Concentrating upon applications that are most relevant to modern physics, this valuable book surveys variational principles and examines their relationship to dynamics and quantum theory. Stressing the history and theory of these mathematical concepts rather than the mechanics, the authors provide many insights into the development of quantum mechanics and present much hard-to-find material in a remarkably lucid, compact form. After summarizing the historical background from Pythagoras to Francis Bacon, Professors Yourgrau and Mandelstram cover Fermat's principle of least time, the (...) principle of least action of Maupertuis, development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. Equipped by this thorough preparation to treat variational principles in general, they proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations. An investigation of electrodynamics in Hamiltonian form covers next, followed by a resume of variational principles in classical dynamics. The authors then launch into an analysis of their most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy. Professional physicists, mathematicians, and advanced students with a strong mathematical background will find this stimulating volume invaluable reading. Extremely popular in its hardcover edition, this volume will find even wider appreciation in its first fine inexpensive paperbound edition. (shrink)

We analyze the quantum mechanical measuring process from the standpoint of information theory. Statistical inference is used in order to define the most likely state of the measured system that is compatible with the readings of the measuring instrument and the a priori information about the correlations between the system and the instrument. This approach has the advantage that no reference to the time evolution of the combined system need be made. It must, however, be emphasized that the result is (...) to be interpreted as the statistically inferred state of the original system rather than the state of the system after measurement. The phenomenon of “reduction of states” appears in this light as a consequence of incomplete information rather than the physical interaction between measured system and measuring instrument. (shrink)

In a world that peers over the brink of disaster more often than not it is difficult to find specific assignments for the scholarly community. One speaks of peace and brotherhood only to realize that for many the only real hope of making a contribution may seem to be in a field of scientific specialization seemingly irrelevant to social causes and problems. Yet the history of man since the beginnings of science in the days of the Greeks does not support (...) this gloomy thesis. Time and again we have seen science precipitate social trends or changes in the humanistic beliefs that have a significant effect on the scientific community. Not infrequently the theoretical scientist, triggered by society's changing goals and understandings, finds ultimate satisfaction in the work of his colleagues in engineering and the other applied fields. Thus the major debate in mid-nineteenth century in which the evidence of natural history and geology at variance with the Biblical feats provided not only courage to a timid Darwin but the kind of audience that was needed to fit his theories into the broad public dialogue on these topics. The impact of "Darwinism" was felt far beyond the scientific community. It affected social thought, upset religious certainties and greatly affected the teaching of science. (shrink)

The fundamental open questions of general relativity theory are the unification of the gravitational field with other fields, aiming at a unified geometrization of physics, as well as the renormalization of relativistic gravitational theory in order to obtain their self-consistent solutions. These solutions are to furnish field-theoretic particle models—a problem first discussed by Einstein. In addition, we are confronted with the issue of a coupling between gravitational and matter fields determined (not only) by Einstein's principle of equivalence, and also with (...) the question of the geometric meaning of a gravitational quantum theory. In our view, all these problems are so closely related that they warrant a general solution. We treat mainly the concepts suggested by Einstein and Weyl. (shrink)

Robert Oppenheimer tells the story about a group of Bible scholars who practised exegesis with grim determination. A visitor, admiring so much earnest learning, inquired whether they did not find certain texts supremely difficult. Answered one Bible student: “Indeed—but what we do not understand we explain to one another.”.

Lichtenberg, the German philosopher and physicist, once remarked: “It is almost impossible to carry the torch of truth through a crowd without singeing someone's beard.” Goethe, coeval with Lichtenberg, possessed by the conviction that he too was the bearer of truth, recked not whose beard was singed. Between his scientific attitude and his philosophic insight, however, a contradiction was patent, as revealed in his maxim that truth is a torch and that it is only with blinking eyes that we try (...) to get past it, whilst in actual terror of being burnt. (shrink)