Quantum Chance and Non-locality: Probability and Non-locality in the Interpretations of Quantum Mechanics

by W. Michael Dickson

• ISBN13: 9780521619479
• ISBN10: 0521619475
• Format: Paperback
• Copyright: 2005-02-17
• Publisher: Cambridge University Press
• More Book Details

Summary

This is a detailed examination of the fundamental questions raised by quantum mechanics. First, is the world indeterministic? Second, are there connections between spatially separated objects? In the first part, the author examines several interpretations, focusing on how each proposes to solve the measurement problem and on how each treats probability. In the second part, the relationship between probability (specifically determinism and indeterminism) and nonlocality are examined, and it is argued that there is a nontrivial relationship between probability and nonlocality. The author then reexamines some of the interpretations in Part One in the light of this argument, and considers how they fare with regard to locality and Lorentz invariance. The book will appeal to anyone with an interest in the interpretation of quantum mechanics, including researchers in the philosophy of physics and theoretical physics, as well as graduate students in those fields.

Table of Contents

Preface	xiii
Acknowledgement	xix
Part one: Quantum chance	1	(126)
Quantum probability and the problem of interpretation	3	(21)
Quantum probability and quantum mechanics	3	(6)
The formalism of quantum probability theory	3	(5)
From quantum probability to quantum mechanics	8	(1)
Interpreting quantum mechanics	9	(9)
The `measurement problem'	9	(1)
Are the quantum probabilities epistemic?	10	(4)
Fable: A brief history of Born's rule	14	(4)
Options for interpretation	18	(6)
The eigenstate-eigenvalue link	18	(1)
Determinism and indeterminism	19	(3)
The lay of the land	22	(2)
Orthodox theories	24	(21)
How is orthodoxy possible?	24	(1)
The projection postulate	24	(7)
Collapse as an analogue of Luder's rule	24	(4)
The projection postulate and its problems	28	(3)
The continuous spontaneous localization (CSL) theory	31	(11)
Intuitive introduction to CSL	31	(1)
CSL as a modification of the Schrodinger equation	32	(2)
Physical clarification of CSL	34	(2)
Does CSL describe our experience?	36	(6)
Probabilities in orthodox interpretations	42	(3)
No-collapse theories	45	(19)
The bare theory	45	(3)
The basic idea	45	(1)
Objections to the bare theory	46	(2)
The many worlds and many minds interpretations	48	(4)
The central idea	48	(2)
Many minds	50	(2)
The consistent histories approach	52	(6)
The formalism of consistent histories	52	(1)
Interpretation of the formalism	53	(1)
Is the consistent histories approach satisfactory?	54	(4)
What is `interpretive minimalism' and is it a virtue?	58	(3)
Probabilities in no-collapse interpretations	61	(3)
Modal interpretations	64	(43)
The quantum logic interpretation	64	(11)
The basic idea	64	(2)
The Kochen-Specker theorem and quantum logic	66	(3)
Further challenges for the quantum logic interpretation	69	(6)
Modal interpretations	75	(29)
General characterization of modal interpretations	75	(1)
Faux-Boolean algebras	76	(3)
Motivating modal interpretations	79	(9)
'Naive realism' about operators	88	(2)
Compound systems and the structure of properties	90	(8)
Dynamics	98	(6)
Probabilities in the modal interpretations	104	(3)
The Bohm theory	107	(20)
Bohm's original idea	107	(1)
Bohmian mechanics	108	(7)
The Bohmian equations of motion	109	(1)
Interpretation of the Bohmian equations	109	(4)
Bohmian mechanics and quantum probability	113	(2)
Classical experience in Bohmian mechanics	115	(5)
The problem of recovering classicality	116	(1)
Recovering classicality	117	(3)
Probability in Bohm's theory	120	(7)
Part two: Quantum non-locality	127	(90)
Non-locality I: Non-dynamical models of the EPR--Bohm experiment	129	(18)
The EPR--Bohm experiment	129	(3)
Analyses of locality	132	(7)
Non-locality in standard quantum mechanics	132	(2)
Bell-factorizability and Jarrett-factorizability	134	(1)
Understanding Jarrett-factorizability	135	(4)
Bell's theorem	139	(1)
Determinism and factorizability	140	(5)
Two-time determinism and factorizability	140	(2)
Model determinism and factorizability	142	(3)
Can there be a local model?	145	(2)
Non-locality II: Dynamical models of the EPR--Bohm experiment	147	(16)
Dynamical determinism	147	(6)
Dynamical models of the EPR-Bohm experiment	147	(2)
Two kinds of dynamical determinism	149	(4)
Dynamical locality	153	(7)
Dynamical factorizability?	153	(1)
Disgression: On the separability of physical objects	154	(3)
To what do the complete states refer?	157	(2)
Two conditions of locality	159	(1)
Determinism and locality in dynamical models	160	(3)
Deriving determinism from locality	160	(2)
Bell's theorem again	162	(1)
Non-locality and special relativity	163	(16)
The theory of relativity	163	(11)
What does relativity require?	163	(2)
Digression: The block-universe argument	165	(9)
Probabilistic locality and metaphysical locality	174	(5)
Probabilistic locality	174	(2)
Metaphysical locality	176	(3)
Probability and non-locality	179	(38)
Review and preview	179	(1)
Orthodox interpretations	180	(7)
Non-locality and the projection postulate	180	(1)
Non-locality in CSL	181	(6)
No-collapse interpretations	187	(9)
The bare theory: Locality at last	187	(1)
Modal interpretations	188	(3)
The Kochen--Dieks--Healey interpretation	191	(5)
Bub's interpretation	196	(1)
Determinism and locality in Bohm's theory	196	(19)
Is Bohm's theory local?	196	(12)
Bohm's theory and relativity	208	(7)
Probability, non-locality, and the sub-phenomenal world	215	(2)
Notes	217	(14)
References	231	(11)
Index	242