I would like to recall my experiences when I joined George Series when on study leave from the University of Otago in 1959. Like George, we had decided, some years previously, to pursue the line of research opened up by the double-resonance experiment of Brossel and Bitter. Up to that time both groups had been applying the new technique to traditional spectroscopic problems, those of measuring the fine structure, hyperhe structure, g -factors and nuclear moments. But here, in Oxford, was something new and exciting - experiments that studied the nature of light itself, questioning some long-held views. George had come to the view that, in a double-resonance experiment, one could demonstrate the inner coherence that could exist between superposition states of an atom. He, and his students Wilf Fox and Mike Taylor, had already obtained promising evidence; but he needed more definite results if he was going to allay the doubts and suspicions of some others in the Clarendon. At the time, people generally thought that light, being a superposition of radiations from many atoms with no obvious phase relation to each other, was an incoherent wave phenomenon. One could observe small scale coherence (for example, in the Young interference experiment) but it would be largely concealed by the incoherent nature of the radiation from many atoms in a source. In the experiments that had been performed the coherence was introduced between a pair of excited states (Zeeman sub-states) by the application of an oscillating magnetic field - was it not likely, according to the doubters, that the modulation observed in the fluorescence was due to "pick-up" in the amplifiers from the source of oscillations? George had to prove that this was not the cause. I well remember him saying at the time "I have a hunch that I am correct". That typified his approach to physics. The work of 1959 demonstrated beyond all doubt that substantial coherence, manifested as strong beats in the intensity of the light, could be obtained. The experiments demonstrated this to be the case. We also worked out the theory of the effect. In the theoretical explanation of the experiments, both George and I were impressed by the success of a semi-classical approach - i.e. by treating the atom as a quantum-mechanical structure and the light as an electromagnetic wave. This viewpoint dominated much of George's work in later times. As he stated in the Memoirs, "I came to the conclusion that the key problem in the interaction of electromagnetic fields and atoms was the nature of spontaneous emission. I accept the quantum field theory as giving an adequate mathematical explanation, but this seems to me to be deficient as a physical explanation". I think it is fair to say that George was always seeking a deeper physical meaning than was provided by a mere mathematical description. This philosophy certainly rubbed off on people who worked with him. That year, 1959, was also the year when coherence in light beams was being studied in other laboratories across the Atlantic. It was the year the laser was born. There was no doubt then about coherence in light. I would also like to mention the great regard that George had for S. Pancharatnam who came to work at the Clarendon in 1964. George and Panch spent many hours in discussions. Although they never published anything jointly, George recalled that, if he was doubtful about some point of physics, he would refer to Panch. As he wrote in a moving review for the Pancharatnam Memorial Issue of Current Science (Vol. 67, August 1994), "Panch was not easily moved from the conventional view [of the nature of the interactions of light and atoms]. I was more impetuous; Panch was generally right". George edited the collected works of Pancharatnam; he went to India as a Raman Visiting Professor in 1982 and was made an Honorary Fellow of the Indian Academy of Sciences in 1984. At Reading [from 1968 to 1982], he increasingly turned to spectroscopy with tuneable lasers, generally with the emphasis on understanding the underlying physics rather than accumulating data. He had a highly original mind, which showed both in his choice of research topics and in his method of approach. He did not follow fashion; his instinct for an interesting problem was at odds with the modem policy of direct funding and the identification of "growth areas". His applications for research grants were often unsuccessful, despite his high international standing and integrity. He was never interested in building up a large research team, and had comparatively few research students, but his enthusiasm and commitment to the quality of his science attracted a succession of overseas visitors to his laboratory. Following my own year at the Clarendon, and some subsequent visits both to Oxford and to Reading, there was a continuing strong association between the Clarendon and Otago Physics that continues until today. George Series was the William Evans Visiting Professor to Otago University in 1972. He never lost his interest in the fundamentals of physics inspired by his first researches into the structure of the hydrogen atom; he wrote on the Rydberg constant, the physics of spontaneous emission, and on the fine-structure constant α = e 2 / hc . He donated a garden seat to St Edmund Hall (Oxford), of which he was a Fellow. On it he placed a plaque* in recognition of the ubiquitous nature of this constant; it almost had magical significance for him. He served physics in many ways outside research. He was for a number of years the Editor of the European Journal of Physics and was also Editor of the Journal of Physics B: Atomic and Molecular Physics , He was also on the Editorial Board of a number of journals. He was elected to Fellowship of a number of physics societies. The Editorial Board of these Memorial Essays dedicate them to George's memory, and to his wife Annette and his family.
