By Robert B. Griffiths
Publisher: Cambridge University Press
Print Publication Year: 2001
Online Publication Date:December 2009
Online ISBN:9780511606052
Hardback ISBN:9780521803496
Paperback ISBN:9780521539296
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511606052.025
Subjects: Quantum Physics, Quantum Information and Quantum Computation, History, Philosophy and Foundations of Physics
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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.
pp. i-vi
pp. vii-xii
pp. xiii-xvi
pp. 1-10
pp. 11-26
3 - Linear algebra in Dirac notation: Read PDF
pp. 27-46
4 - Physical properties: Read PDF
pp. 47-64
5 - Probabilities and physical variables: Read PDF
pp. 65-80
6 - Composite systems and tensor products: Read PDF
pp. 81-93
7 - Unitary dynamics: Read PDF
pp. 94-107
8 - Stochastic histories: Read PDF
pp. 108-120
pp. 121-136
10 - Consistent histories: Read PDF
pp. 137-147
11 - Checking consistency: Read PDF
pp. 148-158
12 - Examples of consistent families: Read PDF
pp. 159-173
13 - Quantum interference: Read PDF
pp. 174-191
14 - Dependent (contextual) events: Read PDF
pp. 192-201
15 - Density matrices: Read PDF
pp. 202-215
16 - Quantum reasoning: Read PDF
pp. 216-227
pp. 228-242
18 - Measurements II: Read PDF
pp. 243-260
19 - Coins and counterfactuals: Read PDF
pp. 261-272
20 - Delayed choice paradox: Read PDF
pp. 273-283
21 - Indirect measurement paradox: Read PDF
pp. 284-295
22 - Incompatibility paradoxes: Read PDF
pp. 296-309
23 - Singlet state correlations: Read PDF
pp. 310-322
24 - EPR paradox and Bell inequalities: Read PDF
pp. 323-335
25 - Hardy's paradox: Read PDF
pp. 336-348
26 - Decoherence and the classical limit: Read PDF
pp. 349-359
27 - Quantum theory and reality: Read PDF
pp. 360-370
pp. 371-376
pp. 377-382
pp. 383-391