Can a Massive Particle Reach Light Speed at Finite Energy? A Hamiltonian Counterexample and Its Physical Limitations

This research investigates whether a massive particle can mathematically attain the speed of light with finite energy and momentum through an alternative Hamiltonian formulation. The proposed Lorentz–Leibniz model predicts a finite threshold at which the particle reaches a characteristic speed equal to the speed of light: Critical momentum: p = πmc/2 Total energy: E = 2mc² Critical velocity: v = c The study compares this alternative formulation with Einstein's special relativity, examining Hamiltonian dynamics, Newtonian limits, energy and momentum conservation, causality, constant-force motion, and the infinite-force limit. Connections to Lorentz-inspired mathematical transformations and persistent homology are also discussed. The results demonstrate the mathematical possibility of constructing a non-Lorentz-covariant Hamiltonian with finite-energy attainment of a limiting speed. However, the proposed model has not been experimentally validated and does not establish a replacement for Einstein's special relativity. Publication status: Preprint — not peer reviewed. Journal submission: European Journal of Physics, Manuscript ID: EJP-111479. Author: Mahir Sogut, Independent Researcher, Çankırı, Türkiye.