Newtonian Kinetic Energy as a Limiting Case of Extended Classical Mechanics

Extended Classical Mechanics (ECM) by Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803
February 07, 2026

Abstract — This paper demonstrates that classical Newtonian kinetic energy emerges naturally as a low-energy limiting case of the ECM mass–energy manifestation law. Kinetic energy is shown to arise from partial displacement of ECM potential energy rather than being a primitive mechanical assumption.

ECM Kinetic Energy Formulation

Eₜₒₜₐₗ = PEᴇᴄᴍ + KEᴇᴄᴍ
KEᴇᴄᴍ = ΔMᴍ c²

Manifested matter mass ΔMᴍ originates from displaced ECM potential energy:

ΔMᴍ = ΔPEᴇᴄᴍ / c²

Low-Velocity Limiting Regime

For weak fields and velocities much smaller than the speed of light (v ≪ c), only partial mass manifestation occurs:

ΔMᴍ → m(v² / c²)

Substituting into the ECM kinetic formulation:

KEᴇᴄᴍ = ΔMᴍ c² → m v²

ECM energy is partitioned inherently and interactionally:

KEᴇᴄᴍ = ½m v² + ½m v²

which recovers classical kinetic energy:

KE = ½ m v²

Conclusion

Newtonian kinetic energy arises as the weak-manifestation limit of ECM’s mass–energy conversion law. Classical mechanics therefore represents a low-energy approximation of the more general ECM framework.

© 2026 Soumendra Nath Thakur — Extended Classical Mechanics (ECM). All rights reserved.