Quantum measures and the coevent interpretation

This paper first reviews quantum measure and integration theory. A new representation of the quantum integral is presented. This representation is illustrated by computing some quantum (Lebesgue)${}^2$ integrals. The rest of the paper only considers finite spaces. Anhomomorphic logics are discussed and the classical domain of a coevent is studied. Pure quantum measures and coevents are considered and it is shown that pure quantum measures are strictly contained in the extremal elements for the set of quantum measures bounded above by one. Moreover, we prove that any quantum measure on a finite event space \ascript can be transferred to an ordinary measure on an anhomomorphic logic \ascript ^*. In this way, the quantum dynamics on \ascript can be described by a classical dynamics on the larger space \ascript ^*.Comment: one file submitte

Quantum Measure Theory: A New Interpretation

Quantum measure theory can be introduced as a histories based reformulation (and generalisation) of Copenhagen quantum mechanics in the image of classical stochastic theories. These classical models lend themselves to a simple interpretation in which a single history (a single element of the sample space) is deemed to be 'real'; we require only that this real history should not be ruled out by the dynamics, the axioms of which ensure that not all histories are precluded. However, applying this interpretation naively to quantum measure theory we can find experimentally realisable systems (notably the Peres-Kochen-Specker system) in which every history is ruled out by the dynamics, challenging us to formulate a deeper realist framework. Our first response is to hold on to our existing interpretative framework and attempt a revision of the dynamics that would reduce quantum measure theory to a classical dynamics. We explore this approach by examining the histories formulation of a stochastic-collapse model on a simple (discrete) null-lattice, concluding that the drawbacks of this approach outweigh the benefits. Our second response is to abandon our classically inspired interpretation in favour of Sorkin's 'co-events', a more general ontology that still allows for strict realism. In this case the 'potentially real' objects of the theory (the 'beables' in Bell's language) are not individual histories but truth valuation maps, or co-events. We develop & evaluate various co-event schemes that have been suggested to date, finally adopting the multiplicative scheme; the current working model of co-event theory and a promising interpretation of quantum measure theory, though still a work in progress. We conclude by exploring the expression of the dynamics & predictions in this new framework.Comment: Thesis, 155 page

Dynamical Wave Function Collapse Models in Quantum Measure Theory

The structure of Collapse Models is investigated in the framework of Quantum Measure Theory, a histories-based approach to quantum mechanics. The underlying structure of coupled classical and quantum systems is elucidated in this approach which puts both systems on a spacetime footing. The nature of the coupling is exposed: the classical histories have no dynamics of their own but are simply tied, more or less closely, to the quantum histories.Comment: 20 pages, 1 figure. Revised after refereein

Quantum measures and integrals

We show that quantum measures and integrals appear naturally in any $L_2$-Hilbert space $H$. We begin by defining a decoherence operator $D(A,B)$ and it's associated $q$-measure operator $\mu (A)=D(A,A)$ on $H$. We show that these operators have certain positivity, additivity and continuity properties. If $\rho$ is a state on $H$, then D_\rho (A,B)=\rmtr\sqbrac{\rho D(A,B)} and $\mu_\rho (A)=D_\rho (A,A)$ have the usual properties of a decoherence functional and $q$-measure, respectively. The quantization of a random variable $f$ is defined to be a certain self-adjoint operator \fhat on $H$. Continuity and additivity properties of the map f\mapsto\fhat are discussed. It is shown that if $f$ is nonnegative, then \fhat is a positive operator. A quantum integral is defined by \int fd\mu_\rho =\rmtr (\rho\fhat\,). A tail-sum formula is proved for the quantum integral. The paper closes with an example that illustrates some of the theory.Comment: 16 page

Quantum Reality Filters

An anhomomorphic logic \ascript ^* is the set of all possible realities for a quantum system. Our main goal is to find the "actual reality" \phi_a\in\ascript ^* for the system. Reality filters are employed to eliminate unwanted potential realities until only $\phi_a$ remains. In this paper, we consider three reality filters that are constructed by means of quantum integrals. A quantum measure $\mu$ can generate or actualize a \phi\in\ascript ^* if $\mu (A)$ is a quantum integral with respect to $\phi$ for a density function $f$ over events $A$. In this sense, $\mu$ is an "average" of the truth values of $\phi$ with weights given by $f$. We mainly discuss relations between these filters and their existence and uniqueness properties. For example, we show that a quadratic reality generated by a quantum measure is unique. In this case we obtain the unique actual quadratic reality.Comment: 25 page

Comparing invasive and non-invasive of isolated Shigella flexneri by electron microscopy of cell culture, SDS-PAGE and congo red method

Background: The aim of this study was to compare invasive and non-invasive strains of Shigella flexneri isolated from Tehran by a 120 kDa protein band by SDS-PAGE, electron microscopy of cell culture and Congo red dye methods. Methods: S. flexneri strains were isolated by standard bacterial methods from fecal specimens of children attending to the 3 children's hospitals. Phenotype analysis for screening virulent of strains of S. flexneri was done on a plate of tryptic soy agar contained 0.003 Congo red dye. Whole membrane protein preparations were used to examine the protein profiles of the inner and outer membrane of these Gram-negative bacteria. The protein mixture was electrophoresed through a polyacrylamide gel. The gel was stained with Coomassie brilliant blue R250 and destained with ethanol and acetic acid. HeLa cell culture was done by two-step preparations: one for light microscopy and the other for electron microscopy. Results: Some of S. flexneri (46) were Congo red positive colonies. S. flexneri with negative Congo red phenotype could not enter the HeLa cell culture. A 120 kDa protein band was found in 46 of these bacteria which could enter into HeLa cell culture. Pseudopod structures which facilitate bacterial cell-to-cell spread were readily identified by electron microscopy. Discussion: Since the existence of 120-kDa protein band was corresponded to enter of S. flexneri into the HeLa cell culture and correlated with Congo red dye positive, for identification of invasive and non-invasive S. flexneri strains, the use of a 120-kDa protein band by SDSPAGE or a simple, rapid and very cheap Congo red dye method is recommended. Because, there are some deaths due to Shigella sp. in our country, notification on the isolation of these bacteria in both children hospitals laboratories and private clinical laboratories is important