Favorite Prefaces V

Concepts in Solids

P. W. Anderson

I reread Concepts in Solids with both pride and embarrassment. Pride, both because it was this set of lectures which inspired Brian Josephson to invent his effect — not every book can point to the precise Nobel prize it inspired — and because l did, in a very brief space, manage to touch some of the key topics which are still not adequately covered in your average solid state theory book. For instance, it is shocking that the main texts used in this country still do not touch on the Mott transition or the “Magnetic State.” I was aiming at conceptual, not mechanical physics, and I hope I got there.

Embarrassment, because after all, there has been 30 years of physics since then. For instance, I note that I guessed absolutely wrong in dismissing tight-binding theory out of hand: it has not yet totally coine into its own but it is, in my present opinion, the right way to think about most bonding in solids. I am not ashamed of skipping localization – only Mott was interested in it, and neither of us yet knew where to go next. I was prescient about broken symmetry — as Josephson realized — but left out phase transitions, as I myself noted.

Nonetheless, I believe that the average student will still be harmed less by this book than by any number of other books I should not name, and I welcome the reissuance.

Favorite Prefaces IV

Classical Mathematical Physics: Dynamical Systems and Field Theories
by Walter Thirring [son of Hans Thirring, who was the co-discoverer of the Lense-Thirring frame effect in general relativity]
(Preface to the second edition).

Since the first edition already contained plenty of material for a one-semester course, new material was added only when some of the original could be dropped or simplified. (…) This involved not only the use of more refined mathematical tools, but also a reevaluation of the word fundamental. What was earlier dismissed as a grubby calculation is now seen as the consequence of a deep principle. Even Kepler’s laws, which determine the radii of the planetary orbits, and which used to be passed over in silence as mystical nonsense, seem to point the way to a truth unattainable by superficial observation: The ratios of the radii of Platonic solids to the radii of inscribed Platonic solids are irrational, but satisfy algebraic equations of lower order. These irrational numbers are precisely the ones that are the least well approximated by rationals, and orbits with radii having these ratios are the most robust against each other’s perturbations, since they are the least affected by resonance effects.

Favorite Prefaces – III

Theory of Relativity
W. Pauli

(…) I do not conceal to the reader my scepticism concerning all attempts of this kind which have been made until now, and also about the future chances of success of theories [unified field theories] with such aims. These questions are closely connected with the problem of the range validity of the classical field concept in its application to the atomic features of Nature. The critical view, which I uttered in the last section of the original text with respect to any solution on these classical lines, has since been very much deepened by the epistemological analysis of quantum mechanics, or wave mechanics, which was formulated in 1927. On the other hand Einstein maintained the hope for a total solution on the lines of a classical field theory until the end of his life. These differences of opinion are merging into the great open problem of the relation of relativity theory to quantum theory, which will presumably occupy physicists for a long while to come. In particular, a clear connection between the general theory of relativity and quantum mechanics is not yet in sight.

(…)

There is a point of view according to which relativity theory is the end-point of “classical physics”, which means physics in the style of Newton-Faraday-Maxwell, governed by the “deterministic” form of causality in space and time, while afterwards the new quantum-mechanical style of the laws of Nature came into play. This point of view seems to me only partly true, and does not sufficiently do justice to the great influence of Einstein, the creator of the theory of relativity, on the general way of thinking of the physicists of today. By its epistemological analysis of the consequences of the finiteness of the velocity of light (and with it, of all signal-velocities), the theory of special relativity was the first step away from naive visualization. The concept of the state of motion of the “luminiferous aether”, as the hypothetical medium was called earlier, had to be given up, not only because it turned out to be unobservable, but because it became superfluous as an element of a mathematical formalism, the group-theoretical properties of which would only be disturbed by it.

By the widening of the transformation group in general relativity the idea of distinguished inertial coordinate systems could also be eliminated by Einstein as inconsistent with the group-theoretical properties of the theory. Without this general critical attitude, which abandoned naive visualizations in favour of a conceptual analysis of the correspondence between observational data and the mathematical quantities in a theoretical formalism, the establishment of the modern form of quantum theory would not have been possible. In the “complementary” quantum theory, the epistemological analysis of the finiteness of the quantum of action led to further steps away from naive visualizations. In this case it was both the classical field concept, and the concept of orbits of particles (electrons) in space and time, which had to be given up in favour of rational generalizations. Again, these concepts were rejected, not only because the orbits are unobservable, but also because they became superfluous and would disturb the symmetry inherent in the general transformation group underlying the mathematical formalism of the theory.

