207 research outputs found
Reichenbach's Common Cause Principle in Algebraic Quantum Field Theory with Locally Finite Degrees of Freedom
In the paper it will be shown that Reichenbach's Weak Common Cause Principle
is not valid in algebraic quantum field theory with locally finite degrees of
freedom in general. Namely, for any pair of projections A and B supported in
spacelike separated double cones O(a) and O(b), respectively, a correlating
state can be given for which there is no nontrivial common cause (system)
located in the union of the backward light cones of O(a) and O(b) and commuting
with the both A and B. Since noncommuting common cause solutions are presented
in these states the abandonment of commutativity can modulate this result:
noncommutative Common Cause Principles might survive in these models
Local Operations and Completely Positive Maps in Algebraic Quantum Field Theory
Einstein introduced the locality principle which states that all physical
effect in some finite space-time region does not influence its space-like
separated finite region. Recently, in algebraic quantum field theory, R\'{e}dei
captured the idea of the locality principle by the notion of operational
separability. The operation in operational separability is performed in some
finite space-time region, and leaves unchanged the state in its space-like
separated finite space-time region. This operation is defined with a completely
positive map. In the present paper, we justify using a completely positive map
as a local operation in algebraic quantum field theory, and show that this
local operation can be approximately written with Kraus operators under the
funnel property
Remarks on Causality in Relativistic Quantum Field Theory
It is shown that the correlations predicted by relativistic quantum field
theory in locally normal states between projections in local von Neumann
algebras \cA(V_1),\cA(V_2) associated with spacelike separated spacetime
regions have a (Reichenbachian) common cause located in the union of
the backward light cones of and . Further comments on causality and
independence in quantum field theory are made.Comment: 10 pages, Latex, Quantum Structures 2002 Conference Proceedings
submission. Minor revision of the order of definitions on p.
Noncommutative causality in algebraic quantum field theory
In the paper it will be argued that embracing noncommuting common causes in the causal explanation of quantum correlations in algebraic quantum field theory has the following two beneficial consequences: it helps (i) to maintain the validity of Reichenbach's Common Causal Principle and (ii) to provide a local common causal explanation for a set of correlations violating the Bell inequality
A portrait of Lewis John Stadler 1896-1954
G. P. REDEI, UNIVERSITY OF MISSOURI, COLUMBIA, MISSOURI
Applying causality principles to the axiomatization of probabilistic cellular automata
Cellular automata (CA) consist of an array of identical cells, each of which
may take one of a finite number of possible states. The entire array evolves in
discrete time steps by iterating a global evolution G. Further, this global
evolution G is required to be shift-invariant (it acts the same everywhere) and
causal (information cannot be transmitted faster than some fixed number of
cells per time step). At least in the classical, reversible and quantum cases,
these two top-down axiomatic conditions are sufficient to entail more
bottom-up, operational descriptions of G. We investigate whether the same is
true in the probabilistic case. Keywords: Characterization, noise, Markov
process, stochastic Einstein locality, screening-off, common cause principle,
non-signalling, Multi-party non-local box.Comment: 13 pages, 6 figures, LaTeX, v2: refs adde
Flower differentiation in arabidopsis
There is a consensus among developmental geneticists that few generalizations are possible at the present status of the field, and even the boundaries are difficult to define. Yet in few special cases, consistent facts have been accumulated which point to systems of controls of differentiation.In the facultative long-day plant Arabidopsis, the differentiation of flower primordia is controlled by several gene loci. Recessive mutations may determine in a qualitatively distinct manner the onset of flower development. Continuous illumination in contrast to 8-9 hours daily cycles of light promotes flowering in all genotypes. Mutants at the ld locus are incapable of flowering under short days and entail a critical day-length. Different alleles at the gi locus require several times as long period for flower induction than the wild type under 24 hours light yet under short days they do not differ, very conspicuously from the standard type. Mutants at the co locus are late flowering and recessive under long days but they are more precocious than the wild type under short days and they display dominance. In total darkness, the wild type and all mutants flower early. The aseptic feeding of 5-bromodeoxyuridine highly accelerates flower differentiation in all genotypes under long days and also under short days with the exception of the ld mutants. The analog is incorporated into the DNA of all types. Bromodeoxyuridine-grown plants accumulate higher amounts of radioactivity, provided by 14[subscript C]-amino acids, into a chromatin fraction. The experimental observations support the view that flowering in this plant is under negative control and bromodeoxyuridineis hampering the synthesis of a postulated suppressor.G. P. REDEI, GREGORIA ACEDO AND G. GAVAZZI, University of Missouri, Columbia, Mo
Extended Representations of Observables and States for a Noncontextual Reinterpretation of QM
A crucial and problematical feature of quantum mechanics (QM) is
nonobjectivity of properties. The ESR model restores objectivity reinterpreting
quantum probabilities as conditional on detection and embodying the
mathematical formalism of QM into a broader noncontextual (hence local)
framework. We propose here an improved presentation of the ESR model containing
a more complete mathematical representation of the basic entities of the model.
We also extend the model to mixtures showing that the mathematical
representations of proper mixtures does not coincide with the mathematical
representation of mixtures provided by QM, while the representation of improper
mixtures does. This feature of the ESR model entails that some interpretative
problems raising in QM when dealing with mixtures are avoided. From an
empirical point of view the predictions of the ESR model depend on some
parameters which may be such that they are very close to the predictions of QM
in most cases. But the nonstandard representation of proper mixtures allows us
to propose the scheme of an experiment that could check whether the predictions
of QM or the predictions of the ESR model are correct.Comment: 17 pages, standard latex. Extensively revised versio
Algebras of Measurements: the logical structure of Quantum Mechanics
In Quantum Physics, a measurement is represented by a projection on some
closed subspace of a Hilbert space. We study algebras of operators that
abstract from the algebra of projections on closed subspaces of a Hilbert
space. The properties of such operators are justified on epistemological
grounds. Commutation of measurements is a central topic of interest. Classical
logical systems may be viewed as measurement algebras in which all measurements
commute. Keywords: Quantum measurements, Measurement algebras, Quantum Logic.
PACS: 02.10.-v.Comment: Submitted, 30 page
Extending structures I: the level of groups
Let be a group and a set such that . We shall describe
and classify up to an isomorphism of groups that stabilizes the set of all
group structures that can be defined on such that is a subgroup of .
A general product, which we call the unified product, is constructed such that
both the crossed product and the bicrossed product of two groups are special
cases of it. It is associated to and to a system called a group extending
structure and we denote it by . There exists a group structure on
containing as a subgroup if and only if there exists an isomorphism of
groups , for some group extending structure
. All such
group structures on are classified up to an isomorphism of groups that
stabilizes by a cohomological type set . A Schreier type theorem is proved and an explicit example is given: it
classifies up to an isomorphism that stabilizes all groups that contain
as a subgroup of index 2.Comment: 17 pages; to appear in Algebras and Representation Theor
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