Galactic Recession, Cosmic Origin, and the Interpretation of Expansion in Extended Classical Mechanics (ECM)

August 12, 2026

In Extended Classical Mechanics (ECM), the Universe is considered to have a physical origin from which its subsequent evolution and observable structures emerge. The observed rapid recession of distant galaxies therefore represents an evolving physical state of a Universe that has an origin; it does not, by itself, require the interpretation that space itself is physically stretching or that space is expanding as an independent material or dynamical substance.

Within the ECM formalism, the observed cosmological expansion is interpreted primarily in terms of the physical recession and increasing separation of galaxies and large-scale matter distributions originating from the evolving state of the Universe.

Accordingly, the expression “expansion of the Universe” may be used observationally to describe the increasing separation of sufficiently distant cosmic structures. However, ECM distinguishes this observable physical recession from the additional theoretical interpretation that the underlying space itself must undergo physical stretching or expansion.

Thus,

Universe with a physical origin → cosmic evolution → formation and evolution of matter → increasing galactic separation → observed galactic recession

provides an ECM-oriented description of the observable progression.

This distinction allows ECM to treat cosmic origin and subsequent galactic recession as physical phenomena while regarding the description of an expanding spatial volume as a theoretical interpretation that should not be conflated with the directly observed recession of astronomical objects.

Accordingly, ECM does not require the Universe to be understood as an initially existing spatial volume that subsequently stretches. Instead, its formulation begins with the physical origin and evolution of the Universe, and interprets the observed large-scale recession of galaxies in terms of the evolving physical state of matter, energy, and their dynamical relationships.

The geometric description of space and its possible expansion may therefore be considered separately from the physical question of what is actually evolving and producing the observed recession.

Frequency, Energy, Phase, and Temporal Interval: A General Mathematical Foundation for the ECM Phase–Frequency Framework

August 12, 2026

Regarding the statement that “quantum mechanics is a specific consequence of the theory of general relativity,” I would respectfully distinguish the two theories. Quantum mechanics is not ordinarily derived as a direct consequence of general relativity. They are distinct theoretical frameworks, although both describe physical phenomena and their relationship remains an important subject in modern physics.

Before discussing how different theories interpret the behaviour of clocks, it is useful to begin with the general mathematical and physical principles underlying a clock.

A clock is a physical system capable of producing a repeatable periodic process. For an oscillator with frequency (f) and period (T),

f = 1/T.

The relation between frequency and energy is given by the Planck relation,

E = hf,

which establishes the fundamental equivalence between frequency and quantum energy.

A periodic process also accumulates phase. If (x°) denotes an accumulated phase expressed in degrees, then one complete cycle corresponds to (360°). Consequently,

x° = 360° f Δt

and hence,

Δt = x° / (360° f)

This relation is simply the mathematical correspondence between frequency, phase advancement, and the associated temporal interval. It does not, by itself, impose any particular interpretation upon the physical origin of the frequency or phase change.

If a physical interaction changes the frequency from (f) to (f + Δf), then, consistently with

E = hf,

the corresponding energy changes by

ΔE = hΔf

The changed frequency consequently changes the rate of phase accumulation. The resulting phase displacement may therefore be represented mathematically by

x° = 360° f Δt

with the appropriate frequency specified for the physical state under consideration.

In the reference state, when there is no frequency difference,

Δf = 0,

the corresponding additional phase displacement is

x° = 0,

and therefore

Δt = 0.

When a physical process produces a frequency difference, the corresponding phase evolution can produce a non-zero temporal interval,

Δt = x° / (360° f).

Extended Classical Mechanics (ECM) uses this mathematical relationship as part of its phase–frequency formulation. In ECM, the emphasis is placed on establishing the physical relationship among frequency, energy, phase, and temporal interval rather than introducing an independent assumption concerning the nature of time.

Thus, the general relationships may be represented as

f → E

f → x° → Δt

with

E = hf, f = 1/T, Δt = x°/(360° f).

Here, E = hf expresses the Planck energy–frequency relation; f = 1/T expresses the general frequency–period relation; and Δt = x°/(360° f) expresses the temporal interval corresponding to an accumulated phase x° at frequency f.