I would like to recall my experiences when I joined George Series when on study leave from the University of Otago in 1959. Like George, we had decided, some years previously, to pursue the line of research opened up by the double-resonance experiment of Brossel and Bitter. Up to that time both groups had been applying the new technique to traditional spectroscopic problems, those of measuring the fine structure, hyperhe structure, g -factors and nuclear moments. But here, in Oxford, was something new and exciting - experiments that studied the nature of light itself, questioning some long-held views. George had come to the view that, in a double-resonance experiment, one could demonstrate the inner coherence that could exist between superposition states of an atom. He, and his students Wilf Fox and Mike Taylor, had already obtained promising evidence; but he needed more definite results if he was going to allay the doubts and suspicions of some others in the Clarendon. At the time, people generally thought that light, being a superposition of radiations from many atoms with no obvious phase relation to each other, was an incoherent wave phenomenon. One could observe small scale coherence (for example, in the Young interference experiment) but it would be largely concealed by the incoherent nature of the radiation from many atoms in a source. In the experiments that had been performed the coherence was introduced between a pair of excited states (Zeeman sub-states) by the application of an oscillating magnetic field - was it not likely, according to the doubters, that the modulation observed in the fluorescence was due to "pick-up" in the amplifiers from the source of oscillations? George had to prove that this was not the cause. I well remember him saying at the time "I have a hunch that I am correct". That typified his approach to physics. The work of 1959 demonstrated beyond all doubt that substantial coherence, manifested as strong beats in the intensity of the light, could be obtained. The experiments demonstrated this to be the case. We also worked out the theory of the effect. In the theoretical explanation of the experiments, both George and I were impressed by the success of a semi-classical approach - i.e. by treating the atom as a quantum-mechanical structure and the light as an electromagnetic wave. This viewpoint dominated much of George's work in later times. As he stated in the Memoirs, "I came to the conclusion that the key problem in the interaction of electromagnetic fields and atoms was the nature of spontaneous emission. I accept the quantum field theory as giving an adequate mathematical explanation, but this seems to me to be deficient as a physical explanation". I think it is fair to say that George was always seeking a deeper physical meaning than was provided by a mere mathematical description. This philosophy certainly rubbed off on people who worked with him. That year, 1959, was also the year when coherence in light beams was being studied in other laboratories across the Atlantic. It was the year the laser was born. There was no doubt then about coherence in light. I would also like to mention the great regard that George had for S. Pancharatnam who came to work at the Clarendon in 1964. George and Panch spent many hours in discussions. Although they never published anything jointly, George recalled that, if he was doubtful about some point of physics, he would refer to Panch. As he wrote in a moving review for the Pancharatnam Memorial Issue of Current Science (Vol. 67, August 1994), "Panch was not easily moved from the conventional view [of the nature of the interactions of light and atoms]. I was more impetuous; Panch was generally right". George edited the collected works of Pancharatnam; he went to India as a Raman Visiting Professor in 1982 and was made an Honorary Fellow of the Indian Academy of Sciences in 1984. At Reading [from 1968 to 1982], he increasingly turned to spectroscopy with tuneable lasers, generally with the emphasis on understanding the underlying physics rather than accumulating data. He had a highly original mind, which showed both in his choice of research topics and in his method of approach. He did not follow fashion; his instinct for an interesting problem was at odds with the modem policy of direct funding and the identification of "growth areas". His applications for research grants were often unsuccessful, despite his high international standing and integrity. He was never interested in building up a large research team, and had comparatively few research students, but his enthusiasm and commitment to the quality of his science attracted a succession of overseas visitors to his laboratory. Following my own year at the Clarendon, and some subsequent visits both to Oxford and to Reading, there was a continuing strong association between the Clarendon and Otago Physics that continues until today. George Series was the William Evans Visiting Professor to Otago University in 1972. He never lost his interest in the fundamentals of physics inspired by his first researches into the structure of the hydrogen atom; he wrote on the Rydberg constant, the physics of spontaneous emission, and on the fine-structure constant α = e 2 / hc . He donated a garden seat to St Edmund Hall (Oxford), of which he was a Fellow. On it he placed a plaque* in recognition of the ubiquitous nature of this constant; it almost had magical significance for him. He served physics in many ways outside research. He was for a number of years the Editor of the European Journal of Physics and was also Editor of the Journal of Physics B: Atomic and Molecular Physics , He was also on the Editorial Board of a number of journals. He was elected to Fellowship of a number of physics societies. The Editorial Board of these Memorial Essays dedicate them to George's memory, and to his wife Annette and his family.
