Basic Physics

The following sections are included:

• DEDICATION
• INTRODUCTION
• FEATURES CONTENTS
• Original Preface
• Original Contents
• Original Acknowledgments
• Original Notes on the text

Four hundred years ago, most men believed that they lived on a stationary earth at the center of the universe. The world beyond the solar system was a mystery. The submicroscopic domain of atoms and molecules was a complete unknown. Even the immediate environment impinging on man’s senses was largely not understood, or else misunderstood. Except for the simplest facts about the balancing of static forces, not a single law of nature governing man’s own world was accurately formulated. The Copernican theory of the solar system, which places the sun at the center, had been published, but it had few adherents and many powerful opponents. There was no science-based technology. There was scarcely any activity that we would today call science. Mathematics was in its infancy…

Today is the particle era in physics. The downward probing of the past few centuries has led finally in the last few decades to the world of elementary particles. Actually no scientist believes that all the particles we now know are truly elementary, but for lack of a better word, and more especially for lack of any deeper knowledge of a lower substratum of matter, they bear the name elementary. It is the effort to understand the particles, to tie them together somehow through deeper and simpler concepts, that occupies the attention of many scientists throughout the world.

It is easy to talk about the “incredibly short” lifetime of an elementary particle or about the “fantastically small” size of an atomic nucleus. It is not so easy to visualize these things. On the submicroscopic frontier of science—as well as on the cosmological frontier—man has proceeded so far away from the familiar scale of the world encompassed by his senses, that he must make a real effort of the imagination to relate these new frontiers to the ordinary world. The reward of being able to think pictorially over the whole panorama, from infinitesimal to enormous, adequately repays the effort.

In a slow and subtle, yet inexorable, way conservation laws have moved in the past few centuries from the role of an interesting sidelight in physics to that of the most central position. What little we now understand about the interactions and transformations of particles comes in large part through certain conservation laws which govern elementary-particle behavior.

A grocer adding a column of figures is doing mathematics. So is an algebraist manipulating symbols that represent abstract concepts unrelated to anything known in the physical world. So is a child wrestling with the problem of how to get a fox and a hare and a cabbage safely across a river in a boat that carries only one of them at a time. From the limit of pure application to the limits of pure abstraction and of pure amusement, mathematics spans a remarkably wide range of human experience, perhaps a wider range than any other single discipline of thought. The all-too-common “nonmathematical” person would probably be startled if confronted with a list of occasions when he regularly uses mathematics or mathematical reasoning— in balancing his bank book (application), in trying to apply logical analysis to some human problem (abstraction), in playing a game of cards (amusement). In most general terms, mathematics is simply logical analysis. Some form of logic has no doubt been a part of the human scene for as long as man has existed. As a recognized distinct field of study, mathematics has existed at least since the earliest civilizations five thousand or more years ago.

A vector is a mathematical object with both numerical and geometrical properties. The physicist has been able to make good use of it in his description of nature. As background for the study of vectors, it is very useful to be able to think graphically about ordinary numbers. Accordingly, we begin this chapter on vectors with a geometrical view of arithmetic.

We are concerned in this chapter with several different topics—mainly practical topics—related to the mathematical description of nature: units and dimensions, special functions, and the presentation of data in graphs, tables, and equations. These topics will find application in all of the later chapters.

In the foregoing chapters, many of the concepts and ideas of mechanics and some of its laws—the conservation laws—have been presented. It is the task of this part of the book to sharpen the definition of some mechanical concepts, to assemble the concepts and laws into the coherent structure called the theory of mechanics, and to apply this theory and its laws to the description and the explanation of various kinds of motion.

