Quantum Theory and Local Causality

Springer Verlag (2018)
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Abstract

​This book summarizes the results of research the authors have pursued in the past years on the problem of implementing Bell's notion of local causality in local physical theories and relating it to other important concepts and principles in the foundations of physics such as the Common Cause Principle, Bell's inequalities, the EPR scenario, and various other locality and causality concepts. The book is intended for philosophers of science with an interest in the formal background of sciences, philosophers of physics and physicists working in foundation of physics.

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Chapters

The Common Cause Principle

In this chapter we turn to Reichenbach’s Common Cause Principle. The principle is generalized to the LPT framework and the status of the various Common Cause Principles in algebraic quantum field theory is investigated. Then we motivate the noncommutative generalization of the principle and compare ... see more

Bell’s Notion of Local Causality

At the beginning of this Chapter Bell’s different formulations of local causality will be reviewed. Next, we analyze the three key concepts featuring in Bell’s final formulation, namely “local beables”, “shielder-off region”, and “complete specification.” We translate them into the LPT framework and... see more

The EPR Scenario

In this Chapter we outline the Einstein–Podolsky–Rosen scenario and show that the violation of Bell’s inequalities does not block the implementation of the EPR situation in a locally causal LQT, neither it excludes a noncommuting common causal explanation for the EPR correlations.

Locality and Causality Principles

This Chapter provides a brief overview of the interconnections between the various causality and locality concepts in algebraic quantum field theory such as causal dynamics, primitive causality, local primitive causality, no-signaling, selective and nonselective measurements, local determinism, stoc... see more

A Noncommutative Locally Causal Model for the EPR Scenario

In this Chapter we explicitly construct a locally causal LQT for the EPR scenario. The model is the 1+1 dimensional local quantum Ising model . We show that the model is not only locally causal in Bell’s sense but also able to implement four pairs of events correlating in the singlet state.

Local Causality: A Historical Introduction

In this chapter we briefly overview the history of local causality starting from the early ideas on the prohibition of the action at a distance and ending with Bell’s formulation of local causality. We state the central message of the book and outline the content of the subsequent chapters.

Summary and Outlook

In this Chapter we summarize the main results of this book and investigate their philosophical consequences. We argue that embracing noncommuting “beables” in our ontology significantly extends our explanatory sources in accounting for correlations. We also examine what price we need to pay for aban... see more

Bell’s Inequalities

This Chapter collects the most important concepts and some of the representative propositions concerning Bell’s inequalities in the general C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \... see more

What Is a Local Physical Theory?

In this Chapter we introduce the mathematical formalism of a local physical theory . Briefly, a LPT is an association of local operator algebras to spacetime regions subjected to the requirements of isotony, microcausality and covariance, all borrowed from algebraic quantum field theory. Depending o... see more

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