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Philosophy of Sciences

2013 year, number 1

PROBABILISTIC AND GEOMETRIC LANGUAGES OF PHYSICS IN THE CONTEXT OF THE PRINCIPLE OF LEAST ACTION

V. E. Terekhovitch
Keywords: principle of least action, Hamilton's principle, Feynman’s path integrals, probability causality

Abstract

The paper discusses the possibility of unification of the geometric language of forces and fields, the geometrical language of four-dimensional space-time and the probabilistic language of quantum mechanics. The author shows that all the three languages are equivalent to one of the forms of the extreme variation principle – the principle of least action. He argues in favor of the capacity of Richard Feynman’s method of path integral for explaining the sense of the particular formulas of the principle of least action. For this purpose, we need to substitute the classical idea of an object moving along a unique path for the idea of its simultaneous motion along an infinite set of possible paths. Hence the author concludes that axioms of classical mechanics and relativistic one are special cases of Feynman’s formulation of quantum mechanics.