Hamilton, Hamiltonian Mechanics, and Causation

TL;DR

The paper explores how Hamilton's philosophical views on causation influenced his formulation of classical mechanics, emphasizing the role of forces and potential energy in establishing causal interpretations within Hamiltonian mechanics.

Contribution

It demonstrates that Hamilton's metaphysics of causation is embedded in Hamiltonian mechanics through the interpretation of forces and potential energy, providing a philosophical foundation for causation in physics.

Findings

Hamilton's causal interpretation is reflected in the force-function as potential energy.

Forces are indispensable in Hamiltonian mechanics and grounded in facts about potential energy.

Hamilton's view supports causation as causes of motion within a mathematical framework.

Abstract

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.