Is the wave-function a physical reality traveling through our apparatus? Is it a real wave, or it is only a mathematical tool for calculating probabilities of results of measurements? Different interpretations of the quantum mechanics (QM) assume different answers to this question. It is shown in this article that the assumption that the wave-function is a real wave entails a contradiction with the predictions of the QM, when the special relativity is invoked. Therefore, this text concentrates on interpretations that conjecture that the reality that moves in our apparatuses is particles, and they move under the constraints of the wave-function. The de Broglie-Bohm interpretation, which matches this picture, assumes that the particle travels along a continuous trajectory. However, the idea of continuous trajectories was proved to lead to a contradiction with the quantum predictions. Therefore this interpretation is not considered here. S. Gao conjectured that the particle is in a permanent random and discontinuous motion (RDM). As it jumps all the time from place to place, the total set of occupied positions at a certain time is given by the absolute square of the wave-function. As motivation for his idea, Gao argued that if a charged particle were simultaneously in two or more locations at the same time, the copies of the particle would repel one another, destroying the wave-function. It is proved here that the quantum formalism renders this motivation wrong. Although refuting this motivation, the RDM interpretation is examined here. A couple of problems of this interpretation are examined and it is proved that they don’t lead to any observable contradictions with the QM predictions, except one problem which seems to have no solution. In all, it appears that none of the wide-spread interpretations of the QM is free of contradictions.
References
[1]
Pusey, M.F., Barrett, J. and Rudolph, T. (2012) On the Reality of the Quantum State, Nature Physics, 8, 475-478. https://doi.org/10.1038/nphys2309
[2]
Leifer, M.S. (2014) Is the Quantum State Real? An Extended Review of ψ-Ontology Theorems. Quanta, 3, 67-155. https://doi.org/10.12743/quanta.v3i1.22
[3]
De Broglie, L. (1926) Ondes et Mouvements. Villars, G., Paris.
[4]
De Broglie, L. (1924) Recherches sur la théorie des quanta. Ph.D. Thesis, Migration Université en cours d’affectation, Français.
https://doi.org/10.1051/anphys/192510030022
[5]
Bohm, D. (1952) A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables I. Physical Review, 85, 166-179.
https://doi.org/10.1103/PhysRev.85.166
[6]
Wechsler, S.D. (2022) A Non-Relativistic Argument against Continuous Trajectories of Particles. Journal of Quantum Information Science, 12, 29-36.
https://doi.org/10.4236/jqis.2022.122004
[7]
Griffiths, R.B. (1984) Consistent Histories and the Interpretation of Quantum Mechanics. Journal of Statistical Physics, 36, 219-272.
https://doi.org/10.1007/BF01015734
[8]
Griffiths, R.B. (2002) Consistent Quantum Theory. Cambridge University Press, Cambridge.
[9]
Griffiths, R.B. (2014) The Consistent Histories Approach to Quantum Mechanics. Stanford Encyclopedia of Philosophy, Stanford.
[10]
Griffiths, R.B. (2002) Consistent Resolution of Some Relativistic Quantum Paradoxes. Physical Review A, 66, Article ID: 062101.
https://doi.org/10.1103/PhysRevA.66.062101
[11]
Cramer, J.G. (1986) The Transactional Interpretation of the Quantum Mechanics. Reviews of Modern Physics, 58, 647-688.
https://doi.org/10.1103/RevModPhys.58.647
[12]
Cramer, J.G. (1988) An Overview of the Transactional Interpretation. International Journal of Theoretical Physics, 27, 227-236. https://doi.org/10.1007/BF00670751
[13]
Cramer, J.G. (2015) The Quantum Handshake: Entanglement, Nonlocality and Transactions. Springer, Cham.
[14]
Kastner, R.E. and Cramer, J.G. (2017) Quantifying Absorption in the Transactional Interpretation. Cornell University, Ithaca. https://doi.org/10.1103/PhysRevD.34.470
[15]
Ghirardi, G.-C., Rimini, A. and Weber, T. (1986) Unified Dynamics for Microscopic and Macroscopic Systems. Physical Review D, 34, Article 470.
[16]
Pearle, P. (1989) Combining Stochastic Dynamical State-Vector Reduction with Spontaneous Localization. Physical Review A, 39, Article ID: 2277.
https://doi.org/10.1103/PhysRevA.39.2277
[17]
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, 42, Article 78. https://doi.org/10.1103/PhysRevA.42.78
[18]
Pearle, P. (2007) Collapse Models. ArXiv: quant-ph/9901077v1.
[19]
Bassi, A. and Ghirardi, G.-C. (2003) Dynamical Reduction Models. Physics Reports, 379, 257-426. https://doi.org/10.1016/S0370-1573(03)00103-0
[20]
Adler, S. (2007) Lower and Upper Bounds on CSL Parameters from Latent Image Formation and IGM Heating. Journal of Physics A, 40, 2935.
https://doi.org/10.1088/1751-8113/40/12/S03
[21]
Adler, S. and Bassi, A. (2007) Collapse Models with Non-White Noises. Journal of Physics A, 40, Article ID: 15083. https://doi.org/10.1088/1751-8113/40/50/012
[22]
Bassi, A. and Salvetti, D.G.M. (2007) The Quantum Theory of Measurement within Dynamical Reduction Models. ArXiv: quant-ph/070201011v1.
