Natural space of the micro-object

A. Yu. Samarin

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2011), pp. 117-128.

Résumé

The immutability of classical dynamical laws for the microscopic object in the space which coordinate axes are the transition matrix elements of the corresponding coordinates is proved. It is stated that measurement is a micro-object localization process in the classical space when it interacts with the device. The description of the wave function reduction is obtained using the path integrals. The mechanism of the probability arising on measurement is offered, where the “hidden parameter” that is the cause of the measurement randomness of microscopic characteristics relates to the interaction process of classical instrument with micro-object. Both types of quantum mechanics processes — evolution and reduction of the wave functions — are described in a unified approach.

Détail

Mots-clés : transition matrix elements
Keywords: path integral, microscopic natural space, the principle of the minimal action, the wave function reduction, hidden parameter, non-locality of the measurement process.

Bibliographie

[1] von Neumann J., Mathematical Foundations of Quantum Mechanics, Princeton Landmarks in Mathematics and Physics, Princeton University Press, Princeton, New Jersy, 1996, 464 pp. ; fon Neiman I., Matematicheskie osnovy kvantovoi mekhaniki, Nauka, M., 1964, 368 pp. | MR | Zbl | MR

[2] Griffits R. B., Consistent quantum theory, Cambridge university press, Cambridge, 2002, 391 pp. | MR

[3] Hartle G. B., “Spacetime quantum mechanics and the quantum mechanics of spacetime”, Gravitation and Quantizations, Proceedings of the 1992 Les Houches Summer School (6 July – 1 Aug., 1992), eds. B. Julia, J. Zinn–Justin, North Holland, Amsterdam, 1995, 285–480, arXiv: gr-qc/9304006 | MR | Zbl

[4] Gell–Mann M., Hartle J. B., “Classical equations for quantum systems”, Phys. Rev. D., 47:8 (1993), 3345–3382 | DOI | MR

[5] Feynman R. P., Hibbs A. R., Quantum Mechanics and Path Integrals, McGraw-Hill Companies, New York, 1965, 365 pp. ; Feinman R., Khibs A., Kvantovaya mekhanika i integraly po traektoriyam, Mir, M., 1968, 382 pp. | Zbl

[6] Zinn–Justin J., Path Integrals in Quantum Mechanics, Oxford University Press, Oxford, 2004, 332 pp. ; Zinn–Zhyusten Zh., Kontinualnyi integral v kvantovoi mekhanike, Fizmatlit, M., 2006, 360 pp. | MR

[7] Samarin A. Yu., “Description of discrete spectrum states transition processes”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2(19) (2009), 226–230 | DOI

[8] Samarin A. Yu., “Wave equation of discrete spectrum states transition processes”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2010, no. 1(20), 188–196 | DOI

[9] Landau L. D. Lifshitz E. M., Quantum Mechanics (Non-Relativistic Theory), Course of Theoretical Physics, v. 3, Pergamon Press, New York, 1977, 689 pp.

[10] Kac M., Probability and Related Topics in Physical Sciences, Lectures in Applied Mathematics Series., 1.1, American Mathematical Society, 1957, 266 pp. ; Kats M., Veroyatnost i smezhnye voprosy v fizike, Mir, M., 1965, 407 pp. | MR | Zbl

[11] Kolmogorov A. N., Probability theory and mathematical statistics. Selected works, ed. Yu. V. Prokhorov, Nauka, Moscow, 1986, 535 pp. | MR

[12] Bell J. S., “On the Einstein Podolsky Rosen Paradox”, Physics, 1:3 (1964), 195–200

[13] Reid M. D., Drummond P. D., “Colloquium: The Einstein–Podolsky–Rosen paradox: From concepts to applications”, Rev. Mod. Phys., 81:4 (2009), 1727–1751 | DOI | MR | Zbl

[14] Aspect A., Grangier P., Roger G., “Experimental Realization of Einstein–Podolsky–Rosen–Bohm Gedankenexperiment: A New Violation of Bell's Inequalities”, Phys. Rev. Lett., 49:1 (1982), 91–94 | DOI | MR

[15] Aspect A., Dalibard J., Roger G., “Experimental Test of Bell's Inequalities Using Time-Varying Analyzers”, Phys. Rev. Lett., 49:25 (1982), 1804–1807 | DOI | MR