Abstract not found

What belongs to quantum theory is no more than what is needed for its derivation. Keeping to this maxim, we record a paradigmatic shift in the foundations of quantum mechanics, where the focus has recently moved from interpreting to reconstructing quantum theory. Several historic and contemporary reconstructions are analyzed, including the work of Hardy, Rovelli, and Clifton, Bub and Halvorson. We conclude by discussing the importance of a novel concept of intentionally incomplete reconstruction.

Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes of possible operations we may perform on a system: ‘‘operational states.’ ’ I discuss general frameworks for ‘‘operational theories’ ’ (sets of possible operational states of a system), in which convexity plays key role. The main technical content of the paper is in a theorem that any such theory naturally gives rise to a ‘‘weak effect algebra’ ’ when outcomes having the same probability in all states are identified and in the introduction of a notion of ‘‘operation algebra’ ’ that also takes account of sequential and conditional operations. Such frameworks are appropriate for investigating what things look like from an ‘‘inside view,’ ’ i.e., for describing perspectival information that one subsystem of the world can have about another. Understandinghow such views can combine, and whether an overall ‘‘geometric’ ’ picture (‘‘outside view’’) coordinating them all can be had, even if this picture is very different in structure from the perspectives within it, is the key to whether we may be able to achieve a unified, ‘‘objective’ ’ physical view in which quantum mechanics is the appropriate description for certain perspectives, or whether quantum mechanics is truly telling us we must go beyond this ‘‘geometric’ ’ conception of physics.

. We provide an overview of the connections between Bell's inequalities and algebraic structure. 1. Introduction Motivated by the desire to bring into the realm of testable hypotheses at least some of the important matters concerning the interpretation of quantum mechanics evoked in the controversy surrounding the EinsteinPodolsky -Rosen paradox [18][5], Bell discovered the first example [3][4] of a family of inequalities which are now generally called Bell's inequalities. These inequalities provide an upper bound on the strength of correlations between systems which are no longer interacting but have interacted in the past. Stated briefly, Bell showed that if the correlation experiments can be modelled by a single classical probability measure, then the strength of the correlations must satisfy a bound which is violated by certain quantum mechanical predictions (and, as has been verified experimentally, by nature - for a review of this original application of Bell's inequalities and ...

In the 1940s, two different views of the brain and the computer were equally important. One was the analog technology and theory that had emerged before the war. The other was the digital technology and theory that was to become the main paradigm of computation. 1 The outcome of the contest between these two competing views derived from technological and epistemological arguments. While digital technology was improving dramatically, the technology of analog machines had already reached a significant level of development. In particular, digital technology offered a more effective way to control the precision of calculations. But the epistemological discussion was, at the time, equally relevant. For the supporters of the analog computer, the digital model — which can only process information transformed and coded in binary — wouldn’t be suitable to represent certain kinds of continuous variation that help determine brain functions. With analog machines, on the contrary, there would be few or no layers between natural objects and the work and structure of computation (cf. [4, 1]). The 1942–52 Macy Conferences in cybernetics helped to validate digital theory and logic as legitimate ways to think about the brain and the machine [4]. In particular, those conferences helped made McCulloch-Pitts ’ digital model

this paper, I want to explore the origin of the modern conception of the idea of consistency in logic in the work of German mathematician David Hilbert. My interest in the development of the modern idea of consistency arises from my belief that an overriding concern with a strict requirement of consistency, borrowed primarily from the rigors of modern developments in logic, has prevented latter day twentieth century philosophers from producing philosophical systems of the type produced in earlier times.

Abstract not found

This work reviews foundations and applications of the complex-energy continuum shell model that provides a consistent many-body description of bound states, resonances, and scattering states. The model can be considered a quasi-stationary open quantum system extension of the standard configuration interaction approach for well-bound (closed) systems.

This work reviews foundations and applications of the complex-energy continuum shell model that provides a consistent many-body description of bound states, resonances, and scattering states. The model can be considered a quasi-stationary open quantum system extension of the standard configuration interaction approach for well-bound (closed) systems.

Sequential effect algebra is an important model for studying quantum measurement theory. In 2005, Professor Gudder presented 25 open problems to motivate its study. The 20th problem asked: In a sequential effect algebra, if the square root of some element exists, is it unique? We can strengthen the problem as following: For each given positive integer n> 1, is there a sequential effect algebra such that the n-th root of its some element c is not unique and the n-th root of c is not the k-th root of c (k < n) ? In this paper, we answer the strengthened problem affirmatively.