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Birkhäuser Boston eBooks

The Infamous Boundary

David Wick

Published Jan 1, 1995• 87 citations
Publisher

Abstract

reprinted in the British trade journal Physics World in 1990, three separate and 5 lengthy replies from establishment physicists were printed in subsequent issues. For outsiders, especially scientists who rely on physicist's theories in their own fields, this situation is disquieting. Moreover, many recall their introduction to quantum mechanics as a startling, if not shocking, experience. A molecular biologist related how he had started in theoretical physics but, after hearing the ideology of quantum mechanics, marched straight to the Reg­ istrar's office and switched fields. A colleague recalled how her undergraduate chemistry professor religiously entertained queries from the class - until one day he began with the words: "No questions will be permitted on today's lecture." The topic, of course, was quantum mechanics. My father, an organic chemist at a Midwestern university, also had to give that dreaded annual lecture. Around age 16, I picked up a little book he used to prepare and was perplexed by the author's tone, which seemed apologetic to the point of pleading. It was my first brush with the quantum theory. 6 Eventually, I went to graduate school in physics. By then I had acquired an historical bent, which developed out of an episode in my freshman year in college. To relieve the tedium of the introductory physics course, I set out to understand Einstein's theory of relativity (the so-called Special Theory of 1905, not the later and more difficult General Theory of 1915). This went badly at first.

DOI
10.1007/978-1-4612-5361-7

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‘Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One’. These views were contained in a letter written by Albert Einstein to Max Born in December 1926. Though the following year would see the completion of work on the theoretical foundation of the modern physics of atoms and particles, Einstein was never to change his judgement and remained firmly convinced that ‘this business […] contains some unreasonableness’. He was unwilling to sacrifice his own ideas as to the cognitive scope of science even in the face of the important results being achieved by the new theory. To the undeterministic findings of quantum mechanics he opposed his belief in the ‘possibility of giving a model of reality, a theory, that is to say, which shall represent events themselves and not merely the probability of their occurrence’. For this reason he chose to live with the isolation of his scepticism and dissent, ironically accepting the reputation as a obstinate heretic that he had won over the years among his colleagues, and worked to the end on his own research programme to develop a unified field theory of rigorously causal nature. As is generally known, Einstein carried on a strong scientific and philosophical dispute with the defenders of the so-called official interpretation of quantum mechanics.

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Many-body physics in condensed matter systems

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The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke `after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is inexperienced in such matters and needs to look at details. This book is addressed to graduate physics and chemistry students and was written thinking of students. However, I would recommend it also to young and mature physicists, even those who are already `into' the subject. It is a comprehensive work, jointly written by five researchers. After a simple introduction to the subject, the book gradually provides deeper concepts, more advanced theory and finally an interesting introduction and explanation of recent experiments. For its multidisciplinary features, this work could not have been written by one single author. The collaborative effort is undoubtedly one of its most interesting qualities. I would definitely recommend it to anyone who wants to learn more on the geometric phase, a topic that is both beautiful and intruiguing.

