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Stochastic Quantum Hydrodynamic Model from the Dark Matter of Vacuum Fluctuations: The Langevin-Schr?dinger Equation and the Large-Scale Classical Limit

DOI: 10.4236/oalib.1106659, PP. 1-36

Subject Areas: Modern Physics

Keywords: Stochastic Quantum Hydrodynamics, Quantum Decoherence Induced by Dark Matter, Quantum to Classical Transition, Quantum Dissipation, Qbits, Mesoscale Dynamics, Wave Function Collapse

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Abstract

The work derives the quantum evolution in a fluctuating vacuum by introducing the related (dark) mass density noise into the Madelung quantum hydrodynamic model. The paper shows that the classical dynamics can spontaneously emerge on the cosmological scale allowing the realization of the classical system-environment super system. The work shows that the dark matter-induced noise is not spatially white and owns a well defined correlation function with the intrinsic vacuum physical length given by the De Broglie one. By departing from the quantum mechanics (the deterministic limit of the theory) in the case of microscopic systems whose dimension is much smaller than the De Broglie length, the model leads to the Langevin-Schrodinger equation whose friction coefficient is not constant. The derivation puts in evidence the range of application of the Langevin-Schrodinger equation and the approximations inherent to its foundation. Increasing the physical length of the system description, the classical physics can be achieved when the scale of the problem is much bigger both than the De Broglie length and the quantum potential range of interaction. The long-distance characteristics as well as the range of interaction of the non-local quantum potential are derived and analyzed in order to have a coarse-grained large-scale description. The process of measurement, in the large-scale classical limit, satisfies the minimum uncertainty conditions if interactions and information do not travel faster than the light speed, reconciling the quantum entanglement with the relativistic macroscopic locality.

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Chiarelli, S. and Chiarelli, P. (2020). Stochastic Quantum Hydrodynamic Model from the Dark Matter of Vacuum Fluctuations: The Langevin-Schr?dinger Equation and the Large-Scale Classical Limit. Open Access Library Journal, 7, e6659. doi: http://dx.doi.org/10.4236/oalib.1106659.