[23]
Bassi, A., Lochan, K., Satin, S., Singh, T.P. and Ulbricht, H. (2013) Models of Wave-function Collapse, Underlying Theories, and Experimental Tests. ArXiv: quant-ph/1204.4325v3.
[24]
Carlesso, M. and Donadi, S. (2019) Collapse Models: Main Properties and the State of Art of the Experimental Tests. In: Vacchini, B., Breuer, H.P. and Bassi, A., Eds., Advances in Open Systems and Fundamental Tests of Quantum Mechanics, Vol. 237, Springer, Cham, 1-13. https://doi.org/10.1007/978-3-030-31146-9_1
[25]
Gisin, N. (1984) Quantum Measurements and Stochastic Processes. Physical Review Letters, 52, Article 1657. https://doi.org/10.1103/PhysRevLett.52.1657
[26]
Gisin, N. (2018) Collapse. What Else? In: Gao, S., Ed., Collapse of the Wave Function, Cambridge University Press, Cambridge, 207.
[27]
Wechsler, S.D. (2020) In Praise and in Criticism of the Model of Continuous Spontaneous Localization of the Wave-Function. Journal of Quantum Information Science, 10, 73-103. https://doi.org/10.4236/jqis.2020.104006
[28]
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
[29]
Diósi, L. (1989) Models for Universal Reduction of Macroscopic Quantum Fluctuations. Physics Reviews A, 40, Article 1165.
https://doi.org/10.1103/PhysRevA.40.1165
[30]
Diósi, L. (2007) Notes on Certain Newton Gravity Mechanisms of Wave Function Localisation and Decoherence. Journal of Physics A: Mathematical and Theoretical, 40, Article 2989. https://doi.org/10.1088/1751-8113/40/12/S07
[31]
Bahrami, M., Smirne, A. and Bassi, A. (2014) Gravity and the Collapse of the Wave Function: A Probe into Diósi-Penrose Model. Physical Review A, 90, Article ID: 062105. https://doi.org/10.1103/PhysRevA.90.062105
[32]
Gasbarri, G., Toroš, M., Donadi, S. and Bassi, A. (2017) Gravity Induced Wave Function Collapse. Physical Review D, 96, Article ID: 104013.
https://doi.org/10.1103/PhysRevD.96.104013
[33]
Donadi, S., Piscicchia, K., Curceanu, C., Diósi, L., Laubenstein, M. and Bassi, A. (2021) Underground Test of Gravity-Related Wave Function Collapse. Nature Physics, 17, 74-78. https://doi.org/10.1038/s41567-020-1008-4
[34]
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
[35]
Gao, S. (2016) The Meaning of the Wave Function: In Search of the Ontology of Quantum Mechanics. ArXiv: quant-ph/1611.02738v1.
[36]
Gao, S. (2018) Is an Electron a Charge Cloud? A Reexamination of Schrödinger’s Charge Density Hypothesis. Foundations of Science, 23, 145-157.
https://doi.org/10.1007/s10699-017-9521-3
[37]
Gao, S. (2020) A Puzzle for the Field Ontologists. Foundations of Physics, 50, 1541-1553. https://doi.org/10.1007/s10701-020-00390-0
[38]
Wechsler, S. (2021) About the Nature of the Quantum System—An Examination of the Random Discontinuous Motion Interpretation of the Quantum Mechanics. Journal of Quantum Information Science, 11, 99-111.
https://doi.org/10.4236/jqis.2021.113008
[39]
Faye, J. (2002) Copenhagen Interpretation of Quantum Mechanics. Stanford Encyclopedia of Philosophy, Stanford.
http://plato.stanford.edu/entries/qm-copenhagen/
[40]
Garziano, L., Macrì, V., Stassi, R., Di Stefano, O., Nori, F. and Savasta, S. (2016) A Single Photon Can Simultaneously Excite Two or More Atoms. ArXiv: quantph/1601.00886v2.
[41]
Wechsler, S. (2019) The Wave-Particle Duality—Does the Concept of Particle Make Sense in Quantum Mechanics? Should We Ask the Second Quantization? Journal of Quantum Information Science, 9, 155-170. https://doi.org/10.4236/jqis.2019.93008
[42]
Lundeen, J.S. and Steinberg, A.M. (2009) Experimental Joint Weak Measurement on a Photon Pair as a Probe of Hardy’s Paradox. ArXiv: quant-ph/0810.4229.
[43]
Hardy, L. (1992) Quantum Mechanics, Local Realistic Theories, and Lorenz-Invariant Realistic Theories. Physical Review Letters, 68, Article 2981.
https://doi.org/10.1103/PhysRevLett.68.2981
[44]
Wechsler, S.D. (2017) Hardy’s Paradox Made Simple—What We Infer from It?
https://www.researchgate.net/publication/318446904_Hardy's_paradox_made_simple_-_what_we_infer_from_it