“Bohr was primarily a philosopher, not a physicist, but he understood that natural philosophy ... carries weight only if its every detail can be subjected to the ... test of experiment” (Heisenberg in [59], p. 95). As a result his approach differed from that of theschool-philosopherswhom he regarded with a somewhat “sceptical attitude, to say the least” ([59], p. 129) and whose lack of interest in “the important viewpoint which had emerged during the development of atomic physics” he noticed with regret ([59], p. 183).But it also differed, and to a considerable degree, from the spirit of what Professor T. S. Kuhn has called a “normal science.” Looking at Bohr's method of research we see that technical problems, however remote, are always related to a philosophical point of view; they are never treated as “tiny puzzles” whose solution is valuable in itself, even if one has not the faintest idea what it means, and where it leads: “For me” Bohr writes to Sommerfeld in 1922 ([59], p. 71) “[the quantum theory] is not a matter for petty didactic details, but a serious attempt to reach ... an inner coherence.” Emphasis is put on matters of principle ([59], p. 36) and minor discrepancies, or “puzzles” in the sense of Kuhn, instead of being deemphasized, and assimilated to the older paradigm,are turned into fundamental difficultiesby looking at them from a new direction, and by testing their background “in its furthest consequences by exaggeration” ([59], p. 329). A noteworthy example of Bohr's “non-normal” and rather metaphysical approach to physics is his scepticism in the face of the success of his own atomic model.
One way of reading this book is as an epilogue-or (more precisely) as a denouement-to a book I wrote more than thirty years ago, which was called Quantum Mechanics and Experience.That earlier book was meant to do two things:1) To introduce its readers to the elementary nuts and bolts of the foundations of quantum mechanics-the idea of superposition, the basics of the standard mathematical formalism of quantum mechanics, the argument of Einstein and Podolsky and Rosen to the effect that that formalism, considered as a description of the fundamental real ity of the world, must be somehow incomplete, Bell's extension of that argument into a general and power ful theorem about locality, the elaboration (by figures like Erwin Schrödinger, and John von Neumann, and Eugene Wigner) of the quantum-mechanical mea surement prob lem, and vari ous proposals (theories of the spontaneous collapse of the wave-function, Bohmian mechanics, the so-called many-worlds interpretations of quantum mechanics, and so on) for solving it.2) To show how the above-mentioned proposals for solving the mea sure ment prob lem, taken together, amount to a
I thank Rodger Walser and his colleagues for organizing this conference to celebrate George \nSudarshan’s birthday and landmark achievements in science. It is an honor for me to be here and \nalso a great pleasure to be back in Austin to join the chorus of the FOGS. \nI would like begin with a brief historical introduction and then turn to topics that we \nhaven’t heard so much about thus far in the symposium, namely experiments in Quantum Optics. \nLet me remind you that blackbody radiation has had a profound impact on physics since the time \nof Planck. However, even in more modern times after the development of quantum mechanics \nand quantum electrodynamics, one really did not know how to describe the underlying field \nfluctuations as required for diverse interference phenomena. Emil Wolf laid critical foundations \nfor this enterprise with his theory of classical coherence developed in collaboration with Max \nBorn in their classic book Principles of Optics. \nA great challenge to the physics community was the experiment by R. H. Brown and R. \nQ. Twiss in 1956 [1], which led to a confusing and controversial time for photons and fields. In \n1958 Leonard Mandel helped to resolve the controversy by explaining how light fluctuations are \nconverted to photocurrents in the detection process, albeit in with a classical description of the \nfield [2]. The confusion arose from the effort to understand, on the one hand, interference \nphenomena that are expressed in terms of the complex amplitude of the electromagnetic field, for \nwhich only a classical description was available. On the other hand, quantum electrodynamics \nhad been developed based upon energy eigenstates (i.e., Fock states) with photons as quanta. It \nwas really difficult to understand how the electric and magnetic fields behave in terms of these \nquantum states. For example, the expectation value of any electromagnetic field is zero in a Fock \nstate. The confusion was compounded by the historic invention of the maser and laser and by the \npressing need for quantum theories of the dynamical processes of these and other laboratory \nadvances.