These relationships should not be regarded as restricted to any particular gravitational, quantum, mechanical, or cosmological situation. Their mathematical applicability follows from the definitions and established relations themselves. The physical interpretation of a particular frequency change, energy change, phase displacement, or temporal interval may then be considered within the appropriate theoretical framework. The mathematical relations are maintained independently of any particular physical interpretation, while ECM applies them within its own phase–frequency formulation.

Accordingly, when comparing clocks under different physical conditions—for example, on Earth, Jupiter, or the Moon—the scientifically appropriate procedure is first to establish the measurable frequency, energy, phase, and temporal relationships and then examine how the respective physical theories account for those observations.

In this sense, ECM does not require the rejection of established mathematical principles or physical laws. Rather, it seeks to formulate and examine observed physical relationships through a phase–frequency framework while retaining the general scientific relations:

E = hf

f = 1/T

x° = 360° f Δt

These relations provide the mathematical basis for connecting energy, frequency, periodicity, phase advancement, and the corresponding temporal interval, while the physical interpretation of these relationships may be considered within the appropriate theoretical framework.

Best Regards,

Soumendra Nath Thakur

ORCID: 0000-0003-1871-7803

Independent Researcher | Tagore's Electronic Lab, India

From Antecedent State to Preceding Physical State: Establishing Mathematically Neutral Terminology in Extended Classical Mechanics

Soumendra Nath Thakur
August 01, 2026

A physical system that undergoes no state transition remains invariant with respect to its defining parameters. The occurrence of any measurable change establishes an ordered sequence of physical states, thereby introducing an identifiable initial state relative to that transition. Every physical transformation may therefore be represented as a mapping between an antecedent state and a subsequent state,

Sᵢ → Sᶠ

where Sᵢ denotes the antecedent state and Sᶠ the resulting state. Within this framework, the concept of an origin is not an arbitrary assumption but a logical consequence of physical change itself. A changing physical state cannot exist independently of an antecedent state from which the transformation proceeds.

The observable universe exhibits continuous transformation across all accessible scales, from microscopic interactions to cosmological evolution. Since its physical state is demonstrably non-invariant, the universe cannot be regarded as existing in an eternal state of physical stasis. Rather, its evolution is represented by a succession of state transitions,

S₀ → S₁ → S₂ → ··· → Sₙ

where each state is physically related to a preceding configuration. This sequence implies that every observable stage of cosmic evolution possesses an antecedent condition. Consequently, the existence of an origin for the observable universe follows as a logical implication of continuous physical transformation, rather than as an independent metaphysical assumption.

The existence of an antecedent condition does not imply complete observational accessibility. As in mathematics, where logical relations exist independently of their human discovery, it is a mathematically and logically unavoidable consequence that any finite observational framework provides only a partial description of physical reality. Human perception and measurement are necessarily finite; therefore, the complete physical state of the universe may include domains that remain beyond present observational or conceptual accessibility.

Within this perspective, phenomena presently identified as dark matter and dark energy may be interpreted as manifestations of physical states lying outside the directly perceptible domain. Extended Classical Mechanics (ECM) further proposes that, preceding the emergence of observable physical events, the universe existed in a pre-manifest phase whose characteristic scale was below the threshold of conventional physical observation. In such an eventless state, chronology possesses no operational meaning because no sequence of distinguishable physical events exists from which temporal intervals can be defined.

The transition from this primordial phase to an event-rich universe marks the onset of physical manifestation. Through successive phase-frequency transformations, the universe evolves from an unmanifested state toward progressively increasing levels of partial and complete manifestation, giving rise to the observable structures and physical processes that define the present cosmos. Within the ECM framework, the currently observable universe represents one stage of this continuous evolutionary sequence, progressing toward its ultimate manifestation limit while preserving the fundamental conservation of the underlying phase-frequency structure.

https://www.researchgate.net/post/From_Antecedent_State_to_Preceding_Physical_State_Establishing_Mathematically_Neutral_Terminology_in_Extended_Classical_mechanics_ECM

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Extended Classical Mechanics (ECM) Approach

The objective of ECM is not to declare victory over established physics, but to develop a mathematically consistent and physically coherent framework whose validity can be evaluated through its internal consistency, explanatory power, predictive capability, and agreement with observation. Where ECM reproduces established results, it demonstrates compatibility; where it offers alternative interpretations or additional insights, those proposals should be judged on their own scientific merits.

