Best Possible Worlds and Random Walks: The Principle of Least Action as a Thought Experiment

Michael Stöltzner (South Carolina) gives a talk at the Irvine-Munich Workshop on the Foundations of Classical and Quantum Field Theories (14 December, 2014) titled "Best Possible Worlds and Random Walks: The Principle of Least Action as a Thought Experiment". Abstract: Over the centuries, no other principle of classical physics has to a larger extent nourished exalted hopes of a universal theory, has constantly been plagued by mathematical counterexamples, and has ignited metaphysical controversies than has the principle of least action (PLA). The aim of this paper is first to survey a series of modern approaches, among them the structural realist readings of Planck and Hilbert, a neo-Kantian relativized a priori principle, and more recent discussions about modality within the context of analytic metaphysics. But these considerations seem outrun by the broad applicability of the PLA beyond classical physics. In the case of Feynman’s path integral, the PLA does no longer amount to the distinction of the actual dynamics among the possible ones, but to the definition of a stochastic process to which all possibilities contribute with a certain probability. To reach a unified philosophical picture of all the various applications of the PLA and its kin, I suggest to consider them as a thought experiment about the applicability of mathematics to a physical problems.