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Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
postmasterenator@gmail.com
Extended Classical Mechanics (ECM) Research & Development Framework
Date: December 18, 2025
Extended Classical Mechanics (ECM) proposes that the Planck scale represents a terminal boundary of physical accountability, beyond which conventional physical descriptors lose operational meaning. At this boundary, energy conservation remains the sole physically valid principle, expressed through frequency and phase. In this framework, frequency is identified as the primitive physical quantity, phase as the organizing mechanism, and time as an emergent ordering arising from phase evolution. The Planck interval emerges as a coherence threshold rather than a geometric or relativistic limit. ECM enforces energetic continuity across the physical–abstract boundary through a conserved frequency–energy equivalence, allowing the energetic state of the observable universe to be consistently related to the abstract energetic origin state. This formulation establishes a coherent basis for understanding the emergence of time, mass equivalence, kinetic and potential energy, and large-scale structure without invoking spacetime curvature or relativistic postulates.
Extended Classical Mechanics; Energy Conservation; Frequency; Phase; Planck Scale; Emergent Time; Foundational Physics
Within Extended Classical Mechanics, the Planck time marks a terminal boundary of physical accountability. Below this scale, conventional physical constructs—such as space, trajectory, force, inertial mass, and geometric structure—lose definability due to the absence of any stable measurement framework. No known physical laws remain operationally meaningful beyond this threshold, with the sole exception of the principle of energy conservation.
At this limit, energy itself remains physically meaningful and manifests exclusively through frequency and phase. Phase represents the smallest measurable manifestation of frequency, while frequency becomes the most primitive descriptor of physical reality. Time does not exist as a fundamental dimension; instead, it emerges only through ordered phase evolution between an initial reference phase and the Planck-scale phase boundary.
ECM identifies frequency as the primitive physical quantity, phase as the organizing principle, and time as the emergent ordering of phase evolution. The mapping from base frequency to phase accumulation and subsequently to time does not describe motion or geometry but expresses an energetic ordering process.
The Planck interval is therefore not an externally imposed unit of time but the smallest physically meaningful phase-ordering interval. Beyond this coherence threshold, ordered phase evolution—and thus physical time—cannot be sustained.
ECM enforces energetic continuity across the Planck boundary through a conserved proportionality between frequency and energy:
E = k f
Here, k is an ECM proportionality constant expressing frequency-equivalent energy in a purely classical conservation sense. The primordial frequency state defines an initial energetic condition, while the Planck-scale frequency defines a corresponding energetic state. These are not separate regimes but energetically equivalent representations of a single conserved quantity.
At the Planck boundary, energy undergoes a transition of representation rather than a discontinuity—from abstract frequency–phase structure to physically manifest kinetic energy, potential energy, and effective mass within the observable universe.
Although the sub-Planck domain lies beyond physical observability, ECM permits speculative mathematical exploration within this regime, provided such exploration remains strictly constrained by energy conservation and does not claim empirical validity.
Quantities such as abstract rates or characteristic “speeds” may be defined mathematically as expressions of phase or energy transition. These do not represent motion through space or propagation in time, since neither space nor time exists at this scale.
A fundamental ECM requirement is that energy conservation must retain consistent physical meaning across both the abstract origin state and the observable universe. The energy associated with the primordial frequency–phase structure must be energetically equivalent to the total kinetic and potential energy content of the observable universe.
Within ECM, changes in kinetic energy, potential energy, and mass equivalence are mutually convertible expressions of the same conserved energy. The kinetic energy associated with the Planck-scale coherence state functions as the energetic seed from which the universe’s total kinetic energy, potential energy, and associated negative apparent mass structure emerge.
This section explores the possibility that the Planck scale may arise from an intrinsic phase-coherence or stability condition rather than serving as an externally imposed boundary. The Planck interval is examined as a potential fixed point of energetic consistency, constrained solely by energy conservation.
Within ECM, the Planck time is reinterpreted as a terminal coherence threshold—the smallest interval over which ordered phase evolution can be physically sustained.
At progressively smaller scales, phase accumulation becomes increasingly sensitive to frequency deviation. The Planck interval corresponds to the minimal coherent expression of phase ordering.
A unique infinitesimal frequency deviation corresponding to the Planck interval may function as a coherence selector rather than a free parameter.
This stability condition arises purely from energetic and phase considerations, independent of spacetime geometry or relativistic assumptions.
If such a fixed-point condition exists, the Planck scale would emerge as a predicted attractor of coherence, elevating ECM from internal consistency to predictive fundamentality.
Extended Classical Mechanics establishes energy, frequency, and phase as the primitive substrate of physical reality. Time, mass equivalence, and large-scale structure emerge through phase ordering constrained by energy conservation. The Planck scale appears as a coherence attractor rather than a geometric boundary, with the identification of a formal fixed-point condition constituting the natural next step in ECM’s foundational development.
© 2025 Soumendra Nath Thakur. All rights reserved.
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