Let us consider this question: Could the concept of a black hole repelling matter have any real-world implications or applications in astronomy or physics?

Disclaimer: The following discussion of a reverse entropic transformation is presented solely as a conceptual exploration for the purpose of addressing the preceding question. It should not be interpreted as a formal or established postulate of Extended Classical Mechanics (ECM). Rather, it serves as a hypothetical extension illustrating how the ECM formalism might consistently describe gravitational collapse without invoking an infinite-density singularity. Any such interpretation remains subject to further theoretical development and independent validation.

With this perspective in mind, one possible ECM-based interpretation is that gravitational collapse need not culminate in an infinite-density singularity. Instead, a black hole may undergo a reverse entropic transformation governed by

fᴏʙꜱᴇʀᴠᴇᴅ − Δfꜱᴏᴜʀᴄᴇ = fꜱᴏᴜʀᴄᴇ → fᴘ − Δf₀ = f₀.

With this perspective in mind, one possible ECM-based interpretation is that gravitational collapse may be described differently from the conventional singularity model. Since ECM avoids the requirement of infinite density, it does not require the existence of a gravitational singularity. Consequently, as a hypothetical extension of the ECM formalism, a black hole may undergo a reverse entropic transformation governed by

fᴏʙꜱᴇʀᴠᴇᴅ − Δfꜱᴏᴜʀᴄᴇ = fꜱᴏᴜʀᴄᴇ → fᴘ − Δf₀ = f₀

where the latent source frequencies (fꜱᴏᴜʀᴄᴇ, f₀) correspond to latent potential energy,

fꜱᴏᴜʀᴄᴇ, f₀ ↔ −ΔPEᴇᴄᴍ.

Within ECM, the reverse entropic transformation represents the inverse of the universal entropic manifestation process. Rather than transforming latent potential energy into manifested matter, the manifested matter component progressively transforms into the kinetic Negative Apparent Mass (NAM) state and subsequently toward the latent phase state. The corresponding mass transformation may be expressed as

Mᴍ → Mᵃᵖᵖ (<0),

with the effective gravitational mass given by

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ) = Mɢ.

The transformation may be represented by

(Δfꜱᴏᴜʀᴄᴇ, Δf₀) ↔ Mᵃᵖᵖ (<0) = −ΔPEᴇᴄᴍ.

As the reverse entropic transformation progresses, the manifested matter component Mᴍ continuously decreases while the kinetic Negative Apparent Mass (NAM) contribution (−Mᵃᵖᵖ) correspondingly increases. Consequently, the effective gravitational mass Mᵉᶠᶠ (= Mɢ) continuously decreases and becomes negative once the apparent negative-mass contribution exceeds the remaining manifested matter component.

Within this interpretation, Mᴍ exhibits attractive gravitation, whereas the kinetic Negative Apparent Mass (NAM) represented by Mᵃᵖᵖ (<0) exhibits effective antigravitational behaviour. Accordingly, photons, dark energy, and other dynamically propagating physical entities associated with Negative Apparent Mass (NAM) are expected to exhibit effective repulsive gravitational behaviour. Likewise, a black hole that has progressed sufficiently through the reverse entropic transformation may transition from a predominantly attractive gravitational state toward an effective antigravitational state.

Therefore, ECM does not suggest that a black hole selectively repels particular kinds of matter. Rather, it proposes that as the reverse entropic transformation advances and the effective gravitational mass becomes negative, a partially or fully latent black hole may exhibit an overall antigravitational influence. If supported by future theoretical and observational studies, this interpretation could have significant implications for black-hole evolution, dark-energy dynamics, large-scale cosmic structure, and the ultimate thermodynamic evolution of the universe.