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

The book offers an exploration of the relationships between epistemology and probability in the work of Niels Bohr, Werner Heisenberg, and Erwin Schrödinger; 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 thinking and knowledge in general. 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, beginning with Schrödinger and, most famously, Einstein, who refused to believe that God would resort to playing dice, as quantum theory appeared to demand. The situation led to an intense debate, in particular the great confrontation between Einstein and Bohr, which began around the time of the discovery of quantum mechanics by Heisenberg and Schrödinger in 1920s and has overshadowed the history of the debate concerning quantum mechanics ever since. The controversy itself surrounding quantum theory and the intensity of the debate concerning it have remained undiminished. No end appears to be in sight. At the same time, in spite of the enormous and ever proliferating amount of commentaries in all genres (technical, philosophical, and popular), some of the deeper philosophical aspects of quantum mechanics and of the philosophical thought of the figures considered in this study often remain explored. The main aim of this book is to contribute to a better understanding of the nature of quantum-theoretical thinking and of the reasons for this extraordinary impact and controversy. Philosophically, the book pursues this task by bringing together in a new way the relationships between epistemology and probability in quantum theory and beyond. Historically, it does so by engaging comprehensively and in a mutually illuminating way with the work of all three key figures responsible for the birth of quantum mechanics - Heisenberg, Schrödinger, and, as concerns quantum epistemology, Bohr - which has not be previously done in literature on quantum mechanics. Among other key contributions of the book is an analysis of the role of mathematics in quantum theory and in the thinking of Bohr, Heisenberg, and Schrödinger; a new treatment of the famous experiment of Einstein, Podolsky, and Rosen (EPR) and of the Bohr-Einstein exchange concerning it; and an exploration of the implications of the epistemological problematics considered by the book for new developments of quantum mechanics itself, such as quantum information theory, on the one hand, and, on the other, for higher-level physical theories, from quantum field theory to string/brane theories and new cosmological theories. The book offers an exploration of the relationships between epistemology and probability in the work of Niels Bohr, Werner Heisenberg, and Erwin SchrÃœdinger; 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 thinking and knowledge in general. 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, beginning with SchrÃœdinger and, most famously, Einstein, who refused to believe that God would resort to playing dice, as quantum theory appeared to demand. The situation led to an intense debate, in particular the great confrontation between Einstein and Bohr, which began around the time of the discovery of quantum mechanics by Heisenberg and SchrÃœdinger in 1920s and has overshadowed the history of the debate concerning quantum mechanics ever since. The controversy itself surrounding quantum theory and the intensity of the debate concerning it have remained undiminished. No end appears to be in sight. At the same time, in spite of the enormous and ever proliferating amount of commentaries in all genres (technical, philosophical, and popular), some of the deeper philosophical aspects of quantum mechanics and of the philosophical thought of the figures considered in this study often remain explored. The main aim of this book is to contribute to a better understanding of the nature of quantum-theoretical thinking and of the reasons for this extraordinary impact and controversy. Philosophically, the book pursues this task by bringing together in a new way the relationships between epistemology and probability in quantum theory and beyond. Historically, it does so by engaging comprehensively and in a mutually illuminating way with the work of all three key figures responsible for the birth of quantum mechanics - Heisenberg, SchrÃœdinger, and, as concerns quantum epistemology, Bohr - which has not be previously done in literature on quantum mechanics. Among other key contributions of the book is an analysis of the role of mathematics in quantum theory and in the thinking of Bohr, Heisenberg, and SchrÃœdinger; a new treatment of the famous experiment of Einstein, Podolsky, and Rosen (EPR) and of the Bohr-Einstein exchange concerning it; and an exploration of the implications of the epistemological problematics considered by the book for new developments of quantum mechanics itself, such as quantum information theory, on the one hand, and, on the other, for higher-level physical theories, from quantum field theory to string/brane theories and new cosmological theories Quantum mechanics, discovered by Werner Heisenberg and Erwin Schrödinger in 1925-1926, is famous for its radical implications for our conception of physics and for our view of human knowledge in general. While these implications have been seen as scientifically productive and intellectually liberating to some, Niels Bohr and Heisenberg, among them, they have been troublesome to many others, including Schrödinger and, most famously, Albert Einstein. The situation led to the intense debate that started in the wake of its discovery and has continued into our own time, with no end appearing to be in sight. Epistemology and Probability aims to contribute to our understanding of quantum mechanics and of the reasons for its extraordinary impact by reconsidering, under the rubric of "nonclassical epistemology," the nature of epistemology and probability, and their relationships in quantum theory. The book brings together the thought of the three figures most responsible for the rise of quantum mechanics--Heisenberg and Schrödinger, on the physical side, and Bohr, on the philosophical side--in order to develop a deeper sense of the physical, mathematical, and philosophical workings of quantum-theoretical thinking. Reciprocally, giving a special emphasis on probability and specifically to the Bayesian concept of probability allows the book to gain new insights into the thought of these figures. The book reconsiders, from this perspective, the Bohr-Einstein debate on the epistemology of quantum physics and, in particular, offers a new treatment of the famous experiment of Einstein, Podolsky, and Rosen (EPR), and of the Bohr-Einstein exchange concerning the subject. It also addresses the relevant aspects of quantum information theory and considers the implications of its epistemological argument for higher-level quantum theories, such as quantum field theory and string and brane theories. One of the main contributions of the book is its analysis of the role of mathematics in quantum theory and in the thinking of Bohr, Heisenberg, and Schrödinger, in particular an examination of the new (vis-à-vis classical physics and relativity) type of the relationships between mathematics and physics introduced by Heisenberg in the course of his discovery of quantum mechanics. Although Epistemology and Probability is aimed at physicists, philosophers and historians of science, and graduate and advanced undergraduate students in these fields, it is also written with a broader audience in mind and is accessible to readers unfamiliar with the higher-level mathematics used in quantum theory Quantum mechanics, discovered by Werner Heisenberg and Erwin Schrödinger in 1925-1926, is famous for its radical implications for our conception of physics and for our view of human knowledge in general. While these implications have been seen as scientifically productive and intellectually liberating to some, Niels Bohr and Heisenberg, among them, they have been troublesome to many others, including Schrödinger and, most famously, Albert Einstein. The situation led to the intense debate that started in the wake of its discovery and has continued into our own time, with no end appearing to be in sight. Epistemology and Probability aims to contribute to our understanding of quantum mechanics and of the reasons for its extraordinary impact by reconsidering, under the rubric of "nonclassical epistemology," the nature of epistemology and probability, and their relationships in quantum theory. The book brings together the thought of the three figures most responsible for the rise of quantum mechanics—Heisenberg and Schrödinger, on the physical side, and Bohr, on the philosophical side—in order to develop a deeper sense of the physical, mathematical, and philosophical workings of quantum-theoretical thinking. Reciprocally, giving a special emphasis on probability and specifically to the Bayesian concept of probability allows the book to gain new insights into the thought of these figures. The book reconsiders, from this perspective, the Bohr-Einstein debate on the epistemology of quantum physics and, in particular, offers a new treatment of the famous experiment of Einstein, Podolsky, and Rosen (EPR), and of the Bohr-Einstein exchange concerning the subject. It also addresses the relevant aspects of quantum information theory and considers the implications of its epistemological argument for higher-level quantum theories, such as quantum field theory and string and brane theories. One of the main contributions of the book is its analysis of the role of mathematics in quantum theory and in the thinking of Bohr, Heisenberg, and Schrödinger, in particular an examination of the new (vis-� -vis classical physics and relativity) type of the relationships between mathematics and physics introduced by Heisenberg in the course of his discovery of quantum mechanics. Although Epistemology and Probability is aimed at physicists, philosophers and historians of science, and graduate and advanced undergraduate students in these fields, it is also written with a broader audience in mind and is accessible to readers unfamiliar with the higher-level mathematics used in quantum theory. 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. Content: Front Matter....Pages i-xxxiii Introduction—Epistemology and Probability in Quantum Theory: Physics, Mathematics, and Philosophy....Pages 1-44 Quantum Phenomena and the Double-Slit Experiment....Pages 45-75 Heisenberg’s Revolutions: New Kinematics, New Mathematics, and New Philosophy....Pages 77-113 From Geometry to Algebra in Physics, with Heisenberg....Pages 115-136 Schrödinger’s Waves: Propagation and Probability....Pages 137-177 Bohr’s Como Argument: Complementarity and the Problem of Causality....Pages 179-217 From Como to Copenhagen: Renunciations....Pages 219-235 Can Quantum-Mechanical Description of Physical Reality Be Considered both Complete and Local?....Pages 237-277 Essential Ambiguity and Essential Influence: Reading Bohr’s Reply to EPR....Pages 279-311 Mysteries Without Mysticism, Correlations Without Correlata, Epistemology Without Ontology, and Probability Without Causality....Pages 313-352 11 Conclusion: “The Mere Touch of Cold Philosophy”....Pages 353-367 Back Matter....Pages 369-402 Offers an exploration of the relationships between epistemology and probability in the work of Niels Bohr, Werner Heisenberg, and Erwin Schrodinger; in quantum mechanics; and in modern physics. This book considers the implications of these relationships and of quantum theory for our understanding of the nature of thinking and knowledge in general