In opening the Levico BEC 2003 meeting, the directors thought it would be useful to say a little about the first BEC workshop held in the same hotel, in the same lecture room, almost exactly ten years ago. I want to give you a personal view of what led up to the historic BEC 93 workshop at Levico and contrast the situation then with the fantastic developments which have occurred over the last decade. BEC 93 was organized by Griffin, Snoke, Stringari, Laloe and Baym. The purpose of the workshop was to bring together people working in different fields of physics but with a common interest in the phenomenon of Bose–Einstein condensation. It is useful to briefly recall the history of BEC studies before the BEC 93 workshop, to understand why it was organized. In 1938 Fritz London suggested that the mysterious phase transition which occurred in liquid 4 He at T = 2.17 K might be related to the formation of a Bose–Einstein condensate (BEC) of 4 He atoms, a phenomenon first predicted by Einstein in 1925 in an ideal gas. After Tisza suggested that the spectacular superfluid effects discovered in 1938 were related to the motion of the Bose condensate, BEC became a hot topic in the years before World War II. In 1941, Landau developed a very successful two-fluid theory of superfluid 4 He, based on the relatively new concept of elementary excitations of a many-body system to describe the 'normal fluid' component. The Landau picture was spectacularly successful in explaining various thermodynamic and transport properties, albeit in a phenomenological manner. However, Landau's magnificent theory made no use of the concept of BEC, or even the fact that the 4 He atoms obeyed Bose statistics. Interest in BEC faded from low temperature conferences in the period 1945–1955, in spite of Bogoliubov's seminal work in 1947 showing that a dilute weakly interacting Bose gas still exhibited BEC. Quite separate from the study of BEC in superfluid 4 He, interest in finding a BEC in a dilute, weakly interacting Bose gas started to develop in the early 1960s. The first system was optically excited excitons in semiconductors (electron-hole pairs, with zero total spin, played the role of the bosons). However, the short lifetime of the excitons in most semiconductors frustrated the early experiments. A second major effort developed in the 1980s with attempts to produce an atomic BEC in spin-polarized hydrogen gas. The initial experiments were very promising, but various problems ultimately stopped people from ever producing (until 1998) high enough densities needed for BEC. However, this work revived interest in the theory of a dilute, weakly interacting Bose gas, and also led to several workshops on 'spin-polarized' quantum gases in the 1980s in which BEC was a major topic. The preceding summary sets the stage for why BEC 93 was organized, namely, to bring together people (both theorists and experimentalists!) interested in BEC in quite different systems, for encouragement as well as stimulation. The topic was largely ignored in the large international low temperature conferences. The organizers were mainly from the condensed matter and low temperature physics communities. Fortunately Franck Laloe was involved, and he was aware of the attempts to produce a BEC in trapped alkali gases using the novel technique of laser-cooling. The titles of the review talks given at BEC 93 show that the popular Bose systems in 1993 were liquid 4 He, excitons, spin-polarized hydrogen and small Cooper pairs in high-temperature superconductors. Work on laser-cooled alkali gases was reviewed by Yvan Castin, but people seemed pessimistic at the time about producing a stable BEC in these very dilute systems in the near future. We also had several excellent talks about Bose condensates involving mesons, as well as Cooper pairing in nuclei. The main reason for this was that crucial financial support for BEC 93 came from the newly formed ECT* Institute in Trento, thanks to Stringari. As a result, several theorists interested in condensates in nuclear and high energy physics were incorporated into