Chapter Eight was built around four central concepts of mechanics—force, mass, length, and time. The number of important mechanical concepts is not large. Counting such derived concepts as velocity and acceleration, probably less than a dozen suffice for a complete foundation of mechanics. It is not far from the truth to say that when these concepts are understood, the science of mechanics is understood. But understanding a concept involves more than knowing simply a definition or an equation. To “understand” a concept thoroughly, one must know its operational definition (how it is defined and how it is measured), its dimension and unit, its relationship through laws and equations to other important concepts, its role in various parts of the physical world, and its typical magnitudes. In addition, one must acquire something of an intuitive “feeling” for the concept, a kind of immediate recognition and appreciation that can come only after the concept has been looked at from enough different angles and seen at work in enough different examples to make it seem a familiar friend. A word of caution: This worthwhile kind of scientific familiarity founded on quantitative study is very different from the illusory familiarity bred by nontechnical everyday usage of words like force and energy and acceleration…

Three basic concepts of mechanics have proved to be hardy perennials, even more deeply rooted in contemporary physics than in the classical physics that gave them birth. Each of the concepts—momentum, angular momentum, and energy—has developed a deeper significance and a wider scope of application than could have been imagined when it was first defined and used in mechanics. Each is the core concept of a fundamental conservation law.

Chapter Nine was devoted to momentum—its conservation and its connection to Newton's third law. In this chapter and in the next we shall be concerned with the key concepts of angular momentum and energy—how each is defined, in what situations each is important, and under what circumstances each is conserved.

The number of concepts that can be defined in physics is limitless. The number that are fundamental for the description of nature is remarkably small. Part of the scientist’s search for simplicity is his search for economy of concepts. To merit attention, a physical concept must be not merely quantitatively definable—that much is easy—but it must also bring something of special value to the description of nature. Either it must appear in a natural way in the description of many different phenomena, or it must facilitate the application of theory to specific problems, or it must tie together different branches of science, or it must under some circumstances be conserved. In some way it must force itself on the attention of the scientist as something he cannot ignore. By every criterion just named, the concept of energy deserves the attention of the scientist and the student.

To bring mechanics to bear on nature requires more than Newton’s laws. Also required are specific laws of force. One force in particular—gravitation—is singled out for attention in this chapter.

Man’s imagination has always been challenged by the domains of nature far removed from his immediate human scales of reference. Concerning the limit of the very large, he has pondered the system of the world. Concerning the limit of the very small, he has puzzled over the ultimate structure of matter. Newton’s mechanics bridged the gap between the macroscopic (human-sized) and cosmological domains. The theory of thermodynamics links the macroscopic and submicroscopic domains.

As profound as any principle in physics is the second law of thermodynamics. Based on uncertainty and probability in the submicroscopic world, it accounts for definite rules of change in the macroscopic world. We shall approach this law, and a new concept, entropy, that goes with it, by considering some aspects of probability. Through the idea of probability comes the deepest understanding of spontaneous change in nature.

More than a century elapsed between Newton’s discovery of the law of gravitational force and Coulomb’s discovery of the law of electrical force. This seems, in retrospect, a very long time, once the spirit and methods of modern science had come alive. However, it is not difficult to find some reasons for the lag of electricity behind mechanics. Mechanics was concerned with the grand sweep of the cosmos and linked earthly laws with universal laws. Electricity, thought at first to be an attribute of only certain substances, seemed to have less to do with the structure and behavior of matter. As a practical matter, electrical phenomena, in spite of ready accessibility, were not easy to deal with quantitatively. An electrified object gradually lost its charge; charges in metals moved about in a manner the experimenter could not control; electric currents persisted only for a moment. Planetary motion was not subject to such vagaries. Whatever the reasons, the fact is that while mathematicians and scientists were perfecting the techniques and the tests of mechanics, electricity remained, literally, a sideshow attraction. Around the middle of the eighteenth century, the sparks and shocks of electricity were more often used by entertainers seeking personal profit than by scientists seeking knowledge…

Why is “electromagnetism” such a ponderously long word? There is a simple scientifichistorical reason for it. In the first half of the nineteenth century, the theories of electricity and of magnetism drew together into a single theory embracing both. As the theories merged into one, their names merged into one. Electromagnetism is not alone in showing its divided past in its modern name. Ideas of heat and of mechanics (or dynamics) drew together in the theory of thermodynamics. Mechanics and the quantum theory were merged in quantum mechanics. More recently, a successful merger of the theories of quantum mechanics and electromagnetism has been christened “quantum electrodynamics.” It is unfortunate that great strides in simplifying and unifying our view of nature must be accompanied by increasing complexity of scientific nomenclature. But perhaps there is merit in allowing history to tinge the names of the fundamental theories of physics. In this chapter we shall explore the ideas and experiments that brought electricity and magnetism together.

