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