the schedule of BEC 93. To my surprise, their talks, relating to Bose condensates in fairly exotic settings, fitted in very well with the other speakers. It was decided to hold BEC 93 in Levico-Terme at the Grand Hotel Bellavista. Stringari scouted many hotels in the area around Trento and Sandro clearly chose wisely, since we returned ten years later for Levico BEC 2003. Because of the interdisciplinary quality of the BEC 93 workshop and the slightly controversial nature of BEC in real systems, however, we found it very difficult to obtain funding for BEC 93. Many of the funding agencies turned down requests for funding so the BEC 93 workshop was funded by the ECT*, a small grant from CNRS in France, a payment from Cambridge University Press (in lieu of royalties for the conference proceedings) and registration fees. We were therefore overjoyed when we received some late applications from people who said they would pay the full registration fee. One of these was Eric Cornell, a young AMO physicist from 'someplace' called JILA in Boulder, Colorado. We gladly accepted his money and his participation. The opening session of BEC 93 in the Grand Hotel Bellavista was a very historic occasion, since almost all the people in the world interested in BEC were present. The excellent review talks and energetic discussions quickly made us realize that the workshop was going to be a success. People heard about the search for BEC in systems quite different from what they were familiar with. It probably was the first time that the CMP and AMO communities were in the same room together. Eric Cornell later told me that it was the first meeting where he met a lot of well known CMP theorists, and heard them arguing about the role of interactions, broken symmetry and order parameters, Goldstone modes, phase rigidity, etc. It dawned on Eric that the physics of a Bose condensate had not been completely settled in Einstein's 1925 paper! One of the star invited speakers was Nozières but at the last moment, he could not attend because of family reasons. However, he gave a lecture a month later at the 60th birthday party for Cohen-Tannoudji in Paris, based on his planned talk for BEC 93. I convinced him that his lecture 'belonged' to BEC 93 so he wrote it up for the BEC book we were preparing. His insightful article became one of the most quoted articles in the book, and many of his phrases (fragmentation of the condensate, phase locking, enemies of Bose–Einstein condensation, etc.) have entered our language. At the conference dinner, we gave out small prizes to some of the best speakers and participants who had made a significant contribution. One of the themes of BEC 93 was to pin down what an unambiguous signature of a Bose condensate was, and the term 'smoking gun' became very popular in discussions. Shlyapnikov received the coveted 'Smoking Gun' award, the prize being a package of cigarettes. The 'Prix d'Or' (1000 Lire), for giving the most convincing evidence for a Bose condensate, was awarded to Wolfe for his group's work on exciton gases. Some years later, in 1999, further work by his group at Urbana showed that an unexpected rapid exciton decay process had not been included in the original data analysis. As a result, the exciton densities had been over-estimated and they had not crossed into the BEC region. Shortly after, I received a letter from Wolfe telling me about the new results, and also the original 1000 Lire banknote he had received as a prize at BEC 93. It made me proud having colleagues like this. Brown, who argued that kaon condensates played a crucial role in the collapse of large stars, received the very special 'Smoking Universe' award. He gave the most impressive 'thank you' speech, worthy of the Academy Awards. At the end of BEC 93, we had an open discussion about whether we should organize another BEC workshop two years later, in 1995. Many people felt that, while BEC 93 had been very stimulating, there probably would not be enough progress to have another BEC meeting 'so soon', but a committee was set up to monitor developments. Walraven took the initiative to organize BEC 95, which was held in Mt St Odile near Strasbourg in France, in June 1995. As luck would have it, a few weeks before BEC 95 convened, rumours circulated that the JILA group at Boulder had clear evidence for a Bose condensate in a trapped gas of 87 Rb atoms. When Eric arrived in Mt St Odile from a meeting in Capri and presented the JILA data 'hot off the press', we