References

[1]  Young, T. (1804) The Bakerian Lecture. Experiments and Calculations Relative to Physical Optics. Philosophical Transactions of the Royal Society of London, 94, 1-16. https://doi.org/10.1098/rstl.1804.0001
[2]  Feynmann, R.P. Leighton, R. and Sands, M. (1963) The Feynman Lectures on Physics: Volume 3. Addison-Wesley, Boston.
[3]  Auletta, G. (2001) An Outline of an Interpretation of Quantum Mechanics. In: Garola, C. and Rossi, A., Eds., The Foundations of Quantum Mechanics: Historical Analysis and Open Questions, World Scientific, Singapore, 31-49. https://doi.org/10.1142/9789812793560_0002
[4]  Greenstein, G. and Zajonc, A.G. (2005) The Quantum Challenge. 2nd Edition, Jones and Bartlett Publishers, Boston.
[5]  Shadbolt, P., Mathews, J.C.F., Laing, A. and O’Brien, J.L. (2014) Testing Foundations of Quantum Mechanics with Photons. Nature Physics, 10, 278-286. https://doi.org/10.1038/nphys2931
[6]  Josson, C. (1974) Electron Diffraction at Multiple Slits. American Journal of Physics, 42, 4.
[7]  Zeilinger, A., Gahler, R., Shull, C.G., Treimer, W. and Mampe, W. (1988) Single- and Double-Slit Diffraction of Neutrons. Reviews of Modern Physics, 60, 1067-1073. https://doi.org/10.1103/RevModPhys.60.1067
[8]  Carnal, O. and Mlynek, J. (1991) Young’s Double-Slit Experiment with Atoms: A Simple Atom Interferometer. Physical Review Letters, 66, 2689-2692. https://doi.org/10.1103/PhysRevLett.66.2689
[9]  Schöllkopf, W. and Toennies, J.P. (1994) Nondestructive Mass Selection of Small van der Waals Clusters. Science, 266, 1345-1348. https://doi.org/10.1126/science.266.5189.1345
[10]  Arndt, M., Nairz, O., Vos-Andreae, J., Keller, C., Van Der Zouw, G. and Zeilinger, A. (1999) Wave-Particle Duality of C60 Molecules. Nature, 401, 680-682. https://doi.org/10.1038/44348.
[11]  Nairz, O., Arndt, M. and Zeilinger, A. (2003) Quantum Interference Experiments with Large Molecules. American Journal of Physics, 71, 319. https://doi.org/10.1119/1.1531580
[12]  Born, M. (1954) The Statistical Interpretation of Quantum Mechanics—Nobel Lecture.
[13]  Ghirardi, G.C., Rimini, A. and Weber, T. (1986) Unified Dynamics for Microscopic and Macroscopic Systems. Physical Review D, 34, 470-491. https://doi.org/10.1103/PhysRevD.34.470
[14]  Ghirardi, G.C. (2000) Local Measurements of Nonlocal Observables and the Relativistic Reduction Process. Foundations of Physics, 30, 1337.
[15]  Pitaevskii, P.P. (1961) Vortex Lines in an Imperfect Bose Gas. Journal of Experimental and Theoretical Physics, 13, 451-454.
[16]  Everette, H. (1957) “Relative State” Formulation of Quantum Mechanics. Reviews of Modern Physics, 29, 454-462. https://doi.org/10.1103/RevModPhys.29.454
[17]  Vaidman, L. (2012) Probability in the Many-Worlds Interpretation of Quantum Mechanics. In: Ben-Menahem, Y. and Hemmo, M. (Eds.), Probability in Physics, The Frontiers Collection XII, Springer, 299-311.
[18]  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
[19]  Goldstein, S. and Ward S. (2007) On the Uniqueness of Quantum Equilibrium in Bohmian Mechanics. Journal of Statistical Physics, 128, 1197-1209.
[20]  Lombardi, O. and Dieks, D. (2016) Particles in a Quantum Ontology of Properties. In: Bigaj, T. and Wüthrich, C. (Eds.), Metaphysics in Contemporary Physics, Brill-Rodopi, Leiden, 123-143.
[21]  Laudisa, F. and Rovelli, C. (2002) Relational Quantum Mechanics. In: Zalta, E.N., Ed., The Stanford Encyclopedia of Philosophy, Springer, Berlin, Heidelberg.
[22]  Griffiths, R.B. (2003) Consistent Quantum Theory. Cambridge University Press, Cambridge.
[23]  Cramer, J.G. (1980) Generalized Absorber Theory and the Einstein-Podolsky-Rosen Paradox. Physical Review D, 22, 362-376. https://doi.org/10.1103/PhysRevD.22.362
[24]  Cramer, J.G. (2016) Quantum Entanglement and Nonlocality. In: Cramer, J.G., Ed., The Quantum Handshake, Springer, Cham, 39-45. https://doi.org/10.1007/978-3-319-24642-0_3
