The paper investigates the non-local property of quantum mechanics by
analyzing the role of the quantum potential in generating the non-local
dynamics and how they are perturbed in presence of noise. The resulting open
quantum dynamics much depend by the strength of the Hamiltonian interaction:
Weakly bounded systems may not be able to maintain the quantum superposition of
states on large distances and lead to the classical stochastic evolution. The
stochastic hydrodynamic quantum approach shows that the wave-function collapse
to an eigenstates can be described by the model itself and that the minimum uncertainty
principle is compatible with the relativistic postulate about the light speed
as the maximum velocity of transmission of interaction. The paper shows that
the Lorenz invariance of the quantum potential does not allow super-luminal
transmission of information in measurements on quantum entangled states.
Einstein, A., Podolsky, B. and Rosen, N. (1935)
Can Quantum-Mechanical Description of Physical
Reality Be Considered Complete? Physical
Review, 47, 777-780. http://dx.doi.org/10.1103/PhysRev.47.777
Greenberger, D.M., Horne, M.A., Shimony, A.
and Zeilinger, A. (1990)
Bell’s Theorem without Inequalities. American Journal
of Physics, 58,
1131-1143. http://dx.doi.org/10.1119/1.16243
Bohm, D.
(1952) A Suggested Interpretation
of the Quantum Theory in Terms of “Hidden” Variables. I. Physical
Review, 85,
166. http://dx.doi.org/10.1103/PhysRev.85.166
Guerra, F. and Ruggero, P. (1973)
New Interpretation of the Euclidean-Markov Field in
the Framework of Physical Minkowski Space-Time. Physical
Review Letters, 31, 1022. http://dx.doi.org/10.1103/PhysRevLett.31.1022
Jona, G., Martinelli, F. and Scoppola, E. (1981)
New Approach to the Semiclassical Limit of Quantum
Mechanics. Communications
in Mathematical Physics, 80, 233-254.
Ruggiero, P.
and Zannetti, M. (1983) Microscopic Derivation of the Stochastic Process for the
Quantum Brownian Oscillator. Physical
Review A, 28,
987. http://dx.doi.org/10.1103/PhysRevA.28.987
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 Lambda Point and That at the
Water-Ice Phase Transition. Physical
Review & Research International, 3, 348-366.
Weiner, J.H. and Askar, A. (1971) Particle
Method for the Numerical Solution of the Time-Dependent Schrodinger Equation. The Journal of Chemical Physics, 54,
3534. http://dx.doi.org/10.1063/1.1675377
Terlecki, G., Grun,
N. and Scheid, W. (1982) Solution of the Time-Dependent Schrodinger Equation with a Trajectory Method and
Application to
H-H Scattering. Physics
Letters A, 88,
33-36. http://dx.doi.org/10.1016/0375-9601(82)90417-0
Gardner, C.L. (1994) The Quantum Hydrodynamic
Model for Semiconductor Devices. SIAM
Journal on Applied Mathematics, 54,
409-427. http://dx.doi.org/10.1137/S0036139992240425
Mariano,
A., Facchi, P.
and Pascazio, S.
(2001) Decoherence
and Fluctuations in Quantum Interference Experiments. Fortschritte
der Physik, 49,
1033-1039.
Cerruti, N.R., Lakshminarayan, A., Lefebvre, T.H.
and Tomsovic, S. (2000) Exploring Phase Space Localization of
Chaotic Eigenstates via Parametric Variation. Physical ReviewE, 63,
016208. http://dx.doi.org/10.1103/PhysRevE.63.016208
Calzetta, E. and Hu, B.L. (1995) Quantum Fluctuations, Decoherence of
the Mean Field, and Structure Formation in the Early Universe. Physical ReviewD, 52, 6770-6788. http://dx.doi.org/10.1103/PhysRevD.52.6770
Wang, C., Bonifacio, P., Bingham, R. and Mendonca, J.T. (2008) Detection of Quantum Decoherence Due to
Spacetime Fluctuations. 37th
COSPAR Scientific Assembly, Montréal, 13-20 July 2008, 3390.
Bousquet, D., Hughes, K.H., Micha, D.A.
and Burghardt, I. (2001) Extended Hydrodynamic Approach to Quantum-Classical
Nonequilibrium Evolution. I. Theory. The Journal of Chemical Physics, 134, 064116. http://dx.doi.org/10.1063/1.3553174
Morato, L.M. and Ugolini, S. (2011) Stochastic Description of a Bose-Einstein
Condensate. Annales
Henri Poincaré, 12, 1601-1612. http://dx.doi.org/10.1007/s00023-011-0116-1
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. http://dx.doi.org/10.11648/j.ajpc.20130206.12
Chiarelli, P. (2013) The Uncertainty Principle Derived by the Finite
Transmission Speed of Light and Information. Journal
of Advanced Physics, 3, 257-266.
Chiarelli, P. (2015) The Quantum Limit to the Black Hole Mass Derived by the Quantization of
Einstein Equation. Class. Quantum Physics. ArXiv: 1504.07102.
