2020/11/16 by Christopher Gregory Weaver, Weaver, Christopher Gregory
Arts and Humanities · Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #History and Philosophy of Physics (physics.hist-ph) #Origins and Evolution of Life #Philosophy and History of Science #Physics Education (physics.ed-ph) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2011.07803
openalex publication_date 2020/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I show how Hamilton's philosophical commitments led him to a causal interpretation of classical mechanics. I argue that Hamilton's metaphysics of causation was injected into his dynamics by way of a causal interpretation of force. I then detail how forces remain indispensable to both Hamilton's formulation of classical mechanics and what we now call Hamiltonian mechanics (i.e., the modern formulation). On this point, my efforts primarily consist of showing that the orthodox interpretation of potential energy is the interpretation found in Hamilton's work. Hamilton called the potential energy function the force-function because he believed that it represents forces at work in the world. Multifarious non-historical arguments for this orthodox interpretation of potential energy are provided, and matters are concluded by showing that in classical Hamiltonian mechanics, facts about potential energies of systems are grounded in facts about forces. Thus, if one can tolerate the view that forces are causes of motions, then Hamilton provides one with a road map for transporting causation into one of the most mathematically sophisticated formulations of classical mechanics, viz., Hamiltonian mechanics.