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A Non-Simple and Not Completed History of Quantum Mechanics and Really Long History of Resolving the Problem of Time as a Quantum Observable

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It shortly described a far from being completed history of quantum mechanics—quantum theory of measurements. Furthermore, there was a relatively recently finished chapter of quantum mechanics which for a long time had not been resolved. This chapter is dedicated to time as a quantum observable, canonically conjugated to energy. And the mathematical reasons for its principal resolving are explained.

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Olkhovsky, V. (2014) A Non-Simple and Not Completed History of Quantum Mechanics and Really Long History of Resolving the Problem of Time as a Quantum Observable.

*Open Access Library Journal*,**1**, 1-15. doi: 10.4236/oalib.1100887.

[1] |
Ginzburg V.L. (1999) What Problems of Physics and Astrophysics Seem Now to Be Especially Important and Interesting (Thirty Years Later, Already on the Verge of XXI Century)? Physics-Uspekhi, 42, 353-373.
http://dx.doi.org/10.1070/PU1999v042n04ABEH000562 |

[2] | Einstein А., Podolsky, В. and Rosen, Т. (1935) Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47, 777-780. |

[3] |
Olkhovsky, V.S., Recami, E. and Jakiel, J. (2004) Unified Time Analysis of Photon and Particle Tunneling. Physics Reports, 398, 133-178. http://dx.doi.org/10.1016/j.physrep.2004.06.001 |

[4] |
Olkhovsky, V.S. and Recami, E. (2007) Time as a Quantum Observable. International Journal of Modern Physics A, 22, 5063-5087. http://dx.doi.org/10.1142/S0217751X0703724X |

[5] |
Olkhovsky, V.S. (2009) Time as a Quantum Observable, Canonically Conjugated to Energy, and Foundations of Self- Consistent Time Analysis of Quantum Processes. Advances in Mathematical Physics. 2009, 83 p.
http://dx.doi.org/10.1155/2009/859710 |

[6] | Bohm, D. (1952) A Suggested Interpretation of the Quantum Theory in Terms of Hidden Variables. Physical Review, 85, 66-179. |

[7] |
Pais, A. (1979) Einstein and the Quantum Theory. Reviews of Modern Physics, 51, 863-914.
http://dx.doi.org/10.1103/RevModPhys.51.863 |

[8] |
Popper, K. (1982) A Critical Note on the Greatest Days of Quantum Theory. Foundations of Physics, 12, 971-976.
http://dx.doi.org/10.1007/BF01889270 |

[9] |
Holland, P.R. (1993) The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511622687 |

[10] |
Paty, M. (1995) The Nature of Einstein’s Objections to the Copenhagen Interpretation of Quantum Mechanics. Foundations of Physics, 25, 183-204. http://dx.doi.org/10.1007/BF02054665 |

[11] |
Everett, H. (1957) “Relative State” Formulation of Quantum Mechanics. Review of Modern Physics, 29, 454-462.
http://dx.doi.org/10.1103/RevModPhys.29.454 |

[12] |
DeWitt, B.S.M. (1970) Quantum Mechanics and Reality. Physics Today, 23, 30-35.
http://dx.doi.org/10.1063/1.3022331 |

[13] | Everett, H. (1973) The Theory of the Universal Wave Function. In: DeWitt, B. and Graham, N., Eds., The Many- Worlds Interpretation of Quantum Mechanics, Princeton University Press, Princeton. |

[14] | Menskii, M.B. (2005) Concept of Consciousness in the Context of Quantum Mechanics. Physics-Uspekhi, 175, 413- 435. |

[15] | Zeh, H.D. (1970) On the Interpretation of Measurement in Quantum Theory. Foundations of Physics, 1, 69-76. |

[16] | Janik, J.A. (1998) Nauka, Religia, Dzieje. IX Seminarium w Castel Andolfo, 5-7 sierpnia 1997, Wydawn. Uniwers. Jagiell., Krako`w, 15-22. |

[17] | Polkinghorne, J. (1991) Reason and Reality: The Relationship between Science and Theology. Trinity Press Internatio- nal, Philadelphia. |

[18] | Pauli, W. (1926) Handbuch der Physik. Vol. 5, by Fluegge, S., Ed., Berlin , 60. |

