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Advances in High Energy Physics
Volume 2013, Article ID 872507, 7 pages
Research Article

Realistic Approach of the Relations of Uncertainty of Heisenberg

Academic Center for Optical Engineering and Photonics, Faculty of Applied Sciences, University POLITEHNICA of Bucharest, 060042 Bucharest, Romania

Received 10 October 2012; Accepted 24 December 2012

Academic Editor: Bogdan Mitrica

Copyright © 2013 Paul E. Sterian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Due to the requirements of the principle of causality in the theory of relativity, one cannot make a device for the simultaneous measuring of the canonical conjugate variables in the conjugate Fourier spaces. Instead of admitting that a particle’s position and its conjugate momentum cannot be accurately measured at the same time, we consider the only probabilities which can be determined when working at subatomic level to be valid. On the other hand, based on Schwinger's action principle and using the quadridimensional form of the unitary transformation generator function of the quantum operators in the paper, the general form of the evolution equation for these operators is established. In the nonrelativistic case one obtains the Heisenberg's type evolution equations which can be particularized to derive Heisenberg's uncertainty relations. The analysis of the uncertainty relations as implicit evolution equations allows us to put into evidence the intrinsic nature of the correlation expressed by these equations in straight relations with the measuring process. The independence of the quantisation postulate from the causal evolution postulate of quantum mechanics is also put into discussion.