Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Wave functions
- 3 Linear algebra in Dirac notation
- 4 Physical properties
- 5 Probabilities and physical variables
- 6 Composite systems and tensor products
- 7 Unitary dynamics
- 8 Stochastic histories
- 9 The Born rule
- 10 Consistent histories
- 11 Checking consistency
- 12 Examples of consistent families
- 13 Quantum interference
- 14 Dependent (contextual) events
- 15 Density matrices
- 16 Quantum reasoning
- 17 Measurements I
- 18 Measurements II
- 19 Coins and counterfactuals
- 20 Delayed choice paradox
- 21 Indirect measurement paradox
- 22 Incompatibility paradoxes
- 23 Singlet state correlations
- 24 EPR paradox and Bell inequalities
- 25 Hardy's paradox
- 26 Decoherence and the classical limit
- 27 Quantum theory and reality
- Bibliography
- References
- Index
24 - EPR paradox and Bell inequalities
Published online by Cambridge University Press: 10 December 2009
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Wave functions
- 3 Linear algebra in Dirac notation
- 4 Physical properties
- 5 Probabilities and physical variables
- 6 Composite systems and tensor products
- 7 Unitary dynamics
- 8 Stochastic histories
- 9 The Born rule
- 10 Consistent histories
- 11 Checking consistency
- 12 Examples of consistent families
- 13 Quantum interference
- 14 Dependent (contextual) events
- 15 Density matrices
- 16 Quantum reasoning
- 17 Measurements I
- 18 Measurements II
- 19 Coins and counterfactuals
- 20 Delayed choice paradox
- 21 Indirect measurement paradox
- 22 Incompatibility paradoxes
- 23 Singlet state correlations
- 24 EPR paradox and Bell inequalities
- 25 Hardy's paradox
- 26 Decoherence and the classical limit
- 27 Quantum theory and reality
- Bibliography
- References
- Index
Summary
Bohm version of the EPR paradox
Einstein, Podolsky, and Rosen (EPR) were concerned with the following issue. Given two spatially separated quantum systems A and B and an appropriate initial entangled state, a measurement of a property on system A can be an indirect measurement of B in the sense that from the outcome of the A measurement one can infer with probability 1 a property of B, because the two systems are correlated. There are cases in which either of two properties of B represented by noncommuting projectors can be measured indirectly in this manner, and EPR argued that this implied that system B could possess two incompatible properties at the same time, contrary to the principles of quantum theory.
In order to understand this argument, it is best to apply it to a specific model system, and we shall do so using Bohm's formulation of the EPR paradox in which the systems A and B are two spin-half particles a and b in two different regions of space, with their spin degrees of freedom initially in a spin singlet state (23.2). As an aid to later discussion, we write the argument in the form of a set of numbered assertions leading to a paradox: a result which seems plausible, but contradicts the basic principles of quantum theory. The assertions E1–E4 are not intended to be exact counterparts of statements in the original EPR paper, even when the latter are translated into the language of spin-half particles. However, the general idea is very similar, and the basic conundrum is the same.
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- Information
- Consistent Quantum Theory , pp. 323 - 335Publisher: Cambridge University PressPrint publication year: 2001