I consider the theory of relativity to be an example showing how a fundamental scientific discovery, sometimes even against the resistance of its creator, gives birth to further fruitful developments, following its own autonomous course.

Note: This preface was written in 1956, two years before Pauli’s death. That edition is a book made from his original paper “Relativitätstheorie”, in Encyklopädie der mathematischen Wissenschaften, Vol. VI9, (B. G. Teubner, Leipzig 1921), written when he extremely young (about 20 years old), and only six years after the publishing of Einstein’s General Relativity theory.

Favorite Prefaces – II

Conceptual Foundations of Quantum Mechanics
by Bernard d’Espagnat

A few words are here in order concerning the guiding idea that inspired this book. It is that quantum mechanics can be formulated axiomatically, that, for clarity sake, it is of course quite appropriate to do so, but that the axioms in question then have to take the form of (precise and general) “rules of the game,” serving to predict what will be observed. This is a difference with classical mechanics, the axioms of which (Newton’s laws and the rest) are most simply expressed as statements bearing on the structure of some mind-independent reality. It is a fact that attempts at doing the same in quantum physics quickly lead to conceptual muddles (“Are wave functions real?,” “Is collapse real?,” etc.), while, in contrast, viewed as a set of observational predictive rules, quantum mechanics is crystal clear. The rules in question must therefore be considered as being—by far—what is most solid in quantum physics. And it is for this matter-of-fact reason—and not because of any a prior allegiance to positivism, empiricism or what not!—that it was here found advisable to begin by just stating these predictive rules and investigating their consequences. Since no allegiance to phenomenalism is made, the question of the possible interpretation of the said rules in terms of some underlying reality of course remains significant. In fact such a study constitutes, in a sense, the very purpose of the present book. But the corresponding analyses must—-and do, here—come in only in a second stage, after the rules have been duly stated and examined.

Note that the just explained standpoint is precisely the one that gives us maximal freedom concerning interpretation problems, since it bars out any a priori prejudice relative to what constitutes reality. Within it, we are not, right at the start, forced to conceive of reality in terms, either of waves, or of particles, or of “wavicles,” or etc. Any way of thinking of it is a priori admissible, provided only that, in the end, it turns out to be compatible with the observational predictions yielded by the basic quantum rules. But, as will be seen, this condition proves to be a demanding one. It does not leave many vistas open. Indeed the book shows that such an approach gently leads to quite definite ideas concerning the conceptual foundations of the incredibly powerful science that is called quantum mechanics.

Favorite prefaces – I

This is the first of a series of posts with short excerpts of prefaces/introductions of books that I find interesting or curious. This is just for fun, but hopefully will lead to a collection of memorable sentences or ideas that compels us further on the subject.

PCT, Spin and Statistics, and All That
by Raymond F. Streater and Arthur S. Wightman

In the beginning, when Dirac, Jordan, Heisenberg, and Pauli created the quantum theory of fields, it was not expected that it would provide a consistent description of Nature. After all, it was only a quantized version of the classical theory of Maxwell and Lorentz, a theory which was well known to be afflicted with diseases arising from the infinite electromagnetic inertia of point particles. Many physicists were of the opinion that any project to make the theory’s mathematical foundation more rigorous was probably ill-advised; first the classical foundation should be set right. Such alterations might so change the basis of the theory that a mathematically rigorous discussion of any preceding version would be entirely irrelevant. More recently, it has been suggested that the trouble is that the theory is too modest; it is not designed to predict the masses of the elementary particles or the values of the coupling constants, and should be fundamentally changed with this in view.

However, attempts to go beyond the theory foundered again and again. What successes were achieved were either phenomenological, or were due to systematic developments of the original formalism. But the quantum theory of fields never reached a stage where one could say with confidence that it was free from internal contradictions–nor the converse. In fact, the Main Problem of quantum field theory turned out to be to kill it or cure it: either to show that the idealizations involved in the fundamental notions of the theory (relativistic invariance, quantum mechanics, local fields, etc.) are incompatible in some physical sense, or to recast the theory in such a form that it provides a practical language for the description of elementary particle dynamics.

The last ten years have seen a number of attempts to meet the situation head on. (The physicists who have engaged in this kind of work are sometimes dubbed the Feldverein. Cynical observers have compared them to the Shakers, a religious sect of New England who built solid barns and led celibate lives, a non-scientific equivalent of proving rigorous theorems and calculating no cross sections.) These efforts have not yet led to a solution of the Main Problem, but they have yielded a number of by-products, very general insights into the structure of a field theory. The present book is devoted to an exposition of some of these general results, the physical ideas they embody, and the mathematics necessary for their proofs.