[19] | Olkhovsky, V.S. (1984) Investrigation of Nuclear Reactions and Decays by Analysis of Their Duration. Soviet Journal of Nuclear Physics, 15, 130-148. |

[20] | Olkhovsky, V.S. (2011) On Time as a Quantum Observable Canonically Conjugate to Energy. Physics-Uspekhi, 181, 829-835. |

[21] | Olkhovsky, V.S. (2012) Time as a Quantum Observable Canonically Conjugate to Energy. Time Analysis of Quantum Processes of Tunneling and Collisions (Nuclear Reactions), LAP LAMBERT Academic Publishing, Saarbrücken, 177 p. |

[22] | Olkhovsky, V.S. and Recami, E. (1968) Space-time Shifts and Cross Sections in Collisions between Relativistic Wave Packets. Nuovo Cim., A53, 610-615. |

[23] | Naimark, M.A. (1940) Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 4, 277. |

[24] | Carleman, T. (1923) Sur les e’quations i’ntegrales a’ noyau re’el et syme’trque. Uppsala. |

[25] | Akhiezer, N.I. and Glazman, I.M. (1981) The Theory of Linear Operators in Hilbert Space. Pitman, Boston. |

[26] | von Neumann, J. (1932) Mathematischen Grundlagen del Quantum Mechanik. Hizzel, Leipzig. |

[27] | Stone, M.H. (1930) Linear Transformations in Hilbert Space: III. Operational Methods and Group Theory. Proceedings of the National Academy of Sciences of the United States of America, 16, 172-175. |

[28] | Haar, D. (1971) Elements of Hamiltonian Mechanics. Oxford. |

[29] |
Judge, D. and Levis, J.L. (1963) On the Commutator ZLZ, φ]. Physics Letters, 5, 190.
http://dx.doi.org/10.1016/S0375-9601(63)96306-0 |

[30] |
Carruthers, P. and Nieto, M.M. (1968) Phase and Angle Variables in Quantum Mechanics. Review of Modern Physics, 40, 411. http://dx.doi.org/10.1103/RevModPhys.40.411 |

[31] | Davydov, A.S. (1976, 1982) Quantum Mechanics. Pergamon, Oxford. |

[32] |
Olkhovsky, V.S., Maydanyuk, S.P. and Recami, E. (2010) Non-Self-Adjoint Operators as Observables in Quantum Theory and Nuclear Physics. Physics of Particles and Nuclei, 41, 508-530.
http://dx.doi.org/10.1134/S1063779610040027 |

[33] | Schweber, S.S. (1961) An Introduction to Relativistic Quantum Field Theory. Row, Peterson and Co., New York. |

[34] | Hоlevo А.S. (1982) Probabilistic and Statistical Aspects of Quantum Theory (Amsterdam). |

[35] | Rosenbaum, D.M. (1969) Super Hilbert Space and the Quantum-Mechanical Time Operators. Journal of Mathematical Physics, 10, 1127. |

[36] | Fujiwara, I. (1979) Well-Defined Time Operators in Quantum Mechanics. Progress of Theoretical Physics, 62, 1179. |

[37] |
Goto, T., et al. (1980) The Time as an Observable in Quantum Mechanics. Progress of Theoretical Physics, 64, 1.
http://dx.doi.org/10.1143/PTP.64.1 |

[38] | Olkhovsky, V.S. and Romanyuk, M.V. (2009) Particle Tunneling and Scattering in a Three-Dimensional Potential with a Hard Core and an External Potential Barrier. Nuclear Physics and Atomic Energy, 10, 273-281. |

[39] | Olkhovsky, V.S. and Romanyuk, M.V. (2011) On Two-Dimensional Above-Barrier Penetration and Sub-Barrier Tu- nneling for Non-Relativistic Particles and Photons. Journal of Modern Physics, 2, 1166-1171. |

[40] |
Olkhovsky, V.S., Dolinska, M.E. and Omelchenko, S.A. (2006) The Possibility of Time Resonance (Explosion) Phenomena in High-Energy Nuclear Reactions. Central European Journal of Physics, 4, 223-240.
http://dx.doi.org/10.2478/s11534-006-0008-z |

