Nonlocality in Quantum Physics

by Grib, Andrey Anatoljevich; Rodrigues, Waldyr Alves, Jr.

• ISBN13: 9780306461828
• ISBN10: 030646182X
• Format: Hardcover
• Copyright: 1999-07-31
• Publisher: Plenum Pub Corp

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