Действующие и целевые причины в принципе наименьшего действия

Vladislav Terekhovich

Published Jan 1, 2012• 0 citations

Abstract

The problem dealt with is that of deterministic and teleological interpretation of least action principle. The author argues that ‘path integral method’ of quantum mechanics could be used as an ontological hypothesis concerning the essence of classical object motion. This makes it possible to replace actual and final causality by probabilistic one.

Related papers

Philosophical and Methodological Problems of the Principle of Least Action.

Vladislav Terekhovich

Twenty extremal principles of the natural sciences are reformulated to the general ontological scheme. The hypothesis is substantiated that the unique role of the principle of least action is based on its probabilistic interpretation. It is shown how most of the variational principles can be reduced to the principle of maximal probability, which is based on a realistic interpretation of Feynman’s path integral method.

Jan 1, 20131 citation

The Principle of Least Action as Interpreted by Nature and by the Observer

Michel Gondran, Alexandre Gondran

In this paper, we show that the difficulties of interpretation of the principle of least action concerning "final causes" or "efficient causes" are due to the existence of two different actions, the "Euler-Lagrange action" (or classical action) and the "Hamilton-Jacobi action". These two actions, which are not clearly differentiated in the texbooks, are solutions to the same Hamilton-Jacobi equation, but with very different initial conditions: smooth conditions for the Hamilton-Jacobi action, singular conditions for the Euler-Lagrange action. There are related by the Minplus Path Integral which is the analog in classical mechanics of the Feynmann Path Integral in quantum mechanics. Finally, we propose a clear-cut interpretation of the principle of least action: the Hamilton-Jacobi action does not use "final causes" and seems to be the action used by Nature; the Euler-Lagrange action uses "final causes" and is the action used by an observer to retrospectively determine the trajectory of the particle.

arXiv:1203.2736Mar 13, 20122 citations

Ontological Foundations of the Variational Principles and the Path Integral Formalism

Vladislav Terekhovich

In this paper, I consider the issue of how two mathematical models of modern physics, the variational principles and the quantum path integral formalism, relate to reality. I assume that the observed phenomena are consistent with the calculations because both of these models have some common ontological foundations. According to the hypothesis of the summation of coexisting alternative possibilities, at the quantum level, the system at once moves along all histories that possible in given boundary conditions. The actual history is a mere result of the summation of all these alternative possible histories. This resultant history differs from others with the minimal action and maximal probability. I observe this history as a macroscopic trajectory of the system.

arXiv:1909.10064Sep 22, 20190 citations

Semi-Classical Limit and Least Action Principle Revisited with (min,+) Path Integral and Action-Particle Duality

Abdelouahab Kenoufi, Michel Gondran, Alexandre Gondran

One shows that the Feynman’s Path Integral designed for quantum mechanics has an analogous in classical mechanics, the so-called (min, +) Path Integral. This former is build on (min, +)-algebra and (min, +)-analysis which permit to handle in a linear way non-linear problems occurring in mathematical physics. The Hamilton-Jacobi equations and their solutions within this mathematical framework, are introduced and yield to a new interpretation expressed in a duality between action field and particle.

Russian Journal of Mathematical PhysicsJan 1, 20202 citations

Quantum mechanics and path integrals

Efstratios Manousakis

Abstract This chapter discusses the Feymann path-integral approach to quantum mechanics. First, it derives a path integral expression for the evolution operator. Next, it shows that the classical equations of motion, that is, those obtained from the principle of least action, are obtained from this path integral formulation in the limit where the variation in the action of the problem at hand is small as compared to the Planck’s constant h. Last, it discusses how the WKB approximation is derived from the path integral formulation.

Nov 1, 2015221 citations

The Theory of Disappearance and Appearance

Mazen Khoder

It is known that quantum mechanics is one of the most successful theories in physics across the entire history of physics, nevertheless, many believe that its foundations are still not really understood like: wave-particle duality, interference, entanglement, quantum tunneling, uncertainty principle, vacuum catastrophe, wave collapse, relation between classical mechanics and quantum mechanics, classical limit, quantum chaos etc., and the continuous failures in the unify between relativity theory and quantum theory may be an indication about a problem in the foundations, this paper aims at discovering the first small step in the path of solving and understanding these quantum puzzles, in fact, the key to solving quantum puzzles is by understanding the reality of the motion and how it occurs. This paper proposes a model of motion with a new action principle like the principle of least action called alike action principle. Actually, we have been able to deduce the principles of quantum mechanics so that the oddity of the quantum becomes easier to understand and interpret, for example, this paper proposes a solution to vacuum catastrophe and gives us the origin of dark energy, and shows that the basic law of motion must be broader than both quantum mechanics and classical mechanics.

Jun 1, 20180 citations