Different attempts to solve the measurement problem of the quantum me-chanics (QM) by denying the collapse principle, and replacing it with changes in the quantum formalism, failed because the changes in the formalism lead to contradictions with QM predictions. To the difference, Ghirardi, Rimini and Weber took the collapse as a real phenomenon, and proposed a calculus by which the wave-function should undergo a sudden localization. Later on, Ghirardi, Pearle and Rimini came with a change of this calculus into the CSL (continuous spontaneous localization) model of collapse. Both these proposals rely on the experimental fact that the reduction of the wave-function occurs when the microscopic system encounters a macroscopic object and involves a big amount of its particles. Both these proposals also change the quantum formalism by introducing in the Schr?dinger equation additional terms with noisy behavior. However, these terms have practically no influence as long as the studied system contains only one or a few components. Only when the amount of components is very big, these terms become significant and lead to the reduction of the wave-function to one of its components. The present work has two purposes: 1) proving that the collapse postulate is unavoidable; 2) ap-plying the CSL model to the process in a detector and showing step by step the modification of the wave-function, until reduction. As a side detail, it is argued here that the noise cannot originate in some classical field, contrary to the thought/hope of some physicists, because no classical field is tailored by the wave-functions of entanglements.
References
[1]
von Neumann, J. (1932) Mathematische Grundlagen der Quantenmechanik. Springer, Berlin.
[2]
Lüders, G. (1950) Über die Zustandsänderung durch den Meßprozeß. Annalen der Physik, 443, 322-328. https://doi.org/10.1002/andp.19504430510
[3]
de Broglie, L. (1926) Ondes et mouvements. Publisher Gauthier-Villars, Paris.
[4]
Bohm, D. (1952) A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables. Part I and II. Physical Review, 85, 166-179.
https://doi.org/10.1103/PhysRev.85.180
[5]
Wechsler, S.D. (2019) The Wave-Particle Duality—Does the Concept of Particle Make Sense in Quantum Mechanics? Should We Ask the Second Quantization? J. of Journal of Quantum Information Science, 9, 155-170.
https://doi.org/10.4236/jqis.2019.93008
[6]
Hardy, L. (1992) On the Existence of Empty Waves in Quantum Theory. Physics Letters A, 167, 11-16. https://doi.org/10.1016/0375-9601(92)90618-V
[7]
Griffiths, R.J. (2002) Consistent Quantum Theory. Cambridge University Press, Cambridge.
[8]
Cramer, J.G. (1986) The Transactional Interpretation of the Quantum Mechanics. Reviews of Modern Physics, 58, 647-688.
[9]
Ghirardi, G.-C., Rimini, A. and Weber, T. (1986) Unified Dynamics for Microscopic and Macroscopic Systems. Physical Review D, 34, 470.
https://doi.org/10.1103/PhysRevD.34.470
[10]
Ghirardi, G.-C., Pearle, P. and Rimini, A. (1990) Markov Processes in Hilbert Space and Continuous Spontaneous Localization of Systems of Identical Particles. Physical Review A: Atomic, Molecular, and Optical Physics, 42, 78-89.
https://doi.org/10.1103/PhysRevA.42.78
[11]
Gisin, N. (1984) Quantum Measurements and Stochastic Processes. Physical Review Letters, 52, 1657-1660. https://doi.org/10.1103/PhysRevLett.52.1657
[12]
Pearle, P. (1989) Combining Stochastic Dynamical Statevector Reduction with Spontaneous Localization. Physical Review A, 39, 2277-2289.
https://doi.org/10.1103/PhysRevA.39.2277
[13]
Gisin, N. (1989) Stochastic Quantum Dynamics and Relativity. Helvetica Physica Acta, 62, 363-371.
[14]
Bassi, A. and Ghirardi, G.-C. (2003) Dynamical Reduction Models. Physics Reports, 379, 257. https://doi.org/10.1016/S0370-1573(03)00103-0
[15]
Bassi, A., Lochan, K., Satin, S., Singh, T.P. and Ulbricht, H. (2013) Models of Wave-Function Collapse, Underlying Theories, and Experimental Tests. Reviews of Modern Physics, 85, 471-527. https://doi.org/10.1103/RevModPhys.85.471
[16]
Bassi, A. and Salvetti, D.G.M. (2007) The Quantum Theory of Measurement within Dynamical Reduction Models. Journal of Physics A: Mathematical and Theoretical, 40, 9859-9876. https://doi.org/10.1088/1751-8113/40/32/011
[17]
Bedingham, D.J. (2009) Dynamical State Reduction in an EPR Experiment. Journal of Physics A: Mathematical and Theoretical, 42, Article ID: 465301.
https://doi.org/10.1088/1751-8113/42/46/465301
[18]
Feynman, R.P. and Hibbs, A.R. (1965) Quantum Mechanics and Path Integral. McGraw-Hill Companies Inc., New York. Emended Edition Daniel F. Styer (2010) Emended Re-Publication Dover Publication, Inc., Mineola, New York.