all gave him a standing ovation. The earth had moved and BEC was about to move to centre stage. Another piece of luck was that our BEC 93 book ( Bose–Einstein Condensation 1995 ed A Griffin, D W Snoke and S Stringari (Cambridge: Cambridge University Press)) finally appeared in March 1995. The discovery of BEC in atomic gases a few months later made the book a modest 'bestseller' and it was quickly re-issued as a paperback (almost unheard of for this type of conference proceedings). Several people later congratulated us on producing such an excellent book on BEC so quickly after the discovery in June 1995! The BEC book (often called the 'Green Book') did fill a vacuum in the early days, providing carefully written reviews about many aspects of BEC. Several of the articles were well ahead of their time, such as the discussion of the BCS–BEC crossover in Fermi gases by Randeria. We are only now seeing a lot of references to his review article, as the search for BCS pairing in trapped Fermi gases has developed over the last year. Probably over half of all publications in the area of BEC and ultracold quantum gases since 1995 have made one or more references to the Green Book. Beginning with BEC 95, these biennial meetings have now become a regular affair, generously financed and sponsored by the European Science Foundation (ESF). BEC 99, 2001 and 2003 have all been held in San Feliu de Guixols, in Spain. Since BEC 95, these workshops have been dominated by people working on trapped atomic gases, for obvious reasons. However, it is nice to see that work has picked up recently in the search for BEC in exciton gases (especially in quantum wells), and the study of trapped Fermi gases has stimulated new connections with people working in nuclear physics as well as highly correlated electron systems. So one can see that the exciting interdisciplinary atmosphere of BEC 93 may return in the near future. The papers given at Levico BEC 2003 already show strong evidence of this trend. In their 2001 Nobel Prize lectures, Cornell, Wieman and Ketterle all emphasized how 'surprised' they were on how rich BEC physics turned out to be. Initially, they expected that these atomic condensates would be small and somewhat delicate, certainly only of minor interest to the larger physics community. In fact, as we all know, interest in ultracold gases has exploded since 1995 like a 'Bosenova' and, like the universe, there is no sign of this expansion stopping. It is rapidly producing a whole new field of research which is an amalgamation of AMO and CMP physics. This in turn is producing a major re-organization of all major physics departments, in terms of the hiring of new faculty and resource allocations. International conferences in more traditional research areas in CMP and AMO have been trying to incorporate this growing subject, but it is probably time to start a new 'International Conference on Ultracold Quantum Gases' which is open to all. Of course, the young physicists who have organized and are the main speakers at Levico BEC 2003 illustrate this on-going revolution. I predict that Bose matter waves, atomic optics and, more generally, phenomena in ultracold quantum gases, will be the basis for all really new technology in the 21st century. I say this with confidence, since I don't see any real competition from developing technologies based on electrons (discovered about 1900) and laser beams (discovered about 1960). As with these older technologies, it will take decades to see how cold quantum gases can be used, in ways that we cannot even imagine today. A crucial reason for the exciting future of ultracold gases is based on the fact that it involves a creative interaction between two major areas of physics, CMP and AMO. Each has their own well developed paradigms for thinking about physics, and this difference surfaces in dealing with cold quantum gases. This creates a certain tension but ultimately it is the basis of a new creativity. Many CMP theorists who had previously worked in the area of quantum fluids and superconductors have entered this new field. This is shown by the recent publication of two excellent books on cold quantum gases (Pethick C and Smith H 2002 Bose–Einstein Condensation in Dilute Gases (Cambridge: Cambridge University Press); Pitaevskii L and Stringari S 2003 Bose–Einstein Condensation (Oxford: Oxford University Press)), both by CMP theorists. This is easy to understand since trapped atomic gases (Bose or Fermi) are beautiful