Cơ học lượng tử: Lý giải và Nền tảng bởi Gennaro Auletta

Gennaro Auletta The Quantum Mechanics Conundrum Interpretation and Foundations The Quantum Mechanics Conundrum www.com Gennaro Auletta The Quantum Mechanics Conundrum Interpretation and Foundations 123 www.com Gennaro Auletta University of Cassino and Southern Lazio Cassino, Frosinone, Italy Ponti cal Gregorian University Rome, Italy ISBN 978-3-030-16648-9 ISBN 978-3-030-16649-6 (eBook) https://doi.1007/978-3-030-16649-6 ' Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, speci cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microlms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a speci c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutionalliations. af This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland www.com Preface The starting point of this book was my tutorship for a doctoral dissertation in the year 2014 at the Pontical Gregorian University in Rome.

The now Ph. Father Lluc Torcal wrote a thesis titled In Search of an Ontology that Underlies Quantum Mechanics: Which Vision of the Physical World Could We Get from Quantum Mechanics?It was essentially a philosophical assessment of the main problems and solutions in interpreting quantum theory with a look at the proposals that I have developed in my own research across more than 20 years starting from the publi- cation of Foundations and Interpretation of Quantum Mechanics: A Critical Historical Analysis of the Problems and a Synthesis of the Results , published in 2000 by World Scientic. At that time, I spent a summer in the monastery of Poblet working together with Father Torcal. Since this gave us the opportunity for examining many crucial points in interpreting quantum mechanics, after the dis- cussion of the mentioned dissertation, both of us envisaged the project of making a book on this subject.

However, when I started to work on it, I became soon aware that the issue at the stake went much further than a simple philosophical assessment. Moreover, Father Torcal, due to his duties in the Cistercian order, could not follow this project. Nevertheless, the current structure of the rst three chapters partly mirrors that of the dissertation. And that was why metaphysics and science were such courageous enterprises, such startling inventions, bigger than the wheel, bigger than agriculture, human artifacts set right against the grain of human nature.

Ian McEwan,Enduring Love Rome, Italy Gennaro Auletta v www.com Introduction As well-known, it was the epistemologist K. Popper to speak of a schism in physics 1 determined by quantum theory. Retrospectively it seems opportune to ask: does the schism consist of the introduction of the subjectivity in the mid of physics, as Popper (following Einstein) seems inclined to think, or in accepting that events occur randomly without any cause or even ground as stressed by Bohr? Or is it rooted in the uncontrolled interactions of the experimenter with quantum systems as suggested by the young Heisenberg? Or even does it consist in the acceptance of non-local correlations as pointed out by Schr dinger? The answer may vary according to personal taste. These aspects essentially deal with the following problems (keeping the same order): reality, causality, measurement, status of for- malism.

They represent a challenge to our rational understanding of Nature. They are all fundamental issues, but I am inclined to think that the crucial problem that is at the root of all these puzzles is the notion of reality. So, we may rephrase Popper s de nition of the schism in physics as the possible break down of the notion of reality as such. It is thus not by chance that quantum mechanics still today (after a century from its beginning) is poorly understood and not universally accepted by the community of scientists and philosophers.

As a matter of fact, many physicists still today consider it as a kind of metaphysical speculation devoid or poor of empirical import, and when they use it in neighbouring elds (e. cosmology or statistical mechanics), they limit such a connection to what is strictly necessary and often, in these applications, forget or minimise what is really typical and fundamental of quantum theory. The present book is addressed to the problem of making quantum mechanics understandable and viable in its rational foundations to the community of scholars. Now, the issue of reality has in turn its roots in a categorial problem.

In fact, if our relation with reality is disturbed, it must be related somehow with the way in which we categorise reality with our notions of physical object, law of nature, probability, cause and so on. Moreover, if, in order to circumvent the problem, we 1 Popper (1982).com viii Introduction deny that there is any reality as such, then we are saying that our categorial structure be simply the way in which we humans (and likely in different ways) build our story. These are two sides of the same coin: to deny reality and to reduce cate- gories to mere subjective constructions or games. Thus, although such a critical philosophical problem arises in the mid of science for the rst time with quantum mechanics, it, directly or indirectly, affects the whole of our knowledge.

The part of the work that is devoted to interpretation is dominated by four giants: Bohr, Einstein, Heisenberg and Schr dinger. On many issues they did not agree. They had strong different scienti c backgrounds and even philosophical ideas: Bohr was very much inuenced by Kant and Kirkegaard and interested in epistemic problems of the theory, Einstein by Spinoza and, for what his realism concerns, by a kind of Aristotelian background, the late Heisenberg was also uenced in by Aristotle but with a constant operational approach, and Schr dinger was fascinated by Schopenhauer and the Oriental philosophy. What they have in common is that they showed a signicant interest in general ideas, a character that seems to be lost in most of the actual scientic debate, apart from very rare exceptions.

