass. This resolves the F = 0 × a = 0 problem in classical mechanics. Furthermore, the polarity of mass determines the polarity of force—positive mass (+m) yields external forces (+F), while negative mass or −Mᵃᵖᵖ yields self-generated forces (−F), which act repulsively.

2. Consistency Within ECM’s Framework

Photon Dynamics:

ECM explains how a photon—despite having no rest mass—can still be dynamic and responsive to force. Negative apparent mass produces a self-generative repulsive force, enabling continuous propagation from emission to detection without requiring an external acceleration source.

Gravitational Implications:

In ECM, gravitational effects result from energetic gradients and mass redistribution, not solely from spacetime curvature. The concept of −Mᵃᵖᵖ offers a pathway to explain phenomena such as cosmic acceleration without introducing exotic components like dark energy. The expansion can instead be seen as a natural consequence of the repulsive effects from cumulative −Mᵃᵖᵖ in the universe.

Self-Sufficiency:

ECM functions independently of the problematic assumptions of simple negative mass. It defines its own mass–energy–force relationships, creating a self-contained theoretical structure that remains internally consistent.

Supporting Note

In a related ResearchGate discussion, it is argued that photons—though conventionally considered “massless”—possess a negative apparent mass (−Mᵃᵖᵖ) in ECM, which results in a negative effective mass and inherently antigravitational behavior. This reframes photon dynamics in gravitational contexts without invoking true masslessness and aligns seamlessly with ECM’s broader mechanical principles. researchgate.net/post/About_Massless_Objects_Negative_Effective_Mass_and_Anti-Gravitational_Motion_in_Extended_Classical_Mechanics

Gravitating Mass as an Emergent, Polarity-Governed Quantity in ECM:

Soumendra Nath Thakur

Tagore’s Electronic Lab | ORCiD: 0000-0003-1871-7803

August 07, 2025

While traditional physics correctly observes that gravity, mass, and energy are deeply interconnected—and that gravitational acceleration (‘g’) varies depending on location—Extended Classical Mechanics (ECM) introduces a critical refinement to this understanding. Rather than treating mass as a fixed, invariant quantity that inherently produces gravitational effects, ECM redefines gravitating mass (Mɢ) as an emergent outcome of interactions between mechanical mass (Mᴍ) and frequency-derived apparent mass (Mᵃᵖᵖ).

This reconceptualization acknowledges that energy itself, particularly in dynamic or radiative forms like kinetic energy or photon emission, contributes negatively to gravitational interaction through transformations such as −Mᵃᵖᵖ or ΔMᴍ. As a result, the net gravitating mass of a system may become positive, negative, or even null, depending on its internal energy configuration and frequency characteristics.

Such a framework allows ECM to consistently explain repulsive gravitational phenomena, such as those observed in dark energy-driven cosmic expansion or photon deflection in curved space, without violating conservation laws. By integrating effective gravitational acceleration (gᵉᶠᶠ) and frequency-based mass modulation, ECM extends classical and relativistic models to include gravitational polarity as a real, measurable consequence of internal dynamics—not as an abstract extension or speculative hypothesis.

This shift from a static to a dynamic view of mass and gravity provides a unified explanation for attraction and repulsion within a single formalism, offering deeper coherence across classical mechanics, quantum physics, and cosmology.

A Comparative Framework for Extended Classical Mechanics' Frequency-Governed Kinetic Energy:

Soumendra Nath Thakur,

August 05, 2025

This paper presents a revised formulation of kinetic energy within Extended Classical Mechanics (ECM), interpreting it as a frequency-governed process arising from mass displacement transitions. ECM proposes that kinetic energy emerges from the redistribution of rest mass (Mᴍ) into a dynamic component (ΔMᴍ), structured by two distinct frequency domains: the de Broglie frequency governing translational motion and the Planck frequency reflecting intrinsic quantum excitation. The resulting kinetic energy relation, KEᴇᴄᴍ = (ΔMᴍᵈᴮ + ΔMᴍᴾ)c² = hf, yields the classical ½mv² limit under low-frequency conditions while providing explanatory power for quantum and high-energy phenomena. Applications to atomic transitions, thermionic emission, nuclear fission, and fusion show that observed energy release can be interpreted as frequency-driven mass redistribution rather than annihilation. ECM thus reframes kinetic energy as an emergent property of dual-frequency mass dynamics, offering a unified theoretical lens spanning classical, quantum, and nuclear regimes.