The workhorse of modern society is its smallest member, the electron. By good fortune, a certain class of materials called metals contain “free” electrons—about 1023 of them in each cubic centimeter. Pushed and pulled through wires, they transmit power and intelligent communication from place to place. In antennas, they create electromagnetic radiation. In the coils of motors, they interact with magnetic fields to do work. Released from the surface of hot metals, electrons can be guided through the space within vacuum tubes to perform tasks of amplification and control and computation. In semiconductors—materials whose electrons are movable but not free—they provide further units of control and of memory.

In modern research not only electrons but other charged particles as well produce fields and react to fields in ways that serve to reveal more about nature. In the following sections, we shall examine several applications of the laws of electromagnetism, some of practical importance, some of research interest.

Interest in the nature of light must go back to prehistory. It is undoubtedly as old as any problem in science, and probably one of the most rewarding scientific problems ever tackled. Interwoven with the whole history of modern physics, from the seventeenth century to the present, is the study of light, which has been closely tied to the development of the theories of electromagnetism, relativity, and quantum mechanics, as well as to the practical science of optics, to numerous discoveries in mathematics and, in the modern period, to such things as radar and lasers. From Römer’s discovery that the speed of light is finite, based on observations of the times of appearance of the moons of Jupiter (1675), to modern measurements of quasi-stellar red shifts and high-energy photon reactions, the history of the study of light has closely paralleled the overall history of physics. In those 300 years the frontiers of physics have diverged from the solar system upward to the universe at large and downward to the world of elementary particles.

In the year 1887, two notable experiments concerned with light took place, one a success, one apparently a failure. In Karlsruhe, Heinrich Hertz demonstrated that the oscillations of electric charge in an ordinary spark give rise to radio waves which travel a great distance through air. In so doing, he provided a key support for electromagnetic theory and bolstered Maxwell’s contention that light is electromagnetic radiation. At the same time, in Cleveland, Ohio, Albert A. Michelson and Edward W. Morley set out to measure what they believed to be another prediction of electromagnetic theory—that the speed of light with respect to the earth should depend upon the motion of the earth through the all-pervasive substratum known as the ether—and they failed. Michelson by himself, as a young visitor in Berlin six years earlier, had tried the same experiment with a similar negative result. Now with the help of Morley, an older professor with a worldwide reputation for accurate measurements, he repeated the experiment with a new and much more precise apparatus. Again no effect. Michelson and Morley were disappointed, indeed almost incredulous. They published their negative findings and went on to other things, little realizing that they had chipped at the foundations of physics.

Because it is simple in conception, and because its result disagrees with the classically expected result, the Michelson-Morley experiment is a useful springboard into relativity theory. The result of the experiment can be conservatively stated in this way: The speed of light seems to be constant with respect to the earth at all times. Since the earth moves now one way relative to the rest of the universe, now another, an earth-fixed observer at two different times can be regarded as two different observers in states of relative motion, and it is not too big a jump to the statement: The speed of light seems to be the same for observers in different states of motion. Some of the early attempts to explain the results of the Michelson- Morley experiment concentrated on the “seems to” in this statement. The explanation offered by the theory of relativity rests instead on a powerful new hypothesis: The speed of light is the same for all observers in inertial frames of reference. (That the earth itself is not a perfect inertial frame of reference is true, but it is unimportant in the interpretation of the Michelson-Morley experiment and in most other terrestrial experiments. The acceleration of the earth may be ignored if the change of velocity of the earth is small during the time a given experiment lasts.)

By 1900 it had become clear that the ether was not easily detectable. Scientists were beginning to feel like Aesop’s fox who could not reach the grapes. Henri Poincaré, perhaps the first to see clearly the potential significance of the failures to discover the ether, was led to say, “Our ether, does it really exist? I do not believe that more precise observations could ever reveal anything more than relative displacements.” Einstein independently rejected the ether. In his first paper on relativity in 1905 (developing what we now call the special theory of relativity), he wrote: “The introduction of a ‘luminiferous ether’ will prove to be superfluous inasmuch as the view to be developed here will not require an ‘absolutely stationary space’ provided with special properties.”