[41] |
Olkhovsky, V.S., Dolinska, M.E. and Omelchenko, S.A. (2011) On New Experimental Data Manifesting the Time Re- sonances (or Explosions). Central European Journal of Physics, 9, 1131-1133.
http://dx.doi.org/10.2478/s11534-011-0009-4 |

[42] | Olkhovsky, V.S. and Omelchenko, S.A. (2011) On the Space-Time Description of Interference Phenomena in Nuclear Reactions with Three Particles in the Final Channel. The Open Particle and Nuclear Physics Journal, 4, 435-438. |

[43] | Olkhovsky, V.S. (2011) On the Time Analysis of Nuclear Reactions. Fundamental Journal of Modern Physics, 1, 63-132. |

[44] |
Abolhasani, M. and Golshani, M. (2000) Tunneling Times in the Copenhagen Interpretation of Quantum Mechanics. Physical Review A, 62, Article ID: 012106. http://dx.doi.org/10.1103/PhysRevA.62.012106 |

[45] |
Cardone, F., Maydanyuk, S.P., Mignani, R. and Olkhovsky, V.S. (2006) Multiple Internal Reflections during Particle and Photon Tunneling. Foundations of Physics Letters, 19, 441-452. http://dx.doi.org/10.1007/s10702-006-0903-y |

[46] | Enders, A. and Nimtz, G. (1992) On Superluminal Barrier Traversal. Journal de Physique I, 2, 1693-1708. |

[47] | Enders, A. and Nimtz, G. (1993) Photonic Tunneling Times. Journal de Physique I, 3, 1089-1098. |

[48] | Enders, A. and Nimtz, G. (1993) Propagation of an Electromagnetic Pulse through a Waveguide with a Barrier. Physical Review, B47, 19605-19618. |

[49] | Enders, A. and Nimtz, G. (1993) Evanescent-Mode Propagation and Quantum Tunneling. Physical Review, E48, 632-643. |

[50] | Nimtz, G. (1997) Tunneling and Its Applications. World Science, Singapore City, 223-237. |

[51] |
Steinberg, A.M., Kwiat, P.G. and Chiao, R.Y. (1993) Measurement of the Single-Photon Tunneling Time. Physical Re- view Letters, 71, 708-711. http://dx.doi.org/10.1103/PhysRevLett.71.708 |

[52] | Chiao, R.Y. and Steinberg, A.M. (1997) Progress in Optics. Vol. 37, Elsevier Science, Amsterdam, 346-405. |

[53] |
Longhi, S., Laporta, P., Belmonte, M. and Recami, E. (2002) Measurement of Superluminal Optical Tunneling Times in Double-Barrier Photonic Band Gaps. Physical Review E, 65, Article ID: 046610.
http://dx.doi.org/10.1103/PhysRevE.65.046610 |

[54] |
Olkhovsky, V.S., Petrillo, V. and Zaichenko, A.K. (2004) Decrease of the Tunneling Time and Violation of the Hartman Effect for Large Barriers. Physical Review A, 70, Article ID: 034103.
http://dx.doi.org/10.1103/PhysRevA.70.034103 |

[55] |
Chew, H., Wang, D.S. and Kerker, M. (1979) Elastic Scattering of Evanescent Electromagnetic Waves. Applied Optics, 18, 2679-2677. http://dx.doi.org/10.1364/AO.18.002679 |

[56] |
Chandiramani, K.L.J. (1974) Diffraction of Evanescent Waves, with Applications to Aerodynamically Scattered Sound and Radiation from Unbaffled Plates. Journal of the Acoustical Society of America, 55, 19-25.
http://dx.doi.org/10.1121/1.1919471 |

[57] | Eremin, N.V., Omelchenko, S.A., Olkhovsky, V.S., et al. (1994) Temporal Description of Interference Phenomena in Nuclear Reactions with Two-Particle Channels. Modern Physics Letters, 9, 22849-2856. |

[58] | Olkhovsky, V.S., Dolinska, M.E. and Omelchenko, S.A. (2011) On Scattering Cross Sections and Durations Near an Isolated Compound-Resonance, Distorted by the Non-Resonant Background, in the Center-of-Mass and Laboratory Systems. Applied Physics Letters, 99, Article ID: 244103. |

