Measurement Problem and Two-State Vector Formalism
Author(s)
Kunihisa Morita
ABSTRACT
In this paper, I show that an interpretation of quantum mechanics using two-state vector formalism proposed by Aharonov, Bergmann, and Lebowitz, can solve one of the measurement problems formulated by Maudlin. According to this interpretation, we can simultaneously insist that the wave function of a system is complete, that the wave function is determined by the Schrödinger equation, and that the measurement of a physical quantity always has determinate outcomes, although Maudlin in his formulation of the measurement problem states that these three claims are mutually inconsistent. Further, I show that my interpretation does not contradict the uncertainty relation and the no-go theorem.
In this paper, I show that an interpretation of quantum mechanics using two-state vector formalism proposed by Aharonov, Bergmann, and Lebowitz, can solve one of the measurement problems formulated by Maudlin. According to this interpretation, we can simultaneously insist that the wave function of a system is complete, that the wave function is determined by the Schrödinger equation, and that the measurement of a physical quantity always has determinate outcomes, although Maudlin in his formulation of the measurement problem states that these three claims are mutually inconsistent. Further, I show that my interpretation does not contradict the uncertainty relation and the no-go theorem.
Cite this paper
Morita, K. (2015) Measurement Problem and Two-State Vector Formalism. Journal of Modern Physics, 6, 1864-1867. doi: 10.4236/jmp.2015.613191.
Morita, K. (2015) Measurement Problem and Two-State Vector Formalism. Journal of Modern Physics, 6, 1864-1867. doi: 10.4236/jmp.2015.613191.
References
[1] Maudlin, T. (1995) Three Measurement Problems. Topoi, 14, 7-15.
http://dx.doi.org/10.1007/BF00763473 [2] Aharonov, Y., Bergmann, P.G. and Lebowitz, J.L. (1964) Time Symmetry in the Quantum Process of Measurement. Physical Review B, 134, 1410-1416.
http://dx.doi.org/10.1103/PhysRev.134.B1410 [3] haronov, Y. and Vaidman, L. (1990) Properties of a Quantum System during the Time Interval between Two Measurements. Physical Review A, 41, 11-20.
http://dx.doi.org/10.1103/PhysRevA.41.11 [4] Yokota, K., Yamamoto, T., Koashi, M. and Imoto, N. (2009) Direct Observation of Hardy’s Paradox by Joint Weak Measurement with an Entangled Photon Pair. New Journal of Physics, 11, Article ID: 033011.
http://dx.doi.org/10.1088/1367-2630/11/3/033011 [5] Hosoya, A. and Koga, M. (2011) Weak Values as Context Dependent Values of Observables and Born’s Rule. Journal of Physics A: Mathematical and Theoretical, 44, Article ID: 415303.
http://dx.doi.org/10.1088/1751-8113/44/41/415303 [6] Morita, K. (2015) Einstein Dilemma and Two-State Vector Formalism. Journal of Quantum Information Science, 5, 41-46.
http://dx.doi.org/10.4236/jqis.2015.52006 [7] Aharonov, Y., Popescu, S. and Tollaksen, J. (2010) A Time-Symmetric Formulation of Quantum Mechanics. Physics Today, 63, 27-32.
http://dx.doi.org/10.1063/1.3518209 [8] Kochen, S.B. and Specker, E.P. (1967) The Problem of Hidden Variables in Quantum Mechanics. Journal of Mathematics and Mechanics, 17, 59-87.
http://dx.doi.org/10.1512/iumj.1968.17.17004 [9] Mermin, N.D. (1993) Hidden Variables and the Two Theorems of John Bell. Reviews of Modern Physics, 65, 803-815.
http://dx.doi.org/10.1103/RevModPhys.65.803 [10] Tollaksen, J. (2007) Pre- and Post-Selection, Weak Values and Contextuality. Journal of Physics A: Mathematical and Theoretical, 40, 9033-9066.
http://dx.doi.org/10.1088/1751-8113/40/30/025
[1] Maudlin, T. (1995) Three Measurement Problems. Topoi, 14, 7-15.
http://dx.doi.org/10.1007/BF00763473 [2] Aharonov, Y., Bergmann, P.G. and Lebowitz, J.L. (1964) Time Symmetry in the Quantum Process of Measurement. Physical Review B, 134, 1410-1416.
http://dx.doi.org/10.1103/PhysRev.134.B1410 [3] haronov, Y. and Vaidman, L. (1990) Properties of a Quantum System during the Time Interval between Two Measurements. Physical Review A, 41, 11-20.
http://dx.doi.org/10.1103/PhysRevA.41.11 [4] Yokota, K., Yamamoto, T., Koashi, M. and Imoto, N. (2009) Direct Observation of Hardy’s Paradox by Joint Weak Measurement with an Entangled Photon Pair. New Journal of Physics, 11, Article ID: 033011.
http://dx.doi.org/10.1088/1367-2630/11/3/033011 [5] Hosoya, A. and Koga, M. (2011) Weak Values as Context Dependent Values of Observables and Born’s Rule. Journal of Physics A: Mathematical and Theoretical, 44, Article ID: 415303.
http://dx.doi.org/10.1088/1751-8113/44/41/415303 [6] Morita, K. (2015) Einstein Dilemma and Two-State Vector Formalism. Journal of Quantum Information Science, 5, 41-46.
http://dx.doi.org/10.4236/jqis.2015.52006 [7] Aharonov, Y., Popescu, S. and Tollaksen, J. (2010) A Time-Symmetric Formulation of Quantum Mechanics. Physics Today, 63, 27-32.
http://dx.doi.org/10.1063/1.3518209 [8] Kochen, S.B. and Specker, E.P. (1967) The Problem of Hidden Variables in Quantum Mechanics. Journal of Mathematics and Mechanics, 17, 59-87.
http://dx.doi.org/10.1512/iumj.1968.17.17004 [9] Mermin, N.D. (1993) Hidden Variables and the Two Theorems of John Bell. Reviews of Modern Physics, 65, 803-815.
http://dx.doi.org/10.1103/RevModPhys.65.803 [10] Tollaksen, J. (2007) Pre- and Post-Selection, Weak Values and Contextuality. Journal of Physics A: Mathematical and Theoretical, 40, 9033-9066.
http://dx.doi.org/10.1088/1751-8113/40/30/025