scholarly journals Violations of locality and free choice are equivalent resources in Bell experiments

2021 ◽  
Vol 118 (17) ◽  
pp. e2020569118
Author(s):  
Pawel Blasiak ◽  
Emmanuel M. Pothos ◽  
James M. Yearsley ◽  
Christoph Gallus ◽  
Ewa Borsuk
Keyword(s):  
Infinite Number ◽  
Free Choice ◽  
Causal Explanation ◽  
Bell Inequalities ◽  
The Other ◽  
Quantum Mechanical ◽  
Causal Explanations ◽  
Experimental Trial ◽  
Experimental Behavior ◽  
Is Theory

Bell inequalities rest on three fundamental assumptions: realism, locality, and free choice, which lead to nontrivial constraints on correlations in very simple experiments. If we retain realism, then violation of the inequalities implies that at least one of the remaining two assumptions must fail, which can have profound consequences for the causal explanation of the experiment. We investigate the extent to which a given assumption needs to be relaxed for the other to hold at all costs, based on the observation that a violation need not occur on every experimental trial, even when describing correlations violating Bell inequalities. How often this needs to be the case determines the degree of, respectively, locality or free choice in the observed experimental behavior. Despite their disparate character, we show that both assumptions are equally costly. Namely, the resources required to explain the experimental statistics (measured by the frequency of causal interventions of either sort) are exactly the same. Furthermore, we compute such defined measures of locality and free choice for any nonsignaling statistics in a Bell experiment with binary settings, showing that it is directly related to the amount of violation of the so-called Clauser–Horne–Shimony–Holt inequalities. This result is theory independent as it refers directly to the experimental statistics. Additionally, we show how the local fraction results for quantum-mechanical frameworks with infinite number of settings translate into analogous statements for the measure of free choice we introduce. Thus, concerning statistics, causal explanations resorting to either locality or free choice violations are fully interchangeable.

Causation and Locality

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Causal Explanation ◽  
Bell Inequalities ◽  
Space Time ◽  
Counterfactual Dependence ◽  
The Other ◽  
Entangled State ◽  
Space Time Structure ◽  
Action At A Distance ◽  
Time Point

By moving to the context of relativistic space-time structure, this chapter completes the argument of Chapter 4 that we can use quantum theory locally to explain correlations that violate Bell inequalities with no instantaneous action at a distance. Chance here must be relativized not just to time but to a space-time point, so that an event may have more than one chance at the same time—it may even be certain relative to one space-time point but ‘at the same time’ completely uncertain relative to another. This renders Bell’s principle of Local Causality either inapplicable or intuitively unmotivated. Counterfactual dependence between the outcomes of measurements on systems assigned an entangled state is not causal since neither outcome is subject to intervention: but it may still be appealed to in a non-causal explanation of one in terms of the other.

scholarly journals Cyclic quantum causal models

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jonathan Barrett ◽  
Robin Lorenz ◽  
Ognyan Oreshkov
Keyword(s):  
Causal Reasoning ◽  
Causal Structure ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Causal Models ◽  
Causal Order ◽  
Quantum Processes ◽  
Causal Explanations ◽  
Causal Structures

AbstractCausal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory encompassing quantum systems and gravity is expected to allow causally nonseparable processes featuring operations in indefinite causal order, defying that events be causally ordered at all. The first challenge has been addressed through the recent development of intrinsically quantum causal models, allowing causal explanations of quantum processes – provided they admit a definite causal order, i.e. have an acyclic causal structure. This work addresses causally nonseparable processes and offers a causal perspective on them through extending quantum causal models to cyclic causal structures. Among other applications of the approach, it is shown that all unitarily extendible bipartite processes are causally separable and that for unitary processes, causal nonseparability and cyclicity of their causal structure are equivalent.

scholarly journals Nonrecurrence and Bell-like inequalities

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 762-768
Author(s):  
Douglas G. Danforth
Keyword(s):  
Infinite Number ◽  
General Class ◽  
Hidden Variables ◽  
Random Variables ◽  
Random Variable ◽  
Bell Inequalities ◽  
Usual Sense ◽  
Real Random Variable ◽  
Action At A Distance ◽  
The Continuum

AbstractThe general class,Λ, of Bell hidden variables is composed of two subclassesΛRandΛNsuch thatΛR⋃ΛN=ΛandΛR∩ΛN= {}. The classΛNis very large and contains random variables whose domain is the continuum, the reals. There are an uncountable infinite number of reals. Every instance of a real random variable is unique. The probability of two instances being equal is zero, exactly zero.ΛNinduces sample independence. All correlations are context dependent but not in the usual sense. There is no “spooky action at a distance”. Random variables, belonging toΛN, are independent from one experiment to the next. The existence of the classΛNmakes it impossible to derive any of the standard Bell inequalities used to define quantum entanglement.