In the following, we shall see that each of these great scientists was somehow right and that their views can be integrated. In fact, meanwhile, we have cumulated a so huge amount of experimental results (and of theoretical developments) to be able to solve most of the questions that were object of discussion at that time. However, for doing this, a philosophical critical assessment is necessary. It could be objected that to satisfy everybody seems too ambitious, especially with a theory that has raised so many different standpoints and even dissatisfaction.

Nevertheless, the essence of the scienti c enterprise is to nd common rational 2 explanations of our world. It is a permanent duty of scholars involved in these problems, and I hope that the following examination could show at least elements that could help for building such a common view according to quantum mechanics. The other issue is rather a foundational inquiry. We shall show that quantum mechanics is basically an information theory.

However, such a reversible theory of information needs to be integrated with a theory of signals when interactions are involved. Here, the relationship with both special and general relativity is crucial. Finally, we shall deal with Category theory and display the categorial structure of quantum mechanics. The method of this work is not axiomatic and in general I prefer to proceed pragmatically instead of from nitions de and axioms.

This method, as we shall see, was anticipated by Einstein when he said that physics is a science going in the direction of increasing simplicity of the logical bases .3 I interpret this statement as meaning that, instead of trying to lead consequences from rst truths, the right method is to start from theories and explanations that are less general and less grounded and to proceed backwards to better foundations and theories that are more general. As we shall see, this is the method followed today by Category theory and this explains its central role in the present work. 2 As pointed out in Deutsch (1997, Chap. Rovelli has insisted on the relevance of foundational issues (Rovelli 2004, p.

See also Auletta (2011, Sects.com Introduction ix Such a subject necessarily involves many aspects and disciplines and certainly a massive use of philosophical methods and notions. In so doing, it is mandatory to ful l the ve criteria of philosophical adequacy set by Abner Shimony: coherence, neness of reasoning, comprehensiveness, openness to evidence, richness of con- tents, of which the latter three require scrupulous taking into account of scienti c results. Eddington said,the compartments into which human thought is divided are not so watertight that fundamental progresses in one is a matter of indifference to the rest.5 I completely support this point of view and have taken inspiration from it for the present book. In this context, he recalled that physics was traditionally called natural philosophy and that a specialisation that has made philosophy and science dumb to each other is not sane.

References Auletta, Gennaro (in collaboration with I. Integrated Cognitive Strategies in a Changing World. Rome: G and B Press.The Fabric of Reality: The Science of Parallel Universes and Its Implications. London: Penguin Books.

Eddington, Arthur Stanley.Philosophy of Physical Science. Cambridge: University Press. Physik und Realit t. Journal of Franklin Institute221: 349 382; Eng.Out of My Later Years, Estate of A.

New York: Wings Books.Quantum Theory and the Schism in Physics. London: Unwin Hyman Ltd; Routledge, 1992, 1995. Cambridge: University Press. The Nature and Function of Scienti c Theories, 79 172, Pittsburgh; rep.Search for a Naturalistic Point of View.

Cambridge: University Press.com Contents 1 Summary of the Basic Elements of the Theory .1 The Beginning of Quantum Mechanics .1 From the Classical to the Quantum World .2 The Quantum Postulate and Matter s Discontinuity.3 The Road to the Schr dinger Equation.2 The Basic Principles of Quantum Mechanics .1 The Superposition Principle .2 The Quantisation Principle .3 Physical Observables and Different Representations .4 Commutativity and Uncertainty Relations .5 Unitary Transformations and Symmetries .3 Some Further Principles .1 Paulis Exclusion Principle and Spin .2 The Correspondence Principle .3 The Complementarity Principle .4 Density Operator and Compound Systems .1 Pure and Mixed States .2 Entangled and Product States .3 Total and Marginal States. 24 2 The Main Problems .1 Quantum-Mechanical Formalism .1 Two Pictures of Quantum Dynamics .2 Probability and Interference .3 What Does the Quantum-Mechanical Formalism Tell Us? .2 The Measurement Problem .com xii Contents 2.1 It is Not a Problem for Classical Physics .2 It is a Double Problem for Quantum Mechanics .3 von Neumanns Problem.4 What Are the Consequences? .5 Schr dinger Cat.3 The Problem of Non-locality .1 The Paradox Proposed by Einstein Podolsky Rosen.2 Classical Physics and Locality .3 Reality and Correlations .4 Possible Replies to EPR .4 The Problem of Causality .5 Summary of the Chapter. 07 3 The Main Interpretations .1 Solutions to the Measurement Problem .3 Role of the Environment .4 Solution of the Cat s Paradox.2 Formalism and Reality: Information .2 A Formalism That Denotes a Reality? .3 Dealing with Information.4 Two Points of View on Entropy and Information .3 Hidden Variables and Non-locality .1 Logical Restatement of the EPR Argument .