The Physical Meaning of the Principle of Least Action

The principle of least action is used in many areas of theoretical physics - in theoretical mechanics, in electrodynamics, in the general theory of relativity, in quantum mechanics. At the beginning of the twentieth century Max Planck discovered the quantum of action. However, so far the action and the principle of least action do not have a single physical meaning. The purpose of this paper is to interpret the principle of least action on the example of modeling the localization and movement of a free particle. The modelling used the idea of the manifestation of reality as a result of the imposition of systems. The particle motion in Minkowski space is modeled by the imposition of independent subsystems. Introduced a homogeneous space of possible states (or possible subsystems), where possible subsystems do not intersect (not superimposed), but are arranged sequentially relative to each other. It is shown that the motion of a free particle in Minkowski space can be considered as the propagation of a plane wave in the space of possible subsystems with a certain phase velocity. In this case, in the nonrelativistic approximation, the wave coincides with the de Broglie wave, where the phase velocity is equal to the velocity of a particle in Minkowski space. In the case of taking into account the finite velocity of propagation of the interaction, the relativistic effects are clearly manifested in the space of possible subsystems. The basic equations of relativistic dynamics are derived from the quantum representations of particle motion, on the basis of the proposed approach. An interpretation is given of the phase velocity of a particle, with which the negative value of the free particle Lagrangian is associated. The connection between the action for a free particle in relativistic dynamics and the action for a de Broglie wave is revealed. The possibility of generalizing the principle of least action in the space of possible subsystems, from which the Fermat principle and the Maupertuis principle follow, is considered. The proposed presentation does not contradict such currently popular fundamental principles as quantum entanglement and quantum nonlocality, but, on the contrary, suggests the existence of these phenomena.

нелокальность, возможные состояния, квантовая теория, волновая функция, запутанные состояния, фазовая скорость, волна де Бройля, релятивистская динамика, лагранжиан, принцип наименьшего действия

1. Полак Л. С. Вариационные принципы механики, их развитие и применение в физике. М: Либроком, 2010. - 600 с.

2. Терехович В. Э. Философские и научные проблемы принципа наименьшего действия / Исторические, философские, политические и юридические науки, культурология и искусствоведение. Вопросы теории и практики. - Тамбов: Грамота, 2013. - 1-1(27). - с. 179-183.

3. Steiner R. History and progress on accurate measurements of the Planck constant // Reports on Progress in Physics, 2013. - Vol.76. - P. 016101.

4. Aspect A., Grangier P. and Roger G. Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A new violation of Bell's inequalities // Phys. Rev. - Lett. 49, 91. - 1982.

5. Greenberger D. M., Horne M. A. and Zeilinger A. In Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, edited by M. Kafatos, Kluwer, Dordrecht. - 1989.

6. Zeilinger A. Quantum teleportation, onwards and upwards. // Nat. Phys. - 14. - 3. - 2018.

7. Richens J. G., Selby J. H., Al-Safi S. W. Entanglement is Necessary for Emergent Classicality in All Physical Theories. // Phys. Rev. - Lett. 119. - 080503. - 2017.

8. Musser G. Spooky Action at a Distance: The Phenomenon that Reimagines Space and Time-and what it Means for Black Holes, the Big Bang, and Theories of Everything. - Scientific American. - Farrar, Straus and Giroux. - New York. - 2015.

9. Яковлев Б. В. К обоснованию фундаментальных принципов квантовой механики и теории относительности (статья депонирована в ВИНИТИ № 27-B2017 от 03.03.2017).

10. Яковлев Б. В. Условие замкнутости системы // Вестник СВФУ. - 2018. - №5(67). - С. 65-71.

11. Yakovlev B. V., and Nikiforova L. V. Finiteness of propagation speed of interactions as condition of system closedness // AIP Conference Proceedings 2041. - 050010 (2018); doi: 10.1063/1.5079379.

12. Ландау Л. Д., Лифшиц Е. М. Теоретическая физика. - Т.6. - Гидродинамика. - М.: Физматлит, 2017. - 736 с.

13. Величко С. П., Герасимова Т. Ю., Иваний В. С., Мороз И. А. Методика построения релятивистской механики на основе принципа наименьшего действия в системе подготовки учителя физики. / ФӘН-НАУКА (Современная наука: актуальные проблемы теории и практики. Серия: Познание). - 6(45). - 2015. - С. 34-38.