Abstract
We discuss a model where a spontaneous quantum collapse is induced by the gravitational interactions, treated classically. Its dynamics couples the standard wave function of a system with the Bohmian positions of its particles, which are considered as the only source of the gravitational attraction. The collapse is obtained by adding a small imaginary component to the gravitational coupling. It predicts extremely small perturbations of microscopic systems, but very fast collapse of QSMDS (quantum superpositions of macroscopically distinct quantum states) of a solid object, varying as the fifth power of its size. The model does not require adding any dimensional constant to those of standard physics.
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A.J. Leggett, Macroscopic quantum systems and the quantum theory of measurement, Suppl. Prog. Theor. Phys. 69, 80 (1980)
A.J. Leggett, Probing quantum mechanics towards the everyday world: where do we stand, Phys. Scr. T102, 80 (2002)
E. Schrödinger, Die gegenwärtige Situation in der Quantenmechanik, Naturwissenchaften 23, 807 (1935); see also [4]
J.D. Trimmer, The present situation in quantum mechanics: a translation of Schrödinger’s cat paradox paper, Proc. Am. Phys. Soc. 124, 323 (1980)
J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932)
J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, 1955)
L. Diosi, A universal master equation for the gravitational violations of quantum mechanics, Phys. Lett. 120, 377 (1987)
L. Diosi, Models for universal reduction of macroscopic quantum fluctuations, Phys. Rev. A 40, 1165 (1989)
G.C. Ghirardi, R. Grassi, A. Rimini, Continuous-spontaneous-reduction models involving gravity, Phys. Rev. A 42, 1057 (1990)
P. Pearle, E. Squires, Gravity, energy conservation, and parameter values in collapse models, Found. Phys. 26, 291 (1996)
R. Penrose, On gravity’s role in quantum state reduction, Gen. Relativ. Gravitation 28, 581 (1996)
L. Diosi, Gravity related spontaneous wave function collapse in bulk matter, New J. Phys. 16, 105006 (2014)
A. Tilloy, L. Diosi, Sourcing semiclassical gravity from spontaneously localized quantum matter, Phys. Rev. D 93, 024026 (2016)
S.L. Adler, Gravitation and the noise needed in objective reduction models, in Quantum nonlocality and reality: 50 years of Bell’s theorem, edited by M. Bell, S. Gao, (Cambridge University Press, 2016)
G. Gasbarri, M. Toros, S. Donadi, A. Bassi, Gravity induced wave function collapse, Phys. Rev. D 96, 104013 (2017)
A. Bassi, K. Lochan, S. Satin, T. Singh, H. Ulbricht, Models of wave function collapse, underlying theories, and experimental tests, Rev. Mod. Phys. 85, 471 (2013)
T.P. Singh, Possible role of gravity in collapse of the wave-function: a brief survey of some ideas, J. Phys.: Conf. Ser. 626, 012009 (2015)
L. de Broglie, La mécanique ondulatoire et la structure atomique de la matière et du rayonnement, J. Phys. Radium 8, 225 (1927)
D. Bohm, A suggested interpretation of the quantum theory in terms of hidden variables, Phys. Rev. 85, 166 (1952)
P. Holland, The Quantum Theory of Motion (Cambridge University Press, 1993)
G. Bacchiagaluppi, A. Valentini, Quantum theory at the crossroads: reconsidering the 1927 Solvay conference (Cambridge University Press, 2009)
D. Dürr, S. Goldstein, N. Zanghi, Quantum physics without quantum philosophy (Springer, 2013)
J. Bricmont, Making sense of quantum mechanics (Springer, 2016)
G. Ghirardi, A. Rimini, T. Weber, Unified dynamics for microscopic and macroscopic systems, Phys. Rev. D 34, 470 (1986)
P. Pearle, Combining stochastic dynamical state-vector reduction with spontaneous localization, Phys. Rev. A 39, 2277 (1989)
V. Allori, S. Goldstein, R. Tumulka, N. Zhanghi, On the common structure of Bohmian mechanics and the Ghirardi-Rimini-Weber theory, Br. J. Philos. Sci. 59, 353 (2008) – see in particular Section 7.2
D. Bedingham, Hidden variable interpretation of spontaneous localization theory, J. Phys. A 44, 275303 (2011)
R. Tumulka, Comment on Hidden variable interpretation of spontaneous localization theory, J. Phys. A 44, 478001 (2011)
F. Laloë, Modified Schrödinger dynamics with attractive densities, Eur. Phys. J. D 69, 162 (2015)
F. Laloë, Quantum collapse dynamics with attractive densities, Phys. Rev. A 99, 052111 (2019)
M. Bahrami, A. Grossardt, S. Donadi, A. Bassi, The Schrödinger-Newton equation and its foundations, New J. Phys. 16, 115007 (2014)
O.V. Prezdho, C. Brooksby, Quantum backreaction through the Bohmian particle, Phys. Rev. Lett. 86, 3215 (2001)
L. Diosi, T.B. Papp, Schrödinger-Newton equation with a complex Newton constant and induced gravity, Phys. Lett. A 373, 3244 (2009)
