TY - JOUR

T1 - Hamilton, Hamiltonian Mechanics, and Causation

AU - Weaver, Christopher Gregory

N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature B.V.

PY - 2023

Y1 - 2023

N2 - I show how Sir William Rowan 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 are 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 contemporary 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. Various 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 the potential energies of systems are grounded in facts about forces. Thus, if one can tolerate the view that forces are causes of motion, 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.

AB - I show how Sir William Rowan 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 are 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 contemporary 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. Various 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 the potential energies of systems are grounded in facts about forces. Thus, if one can tolerate the view that forces are causes of motion, 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.

KW - Causation

KW - Force

KW - Hamilton

KW - Hamiltonian mechanics

KW - Potential energy

UR - http://www.scopus.com/inward/record.url?scp=85175794330&partnerID=8YFLogxK

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U2 - 10.1007/s10699-023-09923-y

DO - 10.1007/s10699-023-09923-y

M3 - Article

AN - SCOPUS:85175794330

SN - 1233-1821

JO - Foundations of Science

JF - Foundations of Science

ER -