3,150 research outputs found
Hypersurface Bohm-Dirac models
We define a class of Lorentz invariant Bohmian quantum models for N entangled
but noninteracting Dirac particles. Lorentz invariance is achieved for these
models through the incorporation of an additional dynamical space-time
structure provided by a foliation of space-time. These models can be regarded
as the extension of Bohm's model for N Dirac particles, corresponding to the
foliation into the equal-time hyperplanes for a distinguished Lorentz frame, to
more general foliations. As with Bohm's model, there exists for these models an
equivariant measure on the leaves of the foliation. This makes possible a
simple statistical analysis of position correlations analogous to the
equilibrium analysis for (the nonrelativistic) Bohmian mechanics.Comment: 17 pages, 3 figures, RevTex. Completely revised versio
J.S. Bell's Concept of Local Causality
John Stewart Bell's famous 1964 theorem is widely regarded as one of the most
important developments in the foundations of physics. It has even been
described as "the most profound discovery of science." Yet even as we approach
the 50th anniversary of Bell's discovery, its meaning and implications remain
controversial. Many textbooks and commentators report that Bell's theorem
refutes the possibility (suggested especially by Einstein, Podolsky, and Rosen
in 1935) of supplementing ordinary quantum theory with additional ("hidden")
variables that might restore determinism and/or some notion of an
observer-independent reality. On this view, Bell's theorem supports the
orthodox Copenhagen interpretation. Bell's own view of his theorem, however,
was quite different. He instead took the theorem as establishing an "essential
conflict" between the now well-tested empirical predictions of quantum theory
and relativistic \emph{local causality}. The goal of the present paper is, in
general, to make Bell's own views more widely known and, in particular, to
explain in detail Bell's little-known mathematical formulation of the concept
of relativistic local causality on which his theorem rests. We thus collect and
organize many of Bell's crucial statements on these topics, which are scattered
throughout his writings, into a self-contained, pedagogical discussion
including elaborations of the concepts "beable", "completeness", and
"causality" which figure in the formulation. We also show how local causality
(as formulated by Bell) can be used to derive an empirically testable Bell-type
inequality, and how it can be used to recapitulate the EPR argument.Comment: 19 pages, 4 figure
- …