Journal of Physics A Mathematical and General•Nov 26, 2003•27 citations
reprinted in the British trade journal Physics World in 1990, three separate and 5 lengthy replies from establishment physicists were printed in subsequent issues. For outsiders, especially scientists who rely on physicist's theories in their own fields, this situation is disquieting. Moreover, many recall their introduction to quantum mechanics as a startling, if not shocking, experience. A molecular biologist related how he had started in theoretical physics but, after hearing the ideology of quantum mechanics, marched straight to the Reg­ istrar's office and switched fields. A colleague recalled how her undergraduate chemistry professor religiously entertained queries from the class - until one day he began with the words: "No questions will be permitted on today's lecture." The topic, of course, was quantum mechanics. My father, an organic chemist at a Midwestern university, also had to give that dreaded annual lecture. Around age 16, I picked up a little book he used to prepare and was perplexed by the author's tone, which seemed apologetic to the point of pleading. It was my first brush with the quantum theory. 6 Eventually, I went to graduate school in physics. By then I had acquired an historical bent, which developed out of an episode in my freshman year in college. To relieve the tedium of the introductory physics course, I set out to understand Einstein's theory of relativity (the so-called Special Theory of 1905, not the later and more difficult General Theory of 1915). This went badly at first.
Vladimir Fock was a Soviet theoretical physicist who, from the 1930s, worked to prove that modern physics was compatible with the Marxist philosophy of dialectical materialism. In 1957, he went to Copenhagen, and a dispute over the interpretation of quantum mechanics began with Niels Bohr. Fock later claimed that he had found points of convergence with his Danish colleague, most of them concerning issues of wording and recognition of the reality of the world independently of our mind. It led to a specific narrative among historians of physics on Fock and his interpretation of quantum mechanics: The Soviet physicist is often described as a member of the Copenhagen school that contributed to the rapprochement of the Soviet philosophy of physics with the ideas of complementarity in stripping away the positivism in its formulation. Our contribution aims to show that this ideological dimension was only one aspect of reality. Returning to the foundations of Fock's epistemology of physics, we argue that he relied on the principles of antireductionism and scientific realism to develop an interpretation of the theory that sought to overcome Bohr's approach and that the differences between the two men cannot be reduced to mere questions of formulation.
‘Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One’. These views were contained in a letter written by Albert Einstein to Max Born in December 1926. Though the following year would see the completion of work on the theoretical foundation of the modern physics of atoms and particles, Einstein was never to change his judgement and remained firmly convinced that ‘this business […] contains some unreasonableness’. He was unwilling to sacrifice his own ideas as to the cognitive scope of science even in the face of the important results being achieved by the new theory. To the undeterministic findings of quantum mechanics he opposed his belief in the ‘possibility of giving a model of reality, a theory, that is to say, which shall represent events themselves and not merely the probability of their occurrence’. For this reason he chose to live with the isolation of his scepticism and dissent, ironically accepting the reputation as a obstinate heretic that he had won over the years among his colleagues, and worked to the end on his own research programme to develop a unified field theory of rigorously causal nature. As is generally known, Einstein carried on a strong scientific and philosophical dispute with the defenders of the so-called official interpretation of quantum mechanics.
This volume collects the lecture notes of an introductory course on the theory of many-body systems, held at the Scuola Normale Superiore di Pisa. It is mainly addressed to fourth and fifth-year undergraduates and to first-year graduates in physics and chemistry. The book is also suitable for researchers in the field wanting to gain a general introductory overview on its modern focal points. Starting from a set of notes first prepared in 1994, which were mainly focused on conduction electrons in metals and semiconductors, these lecture notes are now being reprinted with some major changes and additions in order to provide the reader with an overview of recent developments in the understanding of low-dimensional electron fluids and of confined quantum gases made from bosonic and fermionic atoms and molecules.The book is divided into seven chapters and includes 18 appendices on specialized topics. The introductory chapter illustrates some of the longstanding problems in many-body physics. Chapters 2, 3 and 4 are mainly devoted to topics concerning electron fluids. A formal presentation of the theory of Green's functions and linear response functions for fermions in chapter 2 is followed by a chapter on electron liquids in the normal state and by a further chapter on the magnetism of conduction electrons and strongly correlated electron fluids. Chapter 5 turns to the formal theory of Green's functions and linear response functions for bosons. And finally, Chapters 6 and 7 are on trapped boson gases and on confined fermion gases and gaseous boson-fermion mixtures.
Abstract In the first quarter of this century physicists were slowly and somewhat reluctantly forced to realize that the view of the physical world, so painstakingly built up over the preceding four centuries, was in serious need of revision. In particular, the laws that governed the motion of particles on the atomic scale were not those of classical mechanics. Physics found itself catapulted into the strange new world of quantum theory in which the very notion of position or velocity of a particle became blurred and statistical laws dominated everything.
The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke `after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is inexperienced in such matters and needs to look at details. This book is addressed to graduate physics and chemistry students and was written thinking of students. However, I would recommend it also to young and mature physicists, even those who are already `into' the subject. It is a comprehensive work, jointly written by five researchers. After a simple introduction to the subject, the book gradually provides deeper concepts, more advanced theory and finally an interesting introduction and explanation of recent experiments. For its multidisciplinary features, this work could not have been written by one single author. The collaborative effort is undoubtedly one of its most interesting qualities. I would definitely recommend it to anyone who wants to learn more on the geometric phase, a topic that is both beautiful and intruiguing.