From physical principles to relativistic classical Hamiltonian and Lagrangian particle mechanics

Gabriele Carcassi

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arXiv · 1503.04469

From physical principles to relativistic classical Hamiltonian and Lagrangian particle mechanics

Gabriele Carcassi

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Abstract

We show that classical particle mechanics (Hamiltonian and Lagrangian consistent with relativistic electromagnetism) can be derived from three fundamental assumptions: infinite reducibility, deterministic and reversible evolution, and kinematic equivalence. The core idea is that deterministic and reversible systems preserve the cardinality of a set of states, which puts considerable constraints on the equations of motion. This perspective links different concepts from different branches of math and physics (e.g. cardinality of a set, cotangent bundle for phase space, Hamiltonian flow, locally Minkowskian space-time manifold), providing new insights. The derivation strives to use definitions and mathematical concepts compatible with future extensions to field theories and quantum mechanics.

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Gabriele Carcassi. 2015-03-15. From physical principles to relativistic classical Hamiltonian and Lagrangian particle mechanics. https://arxiv.org/abs/1503.04469

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