In the summer of 1970 I attended as a graduate student from MPI Munich the Brandeis Summer School on Theoretical Physics at Brandeis University. Afterwards I drove in a car which I had to deliver eventually in Long Beach, California, throughout the United States. This trip was not only my first encounter with the magnificent sceneries of the United States. On a short stay at the Physics Center in Aspen, Colorado, I met in a discussion with colleagues on problems of broken scale invariance Murray Gell–Mann for the first time.

The year 1970 was an exciting one in particle physics. After several years of frustration and little progress in experimental studies, the observation of the scaling phenomena in inelastic electron–nucleus scattering at SLAC had started a new era in particle physics. I had the hunch, like numerous other theorists, that the “SLAC scaling” might have something to do with scale invariance in field theory, the topic of my Ph. D. – thesis, which had been given to me by Heinrich Mitter at the MPI in Munich. In 1970 Gell–Mann was working, partially together with Peter Carruthers, on the problem of scale invariance and its breaking in hadron physics, a topic, which at a first sight seemed unrelated to the “scaling phenomenon” seen at SLAC. I remember a number of conversations I had with Murray at the Aspen Physics Center, in which we talked about possible connections.

I find I am three and a half years older than Gell-Mann although I have always prided myself on belonging to the same generation as he does. I shall give you a contemporary's views and some early recollections of Gell-Mann and his influence on the subject of Particle Physics.

I believe I first saw Gell-Mann at the Institute for Advanced Studies in Princeton in April 1951. He had brought from MIT the expression in terms of Heisenberg fields which would give the equation of the Bethe-Salpeter amplitude. I remember him and Francis Low working on this problem and producing the most elegant of papers, which has been the definitive contribution to this subject ever since.

I left the Institute for Advanced Studies in June 1951 and went back to Lahore. Later, in 1954, I returned to Cambridge and found that in the intervening period, the subject of new particles, the so called V0-particles (Λ0, K0) had developed into a full-fledged new activity. There was the Gell-Mann-Nishijima formula which gave the connection between the charge, the isotopic spin and the strangeness - the prototype formula for other similar equations which followed this in later years and whose influence in Particle Physics one cannot exaggerate.

In July 1954, there was a conference in Scotland where Blackett took the chair and where young Gell-Mann was an invited speaker.

I first met Murray when he was a small child, a 19 year old graduate student at the Caltech of the East. I was an ancient of 26 at the time and was quite surprised when he announced upon meeting me that he knew who I was and that he had read all my papers. That was not such a monumental task at that time, but I found out that he had indeed read them. I discovered much more quickly than Viki Weisskopf that Murray was different from me and thee. We became friends and have remained so for nearly forty years.

When I went to Chicago in 1950 I began immediately agitating to hire Murray. It was no easy task to convince my senior colleagues that this was sensible since he had identically zero publications to his name. I did, however, prevail and we began a long collaboration that continued episodically for nearly 20 years. This was an exciting time in particle physics when there was a vast amount of experimental data and a paucity of theoretical tools to cope with it. It was a pleasure to work with Murray as we used everything we could lay our hands on theoretically to try to pick our way toward an understanding of what was a bewildering and complex landscape. His ingenuity, intensity, enthusiasm, and confidence that we could understand a great deal if we stuck to general principles and were not afraid to make bold conjectures was contagious.

A two-day symposium in celebration of Murray Gell-Mann's 60th birthday was held at the California Institute of Technology on January 27–28, 1989. The theme of the Symposium was “Where are Our Efforts Leading?” Each speaker was asked to choose one (or more) of the great challenges in science or human affairs and try to answer, in connection with our present effort to respond to that challenge, “Where do we stand? What kind of progress are we making? In fifty or a hundred years, how do you think today's efforts will appear?”. The topics discussed spanned a very broad range, representative of Murray's remarkably diverse interests and activities. These included particle physics and quantum cosmology, studies of complex adaptive systems, environmental challenges and studies, education and equality of opportunity, arms control and governmental issues.

Given the unusually broad scope of the Symposium, we decided it would be appropriate to publish separately a ‘physics volume,’ including all of the more technical contributions in theoretical physics and related topics. There were many marvelous contributions in other areas that we hope to publish elsewhere. The present volume includes the texts of presentations at the Symposium by Professors J. B. Hartle, E. Witten, H. Fritzsch, T. D. Lee, I. M. Singer, and V. L. Telegdi. It also includes ten additional contributed papers by well-known physicists who are close personal friends of Murray Gell-Mann.

QUANTUM COSMOLOGY

It is an honor, of course, but also a pleasure for me to join in this celebration of Murray Gell-Mann's sixtieth birthday and to address such a distinguished audience. Murray was my teacher and more recently we have worked together in the search for a quantum framework within which to erect a fundamental description of the universe which would encompass all scales – from the microscopic scales of the elementary particle interactions to the most distant reaches of the realm of the galaxies – from the moment of the big bang to the most distant future that one can contemplate. Such a framework is needed if we accept, as we have every reason to, that at a basic level the laws of physics are quantum mechanical. Further, as I shall argue below, there are important features of our observations which require such a framework for their explanation. This application of quantum physics to the universe as a whole has come to be called the subject of quantum cosmology.

