Twentieth Century Physics

Twentieth Century Physics M. A. Reynolds Embry-Riddle University ii Copyright °c 2009 by M. A. Reynolds Cover photographs and text photographs from nobelprize.org iii For Sarah iv v Acknowledgments I am not a modern physicist by trade, but a plasma physicist, so this book has borrowed heavily from many sources. Its originality consists in packaging a course for sophomore physics majors in a manner di®erent than has been done before. I have used what I believe is the best from the standard modern physics texts, but I have also used unique treatments that I have found in unpublished notes, and journals like the American Journal of Physics. When I have borrowed explanations that are unique, I have cited those sources; however, standard treatments of standard concepts I consider to be in the public domain. I learned modern physics from Matt Sands at U.C. Santa Cruz in 1984 where we used the ¯rst edition of Krane's Modern Physics textbook, which I really liked, especially the historical discussions. Now that I have taught the same class from that text, I still like it, but I feel that it su®ers from the same problems that most modern textbooks su®er from, a too-heavy reliance on the historical approach. I learned quantum mechanics from George Gaspari at U.C. Santa Cruz in 1986-87 and from Ernest Abers at U.C.L.A. in 1987-88. Abers has recently produced a wonderful graduate-level textbook based on his lecture notes,1 and I have used some of that material that is accessible to undergraduates. 1Abers, Quantum Mechanics, 2006. vi vii Preface Tomorrow is going to be wonderful because tonight I do not understand anything. | Niels Bohr Introductory physics is usually taught in historical order. The ¯rst course is mechanics, which was developed in the 17th century, followed by fluids, thermodynamics and electromagnetism, which were developed in the 18th and 19th centuries. The ¯nal piece of the puzzle, modern physics (or 20th century physics), is left until last, and is also usually presented in a historical manner. It starts with special relativity, and then progresses through \old quantum theory" and basic quantum mechanics. Finally, if there is time in the typical one-semester course, a brief overview of nuclear physics, the standard model of particle physics, and possible some cosmology is presented. This standard procedure illustrates the (now discredited) biological dictum, \ontogeny recapitulates phylogeny."2 However, the brief emphasis placed on particle physics does not give the students a sense of the \big picture" of the standard model, which is our current best guess for how things are put together. While a fundamental understanding of the standard model requires advanced relativity and quantum mechanics, I believe that to be truly a course in \modern physics," we must place this modern understanding in a prominent role. Also, after two or three semesters of physics, students deserve to be shown how all the physics that they have learned ¯ts together, rather than simply viewing the Bohr model, the Schrodinger equation, and special relativity, etc., as simply more in a long list of (separate) topics. For this reason, I start this book with a discussion of the most fundamental particles, quarks and leptons, and then I progress outward to larger, composite, objects: nuclei, and then atoms. This is in reverse historical order, but gives the students a coherent picture of our current knowledge. Of course, some ideas from relativity and quantum mechanics are needed to understand these fundamental particles, so I have placed a basic introduction in Chapter 1, and have also introduced physical concepts as needed. Finally, in the latter part of the book, while covering relativity and quantum theory, I am able to prove some statements that I had previously only quoted. Therefore, the endpoint of our study of relativity and quanta is an explanation of our understanding at the most basic level, i.e., the important applications, rather than simply solving the 1D Schrodinger equation for various potentials, for example, with no apparent motivation. It is true that there is much to be learned studying history, and one of the most important results of a study of physics is to understand precisely how we have come to our conclusions, and why we think they are correct. That is, how do we know what we claim to know? What are the experimental clues that lead us to believe that our current 2An idea from developmental biology which states that the embryonic development of an organism (ontogeny) mirrors the evolutionary development of the species (phylogeny). This theory was ¯rst put forth by Ernst Haeckel (1834-1919). As Haeckel himself wrote in his book Riddle of the Universe at the Close of the Nineteenth Century (1899), \I established the opposite view, that this history of the embryo (ontogeny) must be completed by a second, equally valuable, and closely connected branch of thought - the history of race (phylogeny). Both of these branches of evolutionary science, are, in my opinion, in the closest causal connection; this arises from the reciprocal action of the laws of heredity and adaptation ... òntogenesis is a brief and rapid recapitulation of phylogenesis, determined by the physiological functions of heredity (generation) and adaptation (maintenance).' " viii model is the best one? And what were the previous models that experiments ruled out?3 Understanding these experimental facts and the logic behind them are as important as understanding the theoretical constructs upon which we base our models. As Robert Millikan [Nobel Prize, Physics, 1923] said, \Science walks forward on two feet, namely theory and experi- ment ... Sometimes it is one foot which is put forward ¯rst, sometimes the other, but continuous progress is only made by the use of both { by theorizing and then testing, or by ¯nding new relations in the process of experimenting and then bringing the theoretical foot up and pushing it on beyond, and so on in unending alternations."4 In fact, a thorough investigation into incorrect models, and the experiments that ¯nally re- vised (or perhaps completely overthrew) those models, is extremely useful. Those stories are not the main thrust of this book, however, and have been relegated either to foot- notes, boxed historical asides, or appendices. Several of the appendices should be studied thoroughly, as they comprise a signi¯cant fraction of the text. The main point, though, is to describe our current thinking about how the world is put together, what it is made of, and how the pieces interact. In telling that story the key historical observations and experiments will be delved into, and pointers to the appropriate appendix will be made for further study. This book is divided approximately into three parts. First, Chapter 1 consists of a brief overview, with statements (not proof) of some of the basic principles of relativity and quantum mechanics that are needed as a foundation. Second, Chapters 2-4 are in- troductions to particle physics, nuclear physics, and atomic physics, which bring you up to speed on the current state-of-the-art. Finally, Chapters 5-7 develop the mathematics that explain the results stated previously: Chapter 5 is a development of special relativity; Chapter 6 is a development of \old quantum theory, and Chapter 7 derives the full-fledged non-relativistic quantum mechanics, 3Epistemological questions such as these tend to be swept under the rug during a study of classical physics, partially because the answers seem so self-evident among familiar surroundings. When you study physics that is further removed from everyday experience, however, such as subatomic particles, these questions come to the fore, unbidden. A careful consideration of such questions clari¯es the role of classical physics and gives us a deeper understanding of the universe and its inner workings. 4Nobel Lecture, May 23, 1924, The electron and the light-quant from the experimental point of view. ix How to Study There are as many study methods as there are students, but a few principles are universal, and there are a few new ones that apply speci¯cally to modern physics. First, do a lot of outside reading. Unlike in your previous physics courses, which mostly covered classical physics, which is \normal" and \intuitive," in modern physics there will be quite a few new concepts, many of them completely unfamiliar and counter-intuitive, along with lots of new jargon. One way to become familiar with the concepts and comfortable with the language is to expose yourself to as many di®erent viewpoints as possible. Not only should you read this text carefully, but you should read other textbooks and popular accounts. Second, true physical understanding comes through familiarity with the mathematics. So, just as in classical physics, problem solving is crucial to building physical intuition. How best to solve problems? Just as with study habits, there many problem solving methods, but Descartes developed a method 400 years ago that still works. Ren¶eDescartes was one of the ¯rst to discuss the so-called \scienti¯c method." Such a method works as well for solving problems as it does for investigating nature | this is because they are the same activity! Descartes said in Discourse on the Method: A multitude of laws often hampers justice, so that a state is best governed when it has only a few laws which are strictly administered; similarly, instead of the large number of laws which make up logic, I was of the opinion that the four following laws were perfectly su±cient for me, provided I took the ¯rm and unwavering resolution to stick to them clearly at all times.

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