| Name | David J. Tannor |
|---|---|
| Affiliation/Institute | Weizmann Institute of Science |
| Title | Two Hundred Years after Hamilton: The Simple Axiom that Underlies Classical Mechanics |
| Abstract (text only) | In 1834-1835, Hamilton published two papers that revolutionized classical mechanics [1]. In these papers he introduced the Hamilton-Jacobi equation, Hamilton’s equations of motion and Hamilton’s principle of least action. These three reformulations of classical mechanics became the three forerunners of quantum mechanics. Yet none of these is what Hamilton was looking for -- he was looking for a function he called the principal function, S(q’,q’’,T), from which the entire trajectory history can be obtained just by differentiation [2-3]. Here we show that all three of Hamilton’s formulations can be derived just by assuming that the principal function is additive with no input of physics. It appears that analytical mechanics is simply a footnote to the most basic problem in the calculus of variations of finding the shortest path between two points. The simplicity of the formulation could provide new perspectives on some of the major themes in classical mechanics including symplectic geometry [4], periodic orbit theory [5] and Morse theory, as well as giving new perspectives on quantum mechanics [6]. Moreover, it could potentially provide a unified description of different areas of physics leading, for example, to insight into the transition from deterministic dynamics to statistical mechanics. |
