Plotnitsky Epistemology and Probability

Bohr, Heisenberg, Schrödinger, and the Nature of Quantum-Theoretical Thinking
2010
ISBN: 978-0-387-85334-5
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 161, 402 Seiten

Reihe: Fundamental Theories of Physics

This book offers an exploration of the relationships between epistemology and probability in the work of Niels Bohr, Werner Heisenberg, and Erwin Schro- ¨ dinger, and in quantum mechanics and in modern physics as a whole. It also considers the implications of these relationships and of quantum theory itself for our understanding of the nature of human thinking and knowledge in general, or the ''epistemological lesson of quantum mechanics,'' as Bohr liked 1 to say. These implications are radical and controversial. While they have been seen as scientifically productive and intellectually liberating to some, Bohr and Heisenberg among them, they have been troublesome to many others, such as Schro¨ dinger and, most prominently, Albert Einstein. Einstein famously refused to believe that God would resort to playing dice or rather to playing with nature in the way quantum mechanics appeared to suggest, which is indeed quite different from playing dice. According to his later (sometime around 1953) remark, a lesser known or commented upon but arguably more important one: ''That the Lord should play [dice], all right; but that He should gamble according to definite rules [i. e. , according to the rules of quantum mechanics, rather than 2 by merely throwing dice], that is beyond me. '' Although Einstein's invocation of God is taken literally sometimes, he was not talking about God but about the way nature works. Bohr's reply on an earlier occasion to Einstein's question 1 Cf.

Autoren/Hrsg.

Plotnitsky, Arkady

Inhaltsverzeichnis

1;Preface;6
2;Acknowledgments;27
3;Contents;29
4;Abbreviations;32
5;Introduction-Epistemology and Probability in Quantum Theory: Physics, Mathematics, and Philosophy;33
5.1;1.1 Classical and Nonclassical Epistemology;33
5.2;1.2 Nonclassical Epistemology and Quantum Probability;44
5.3;1.3 Physics, Mathematics, and Philosophy in Quantum Theory;53
5.4;1.4 The Architecture of Quantum-Theoretical Concepts;58
5.5;1.5 Epistemology and Interpretation;71
6;Quantum Phenomena and the Double-Slit Experiment;77
6.1;2.1 The Double-Slit Experiment: From an (Almost) Classical to a Nonclassical View;77
6.2;2.2 The Double-Slit Experiment, the Uncertainty Relations, and Probability;89
6.3;2.3 The Delayed-Choice Experiment;97
6.4;2.4 The Quantum Eraser;102
6.5;2.5 Repetition and Erasure, Classical and Quantum;105
7;Heisenberg’s Revolutions: New Kinematics, New Mathematics, and New Philosophy;108
7.1;3.1 ‘‘A Step of Probably Fundamental Importance’’: From Bohr to Heisenberg;109
7.2;3.2 The Founding Physical and Philosophical Principles of Heisenberg’s Quantum Mechanics;123
7.3;3.3 The Correspondence Principle Between Physics and Mathematics;131
7.4;3.4 ‘‘Ensembles of Quantities’’: From Experiment to Mathematics to Physics;138
8;From Geometry to Algebra in Physics, with Heisenberg;145
8.1;4.1 ‘‘A Purely Algebraic Method of Description of Nature’’;145
8.2;4.2 ‘‘A New Era of Mutual Stimulation of Mechanics and Mathematics’’;158
9;Schrödinger’s Waves: Propagation and Probability;167
9.1;5.1 Quantum Waves and Quantum Probability;168
9.2;5.2 ‘‘The Wave Radiation Forming the Basis of the Universe’’;174
9.3;5.3 Schrödinger’s Equation;185
9.4;5.4 Wave Mechanics Between Optics and Mechanics;191
9.5;5.5 Quantum Mechanics Beyond Mechanics and Optics;195
9.6;5.6 The Ends of the Wave Function: From Quantum States to Entangled Knowledge;201
10;Bohr’s Como Argument: Complementarity and the Problem of Causality;208
10.1;6.1 Complementarity: Between Concepts and Experiments;208
10.2;6.2 The Quantum Postulate: Discontinuity and Irrationality;215
10.3;6.3 Complementarity and Causality;220
10.4;6.4 Quantum Causality in Dirac, Heisenberg, and von Neumann;231
10.5;6.5 A Brief History of Quantum Causality;243
11;From Como to Copenhagen: Renunciations;247
12;Can Quantum-Mechanical Description of Physical Reality Be Considered both Complete and Local?;264
12.1;8.1 Correlations, Completeness, and Locality;265
12.2;8.2 Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? EPR’s Argument;275
12.3;8.3 Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Bohr’s Argument;279
12.4;8.4 Can Quantum-Mechanical Description of Physical Reality Be Considered Local?;295
13;Essential Ambiguity and Essential Influence: Reading Bohr’s Reply to EPR;305
13.1;9.1 Framing the Argument;305
13.2;9.2 Measurement and Complementarity;310
13.3;9.3 Restaging the EPR Experiment;320
13.4;9.4 Essential Ambiguity and Essential Influence;327
13.5;9.5 From Temporality to Relativity;332
14;Mysteries Without Mysticism, Correlations Without Correlata, Epistemology Without Ontology, and Probability Without Causality;338
14.1;10.1 Mysteries Without Mysticism;338
14.2;10.2 Correlations Without Correlata;348
14.3;10.3 Epistemology Without Ontology;352
14.4;10.4 Probability Without Causality;361
15;Conclusion: ‘‘The Mere Touch of Cold Philosophy’’;378
16;References;393
17;Name Index;403
18;Subject Index;407