The special theory of relativity, in spite of its all-embracing scope as a theory of theories, is indeed “special” in the sense that it describes transformations of observations only among inertial frames of reference, and imposes an invariance requirement on physical laws only in inertial frames. This circumstance, of course, need not be regarded as a defect of the theory, any more than Newton’s laws of motion were regarded as defective for the same reason—since they too apply directly only to motion in inertial frames. Nevertheless, Einstein did regard it as a defect, and his conviction that the laws of nature should be expressed in a form invariant in all frames of reference, accelerated or not, was the primary motivating force which led to the general theory of relativity, a structure of magnificent beauty and simplicity from the mathematician’s point of view, yet more difficult to understand, interpret, and apply than any other theory in the history of science.

In December, 1900, Max Planck introduced an idea destined to shake the foundations of physics, the idea that material energy can be transformed into radiant energy only in units of a certain size, “quantum units.” A dozen years later, Niels Bohr generalized Planck’s idea into a quantum principle of nature and used the principle with astonishing success to account for the structure of the hydrogen atom (Chapter Twenty-Four). Bohr’s principle is this: Some of nature’s variables can take on only discrete values, and accordingly can change only in finite jumps. Building on this principle of discreteness or quantization in nature, Werner Heisenberg, Erwin Schrödinger, Max Born, Wolfgang Pauli, Paul Dirac, and Bohr created in the years 1925-1928 the edifice that we now call the theory of quantum mechanics. The giant stride of physics in those few years has not been equaled since.

The photon was “discovered” by a theoretical physicist, Albert Einstein, in 1905. Five years earlier another theoretical physicist, Max Planck, had introduced the quantum idea on which Einstein capitalized. Because these two men took the vital first quantum steps down the road that led eventually to a full theory of atomic structure, we place the photon first in a chapter on atoms.

Twice in history the atomic nucleus has forced itself upon the attention of man. In 1896, Henri Becquerel in Paris was astonished to discover that a salt containing uranium emitted a new kind of radiation powerful enough to darken a photographic plate through its opaque wrapping. In 1945, all mankind came to know and fear the nucleus when 1 kg of uranium devastated Hiroshima…

Almost seventy years have gone by since Planck introduced into the description of nature a new quantum constant. More than forty years have passed since quantum mechanics reached near final form. In recent decades knowledge has multiplied and facts have exploded. Yet the search for fundamental understanding, for a new theory with the simplicity and generality to match relativity or quantum mechanics, continues at the slow and difficult pace that has always characterized man’s struggle at the frontier of the unknown. Few physicists doubt that such a new theory awaits discovery, for the clues are too numerous, the hints too tantalizing, to allow either complacency about what we know already or discouragement about what we do not yet know. And few doubt that a great step will take place at the submicroscopic frontier, where the profusion of particles and the variety of interactions cry out for unification.

In this chapter and the next, we explore the frontier of the very small, where elementary particles serve admirably to bridge the gap from the known to the unknown. The particles illustrate, often simply and directly, the key ideas of quantum mechanics. At the same time they reveal new facts and new puzzles, pointing the way to future discovery. The theme of this chapter is the intimate connection between the nature of the individual particles and the way in which they interact with each other.

At the frontier of the very large are the stars, the galaxies, and the universe itself. At the frontier of the very complex are solids, liquids, plasmas, and organic molecules. At the frontier of the very small are the elementary particles. In this final chapter, we shall explore some aspects of the contemporary scene at the third frontier—the frontier of the very small. Here, in the submicroscopic area of particle interactions, are to be found both insights and puzzles as profound as any in science…

Thrilling insights and awesome power. These are the fruits of science. In this final chapter, we shall examine the nature and progress of man’s most successful enterprise, scientific inquiry, and hazard some guesses about its future…

The following sections are included:

• APPENDIX ONE: Greek alphabet
• APPENDIX TWO: Numerical data
• APPENDIX THREE: Conversion of units
• INDEX
• FEATURES INDEX