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9780306461828

Nonlocality in Quantum Physics

by ;
  • ISBN13:

    9780306461828

  • ISBN10:

    030646182X

  • Format: Hardcover
  • Copyright: 1999-07-31
  • Publisher: Plenum Pub Corp
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Summary

The nonlocality phenomena exhibited by entangled quantum systems are certainly one of the most extraordinary aspects of quantum theory. This book discusses this phenomenon according to several points of view, i.e., according to different interpretations of the mathematics of the quantum formalism. The several interpretations of the Copenhagen interpretation, the many worlds, the de Broglie-Bohm, quantum logics, the decohering by the environment approach and the histories approach interpretations are scrutinized and criticized in detail. Recent results on cryptography, quantum bit commitment, quantum erasers and teleportation are also presented and discussed.

Table of Contents

Introduction
1(7)
Chapter References
5(2)
Fundamentals
7(22)
The rules of the game
7(5)
The whole and its parts
12(2)
Classical limit and decoherence
14(9)
Ehrenfest theorem
15(1)
Classical dynamical variables and collective observables
15(4)
The WKB approximation
19(1)
Decoherence and Schrodinger's cat paradox
20(3)
Proofs of the frequency interpretation
23(3)
Chapter References
26(3)
How Ψ Collapses
29(6)
The problem
29(1)
Collapse and unitary evolution
30(3)
Chapter References
33(2)
Bell's Inequalities
35(8)
The Einstein, Podolski and Rosen (EPR) argument
35(1)
D'Espagnat's version of Bell's inequalities
36(1)
Stapp's formulation of Bell's inequalities
37(2)
Bell's proof
39(2)
Chapter References
41(2)
Copenhagen Interpretation
43(16)
Absence of quantum objects
45(4)
Nonlocality
46(1)
Criticisms
47(2)
Objectively existing potentialities world
49(6)
Nonlocality
51(2)
Criticisms
53(1)
The Wigner friend paradox
53(1)
The problem of quantum processes before the existence of conscious observers
53(2)
Chapter References
55(4)
Many Worlds Interpretation (MWI)
59(8)
The role of the observer
59(2)
Nonlocality
61(1)
Criticisms
62(2)
Chapter References
64(3)
Quantum Logic (QL)
67(16)
Proposal
67(7)
Weak modularity postulate and proposition calculus
70(1)
The Boolean lattice of a classical system
71(1)
The non distributive lattice associated to a quantum system
72(2)
Hasse diagrams
74(2)
Spin one system for which two spin projections, Sx and Sz, are measured
75(1)
The birth of time
76(4)
Chapter References
80(3)
Macroscopic Realizations of QL
83(14)
Lattices and graphs
83(8)
Grib and Zapatrin rule for construction of the lattice corresponding to a given graph and vice-versa
Breakdown of Bell's inequalities
91(4)
The Problem of Nonlocality
95(1)
Chapter References
95(2)
Hidden Variables Theoreis (HVT)
97(18)
What is a hidden variables theory?
97(4)
Comments on HVT of the first kind
99(2)
Theories of the second and zeroth kinds
101(1)
Von Neumann's theorem
101(2)
Spin 1/2 hidden variable's model
103(1)
Gleason's theorem. Kochen-Specker paradox
104(8)
Gleason's theorem
105(3)
Kochen-Specker theorem
108(1)
Contextuality in HVT and the Mermin example
108(2)
Kochen-Specker paradox
110(2)
Chapter References
112(3)
De Broglie-Bohm Non Relativistic HVT
115(8)
Non relativistic de Broglie-Bohm theory
115(3)
Stationary states
117(1)
Non conservation of energy and momentum in non stationary states
117(1)
The many particle system
118(1)
Remarks on the non relativistic BBT
119(2)
Chapter References
121(2)
De Broglie-Bohm Relativistic HVT
123(10)
HVT interpretation of the boson equations
123(2)
The BBT interpretation of the Dirac equation
125(1)
Relativistic BBT many-fermion theory
126(1)
Necessity of superluminal processes
127(2)
Chapter References
129(4)
Statistical Interpretation
133(10)
Introduction
133(2)
When is the SIQT possible?
135(2)
SIQT × orthodox quantum theory
137(4)
Chapter References
141(2)
Non-Unitary Evolution?
143(8)
Prigogine and Ghirardi et al. theories
144(2)
Criticisms
146(2)
Chapter References
148(3)
Histories Approach
151(8)
What is a history?
151(1)
Consistent histories
152(3)
Criticisms
155(2)
Chapter References
157(2)
Quantum Miracles and Cryptography
159(22)
Greenberger et al. example
159(2)
Hardy's example
161(2)
Negative experiments. Elitzur-Vaidman proposal
163(1)
Delayed choice experiments
164(1)
Quantum erasers
165(3)
Quantum cryptography
168(5)
Quantum bit commitment
169(4)
Teleportation
173(5)
Chapter References
178(3)
Where are We Now?
181(36)
Chapter References
184(3)
Appendices
A-- Set Theory and Lattices
187(12)
A.1 Main definitions
187(2)
A.2 Posets
189(1)
A.3 Lattices
190(4)
A.4 The Boolean algebra of sets
194(1)
A.5 Borel sets, measures and integration
194(5)
Chapter References
199(2)
B-- Hilbert Spaces
201(15)
B.1 Definition of Hilbert Space
201(2)
B.2 Linear manifolds and subspaces
203(4)
B.2.1 The lattice of subspaces
207(1)
B.3 Dual and conjugate dual spaces
207(2)
B.4 Tensor products
209(1)
B.5 Linear operators
210(3)
B.6 Projection operators and lattice structure
213(3)
Chapter References
216(1)
Index 217

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