Orthonormal basis of wavelets with customizable frequency bands

2016 ◽  
Vol 14 (06) ◽  
pp. 1650050 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang
Keyword(s):  
Frequency Domain ◽  
Infinite Number ◽  
Orthonormal Basis ◽  
The Other ◽  
Just Intonation ◽  
Frequency Bands ◽  
Orthonormal Bases ◽  
Major Scale ◽  
Dilation Factor ◽  
New Type

We already proved the existence of an orthonormal basis of wavelets having an irrational dilation factor with an infinite number of wavelet shapes, and based on its theory, we proposed an orthonormal basis of wavelets with an arbitrary real dilation factor. In this paper, with the development of these fundamentals, we propose a new type of orthonormal basis of wavelets with customizable frequency bands. Its frequency bands can be freely designed with arbitrary bounds in the frequency domain. For example, we show two types of orthonormal bases of wavelets. One of them has an irrational dilation factor, and the other is designed based on the major scale in just intonation.

Determination of Stresses in Cemented Lap Joints

1953 ◽  
Vol 20 (3) ◽  
pp. 355-364
Author(s):  
R. W. Cornell
Keyword(s):  
Differential Equations ◽  
Infinite Number ◽  
Lap Joints ◽  
The Other ◽  
Complete Analysis ◽  
Stress Distributions ◽  
Lap Joint ◽  
Analogy Method ◽  
Set Up

Abstract A variation and extension of Goland and Reissner’s (1) method of approach is presented for determining the stresses in cemented lap joints by assuming that the two lap-joint plates act like simple beams and the more elastic cement layer is an infinite number of shear and tension springs. Differential equations are set up which describe the transfer of the load in one beam through the springs to the other beam. From the solution of these differential equations a fairly complete analysis of the stresses in the lap joint is obtained. The spring-beam analogy method is applied to a particular type of lap joint, and an analysis of the stresses at the discontinuity, stress distributions, and the effects of variables on these stresses are presented. In order to check the analytical results, they are compared to photoelastic and brittle lacquer experimental results. The spring-beam analogy solution was found to give a fairly accurate presentation of the stresses in the lap joint investigated and should be useful in analyzing other cemented lap-joint structures.

Applications to Silicate, Carbonate, and Borate Minerals and Related Species

1992 ◽  
Author(s):  
John A. Tossell ◽  
David J. Vaughan
Keyword(s):  
Related Species ◽  
The Other ◽  
Quantum Mechanical ◽  
Quantum Mechanical Calculations ◽  
Solid Solution Series ◽  
Silicate Minerals ◽  
Borate Minerals ◽  
Cluster Unit ◽  
Silicate Carbonate

The most abundant materials making up the crust of the earth (i.e., the “rock-forming minerals”) can be regarded as dominated by oxyanion units; notably, the units that can be formally represented by SiO44- and AlO45- clusters of the silicate minerals, and the CO32- unit of the carbonates. less common, but geochemically interesting, oxyanion units include, for example, BO33-, BeO46- , and PO43-. in this chapter, applications of quantum-mechanical calculations and experimental techniques to such materials are considered. first, the silicates are discussed, commencing with the large amount of work undertaken on the olivines, before considering such work as has so far been done on the other silicate minerals and related materials. second, the most important of the nonsilicate rock-forming mineral groups, the carbonates, are discussed. finally, although of less petrological importance but interesting geochemically and in terms of contrast with the othergroups, the borates and related species are considered. in each case, geometric aspects of structure and the problems of calculating structural properties are considered before going on to consider electronic structures and the factors controlling stabilities and a wider range of physical properties. in all of these materials, there is considerable interest in the, bonding in the oxyanion unit and how this is affected by, and controls, the interaction with counterions or the polymeric units. the building up of the minerals by such interactions exerts the dominant control over their crystal chemistries and properties and thus forms a central theme of this chapter. the silicate minerals are, of course, characterized by the presence of the tetrahedral siO4 cluster unit and the crystal chemistry and classification of silicates dominated by the structures built up by the linking together (polymerization) of these units. in the “simplest” of the silicates, the island silicates such as the olivine minerals (dominated by the forsterite (Mg2 SiO4)-fayalite (Fe2SiO4) solid solution series), the sio4 units are isolated by counterions such as Mg2+, Fe2+, Ca2+.