examples of interacting, highly coherent, quantum many-body systems, precisely the subject that CMP theorists have been struggling to understand since the 1950s. The new concepts and techniques needed to understand such many-body systems were developed and fought over in the period 1955–1965, when it was realized that there was more to the quantum theory of matter than solving Schrödinger's wave equation. A major contribution was made by the Landau school in Moscow. This battle of ideas was focused on the attempts to understand both superconductivity and superfluid 4 He. While the BCS theory of superconductivity in metals which appeared in 1957 clearly had the right physics to explain the key properties of superconductors, it still took some time for most theorists to really understand the BCS theory at a deeper level, in terms of broken symmetry, order parameters and Goldstone modes. The BCS theory gave CMP physics a simple microscopic model for superfluidity in a real system, in terms of the coherent motion of Cooper pairs. Very quickly, the close analogy was made between Bogoliubov's theory of a Bose-condensed gas and the BCS theory of superconductors. Strangely enough, however, it was only in the 1980s that pioneering work by Leggett, Nozières and others re-emphasized that one should think of the BCS theory as a Bose condensate of Cooper pairs. This led to an understanding of the BCS–BEC crossover, and also that the Bogoliubov theory of a weakly interacting Bose-condensed gas was 'buried' in the full BCS theory. It is fitting that, in 2003, this BCS–BEC crossover is becoming a central topic in the field of ultracold atoms. I say this because it represents a beautiful synthesis of both AMO physics (the formation of diatomic molecules using Feshbach resonances) and CMP physics (many-body effects giving rise to Cooper pairs) in a novel setting. As Levico BEC 2003 and the articles published in this special section show, we can expect more exciting advances of this kind in the near future. Acknowledgments I would like to thank the organizers of the Levico BEC 2003 workshop for inviting me to participate as a senior lecturer and also to commemorate the tenth anniversary of the first BEC workshop held in Levico-Terme. My research is funded by NSERC of Canada.
FOR twenty years and more we have been hearing continually about the conflict between the corpuscular and the undulatory theories of light, and it is possible that for years to come we may be hearing about a similar contest between the wave-theory and the particle-theory of matter. Furthermore, there are intimations that if an adequate theory either of light or of matter ever is attained, it will involve conceptions of waves which in certain limiting cases approach to conceptions of particles. Already it is established that the appropriate way to attack the typical problems of the atom consists in setting up a wave-equation, and dealing with it in the same manner as one adopts to solve the typical problem of acoustics: how to determine the resonance-frequencies of a piece of elastic matter, such as a taut wire or a drumhead or a column of air in a tube. Therefore it seems opportune to restudy, with care and in detail, the great classical example of a wave-theory highly developed and widely successfulthe great theory of light dimly foreshadowed by Huygens, endowed with its essen tial attributes by Young and Fresnel and Kirchhoff and a host of their coevals, utilized in the design of a multitude of ingenious instruments, perfected by Maxwell and connected with the theory of electricity and magnetism, and serving to this day as the basis for the theory of quanta. So doing, we shall be reminded of many triumphs of the past century of physical research, discoveries which in their time were as exciting as new quantum phenomena in ours; we shall notice certain achievements themselves as recent as those of quanta, and perhaps not less impressive; we shall retrace the reasonings which led to certain conclusions which the quantum-theories, unable to do without them and yet incompetent to derive them, have taken bodily over from their forerunner; we shall reconsider the evidence which in the litigation of a century ago caused the verdict to be rendered in favour of the wave-theory over the particle-theory; and perhaps incidentally we shall be drilling ourselves to test the evidence lately submitted and still to be submitted in the appeal of that case, and in the hearing of that other which impends.