Fundamental Role of Frequency in Physical Description: A Dimensional and Conceptual Justification

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

Date: July 20, 2025

Scientific Statement:

In Extended Classical Mechanics (ECM), frequency is posited as the most fundamental descriptor of physical state, more primary than both energy (E) and time (Δt), based on its direct association with intrinsic dynamical evolution, independence from external reference systems, and dimensional precedence in the construction of observable quantities.

Description:

In the classical Planck relation E = hf, energy appears as the product of a constant h and frequency f, suggesting an equivalence. However, ECM reinterprets this relation: energy is not a primary physical quantity, but rather an emergent one - a secondary representation of the system's intrinsic frequency of phase transition or oscillation, scaled by a conversion constant (e.g., ECMs k = 5.558 x 10⁻34 Js).

Unlike energy, which depends on system configuration (mass, motion, potential), and time Δt, which is relational and observer-dependent, frequency is inherent to the systems dynamical state. Whether referring to the oscillation of a field, the cycling of a phase, or the emission profile of a particle, frequency directly characterizes the ongoing evolution of the system without requiring an external timekeeper.

This primacy is reinforced by the role of frequency in ECM cosmology, where redshift and energetic shifts are framed in terms of Δf rather than time-based expansion. The apparent energetic imbalance ΔE or mass variation ΔM over a duration Δt is governed by the fundamental phase-frequency evolution, not by the passage of time itself.

Footnote: Frequency as Fundamental

Frequency is more fundamental than energy. It is synonymous with vibration or oscillation, since frequency is the only valid way to mathematically represent such repetitive motion. Vibration cannot be defined without frequency; hence, frequency precedes energy as the primary descriptor of oscillatory systems.

Dimensional Analysis:

Quantity	Symbol	Dimensional Form
Frequency	f	[T⁻1]
Time	Δt	[T]
Energy	E	[ML2T⁻2]
Planck constant or ECM constant	h or k	[ML 2 T⁻1]

From the relation E = hf ⇒ [E] = [h][f]
Substituting dimensions: [ML2T⁻2] = [ML2T⁻1] x [T⁻1]

This confirms frequency is the more elementary term: both energy and Planck's constant depend dimensionally on it. Furthermore, frequency derives solely from inverse time, while energy couples mass, length, and squared inverse time.

Importantly, frequency does not depend on energy, but energy cannot be defined without frequency, if one accepts E = hf as fundamental. Similarly, Δt is just the inverse of frequency, and thus frequency subsumes the role of time as well:

f = 1 / Δt      ⇒      Δt = 1 / f

Therefore, both E and Δt are derived quantities, contingent upon f.

External Validation of Frequency s Primacy in Physical Definition

The ECM position-that frequency is more fundamental than both energy and time-finds clear support in both experimental standards and foundational quantum theory.

1. Time Defined via Frequency in SI Units
   The International System of Units defines the second via the fixed frequency of radiation from cesium-133 atoms:
   

   The second is defined by taking the fixed numerical value of the caesium frequency ∆ν(Cs) to be 9,192,631,770 when expressed in the unit Hz (s⁻¹). - NIST

   This makes time a derived quantity from frequency, not vice versa.
2. Quantum Energy as Frequency of Phase Evolution
   In quantum mechanics, energy is expressed through phase evolution:
   ψ(t) ∝ e−iEt/ħ = e−2πift
   Energy (E) is interpreted as the product of frequency (f) and Planck's constant. This supports the ECM position that frequency governs state evolution.
3. Dimensional Coherence Reinforced
   From E = hf:
   [E] = [h][f] = [ML2T⁻1] x [T⁻1] = [ML2T⁻2]
   Again showing energy is a frequency-scaled quantity.
4. Experimental Clocks Rely on Frequency
   All modern atomic clocks define time intervals by counting cycles of atomic transitions-i.e., frequency. This operational priority supports the ECM claim that time Δt is secondary to frequency.
5. Uncertainty Principle Prioritizes Frequency's Accuracy
   In the energy-time uncertainty relation, a precise energy value requires a long-duration observation of a stable frequency. Thus, frequency accuracy is logically prior to energy definition.

Conclusion:
These empirical and theoretical pillars collectively reinforce the ECM stance:

Frequency is not merely a useful parameter but the ontological basis of time, energy, and mass relations.