Headless Relative Clauses in K'iche'

2021 ◽  
pp. 260-289
Author(s):  
Telma Angelina Can Pixabaj
Keyword(s):  
Relative Clauses ◽  
Free Choice ◽  
The Other ◽  
Free Relative ◽  
Preliminary Description

This chapter offers a preliminary description of headless relative clauses in K’iche’. The language exhibits all three varieties of free relative clauses that are attested crosslinguistically: maximal, existential, and free-choice. It also has two other kinds of headless relative clauses: light-headed relative clauses introduced by determiners (without wh-expressions) and headless relative clauses with no marking of any kind (neither wh-expressions nor determiners). Overall, the picture that emerges is that all three varieties of free relative clauses exhibit clear morpho-syntactic and semantic differences that differentiate them both from each other as well as from headed relative clauses. One characteristic that helps to differentiate between them is the different subsets of wh-expressions they make use of. All of these wh- clausal constructions are related but, crucially, independent. Of the two kinds of headless relative clauses that do not make use of wh-expressions, one kind—light-headed relative clauses—is introduced by a determiner, while the other kind has no special marking. Both exhibit distributional and semantic restrictions that distinguish them from headed relative clauses.

scholarly journals Mechanism, process and the wider context of economic geography

2019 ◽  
Vol 9 (3) ◽  
pp. 273-278 ◽  
Author(s):  
Julie MacLeavy
Keyword(s):  
Reflective Practice ◽  
Economic Geography ◽  
Lived Experiences ◽  
Critical Realism ◽  
Causal Explanation ◽  
Transformative Change ◽  
Methodological Development ◽  
Causal Explanations ◽  
Critical Realist ◽  
Analytical Approaches

This commentary responds to Henry Wai-chung Yeung’s call to develop clearer causal explanations in geography through mechanism-based thinking. His suggested use of a critical realist framework to ground geographical research on economies is, on one level, appealing and may help to counteract taken-for-granted assumptions about socio-spatial conditions and the significance of economic structures for everyday lived experiences. However, the general lack of applied critical realist research means the distinction between ‘mechanism’ and ‘process’ is often difficult to define in analyses of specific empirical events or geographical episodes. Not only is there a need for methodological development but, I suggest, also for greater recognition of critical realism as a reflective practice. We need to consider the means by which scholars distinguish between contingent and necessary relations, identify structures and counterfactuals and infer how mechanisms work out in particular places. The critical realist goal of advancing transformative change through the provision of causal explanation relies upon inferences made on the basis of researcher experience. Hence, we need to recognise that research is always a political practice and be careful not to discount knowledge borne from other analytical approaches.

Vibration of an Infinitely Extending Plate Resting on an Elastic Foundation

1963 ◽  
Vol 30 (3) ◽  
pp. 355-362 ◽  
Author(s):  
Kazuyosi Ono
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Infinite Number ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
The Other ◽  
Damped Oscillation

Free vibrations and forced vibrations of an infinitely extending plate resting on an elastic foundation and carrying a mass are solved. Then the amplitudes of the free vibrations produced by an impulse applied to the mass on the plate are determined, and it is found that two kinds of vibration are produced in the plate: One is a free vibration and the other is a special vibration, which consists of an infinite number of free vibrations and resembles a damped oscillation.

scholarly journals The vacuum in Dirac's theory of the positive electron

1934 ◽  
Vol 146 (857) ◽  
pp. 420-441 ◽  
Keyword(s):  
Kinetic Energy ◽  
Infinite Number ◽  
Strong Support ◽  
Negative Energy ◽  
Positive Energy ◽  
Quantum Mechanical ◽  
Normal Density ◽  
Physical Picture ◽  
Negative Energy States ◽  
Energy States

According to a theory proposed by Dirac one has to picture the vacuum as filled with an infinite number of electrons of negative kinetic energy, the electric density of which is, however, unobservable. One can observe only deviations from this "normal" density which either consist of an addition of electrons in states of positive energy or absence of electrons from some of the negative energy states (positive electrons). The discovery of the positive electron and the observed magnitude of the processes involving it give strong support to this view. This theory, as it stands, however, is not complete because it makes use of infinite quantities which are inadmissible in physical equations. It therefore must be understood (and was meant so by Dirac) to be a physical picture showing a way in which the quantum mechanical equations can probably be modified in order to give account of the positive electron and to solve the difficulty connected with the states of negative energy.

Sign in / Sign up

Export Citation Format

Share Document