Epistemology and Probability (eBook)

Bohr, Heisenberg, Schrödinger, and the Nature of Quantum-Theoretical Thinking

Arkady Plotnitsky (Autor)

eBook Download: PDF

2009 | 2010
XXXIV, 402 Seiten
Springer New York (Verlag)
978-0-387-85334-5 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 20.10.2009
• Reihe/Serie: Fundamental Theories of Physics
• Reihe/Serie: Fundamental Theories of Physics
• Zusatzinfo: XXXIV, 402 p. 2 illus.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Geisteswissenschaften ► Philosophie ► Erkenntnistheorie / Wissenschaftstheorie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
• Themenwelt: Technik
• Schlagworte: Bohr Einstein exchange • Bohr theory meaning • epistemological problem • Epistemology • Epistemology and Probability • EPR discussion • Heisenberg theory meaning • Knowledge • Mathematics • pH • Philosophy of Physics • Physics • Probability • quantum mechanics • Quantum Theoretical • Quantum Theory • reason • Schrodinger equation • Schrodinger meaning • Schrödinger meaning
• ISBN-10: 0-387-85334-0 / 0387853340
• ISBN-13: 978-0-387-85334-5 / 9780387853345