The Definition of Universal Momentum Operator of Quantum Mechanics and the Essence of Micro-Particle’s Spin——To Reveal the Real Reason That the Bell Inequality Is Not Supported by Experiments

Affiliation(s)

nstitute of Innovative Physics in Fuzhou, Department of Physics, Fuzhou University, Fuzhou, China.

Institute of Innovative Physics in Fuzhou, Department of Physics, Fuzhou University, Fuzhou, China.

nstitute of Innovative Physics in Fuzhou, Department of Physics, Fuzhou University, Fuzhou, China.

Institute of Innovative Physics in Fuzhou, Department of Physics, Fuzhou University, Fuzhou, China.

ABSTRACT

The definition of momentum operator in quantum mechanics has some foundational problems and needs to be improved. For example, the results are different in general by using momentum operator and kinetic operator to calculate microparticle’s kinetic energy. In the curved coordinate systems, momentum operators can not be defined properly. When momentum operator is acted on non-eigen wave functions in coordinate space, the resulting non-eigen values are complex numbers in general. In this case, momentum operator is not the Hermitian operator again. The average values of momentum operator are complex numbers unless they are zero. The same problems exist for angle momentum operator. Universal momentum operator is proposed in this paper. Based on it, all problems above can be solved well. The logical foundation of quantum mechanics becomes more complete and the EPY momentum paradox can be eliminated thoroughly. By considering the fact that there exist a difference between the theoretical value and the real value of momentum, the concepts of auxiliary momentum and auxiliary angle momentum are introduced. The relation between auxiliary angle momentum and spin is deduced and the essence of micro-particle’s spin is revealed. In this way, the fact that spin gyro-magnetic ratio is two times of orbit gyro-magnetic ratio, as well as why the electrons of ground state without obit angle momentum do not fall into atomic nuclear can be explained well. The real reason that the Bell inequality is not supported by experiments is revealed, which has nothing to do with whether or not hidden variables exist, as well as whether or not locality is violated in microcosmic processes.

The definition of momentum operator in quantum mechanics has some foundational problems and needs to be improved. For example, the results are different in general by using momentum operator and kinetic operator to calculate microparticle’s kinetic energy. In the curved coordinate systems, momentum operators can not be defined properly. When momentum operator is acted on non-eigen wave functions in coordinate space, the resulting non-eigen values are complex numbers in general. In this case, momentum operator is not the Hermitian operator again. The average values of momentum operator are complex numbers unless they are zero. The same problems exist for angle momentum operator. Universal momentum operator is proposed in this paper. Based on it, all problems above can be solved well. The logical foundation of quantum mechanics becomes more complete and the EPY momentum paradox can be eliminated thoroughly. By considering the fact that there exist a difference between the theoretical value and the real value of momentum, the concepts of auxiliary momentum and auxiliary angle momentum are introduced. The relation between auxiliary angle momentum and spin is deduced and the essence of micro-particle’s spin is revealed. In this way, the fact that spin gyro-magnetic ratio is two times of orbit gyro-magnetic ratio, as well as why the electrons of ground state without obit angle momentum do not fall into atomic nuclear can be explained well. The real reason that the Bell inequality is not supported by experiments is revealed, which has nothing to do with whether or not hidden variables exist, as well as whether or not locality is violated in microcosmic processes.

Cite this paper

X. Mei and P. Yu, "The Definition of Universal Momentum Operator of Quantum Mechanics and the Essence of Micro-Particle’s Spin——To Reveal the Real Reason That the Bell Inequality Is Not Supported by Experiments,"*Journal of Modern Physics*, Vol. 3 No. 6, 2012, pp. 451-470. doi: 10.4236/jmp.2012.36062.

X. Mei and P. Yu, "The Definition of Universal Momentum Operator of Quantum Mechanics and the Essence of Micro-Particle’s Spin——To Reveal the Real Reason That the Bell Inequality Is Not Supported by Experiments,"

References

[1] A. Einstein, “Science Paper Presented to Max Born, on His Retirement from the Tait Chair of Natural Philosopby in the University of Edinburgh,” 1953.

[2] W. Pauli, “Pauli Lecture on Physics,” MIT Press, Cambridge, 1973.

[3] H. Yukawa, “Quantum Mechanics,” 2nd Edition, YanBo, Bookshop, Tokyo, 1978.

