Foundations of Quantum Mechanics
Do Bell inequality violations imply absence of local realism?
[P69] A.E. Allahverdyan, A. Khrennikov and Th.M. N., Brownian Entanglement ,
Phys. Rev. A 72, 032102 (2005)
Many experiments have shown violation of Bell inequalities, the first ones were
by the Clauser and the Aspect groups. There are several loopholes, which to date have
not been closed simultaneously in a single experiment.
If one believes in the applicability of quantum mechanics, the loophole issue
should be solvable one day. But even then one may wonder whether Bell made the
proper connection to absence of local realism.
On the basis of a physical reasoning we argue that this connection is based on
a misconception:
[C44] Th. M. Nieuwenhuizen,
Where Bell went wrong ,
arXiv:0812.3058,
AIP Conf. Proc. 1101: Foundations of Probability and Physics - 5;
Luigi Accardi, Guillaume Adenier, Christopher A. Fuchs, Gregg Jaeger, Andrei Yu. Khrennikov,
Jan-Ake Larsson and Stig Stenholm, eds,
(Am. Inst. Phys., Melville, NY, 2009), pp 127-133.
Sub-quantum mechanics
An insight underlined by our results on quantum measurements
is that quantum mechanics only describes statistics of outcomes of experiments:
Individual experiments occur in nature, but we have no theory to describe them.
This has led me to consider more complete theories.
In the present approach I consider a classical description for the quantum mechanical
hydrogen atom. It deals with the electron's Newtonian motion in the Coulomb potential of the nucleus,
its Lorentz damping and an unspecified but weak noise mechanism, that prevents the electron to fall
in the nucleus by kicking it away. A stable ground state is supposed to arise from this setup.
In this work I propose phase space densities, that, by construction, reproduce the quantum probabilities
(squares of wavefunctions) in coordinate space.
But they are non-negative everywhere and their representation in momentum space differs from the one given by
the Wigner function.
Some insights follow, while, to put it mildly, at least one puzzle shows up.
ITFA-2005-29: Th. M. Nieuwenhuizen,
Classical phase space density for the relativistic hydrogen atom,
Proceedings of
Quantum Theory: reconsideration of foundations-3, June 6-11, 2005,
V�xj� University, Sweden. AIP Conference Series, to appear.
Entanglement in classical physics
Quantum entanglement is today's paradigm of quantum mechanics.
But entanglement can also occur in classical physics, as we demonstrated on the case of Brownian motion.
It shows up there if one looks at the coarsed timescale, where the momentum has become a statistical variable.
In other words: on timescales where the Brownian particles undergo may scatterings with the
fluid particles, and the instantaneous velocity has no meaning. See [p69].
This work may shed light on the possible relation between this type of entanglement and the one
that may arise when going from sub-quantum mechanics to quantum mechanics.