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Classical mechanics employs energy as a bookkeeping construct, multiplying mass by specific mechanical energy to track motion. However, this approach introduces a structural inconsistency: mass is treated as a real stored capacity, while energy-per-mass remains a non-substantial abstraction. Extended Classical Mechanics (ECM) resolves this inconsistency by treating kinetic energy as a physically manifested portion of stored mass-existence, establishing a consistent mass-energy partition framework applicable to motion and gravitational potentials.
Newton's second law provides the basic relationship between force, mass, and acceleration:
F = ma
For a constant force and non-zero mass:
a ∝ m⁻¹
Thus, as mass increases, acceleration decreases, indicating that mass functions as a stored resistance to motion.
Classical mechanics defines potential and kinetic energy as:
PE = mgh , KE = ½mv²
Total mechanical energy is expressed as:
E = m(gh + ½v²)
Here, (gh + ½v²) is a bookkeeping quantity, a numerical abstraction per unit mass.
Yet, classical theory simultaneously assumes PE ≥ KE, meaning only part of stored capacity manifests as motion.
True bookkeeping requires symmetric cancellation:
(gh + ½v²)/(gh + ½v²) = 1
However, the ratio m/(gh + ½v²) has incompatible units and lacks physical meaning, revealing a structural inconsistency.
Mass is treated as a real stored capacity, while energy-per-mass is a non-substantial abstraction.
Conservation of energy becomes numerical rather than physical.
m⁻¹ → Δm when a > 0, with m ≥ Δm
Kinetic energy is thus interpreted as a physically manifested mass-equivalent portion, ensuring that stored capacity and motion are connected, not merely multiplied numerically.
ECM formalizes this partition as:
(PEᴇᴄᴍ − ΔPEᴇᴄᴍ) + ΔKEᴇᴄᴍ, with ΔKEᴇᴄᴍ = −ΔPEᴇᴄᴍ
Translating to mass-existence terms:
(Mᴍ − ΔMᴍ) + ΔMᴍ when aᵉᶠᶠ > 0
This yields a dynamic system of:
Mᵉᶠᶠ + ΔMᴍ
representing motion or gravitational potential difference, where mass-energy transfer is physically realized rather than treated abstractly.
Classical mechanics, while effective at predicting motion, treats energy as a numerical bookkeeping tool rather than a physical substance. ECM restores physical meaning by partitioning stored mass-existence into manifested kinetic energy, ensuring consistent bookkeeping, dynamical response, and gravitational interpretation. This principle-driven approach bridges classical foundations with physically grounded mass-energy dynamics.
[References to be included here — links or DOIs]