Many worlds and modality in the interpretation of quantum mechanics: an algebraic approach

Many worlds interpretations (MWI) of quantum mechanics avoid the measurement problem by considering every term in the quantum superposition as actual. A seemingly opposed solution is proposed by modal interpretations (MI) which state that quantum mechanics does not provide an account of what `actually is the case', but rather deals with what `might be the case', i.e. with possibilities. In this paper we provide an algebraic framework which allows us to analyze in depth the modal aspects of MWI. Within our general formal scheme we also provide a formal comparison between MWI and MI, in particular, we provide a formal understanding of why --even though both interpretations share the same formal structure-- MI fall pray of Kochen-Specker (KS) type contradictions while MWI escape them.Comment: submitted to the Journal of Mathematical Physic

Involutive Categories and Monoids, with a GNS-correspondence

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. The core of the so-called Gelfand-Naimark-Segal (GNS) construction is identified as a bijective correspondence between states on involutive monoids and inner products. This correspondence exists in arbritrary involutive categories

On the lattice structure of probability spaces in quantum mechanics

Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models' approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.Comment: arXiv admin note: substantial text overlap with arXiv:1008.416

Nonlinear self-action of light through biological suspensions

It is commonly thought that biological media cannot exhibit an appreciable nonlinear optical response. We demonstrate, for the first time to our knowledge, a tunable optical nonlinearity in suspensions of cyanobacteria that leads to robust propagation and strong self-action of a light beam. By deliberately altering the host environment of the marine bacteria, we show experimentally that nonlinear interaction can result in either deep penetration or enhanced scattering of light through the bacterial suspension, while the viability of the cells remains intact. A theoretical model is developed to show that a nonlocal nonlinearity mediated by optical forces (including both gradient and forward-scattering forces) acting on the bacteria explains our experimental observation

Hadronization of a Quark-Gluon Plasma in the Chromodielectric Model

We have carried out simulations of the hadronization of a hot, ideal but effectively massive quark-gluon gas into color neutral clusters in the framework of the semi-classical SU(3) chromodielectric model. We have studied the possible quark-gluon compositions of clusters as well as the final mass distribution and spectra, aiming to obtain an insight into relations between hadronic spectral properties and the confinement mechanism in this model.Comment: 34 pages, 37 figure

A geometrical origin for the covariant entropy bound

Causal diamond-shaped subsets of space-time are naturally associated with operator algebras in quantum field theory, and they are also related to the Bousso covariant entropy bound. In this work we argue that the net of these causal sets to which are assigned the local operator algebras of quantum theories should be taken to be non orthomodular if there is some lowest scale for the description of space-time as a manifold. This geometry can be related to a reduction in the degrees of freedom of the holographic type under certain natural conditions for the local algebras. A non orthomodular net of causal sets that implements the cutoff in a covariant manner is constructed. It gives an explanation, in a simple example, of the non positive expansion condition for light-sheet selection in the covariant entropy bound. It also suggests a different covariant formulation of entropy bound.Comment: 20 pages, 8 figures, final versio

Potential for sulfide-hosted by-products from the iron oxide-apatite deposits at Kiruna? A mineralogical perspective

Sulfide mineralisation types in the Kiirunavaara and Per Geijer iron oxide-apatite deposits in the Kiruna district have been studied by mineralogical means to infer a preliminary potential for future by-products of Co, Cu, and sulfuric acid. Based on the dominance of pyrite over other sulfides, e.g., chalcopyrite and bornite-digenite solid solution series minerals, the main potential can be attributed to pyrite as the source of sulfuric acid. Significant concentrations of cobalt in pyrite types from both deposits may indicate an economic potential if proven processable in the future. Copper minerals have low concentrations of deleterious elements but occur less frequently compared to pyrite, so their potential is not yet tangible. Further studies are planned to evaluate the full potential of sulfides