A. Valentini, H. Westman, Dynamical origin of quantum probabilities, Proc. Roy. Soc. A 461, 253 (2004)
M.D. Towler, N.J. Russell, A. Valentini, Time scales for dynamical relaxation to the Born rule, Proc. R. Soc. A 468, 990 (2012)
K. Hornberger, S. Gerlich, P. Haslinger, S. Nimmrichter, M. Arndt, Quantum interference of clusters and molecules, Rev. Mod. Phys. 84, 157 (2012)
P.C.E. Stamp, Rationale for a correlated worldline theory of quantum gravity, New. J. Phys. 17, 065017 (2015)
P.C.E. Stamp, in 4th lecture given at the College de France (Paris, 2016)
G. Tastevin, F. Laloë, Surrealistic Bohmian trajectories do not occur with macroscopic pointers, Eur. Phys. J. D 72, 183 (1981)
J.S. Bell, Bertlmann’s socks and the nature of reality, J. Phys. Colloques C2, 41 (1981). [Reprinted in pp. 139–158 of [41]]
J.S. Bell, Speakable and Unspeakable in Quantum Mechanics, (Cambridge University Press, 1987); second augmented edition (2004)
N. Gisin, Stochastic quantum dynamics and relativity, Helv. Phys. Acta 62, 363 (1989)
A. Bassi, K. Hejazi, No-faster-than-light-signaling implies linear evolutions. A rederivation, Eur. J. Phys. 36, 055027 (2015)
L. Diosi, Nonlinear Schrödinger equation in foundations: summary of 4 catches, J. Phys.: Conf. Ser. 701, 012019 (2016)
S. Nimmrichter, K. Hornberger, Stochastic extensions of the regularized Schrödinger-Newton equation, Phys. Rev. D 91, 024016 (2015)
A. Shimony, Events and processes in the quantum world pp. 182–203 in: Quantum concepts in Space and Timeedited by R. Penrose, C. Isham, (Clarendon Press, Oxford, 1986)
P. Pearle, E. Squires, Bound state excitation, nucleon decay experiments, and models of wave function collapse, Phys. Rev. Lett. 73, 1 (1993)
Ph. Blanchard, A. Jadczyk, A. Ruschhaupt, How events come into being: EEQT, particle tracks, quantum chaos and tunneling time, in Mysteries, Puzzles and Paradoxes in Quantum Mechanics, edited by R. Bonifacio, American Institute of Physics, AIP Conference Proceedings, no. 461 (1999) [J. Mod. Opt. 47, 2247 (2000)]
D. Bohm, J. Bub, A proposed solution of the measurement problem in quantum mechanics by hidden variable theory, Rev. Mod. Phys. 38, 453 (1966)
A. Tilloy, Ghirardi-Rimini-Weber model with massive flashes, Phys. Rev. D 97, 021502 (2017)
W. Struyve, Semi-classical approximations based on Bohmian mechanics (2015) https://arXiv:1507.04771
W. Struyve, Towards a novel approach to semi-classical gravity, in The philosophy of cosmology, edited by K. Chamcham, J. Silk, J.D. Barrow, S. Saunders, (Cambridge University Press, 2017); https://arXiv:1902.02188 (2019)
P. Peter, E. Pinho, N. Pinto-Neto, Tensor perturbations in quantum cosmological backgrounds, J. Cosmol. Astropart. Phys. 07, 014 (2005)
P. Peter, E. Pinho, N. Pinto-Neto, Gravitational wave background in perfect fluid quantum cosmologies, Phys. Rev. D 73, 104017 (2006)
E. Pinho, N. Pinto-Neto, Scalar and vector perturbations in quantum cosmological backgrounds, Phys. Rev. D 76, 023506 (2007)
C. Møller, Les théories relativistes de la gravitation (Colloques internationaux du CNRS, Paris, 1959)
L. Rosenfeld, On the quantization of fields, Nucl. Phys. 40, 353 (1963)
L. Rosenfeld, in Quantentheorie und Gravitation in Einstein symposium 1965 (Akademie, Berlin 1966) [English translation in page 599 of selected papers of L. Rosenfeld, Boston studies in the philosophy of science, edited by R.S. Cohen, J.J. Stachelin (Reidel, 1979)]
K. Eppley, E. Hahhah, The necessity of quantizing the gravitational field, Found. Phys. 7, 51 (1977)
G. Baym, T. Ozawa, Two-slit diffraction with highly charged particles: Niels Bohr’s consistency argument that the electromagnetic field must be quantized, Proc. Nat. Acad. Sci. USA 106, 3035 (2009)
S. Bose, A. Mazumdar, G.W. Morley, H. Ulbricht, M. Toros, M. Paternostro, A.A. Geraci, P.F. Barker, M.S. Kim, G. Milnurn, Spin entanglement witness for quantum gravity, Phys. Rev. Lett. 119, 240401 (2017)
C. Marletto, V. Vedral, Gravitationnally induced entanglement between two massive particles is sufficient evidence of quantum effects of gravity, Phys. Rev. Lett. 119, 240402 (2017)
A. Belenchia, R.M. Wald, F. Giacomini, E. Castro-Ruiz, C. Brukner, M. Aspelmeyer, Quantum superposition of massive objects and the quantization of gravity, Phys. Rev. D 98, 126009 (2018)
A. Tilloy, Does gravity have to be quantized? Lessons from non-relativistic toy models, https://arXiv:1903.01823 (2019)
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Laloë, F. A model of quantum collapse induced by gravity. Eur. Phys. J. D 74, 25 (2020). https://doi.org/10.1140/epjd/e2019-100434-1
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DOI: https://doi.org/10.1140/epjd/e2019-100434-1