[4] X. L. Ge, “Quantization of Canonical Coordinates,” 2001.

[5] Y. B. Zhang, “Momentum Operator and Kinetic Operator in Curved Coordinates,” 1988.

[6] Z. Xu, “Discuss on Canonical Operators,” 1991.

[7] C. B. Liang, “Quantization of Classical Systems,” Journal of Beijing Normal University, Vol. l, 1994, p. 67.

[8] H. Guang, “Foundation of Quantum Mechanics,” 1996.

[9] J. M. Domingos and M. H. Caldeira, “Self-Adjiontness of Momentum Operators in Generalized Coordinates,” Foundation of Physics, Vol. 14, No. 2, 1984, pp. 147-154. doi:10.1007/BF00729971

[10] M. Vos and I. McCarthy, “Electron-Momentum Spectroscopy and the Measurement of Orbits,” American Journal of Physics, Vol. 65, No. 6, 1997, p. 544. doi:10.1119/1.18586

[11] Y. D. Zhang, “Quantum Mechnics,”, 2008.

[12] J. S. Bell, “On the Problem of Hidden Variables in Quantum Mechanics,” Reviews of Modern Physics, Vol. 38, No. 3, 1966, pp. 447-452.

[13] E. P. Wigner, “Survival and the Bomb; Methods of Civil Defense,” American Journal of Physics, Vol. 38, No. 11, 1970, p. 1367. doi:10.1119/1.1976129

[14] J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Physical Review Letters, Vol. 23, No. 15, 1969, pp. 880-884. doi:10.1103/PhysRevLett.23.880

[15] S. J. Freedman and J. F. Clauser, “Experimental Test of Local Hidden-Variable Theories,” Physical Review Letters, Vol. 28, No. 14, 1973, pp. 938-941. doi:10.1103/PhysRevLett.28.938

[16] Z. Y. Tao, “An Question on the Foundation of Quantum Mechanics,” Academic Journal of Photons, Vol. 26, 1997, p. 769.

[1] A. Einstein, “Science Paper Presented to Max Born, on His Retirement from the Tait Chair of Natural Philosopby in the University of Edinburgh,” 1953.

[2] W. Pauli, “Pauli Lecture on Physics,” MIT Press, Cambridge, 1973.

[3] H. Yukawa, “Quantum Mechanics,” 2nd Edition, YanBo, Bookshop, Tokyo, 1978.

[4] X. L. Ge, “Quantization of Canonical Coordinates,” 2001.

[5] Y. B. Zhang, “Momentum Operator and Kinetic Operator in Curved Coordinates,” 1988.

[6] Z. Xu, “Discuss on Canonical Operators,” 1991.

[7] C. B. Liang, “Quantization of Classical Systems,” Journal of Beijing Normal University, Vol. l, 1994, p. 67.

[8] H. Guang, “Foundation of Quantum Mechanics,” 1996.

[9] J. M. Domingos and M. H. Caldeira, “Self-Adjiontness of Momentum Operators in Generalized Coordinates,” Foundation of Physics, Vol. 14, No. 2, 1984, pp. 147-154. doi:10.1007/BF00729971

[10] M. Vos and I. McCarthy, “Electron-Momentum Spectroscopy and the Measurement of Orbits,” American Journal of Physics, Vol. 65, No. 6, 1997, p. 544. doi:10.1119/1.18586

[11] Y. D. Zhang, “Quantum Mechnics,”, 2008.

[12] J. S. Bell, “On the Problem of Hidden Variables in Quantum Mechanics,” Reviews of Modern Physics, Vol. 38, No. 3, 1966, pp. 447-452.

[13] E. P. Wigner, “Survival and the Bomb; Methods of Civil Defense,” American Journal of Physics, Vol. 38, No. 11, 1970, p. 1367. doi:10.1119/1.1976129

[14] J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Physical Review Letters, Vol. 23, No. 15, 1969, pp. 880-884. doi:10.1103/PhysRevLett.23.880

[15] S. J. Freedman and J. F. Clauser, “Experimental Test of Local Hidden-Variable Theories,” Physical Review Letters, Vol. 28, No. 14, 1973, pp. 938-941. doi:10.1103/PhysRevLett.28.938

[16] Z. Y. Tao, “An Question on the Foundation of Quantum Mechanics,” Academic Journal of Photons, Vol. 26, 1997, p. 769.