26,631 research outputs found
Hidden assumptions in the derivation of the Theorem of Bell
John Bell's inequalities have already been considered by Boole in 1862. Boole
established a one-to-one correspondence between experimental outcomes and
mathematical abstractions of his probability theory. His abstractions are
two-valued functions that permit the logical operations AND, OR and NOT and are
the elements of an algebra. Violation of the inequalities indicated to Boole an
inconsistency of definition of the abstractions and/or the necessity to revise
the algebra. It is demonstrated in this paper, that a violation of Bell's
inequality by Einstein-Podolsky-Rosen type of experiments can be explained by
Boole's ideas. Violations of Bell's inequality also call for a revision of the
mathematical abstractions and corresponding algebra. It will be shown that this
particular view of Bell's inequalities points toward an incompleteness of
quantum mechanics, rather than to any superluminal propagation or influences at
a distance
Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
I report, emphasizing some key open issues and some aspects that are
particularly relevant for phenomenology, on the status of the development of
"doubly-special" relativistic ("DSR") theories with both an
observer-independent high-velocity scale and an observer-independent
small-length/large-momentum scale, possibly relevant for the
Planck-scale/quantum-gravity realm. I also give a true/false characterization
of the structure of these theories. In particular, I discuss a DSR scenario
without modification of the energy-momentum dispersion relation and without the
-Poincar\'e Hopf algebra, a scenario with deformed Poincar\'e
symmetries which is not a DSR scenario, some scenarios with both an invariant
length scale and an invariant velocity scale which are not DSR scenarios, and a
DSR scenario in which it is easy to verify that some observable relativistic
(but non-special-relativistic) features are insensitive to possible nonlinear
redefinitions of symmetry generators.Comment: This is the preprint version of a paper prepared for a special issue
"Feature Papers: Symmetry Concepts and Applications" of the journal Symmetr
- …