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.
Cite this paper
Olkhovsky, V. S. (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, e887. doi: http://dx.doi.org/10.4236/oalib.1100887.
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
Einstein А., Podolsky, В. and Rosen, Т. (1935) Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47, 777-780.
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
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
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
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
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
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
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.
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.
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.
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
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
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.
Olkhovsky, V.S. and Romanyuk, M.V. (2011) On Two-Dimensional Above-Barrier Penetration and Sub-Barrier Tunneling for Non-Relativistic Particles and Photons. Journal of Modern Physics, 2, 1166-1171.
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
Olkhovsky, V.S., Dolinska, M.E. and Omelchenko, S.A. (2011) On New Experimental Data Manifesting the Time Resonances (or Explosions). Central European Journal of Physics, 9, 1131-1133.
http://dx.doi.org/10.2478/s11534-011-0009-4
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.
Abolhasani, M. and Golshani, M. (2000) Tunneling Times in the Co-penhagen Interpretation of Quantum Mechanics. Physical Review A, 62, Article ID: 012106.
http://dx.doi.org/10.1103/PhysRevA.62.012106
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
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
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
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
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.
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 La-boratory Systems. Applied Physics Letters, 99, Article ID: 244103.
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 Cen-ter-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.
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.
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.
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.
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.
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
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
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
Muga, J., Papao, J. and Leavens, C. (1999) Arrival Time Distributions and Perfect Absorption in Classical and Quantum Mechanics. Physics Letters A, 253, 21-27.
http://dx.doi.org/10.1016/S0375-9601(99)00020-1
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
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