Not throwing out the baby with the bathwater: Bell's condition of local causality mathematically 'sharp and clean'

The starting point of the present paper is Bell's notion of local causality and his own sharpening of it so as to provide for mathematical formalisation. Starting with Norsen's (2007, 2009) analysis of this formalisation, it is subjected to a critique that reveals two crucial aspects that have so far not been properly taken into account. These are (i) the correct understanding of the notions of sufficiency, completeness and redundancy involved; and (ii) the fact that the apparatus settings and measurement outcomes have very different theoretical roles in the candidate theories under study. Both aspects are not adequately incorporated in the standard formalisation, and we will therefore do so. The upshot of our analysis is a more detailed, sharp and clean mathematical expression of the condition of local causality. A preliminary analysis of the repercussions of our proposal shows that it is able to locate exactly where and how the notions of locality and causality are involved in formalising Bell's condition of local causality.Comment: 14 pages. To be published in PSE volume "Explanation, Prediction, and Confirmation", edited by Dieks, et a

Two-particle entanglement as a property of three-particle entangled states

In a recent article [Phys. Rev. A 54, 1793 (1996)] Krenn and Zeilinger investigated the conditional two-particle correlations for the subensemble of data obtained by selecting the results of the spin measurements by two observers 1 and 2 with respect to the result found in the corresponding measurement by a third observer. In this paper we write out explicitly the condition required in order for the selected results of observers 1 and 2 to violate Bell's inequality for general measurement directions. It is shown that there are infinitely many sets of directions giving the maximum level of violation. Further, we extend the analysis by the authors to the class of triorthogonal states |Psi> = c_1 |z_1>|z_2>|z_3> + c_2 |-z_1>|-z_2>|-z_3>. It is found that a maximal violation of Bell's inequality occurs provided the corresponding three-particle state yields a direct ("all or nothing") nonlocality contradiction.Comment: REVTeX, 7 pages, no figure

A Deeper Look at Student Learning of Quantum Mechanics: the Case of Tunneling

We report on a large-scale study of student learning of quantum tunneling in 4 traditional and 4 transformed modern physics courses. In the transformed courses, which were designed to address student difficulties found in previous research, students still struggle with many of the same issues found in other courses. However, the reasons for these difficulties are more subtle, and many new issues are brought to the surface. By explicitly addressing how to build models of wave functions and energy and how to relate these models to real physical systems, we have opened up a floodgate of deep and difficult questions as students struggle to make sense of these models. We conclude that the difficulties found in previous research are the tip of the iceberg, and the real issue at the heart of student difficulties in learning quantum tunneling is the struggle to build the complex models that are implicit in experts' understanding but often not explicitly addressed in instruction.Comment: v2, v3 updated with more detailed analysis of data and discussion; submitted to Phys. Rev. ST: PE

Gesture analysis for physics education researchers

Systematic observations of student gestures can not only fill in gaps in students' verbal expressions, but can also offer valuable information about student ideas, including their source, their novelty to the speaker, and their construction in real time. This paper provides a review of the research in gesture analysis that is most relevant to physics education researchers and illustrates gesture analysis for the purpose of better understanding student thinking about physics.Comment: 14 page

The Conway-Kochen argument and relativistic GRW models

In a recent paper, Conway and Kochen proposed what is now known as the "Free Will theorem" which, among other things, should prove the impossibility of combining GRW models with special relativity, i.e., of formulating relativistically invariant models of spontaneous wavefunction collapse. Since their argument basically amounts to a non-locality proof for any theory aiming at reproducing quantum correlations, and since it was clear since very a long time that any relativistic collapse model must be non-local in some way, we discuss why the theorem of Conway and Kochen does not affect the program of formulating relativistic GRW models.Comment: 16 pages, RevTe

Using resource graphs to represent conceptual change

We introduce resource graphs, a representation of linked ideas used when reasoning about specific contexts in physics. Our model is consistent with previous descriptions of resources and coordination classes. It can represent mesoscopic scales that are neither knowledge-in-pieces or large-scale concepts. We use resource graphs to describe several forms of conceptual change: incremental, cascade, wholesale, and dual construction. For each, we give evidence from the physics education research literature to show examples of each form of conceptual change. Where possible, we compare our representation to models used by other researchers. Building on our representation, we introduce a new form of conceptual change, differentiation, and suggest several experimental studies that would help understand the differences between reform-based curricula.Comment: 27 pages, 14 figures, no tables. Submitted for publication to the Physical Review Special Topics Physics Education Research on March 8, 200

Optimal Monitoring of Position in Nonlinear Quantum Systems

We discuss a model of repeated measurements of position in a quantum system which is monitored for a finite amount of time with a finite instrumental error. In this framework we recover the optimum monitoring of a harmonic oscillator proposed in the case of an instantaneous collapse of the wavefunction into an infinite-accuracy measurement result. We also establish numerically the existence of an optimal measurement strategy in the case of a nonlinear system. This optimal strategy is completely defined by the spectral properties of the nonlinear system.Comment: 4 pages, REVTeX 3.0, 4 PostScript figure

Decoherence, einselection, and the quantum origins of the classical

Decoherence is caused by the interaction with the environment. Environment monitors certain observables of the system, destroying interference between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the Universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly non-local "Schr\"odinger cat" states. Classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit: Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation.Comment: Final version of the review, with brutally compressed figures. Apart from the changes introduced in the editorial process the text is identical with that in the Rev. Mod. Phys. July issue. Also available from http://www.vjquantuminfo.or