Foundations of Modern Physics
This book grew out of the notes for a course I gave for undergraduate physics students at the University of Texas. In this book I think I go farther forward than is usual in undergraduate courses, giving readers a taste of nuclear physics and quantum ﬁeld theory. I also go farther back than is usual, starting with the struggle in the nineteenth century to establish the existence and properties of atoms, including the development of thermodynamics that both aided in this struggle and offered an alternative program.
I fear that some readers may want to skim through this early part and hurry on to what they regard as the good stuff, quantum mechanics and relativity. That would be a pity. In my experience physics students who aim at a career in atomic or nuclear or elementary particle physics often manage to get through their formal education without ever becoming familiar with entropy, or equipartition, or viscosity, or diffusion. That was true in my own case. This book, or a course based on it, may provide some students with their last chance to learn about these and other matters needed to understand the macroscopic world.
Readers may ﬁnd this book unusual also in its strong emphasis on history. I make a point of saying a little about the welter of theoretical guesswork and ill-understood experiments out of which modern physics emerged in the twentieth century. This, it seems to me, is a help in understanding what otherwise may seem an arbitrary set of postulates for relativity and quantum mechanics. It is also a matter of personal taste. Research in physics seems to me to lose some of its excitement if we do not see it as part of a great historical progression. Some valuable historical works are listed in a bibliography, along with collections of original articles that I have found most helpful.
But this is not a work of history. Historians aim at uncovering how the scien-tists of the past thought about their own problems – for instance, how Einstein in 1905 thought about the measurement of space and time separations in de-veloping the special theory of relativity. For this aim of historical writing it is necessary to go deeply into personal accounts, institutional development, and false starts, and to put aside our knowledge of subsequent progress. I try to be accurate in describing the state of physics in past times, but the aim of this book in discussing the problems of the past is different: it is to make clear how physicists think about these things today.
This book is intended chieﬂy for physics students who are well into their time as undergraduates, and for working scientists who want a brief introduction to some area of modern physics. I have therefore not hesitated to use calculus and matrix algebra, though not in advanced versions. As required by the subject matter, the mathematical level here slopes upwards through the book. Where possible I have chosen concrete rather than abstract formulations of physical theories. For instance, in Chapter 5, on quantum mechanics, I mostly represent physical states as wave functions, only coming at the end of the chapter to their representation as vectors in Hilbert space. In some sections detailed material that can be skipped without losing the thread of the theory is put into appendices. Two of these appendices present what in my unbiased opinion are improved derivations of important results: the appendix to Section 2.6 gives a revised version of Einstein’s derivation of his formula for the diffusion constant in Brownian motion, and the appendix to Section 6.4 presents a revision of Fermi’s calculation of the rate of alpha decay.
In my experience, with some judicious pruning, the material of the book up to about the middle of Chapter 5 can be covered in a one-term undergraduate course. But I think that to go over the whole book would take a full two-term academic year.
This book treats such a broad range of topics that it is impossible to go very far into any of them. Certainly its treatment of quantum mechanics, statistical mechanics, transport theory, nuclear physics, and quantum ﬁeld theory is no substitute for graduate-level courses on these topics, any one of which would occupy at least a whole year. This book presents what I think, in an ideal world, the ambitious physics student would already know when he or she enters graduate school. At least, it is what I wish that I had known when I entered graduate school.
In any case, I hope that the student or reader may be sufﬁciently interested in what I do discuss that they will want to go into these topics in greater detail in more specialized books or courses, and that they will ﬁnd in this book a good preparation for such further studies.
I am grateful to many students and colleagues for pointing out errors in the lecture notes on which this book is based and for the expert and friendly assistance I have received from Simon Capelin and Vince Higgs, the editors at Cambridge University Press who guided the publication of this book.
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|September 18, 2021|
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