To the question on application of Zeno’s paradox for the studying of the nature of mechanical movement


  • Oleksandr Nikolenko


Nature of physical motion, Zeno's paradox, classical mechanics, quantum mechanics, wave properties of particles, wave-particle dualism.


The nature of the reasons of occurrence of wave-particle dualism at particles are under consideration. It is shown what to formulate to the classical mechanics as the consistent axiomatic theory it is impossible. The proof is based on Zeno's paradoxes that strictly follow from the classical definition of mechanical motion. Impossibility of continuous mechanical motion within the framework of the classical mechanics has been shown. Within the frame of the classical mechanics these paradoxes are unsolvable due to additivity of integrals of motion. The offered decision consists that the statement of Zeno’s paradox can be applied to only a part of the motion interval which represents additive motion, and to get over the remaining non-additive part of the interval requires the funds that go beyond classical mechanics. These tools are given by quantum mechanics. A conclusion has been drawn that continuous mechanical motion is possible only as a consequence of wave properties of material particles, and such a motion is the most pictorial manifestation of the quantum mechanical effects in the macrouniverse. The possession wave properties is inevitable necessity for maintenance of mobility of such particles and material bodies consisting of them. It is shown, that Zeno’s paradox contains exceptions: at certain speeds of particles it does not operate.


Аристотель, Физика, М.: Мысль, 1976.

А. М. Анисов, Апории Зенона и проблема движения // Труды научно-исследовательского семинара Логического центра Института философии РАН / РАН. Ин-т философии, Обществ. ин-т логики, когнитологии и развития личности. — М.: 2000. — Вып. 14 / Редкол.: А. С. Карпенко (отв. ред.) и др. — Стр. 139—153.

Дж. Уитроу, Естественная философия времени, М.: УРСС, 2003.

Д. Гильберт, П. Бернайс , Основания математики, М.: Наука, 1979.

Р. Курант, Г. Роббинс, Что такое математика, 3-е изд., М.: МЦНМО, 2001.

М. Клайн, Математика. Утрата определённости, М.: Мир, 1984.

Л. Д. Ландау, Е. М. Лифшиц, Квантовая механика, М.: Наука, 1972.

Ю. Ф. Вилесов, Вестник МГУ, сер. 7 Философия, 6, 20 (2002).

Л. А. Халфин, УФН 160(10), 185 (1990).

Saduarshan E. C. G., Misra B., J. Math. Phys. 18,756 (1977).

How to Cite

Nikolenko, O. (2012). To the question on application of Zeno’s paradox for the studying of the nature of mechanical movement. Physics of Consciousness and Life, Cosmology and Astrophysics, 12(1), 55–64. Retrieved from