[59] | Olkhovsky, V.S., Doroshko, N.L. and Lokotko, T.I. (2013) On the Cross Section and Duration of the Neutron-Nucleus Scattering with Two Overlapped Resonances in the Center-of-Mass System and Laboratory System. Proceedings of the 4th International Conference on Current Problems in Nuclear Physics and Atomic Energy (NPAE-2012), Kyiv, 3-7 September 2012, 192-197. |

[60] | Olkhovsky, V.S., Dolinska, M.E. and Omelchenko, S.A. (2013) On the Cross Section and Duration of the Neutron-Nucleus Scattering with a Resonance, Distorted by a Non-Resonant Background, in the Center-of-Mass System and Laboratory System. Proceedings of the 4th International Conference on Current Problems in Nuclear Physics and Atomic Energy (NPAE-2012), Kyiv, 3-7 September 2012, 198-201. |

[61] | Olkhovsky V.S., Dolinska M.E. and Omelchenko S.A. (2006) The Possibility of Time Resonance (Explosion) Phenomena in High-Energy Nuclear Reactions. Central European Journal of Physics, 4, 1-18. |

[62] | Olkhovsky, V.S. and Omelchenko, S.A. (2011) On the Space-Time Description of Interference Phenomena in Nuclear Reactions with Three Particles in the Final Channel. The Open Particle and Nuclear Physics Journal, 4, 35-38. |

[63] | Olkhovsky, V.S. and Dolinska, M.E. (2010) Вiсник Киïвського унiверситету. Серiя: Фiз.-мат. науки, вип.3, 82-86 [The Proceedings of International Conference “Humboldt Cosmos: Science and Society”, HCS2 Kiev2009]. |

[64] | Olkhovsky, V.S. and Dolinska, M.E. (2010) On the Modification of Methods of Nuclear Chronometry in Astrophysics and Geophysics. Сеntr. Europ. J. Phys., 8, 95-100. |

[65] | Olkhovsky, V.S. (2014) On the Modification of Nuclear Chronometry in Astrophysics and Geophysics. Development in Earth Science (DES), 2, 1-7. |

[66] |
Kobe, D.H. and Aguilera-Navarro, V.C. (1994) Derivation of the Energy-Time Uncertainty Relation. Physical Review A, 50, 933-941. http://dx.doi.org/10.1103/PhysRevA.50.933 |

[67] |
Grot, N., Rovelli, C. and Tate, R.S. (1996) Time of Arrival in Quantum Mechanics. Physical Review A, 54, 4676-4687.
http://dx.doi.org/10.1103/PhysRevA.54.4676 |

[68] | Leo’n, J. (1997) Time Operator in the Positive-Operator-Value-Measure Approach. Journal of Physics A: Mathematical and General, 30, 4791-4799. |

[69] |
Aharonov, Y., Oppenheim, J., Popescu, S., Reznik, B. and Unruh, W.G. (1998) Measurement of Time of Arrival in Quantum Mechanics. Physical Review A, 57, 4130-4142. http://dx.doi.org/10.1103/PhysRevA.57.4130 |

[70] |
Muga, J., Papao, J. and Leavens, C. (1999) Arrival Time Distributions and Perfect Absorption in Classical and Quan- tum Mechanics. Physics Letters A, 253, 21-27. http://dx.doi.org/10.1016/S0375-9601(99)00020-1 |

[71] |
Muga, J., Egusquiza, I.L., Damborenea, J.A. and Delgado, F. (2002) Bounds and Enhancements for Negative Scattering Time Delays. Physical Review A, 66, Article ID: 042115. http://dx.doi.org/10.1103/PhysRevA.66.042115 |

[72] | Muga, J.G., Mayato, R.S. and Egusquiza, I.L. (2007) Time in Quantum Mechanics—Lecture Notes in Physics, v.1, 2007, v.2, 2009, Springer, Berlin. |

[73] |
Aharonov, Y. and Bohm, D. (1961) Time in the Quantum Theory and the Uncertainty Relation for Time and Energy. Physical Review, 122, 1649-1657. http://dx.doi.org/10.1103/PhysRev.122.1649 |

[74] | Naimark, М.А. (1943) Izv.АN SSSR. Seria Matematicheskaya, 7, 237. |

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