[25]  Von Baeyer, H.C. (2016) QBism: The Future of Quantum Physics. Harvard University Press, Cambridge. https://doi.org/10.4159/9780674545342
[26]  Madelung, E. (1926) Quantentheorie in Hydrodynamischer Form. Zeitschrift für Physik, 40, 322-326. https://doi.org/10.1007/BF01400372
[27]  Jánossy, L. (1962) Zum Hydrodynamischen Modell der Quantenmechanik. Zeitschrift für Physik, 169, 79-89. https://doi.org/10.1007/BF01378286
[28]  Weiner, J.H. (1983) Statistical Mechanics of Elasticity. John Wiley & Sons, New York, 315-7.
[29]  Lidar, D.A., Chuang, I.L. and Whaley, K.B. (1998) Decoherence-Free Subspaces for Quantum Computation. Physical Review Letters, 81, 2594-2597. https://doi.org/10.1103/PhysRevLett.81.2594
[30]  Tsekov, R. (2011) Bohmian Mechanics versus Madelung Quantum Hydrodynamics. 112-119.
[31]  Bialyniki-Birula, I., Cieplak, M. and Kaminski, J. (1992) Theory of Quanta. Oxford University Press, Oxford, 87-111.
[32]  Cerruti, N.R., Lakshminarayan, A., Lefebvre, T.H. and Tomsovic, S. (2000) Exploring Phase Space Localization of Chaotic Eigenstates via Parametric Variation. Physical Review E, 63, Article ID: 016208. https://doi.org/10.1103/PhysRevE.63.016208
[33]  Calzetta, E. and Hu, B.L. (1995) Quantum Fluctuations, Decoherence of the Mean Field, and Structure Formation in the Early Universe. Physical Review D, 52, 6770-6788. https://doi.org/10.1103/PhysRevD.52.6770
[34]  Wang, C., Bonifacio, P., Bingham, R. and Tito Mendonca, J. (2008) Detection of Quantum Decoherence due to Spacetime Fluctuations. 37th COSPAR Scientific Assembly, Montréal, 13-20 July 2008, 3390.
[35]  Lombardo, F.C. and Villar, P.I. (2005) Decoherence Induced by Zero-Point Fluctuations in Quantum Brownian Motion. Physics Letters A, 336, 16-24. https://doi.org/10.1016/j.physleta.2004.12.065
[36]  Chiarelli, P. (2013) Can Fluctuating Quantum States Acquire the Classical Behavior on Large Scale? Journal of Advances in Physics, 2, 139-163.
[37]  Chiarelli, P. (2020) Stability of Quantum Eigenstates and Kinetics of Wave Function Collapse in a Fluctuating Vacuum, in Progress.
[38]  Chiarelli, P. (2013) Quantum to Classical Transition in the Stochastic Hydrodynamic Analogy: The Explanation of the Lindemann Relation and the Analogies Between the Maximum of Density at He Lambda Point and that One at Water-Ice Phase Transition. Physical Review & Research International, 3, 348-366.
[39]  Bressanini, D. (2011) An Accurate and Compact Wave Function for the 4He Dimer. EPL, 96, Article ID: 23001. https://doi.org/10.1209/0295-5075/96/23001
[40]  Chiarelli, P. (2014) The Quantum Potential: The Missing Interaction in the Density Maximum of He4 at the Lambda Point? American Journal of Physical Chemistry, 2, 122-131. https://doi.org/10.11648/j.ajpc.20130206.12
[41]  Gross, E.P. (1961) Structure of a Quantized Vortex in Boson Systems. Il Nuovo Cimento, 20, 454-457. https://doi.org/10.1007/BF02731494
[42]  Gardiner, C.W. (1985) Handbook of Stochastic Method. 2nd Edition, Springer, Berlin, 331-341.
[43]  Einstein, A., Podolsky, B. and Rosen, N. (1935) Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47, 777-780. https://doi.org/10.1103/PhysRev.47.777
[44]  Weiner, J.H. and Forman, R. (1974) Rate Theory for Solids. V. Quantum Brownian Motion Model. Physical Review B, 10, 325-337. https://doi.org/10.1103/PhysRevB.10.325
[45]  Ruggiero, P. and Zannetti, M. (1981) Critical Phenomena at T=0 and Stochastic Quantization. Physical Review Letters, 47, 1231-1234. https://doi.org/10.1103/PhysRevLett.47.1231
[46]  Ruggiero, P. and Zannetti, M. (1983) Microscopic Derivation of the Stochastic Process for the Quantum Brownian Oscillator. Physical Review A, 28, 987-993. https://doi.org/10.1103/PhysRevA.28.987
[47]  Rumer, Y.B. and Ryvkin, M.S. (1980) Thermodynamics, Statistical Physics, and Kinetics. Mir Publishers, Moscow, 269.

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