Frequency and Energy in Extended Classical Mechanics (ECM):

Frequency and Energy in Extended Classical Mechanics (ECM):

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

Email: postmasterenator@gmail.com

Date: July 21, 2025

In Extended Classical Mechanics (ECM), the concepts of frequency and energy are reinterpreted with frequency (f) taking precedence as the most fundamental descriptor of a physical state. This framework positions frequency as more intrinsic to a system's dynamical evolution, independent of external reference frames, and dimensionally foundational for constructing observable quantities.

Frequency as the Primary Descriptor of Oscillation

In ECM, the argument for frequency's primacy is robust:

Synonymous with Vibration: Frequency isn't just a measure of vibration; it's considered synonymous with it. To talk about something vibrating or oscillating is, by definition, to imply a recurring event, and frequency quantifies that recurrence.

Mathematical Representation: ECM posits that frequency is the "only valid mathematical representation" of repetitive motion. Without a defined frequency, the concept of a regular, repeating vibration or oscillation becomes ill-defined. Consider a simple pendulum: its swing is described by its frequency (or period), not just its displacement.

Definitional Precedence: The idea is that vibration cannot be defined without frequency. This establishes frequency as the primary descriptor for any oscillatory system. It's the intrinsic characteristic that defines the very essence of its repetitive movement.

This perspective elevates frequency from being merely a derived quantity (like energy in the E = hf relation) to being the foundational property from which other related concepts emerge.

Reinterpreting the Planck Relation

The classical Planck relation, E = hf, is fundamentally reinterpreted in ECM. Here's how:

Energy as an Emergent Quantity: Unlike traditional physics where energy is a primary physical quantity, ECM views energy as an emergent concept. It's considered a secondary representation derived from a system's intrinsic frequency of phase transition or oscillation.

Conversion Constant: Instead of Planck's constant (h), ECM introduces its own conversion constant, for example, k = 5.558 × 10^−34 Js, which scales the system's intrinsic frequency to yield energy. This suggests that energy is a consequence of frequency, rather than frequency being a characteristic of energy.

Primacy of Frequency

ECM emphasizes the primacy of frequency over both energy and time (Δt) for several reasons:

Inherent to Dynamical State: Frequency is considered inherent to a system's dynamical state. It directly characterizes the ongoing evolution of a system without requiring an external timekeeper. This contrasts with energy, which depends on factors like system configuration (mass, motion, potential), and time, which is seen as relational and observer-dependent.

Fundamental for Oscillation: Frequency is deemed synonymous with vibration or oscillation and is presented as the only valid mathematical representation of such repetitive motion. It is argued that vibration cannot be defined without frequency, thus establishing frequency as the primary descriptor for oscillatory systems.

Cosmological Implications: In ECM cosmology, phenomena like redshift and energetic shifts are framed in terms of Δf (change in frequency) rather than time-based expansion. This perspective suggests that apparent energetic imbalances (ΔE) or mass variations (ΔM) over a duration (Δt) are governed by the fundamental phase-frequency evolution, not by the passage of time itself.

In essence, ECM proposes a shift from an energy-centric view to one where frequency is the foundational element driving physical processes and defining the nature of reality.