Brownian motion and polarized three-dimensional quantum vacuum
Keywords:Brownian motion, three-dimensional quantum vacuum, variable quantum vacuum energy density, perturbative fluctuation of the quantum vacuum energy density
A nonlinear model of Brownian motion is developed in a three-dimensional quantum vacuum defined by a variable quantum vacuum energy density corresponding to processes of creation/annihilation of virtual particles. In this model, the polarization of the quantum vacuum determined by a perturbative fluctuation of the quantum vacuum energy density associated with a fluctuating viscosity, which mimics the action of dark matter, emerges as the fundamental entity which generates the Brownian motion.
R. Brown, “XXVII. A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies”, Philosophical Magazine 4, 21, 161-173 (1828); Ann. Phys. Chem. 14, 294 (1828).
A. Einstein, “On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat”, Annalen der Physik 17, 549-560 (1905).
W. Sutherland, “A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin”, Philosophical Magazine 9, 54, 781-785 (1905).
M. von Smoluchowski, "Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen", Annalen der Physik 21, 14, 756-780 (1906).
P. Langevin, “On the theory of Brownian motion”, C. R. Acad. Sci. Paris 146, 530-533 (1908).
J. Perrin, “L’agitation moléculaire et le mouvement brownien”, Comptes Rendus (Paris) 146, 967 (1908).
J. Perrin, “Mouvement Brownien et Realite Moleculaire”, Annales de Chimie et de Physique 18, 5 (1909).
I. Nordlund, Zeitschrift für Physikalische Chemie 87, 40 (1914).
E. Kappler, Annalen der Physik 11, 233 (1931).
T. Cheng, R. Primulando and M. Spinrath, “Dark matter induced Brownian motion”, The European Physical Journal C 80, 519 (2020); e-print arXiv:1906.07356v2 [hep-ph].
D. Fiscaletti and A. Sorli, “Perspectives about quantum mechanics in a model of a three-dimensional quantum vacuum where time is a mathematical dimension”, SOP Transactions on Theoretical Physics 1, 3, 11-38 (2014).
D. Fiscaletti and A. Sorli, “Space-time curvature of general relativity and energy density of a three-dimensional quantum vacuum”, Annales UMCS Sectio AAA: Physica LXIX, 55-81 (2014).
D. Fiscaletti, The timeless approach. Frontier perspectives in 21st century physics, 1st ed., World Scientific, Singapore (2015).
D. Fiscaletti, “About dark energy and dark matter in a three-dimensional quantum vacuum model”, Foundations of Physics 46, 10, 1307-1340 (2016).
D. Fiscaletti and A. Sorli, “About a three-dimensional quantum vacuum as the ultimate origin of gravity, electromagnetic field, dark energy … and quantum behaviour”, Ukrainian Journal of Physics 61, 5, 413-431 (2016).
D. Fiscaletti and A. Sorli, “Dynamic quantum vacuum and relativity”, Annales UMCS Sectio AAA: Physica LXXI, 11-52 (2016).
D. Fiscaletti, “What is the actual behaviour of the electron? From Bohm’s approach to the transactional interpretation… to a three-dimensional timeless non-local quantum vacuum”, Electronic Journal of Theoretical Physics 13, 35, 1-26 (2016).
D. Fiscaletti and A. Sorli, “About electroweak symmetry breaking, electroweak vacuum and dark matter in a new suggested proposal of completion of the Standard Model in terms of energy fluctuations of a timeless three-dimensional quantum vacuum”, Quantum Physics Letters 5, 3, 55-69 (2016).
D. Fiscaletti and A. Sorli, “Quantum vacuum energy density and unifying perspectives between gravity and quantum behaviour of matter”, Annales de la Fondation Louis de Broglie 42, 2, 251-297 (2017).
D. Fiscaletti and A. Sorli, “Quantum relativity: variable energy density of quantum vacuum as the origin of mass, gravity and the quantum behaviour”, Ukrainian Journal of Physics 63, 7, 623-644 (2018).
I. Licata and L. Chiatti, “Timeless approach to quantum jumps”, Quanta 4, 10-26 (2015).
L. Chiatti and I. Licata, “Particle model from quantum foundations”, Quantum Studies: Mathematics and Foundations 4, 181-204 (2016).
D. Fiscaletti, “About dark matter as an emerging entity from elementary energy density fluctuations of a three-dimensional quantum vacuum”, Journal of Theoretical and Applied Physics 14, 3, 203-222 (2020).
V. Sbitnev, “Dark matter is a manifestation of the vacuum Bose-Einstein condensate”, arXiv:1601:04536v2 [physics.gen-ph] (2016).
R. Tsekov, “Nonlinear theory of quantum Brownian motion”, International Journal of Theoretical Physics 48, 85-94 (2009).
LHC Guide, CERN Brochure, 2017, http://cds.cern.ch/record/2255762.
J. Aasi et al. [LIGO Scientific], Classical and Quantum Gravity 32, 074001 (2015) [arXiv:1411.4547 [gr-qc]].
K. Somiya [KAGRA], Classical and Quantum Gravity 29, 124007 (2012) [arXiv:1111.7185 [gr-qc]].
Planck Collaboration, P.A.R. Ade et al., “Planck 2015 results - XVIII. Background geometry and topology of the Universe”, Astron. Astrophys., 594 (2016) A18, [arXiv:1502.0159].
S. Weinberg, Cosmology, Oxford University Press, Oxford (2008).
C.H.G. Bessa, V.B. Bezerra, E.R. Bezerra de Mello and H.F. Mota, “Quantum Brownian motion in an analog Friedmann-Robertson-Walker geometry”, Physical Review D 95, 085020 (2017); e-print arXiv:1703.06525v2 [hep-th].
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