[19]
Adler, S.L. and Bassi, A. (2020) Minimum Measurement Time: Lower Bound on the Frequency Cutoff for Collapse Models. Journal of Physics A: Mathematical and Theoretical, 53, Article ID: 215302. https://doi.org/10.1088/1751-8121/ab8673
[20]
Gisin, N. (2017) Collapse. What Else?
[21]
Diósi, L. (1989) Models for Universal Reduction of Macroscopic Quantum Fluctuations. Physical Review A, 40, 1165-1174. https://doi.org/10.1103/PhysRevA.40.1165
[22]
Diósi, L. (1987) A Universal Master Equation for the Gravitational Violation of Quantum Mechanics. Physics Letters A, 120, 377-381.
https://doi.org/10.1016/0375-9601(87)90681-5
[23]
Diósi, L. and Lukacs, B. (1987) In Favor of a Newtonian Quantum Gravity. Annalen der Physik, 499, 488-492. https://doi.org/10.1002/andp.19874990703
[24]
Ghirardi, G.-C., Grassi, R. and Rimini, A. (1990) Continuous-Spontaneous-Reduction Model Involving Gravity. Physical Review A, 42, 1057-1064.
https://doi.org/10.1103/PhysRevA.42.1057
[25]
Bassi, A. and Ghirardi, G.-C. (2002) Dynamical Reduction Models with General Gaussian Noises. Physical Review A, 65, Article ID: 042114.
https://doi.org/10.1103/PhysRevA.65.042114
[26]
Knoll, G.F. (2000) Radiation Detection and Measurement. 3rd Edition, John Willey and Sons Inc., Hoboken.
Diethorn, W. (1956) A Methane Proportional Counter System for Natural Radiocarbon Measurements. Thesis, Carnegie Inst. of Tech., Pittsburgh, Report Number NYO-6628.
[29]
Milburn, G.J. (2010) Quantum Measurement and Control of Single Spins in Diamond. Science, 330, 1188-1189. https://doi.org/10.1126/science.1198299
[30]
Elitzur, A.C. and Vaidman, L. (1993) Quantum Mechanical Interaction-Free Measurement. Foundations of Physics, 23, 987-997. https://doi.org/10.1007/BF00736012
[31]
Sciarrino, F., Lombardi, E., Milani, G. and de Martini, F. (2002) Delayed-Choice Entanglement Swapping with Vacuum-One-Photon Quantum States. Physical Review A, 66, Article ID: 024309.
[32]
Lombardi, E., Sciarrino, F., Popescu, S. and De Martini, F. (2001)Teleportation of Entangled States of a Vacuum-One Photon Qubit.
https://arxiv.org/abs/quant-ph/0109160
[33]
Schellekens, M., Hoppeler, R., Perrin, A., Viana Gomes, J., Boiron, D., Aspect, A. and Westbrook, C.I. (2005) Hanbury Brown Twiss Effect for Ultracold Quantum Gases. Science, 310, 648-651. https://doi.org/10.1126/science.1118024
[34]
Jeltes, T., McNamara, J.M., Hogervorst, W., Vassen, W., Krachmalnicoff, V., Schellekens, M., Perrin, A., Chang, H., Boiron, D., Aspect, A. and Westbrook, C.I. (2007) Comparison of the Hanbury Brown-Twiss Effect for Bosons and Fermions. Nature (Letters), 445, 402-405. https://doi.org/10.1038/nature05513
[35]
MIT OpenCourseWare, Itô Calculus. From MIT 18.S096 Topics in Mathematics with Applications in Finance. Taught by Dr. Peter Kempthorne, Dr. Choongbum Lee, Dr. Vasily Strela, and Dr. Jake Xia in Fall 2013 (2013), Uploaded by MIT OpenCourseWare in Jan 2015.
https://ocw.mit.edu/courses/mathematics/18-s096-topics-in-mathematics-with-applications-in-finance-fall-2013/video-lectures/lecture-18-ito-calculus
[36]
Adler, S.L. and Bassi, A. (2009) Is Quantum Theory Exact? Science, 325, 275-276.
https://doi.org/10.1126/science.1176858
[37]
Adler, S. (2004) Proof of Reduction with Born Rule Probabilities. In: Adler, S., Ed., Quantum Theory as an Emergent Phenomenon, Cambridge University Press, Cambridge, Section 6.2. https://doi.org/10.1017/CBO9780511535277
[38]
Peres, A. (1993) Maximal Quantum Tests. In: Quantum Theory: Concepts and Methods, Kluwer Academic Publishers, Dordrecht.