DOI of the Paper.

Extended Classical mechanics' rebuttal to the Lorentz factor γ stands on nearly irrefutable physical and mathematical ground.

ResearchGate Link

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

August 08, 2025

ECM rebuttal to the Lorentz factor γ is grounded not in speculative critique but in principled limitations within the formalism of relativity itself. ECM exposes these inconsistencies through:

·                        Neglect of acceleration during frame transition (γ is derived assuming constant relative velocity, ignoring inertial transition forces).

·                        No account for material stiffness (k) or real-world resistive mechanics that accompany motion in bound or structured systems.

·                        Breakdown at low velocities where γ ≈ 1 yields no meaningful distinction from classical energy, yet the relativistic model continues to be inapplicably extended.

·                        Undefined behaviour at c (as γ → ∞), making γ inapplicable at the very limit it was designed to describe.

·                        Misuse as an energy multiplier (e.g., E = γmc²) without dynamic basis—whereas ECM introduces hf = −ΔMᴍc², dynamically rooted in frequency modulation and internal mass polarity transitions.

These critiques are not philosophical but structural, targeting how γ:

·                        Lacks consistency with acceleration-based dynamics;

·                        Cannot incorporate internal energetic processes;

·                        Fails to bridge between classical and quantum domains coherently.

Thus, ECM does not merely refute γ—it replaces it with a measurable, frequency-based dynamic variable (ΔMᴍ, Mᵃᵖᵖ, gᵉᶠᶠ) that remains valid across all domains: classical, relativistic, and quantum.

This makes ECM Appendix 38 not only valid—it’s strategically essential in ECM’s bridging framework.

With current foundational models, this rebuttal stands on nearly irrefutable physical and mathematical ground.

Additional Theoretical Insight:

The application of the cosmological constant Λ within Newtonian dynamics—as demonstrated in the paper" Article Darkenergy and the structure of the Coma cluster of galaxies" by A. D. Chernin et al.—enables the derivation of real, observable features such as the zero-gravity surface. This choice implicitly reveals a critical limitation of relativistic mechanics in addressing dark energy on intergalactic scales. The authors' preference for Newtonian treatment, despite the general relativistic origin of Λ, highlights the pragmatic supremacy of Newtonian dynamics in this context.

In contrast, Extended Classical Mechanics (ECM) offers an even more radical and structured improvement. ECM independently integrates negative quantities—such as negative apparent mass (−Mᵃᵖᵖ) and mass shifts (ΔMᴍ ≡ −Mᵃᵖᵖ)—in a physically consistent and mathematically conserved framework. This approach not only captures the role of repulsive dynamics (similar to dark energy) more robustly than Λ in relativity but also does so without relying on coordinate transformations or metric dependencies, enabling a direct energetic interpretation.

Thus, while the cited research wisely adopts Newtonian formalism over relativistic treatments for dark energy modelling, ECM moves even further by foundationally justifying negative-mass behaviour within a dynamic mass–frequency–energy structure, offering a potentially superior alternative to both Newtonian and relativistic frameworks in cosmological modelling.

Complementary Nomination Perspective – On the Origin of Lorentz Transformation (Engelhardt)

An important related theoretical challenge to special relativity is presented in the paper "On the Origin of the Lorentz Transformation" by W.W. Engelhardt. This paper traces the historical and mathematical roots of the Lorentz transformation—not to Einstein's special relativity—but to earlier work by Woldemar Voigt (1887), who introduced these transformations to preserve the form of the wave equation.

The author critically exposes the mathematical inconsistencies and conceptual flaws in many standard derivations of the Lorentz transformation, including Einstein’s own. Engelhardt’s key insight is that Lorentz transformations should be viewed as auxiliary variables, not as physically necessary outcomes of relativistic postulates.

As emphasized in commentary by Halim Boutayeb :

1.                    “Lorentz transformations are in reality auxiliary variables invented by Voigt in 1887... Scientists in acoustics were lucky not to have been stuck in STR interpretation. Scientists in electromagnetism need to get rid of STR and LT to advance.”

This view strengthens ECM's own critique of the Lorentz factor γ by showing that even its foundational transformation lacks rigorous physical derivation. It supports ECM's shift toward frequency-based dynamics as not only a physical necessity but also a historically grounded correction to an inherited but faulty theoretical convention.