The assignment of the organizers was to speak on the topic “Where are our efforts leading?” I took this as an invitation to speculate, for I think that it is characteristic of the frontier areas of science that, while we may know what direction we are headed, we seldom know where we will wind up.

When Murray Gell-Mann was starting out in physics, one of the big mysteries in the field was to understand the strong interactions, and especially the hadron resonances that proliferated in the 1950's. The existence of these resonances showed clearly that something very new was happening in physics at an energy scale of order one GeV. Another important mystery was to find the correct description of the weak interactions, and among other things to overcome the problems associated with the unrenormalizability of the simple though relatively successful Fermi theory. This problem pointed to a new development at a significantly higher energy scale.

Murray Gell-Mann played a tremendous role in advancing the understanding of these mysteries. His great contributions include his work on the strange particles; the “renormalization group” introduced by Gell-Mann and Low; early ideas about intermediate weak bosons; contributions to the proper description of the structure of the weak current; the unearthing of the SU(3) symmetry of strong interactions, and his contributions to the understanding of current algebra; the introduction of the quark model, and early ideas about QCD. His insights on these and other scientific problems are part of the foundation on which we now attempt to build, and his enthusiasm for science is an inspiration to all of us.

If we ask today what are some of the key new mysteries in particle physics, there are at least three that seem particularly pressing.

ABSTRACT:

We discuss how Murray Gell-Mann contributed to the theory of nuclear rotational motion.

Introduction

Nuclear physics could hardly be called one of Murray Gell-Mann's primary interests, but it is our aim in the present note to show, nonetheless, that Murray did in fact make basic contributions to the theory of nuclear rotational motion. Of course—from the perspective of the next century—Murray Gell-Mann's introduction of quarks and SU3(color) will be seen as laying the very foundations of theoretical nuclear physics itself, so it will not be surprising to anyone (in that era) that he contributed to nuclear rotational theory.

Murray Gell-Mann developed his ideas, which we will discuss below, in the 1960's entirely in the context of particle physics and, although aware of their importance for other fields, he did not himself publish applications outside particle physics or field theory. By good fortune one of us (LCB) was a visiting faculty member at Cal Tech at this critical time and one day an invitation came to visit his office. During this visit he explained at some length the significance of his approach for nuclear physics, and for nuclear rotational motion in particular, and suggested that these ideas be followed up. It was in this way that Murray's ideas made their way into the nuclear physics literature.

Abstract

We consider heat engines that take both energy and information from their environment. To operate in the most efficient fashion, such engines must compress the information that they take in to its most concise form. But the most concise form to which a piece of information can be compressed is an uncomputable function of that information. Hence there is no way for such an engine systematically to achieve its maximum efficiency.

Heat engines take heat from their environment and turn it into work. We consider here engines that gather both heat and information and turn them into work. An example of such an engine is the Szilard engine, a one-molecule heat engine that turns information into work. Practical examples include engines that run off of fluctuations, and car engines that use microprocessors to achieve greater efficiency.

For an ordinary heat engine a Carnot cycle can in principle be carried out reversibly. Following a suggestion of Zurek, we show that engines that process both heat and information cannot attain the Carnot efficiency even in principle. We prove that to operate at the maximum efficiency over a cycle, such an engine must reversibly compress the information that it has acquired to its most compact form. But Gödel's theorem implies that the most compact form to which a given piece of information can be compressed is an uncomputable function of that information. Accordingly, there is no systematic way for an engine to achieve its maximum efficiency.

General relativity is the flagship of applied mathematics. Although from its inception this has been regarded as an extraordinarily difficult theory, it is in fact the simplest theory to consummate the union of special relativity and Newtonian gravity. Einstein's ‘popular articles’ set a high standard which is now emulated by many in the range of introductory textbooks. Having mastered one of these the new reader is recommended to move next to one of the more specialized monographs, e.g. Chandrasekhar, 1983, Kramer et al., 1980, before considering review anthologies such as Einstein (centenary), Hawking and Israel, 1979, Held, 1980 and Newton (tercentenary), Hawking and Israel, 1987. As plausible gravitational wave detectors come on line in the next decade (or two) interest will focus on gravitational radiation from isolated sources, e.g., a collapsing star or a binary system including one, and I have therefore chosen to concentrate in this book on the theoretical background to this topic.

The material for the first three chapters is based on my lecture courses for graduate students. The first chapter of this book presents an account of local differential geometry for the benefit of the beginner and as a reminder of notation for more experienced readers. Chapter 2 is devoted to two-component spinors which give a representation of the Lorentz group appropriate for the description of gravitational radiation. (The relationship to the more common Dirac four-component spinors is discussed in an appendix.) Far from an isolated gravitating object one might expect spacetime to become asymptotically Minkowskian, so that the description of the gravitational field would be especially simple.