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Force-Based Phase-Frequency Continuum and Axiomatic Lorentz Transformation Alternatives in Extended Classical Mechanics

Extended Classical Mechanics (ECM) formulates a force-based, phase-frequency continuum as an alternative mathematical framework for describing large-scale cosmic motion, galactic dynamics, and velocity-dependent phenomena without invoking metric spacetime curvature. The framework...

Force-Based Phase-Frequency Continuum and Axiomatic Lorentz Transformation Alternatives in Extended Classical Mechanics

Extended Classical Mechanics (ECM) formulates a force-based, phase-frequency continuum as an alternative mathematical framework for describing large-scale cosmic motion, galactic dynamics, and velocity-dependent phenomena without invoking metric spacetime curvature. The framework...

From Absolute Space to Angular Phase: An Extended Classical Mechanics (ECM) Reassessment of the Physics–Mathematics Relationship in Gravitational Theory and the Genesis of Manifested Reality

This monograph re-examines the epistemological relationship between physics and mathematics, tracing the historical development of gravitational theory from Newtonian mechanics through Einstein's general relativity, and evaluates the empirical standing of the spacetime concept. I...

From Absolute Space to Angular Phase: An Extended Classical Mechanics (ECM) Reassessment of the Physics–Mathematics Relationship in Gravitational Theory and the Genesis of Manifested Reality

This monograph re-examines the epistemological relationship between physics and mathematics, tracing the historical development of gravitational theory from Newtonian mechanics through Einstein's general relativity, and evaluates the empirical standing of the spacetime concept. I...

From Absolute Space to Angular Phase: An Extended Classical Mechanics (ECM) Reassessment of the Physics–Mathematics Relationship in Gravitational Theory and the Genesis of Manifested Reality

This monograph re-examines the epistemological relationship between physics and mathematics, tracing the historical development of gravitational theory from Newtonian mechanics through Einstein's general relativity, and evaluates the empirical standing of the spacetime concept. I...

Phase-State Primacy in Extended Classical Mechanics: A Formal Response to Geometric, Energetic, and Cosmological Objections

Extended Classical Mechanics (ECM) introduces a phase-state variable x° whose domain precedes the emergence of dimensional geometric structure. This paper provides a formal response to three classes of objection: (i) geometric objections that impose the conventional angular-phase...

Energetic Phase Measure x° and Its Relation to Frequency, Wavelength, Matter Mass, and Kinetic Energy in Extended Classical Mechanics

This work introduces x° as an energetic phase measure in Extended Classical Mechanics (ECM) and examines its dynamic correspondence with frequency variation, phase wavelength, matter-mass manifestation, and kinetic-energy transformation.

Dimensional Consistency of k₍ₓ°₎ = h(fᴘ₍ₓ°₎ / f₀₍ₓ°₎) in Extended Classical Mechanics

This work examines the dimensional consistency of the proposed ECM relation k₍ₓ°₎ = h(fᴘ₍ₓ°₎ / f₀₍ₓ°₎), establishing how the frequency ratio remains dimensionless while k₍ₓ°₎ retains the dimensions of Planck’s constant h across the dynamic phase-state domain.

Energetic Phase Measure x° and Its Relation to Frequency, Wavelength, Matter Mass, and Kinetic Energy in Extended Classical Mechanics

This work introduces x° as an energetic phase measure in Extended Classical Mechanics (ECM) and examines its dynamic correspondence with frequency variation, phase wavelength, matter-mass manifestation, and kinetic-energy transformation.

A Phase-Geometric Framework with Fixed Planck Length, Mathematical Subdivided Coordinates, and Cyclic Cosmic Evolution: Extended Classical Mechanics

Extended Classical Mechanics (ECM) presents a phase-, frequency-, energy-, and propagation-based framework for describing physical emergence from an initial zero-length potential-energy state. The formulation retains the Planck length ℓₚ = 1.616255 × 10⁻³⁵ m as a fixed physical r...

Propagation-State Transformation Matrix in Extended Classical Mechanics

Version 1.2 The propagation-state formalism recently introduced within the framework of Extended Classical Mechanics (ECM) provides an alternative physical interpretation of the relativistic Doppler effect by distinguishing the normalized propagation state from the observed propa...

Core Operational Relations of Extended Classical Mechanics (ECM)

Extended Classical Mechanics (ECM) formulates a unified operational framework in which time, frequency, energy, mass, and force are represented as physically connected manifestations of phase-dependent transformation rather than as independent quantities. The framework begins wit...