384 research outputs found
EPR-Bell Nonlocality, Lorentz Invariance, and Bohmian Quantum Theory
We discuss the problem of finding a Lorentz invariant extension of Bohmian
mechanics. Due to the nonlocality of the theory there is (for systems of more
than one particle) no obvious way to achieve such an extension. We present a
model invariant under a certain limit of Lorentz transformations, a limit
retaining the characteristic feature of relativity, the non-existence of
absolute time resp. simultaneity. The analysis of this model exemplifies an
important property of any Bohmian quantum theory: the quantum equilibrium
distribution cannot simultaneously be realized in all
Lorentz frames of reference.Comment: 24 pages, LaTex, 4 figure
Bohm's interpretation and maximally entangled states
Several no-go theorems showed the incompatibility between the locality
assumption and quantum correlations obtained from maximally entangled spin
states. We analyze these no-go theorems in the framework of Bohm's
interpretation. The mechanism by which non-local correlations appear during the
results of measurements performed on distant parts of entangled systems is
explicitly put into evidence in terms of Bohmian trajectories. It is shown that
a GHZ like contradiction of the type+1=-1 occurs for well-chosen initial
positions of the Bohmian trajectories and that it is this essential
non-classical feature that makes it possible to violate the locality condition.Comment: 18 page
Modal quantum theory
We present a discrete model theory similar in structure to ordinary quantum
mechanics, but based on a finite field instead of complex amplitudes. The
interpretation of this theory involves only the "modal" concepts of possibility
and necessity rather than quantitative probability measures. Despite its
simplicity, our model theory includes entangled states and has versions of both
Bell's theorem and the no cloning theorem.Comment: Presented at the 7th Workshop on Quantum Physics and Logic, Oxford
University (29-30 May 2010). Revised 1 Aug 2011 in response to referee
comment
The quantum world is not built up from correlations
It is known that the global state of a composite quantum system can be
completely determined by specifying correlations between measurements performed
on subsystems only. Despite the fact that the quantum correlations thus suffice
to reconstruct the quantum state, we show, using a Bell inequality argument,
that they cannot be regarded as objective local properties of the composite
system in question. It is well known since the work of J.S. Bell, that one
cannot have locally preexistent values for all physical quantities, whether
they are deterministic or stochastic. The Bell inequality argument we present
here shows this is also impossible for correlations among subsystems of an
individual isolated composite system. Neither of them can be used to build up a
world consisting of some local realistic structure. As a corrolary to the
result we argue that entanglement cannot be considered ontologically robust.
The argument has an important advantage over others because it does not need
perfect correlations but only statistical correlations. It can therefore easily
be tested in currently feasible experiments using four particle entanglement.Comment: Published version. Title change
A toy model for quantum mechanics
The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)]
to argue in favor of an epistemic view of quantum mechanics is extended by
generalizing his definition of pure states (i.e. states of maximal knowledge)
and by associating measurements with all pure states. The new toy model does
not allow signaling but, in contrast to the Spekkens model, does violate
Bell-CHSH inequalities. Negative probabilities are found to arise naturally
within the model, and can be used to explain the Bell-CHSH inequality
violations.Comment: in which the author breaks his vow to never use the words "ontic" and
"epistemic" in publi
Experimental Realization of the Quantum Box Problem
The three-box problem is a gedankenexperiment designed to elucidate some
interesting features of quantum measurement and locality. A particle is
prepared in a particular superposition of three boxes, and later found in a
different (but nonorthogonal) superposition. It was predicted that appropriate
"weak" measurements of particle position in the interval between preparation
and post-selection would find the particle in two different places, each with
certainty. We verify these predictions in an optical experiment and address the
issues of locality and of negative probability.Comment: 5 pages, 4 figure
Rotationally invariant proof of Bell's theorem without inequalities
The singlet state of two spin-3/2 particles allows a proof of Bell's theorem
without inequalities with two distinguishing features: any local observable can
be regarded as an Einstein-Podolsky-Rosen element of reality, and the
contradiction with local realism occurs not only for some specific local
observables but for any rotation whereof.Comment: REVTeX4, 3 page
Bell inequalities as constraints on unmeasurable correlations
The interpretation of the violation of Bell-Clauser-Horne inequalities is
revisited, in relation with the notion of extension of QM predictions to
unmeasurable correlations. Such extensions are compatible with QM predictions
in many cases, in particular for observables with compatibility relations
described by tree graphs. This implies classical representability of any set of
correlations , , , and the equivalence of the
Bell-Clauser-Horne inequalities to a non void intersection between the ranges
of values for the unmeasurable correlation associated to different
choices for B. The same analysis applies to the Hardy model and to the "perfect
correlations" discussed by Greenberger, Horne, Shimony and Zeilinger. In all
the cases, the dependence of an unmeasurable correlation on a set of variables
allowing for a classical representation is the only basis for arguments about
violations of locality and causality.Comment: Some modifications have been done in order to improve clarity of
presentation and comparison with other approache
Hidden variables with nonlocal time
To relax the apparent tension between nonlocal hidden variables and
relativity, we propose that the observable proper time is not the same quantity
as the usual proper-time parameter appearing in local relativistic equations.
Instead, the two proper times are related by a nonlocal rescaling parameter
proportional to |psi|^2, so that they coincide in the classical limit. In this
way particle trajectories may obey local relativistic equations of motion in a
manner consistent with the appearance of nonlocal quantum correlations. To
illustrate the main idea, we first present two simple toy models of local
particle trajectories with nonlocal time, which reproduce some nonlocal quantum
phenomena. After that, we present a realistic theory with a capacity to
reproduce all predictions of quantum theory.Comment: 16 pages, accepted for publication in Found. Phys., misprints
corrected, references update
Sturmian morphisms, the braid group B_4, Christoffel words and bases of F_2
We give a presentation by generators and relations of a certain monoid
generating a subgroup of index two in the group Aut(F_2) of automorphisms of
the rank two free group F_2 and show that it can be realized as a monoid in the
group B_4 of braids on four strings. In the second part we use Christoffel
words to construct an explicit basis of F_2 lifting any given basis of the free
abelian group Z^2. We further give an algorithm allowing to decide whether two
elements of F_2 form a basis or not. We also show that, under suitable
conditions, a basis has a unique conjugate consisting of two palindromes.Comment: 25 pages, 4 figure
- …