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In this splendidly lucid and profusely illustrated book, a Nobel laureate relates the fascinating story of Einstein, the general and special theories of relativity, and the scientists before and since who influenced relativity's genesis and development. Eschewing technical terms in favor of ordinary language, the book offers a perfect introduction to relativity for readers without specialized knowledge of mathematics and science.
The author follows Einstein's own dictum to make explanations "as simple as possible, but not more so." His periodic use of equations as points of clarification involve nothing more than simple algebra; these can be disregarded by math-averse readers. Dr. Schwinger begins with a discussion of the conflict between two principles of electromagnetic theory that are irreconcilable in Newtonian physics, and how Einstein's attempts to resolve this conflict led to the theory of relativity. Readers learn about the meaning of time and the paradoxes of space travel at speeds close to that of light, following the development of Einstein's relativistic thought and his epochal perception that E=mc2. Further chapters examine gravity and its effect on light; non-Euclidean geometry and the curving of space-time; and the impact of radio astronomy and space-age discoveries upon Einstein's model of the universe.
Amusing quotes, suppositions, and illustrative fictions — along with numerous sidebars and boxes explaining physical principles, anomalies, events, and inventions — enhance this accessible introduction, and provide stimulating food for thought. Preface. 189 black-and-white illustrations. Sources of the Illustrations. Index.
Product Details
| ISBN-13: | 9780486146744 |
|---|---|
| Publisher: | Dover Publications |
| Publication date: | 04/26/2012 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| Pages: | 160 |
| File size: | 9 MB |
Read an Excerpt
Einstein's Legacy
The Unity of Space and Time
By Julian Schwinger
Dover Publications, Inc.
Copyright © 1986 Clarice SchwingerAll rights reserved.
ISBN: 978-0-486-14674-4
CHAPTER 1
A CONFLICT BROUGHT TO LIGHT
DRAMATIS PERSONAE
Issac Newton—whose name is celebrated in his three laws of motion and his theory of universal gravitation—once wrote that, if he had seen a little farther than others, it was because he had stood on the shoulders of giants. Albert Einstein also stood on the shoulders of giants—those of Isaac Newton and James Clerk Maxwell.
All three men, in their own lifetimes, were members of the Royal Society of London for Improving Natural Knowledge, or, simply, the Royal Society. This, the oldest scientific society in Great Britain, began informally in 1645 with weekly meetings of "divers worthy persons, inquisitive into natural philosophy and other parts of human learning, and particularly of what hath been called the New Philosophy or Experimental Philosophy." Some of the first meetings were held at the Bull Head Tavern, Cheapside, one of several homes that preceded the present one at Carlton House Terrace, not far from Trafalgar Square. The Society was formally recognized in 1660 by Charles II, and it was incorporated by Royal Charter in 1662.
Early in 1672, Newton sent a description of his new reflecting telescope to the Royal Society; it was read to the members during the meeting at which he was elected a Fellow of the Society. In replying to the notice of election, Newton proposed to present "an account of a philosophical discovery, which induced me to the making of the said telescope ... being in my judgement the oddest if not the most considerable detection which hath hitherto been made into the operations of nature." Newton had physically separated white light into its component colors by passing the light through a glass prism. This, and related discoveries, led him, the following year, to devise his theory of light being a stream of corpuscles, or particles.
Perhaps the most important contribution to science that the Royal Society has made in its three centuries of existence is its early role in publishing Newton's masterful account of his discoveries: Mathematical Principles of Natural Philosophy—the Principia. The book was licensed for publication in 1686 by the then president of the Royal Society, Samuel Pepys—amateur scientist, amateur musician, treasurer of the Royal Fishery, member of Parliament, Secretary of the Admiralty—best known today for his daringly honest, secret account of his times, the Diary.
Just as Isaac Newton dominated the scientific scene in the seventeenth century, so Albert Einstein dominates that of the twentieth century. World renowned for his introduction and development of the theory of relativity, Einstein became a foreign member of the Royal Society in 1921, the same year for which he received the Nobel Prize, although it was not awarded until 1922. The citation for that prize does not mention the theory of relativity explicitly; it reads "for his services to Theoretical Physics and especially for his discovery of the law of the photoelectric effect."
The latter refers to Einstein's role in reintroducing the particle nature of light, which Newton had proposed more than two centuries earlier. Against it was ranged the wave theory suggested by Christian Huygens (1629–1695) in 1690. Although there were doubters—Benjamin Franklin was one—Newton's authority had kept the particle theory in the forefront until the nineteenth century, when the wave theory won general acceptance (see Box 1 1). Einstein's discovery was not a return to Newton, however; the truth that ultimately emerged is more subtle than either of the two alternatives and transcends both of them. This part of Einstein's legacy—it concerns the laws of atomic physics—receives occasional mention in subsequent chapters. It is, however, outside the general framework of this book, which is focused on Einstein and relativity.
Einstein is a household word. Newton has his fan club.
Nature and Nature's laws lay hid in night: God said, Let Newton be! and all was light.
ALEXANDER POPE (1688–1744)
But James Clerk Maxwell (1831–1879), whose scientific accomplishments have had much greater effect on our daily lives, is comparatively unknown. Who was this man, and what did he do?
He was the last of a line of the well-to-do, land-owning Clerk family of Scotland; the Maxwell name had been added in order to retain lands acquired by marriage. The only surviving child of middle-aged parents, he was born in Edinburgh in the same summer in which Michael Faraday made an epochal discovery, one that Maxwell would later use as a cornerstone of his greatest achievement. The child soon displayed an omnivorous curiosity and a remarkable memory—he was different. Those characteristics, combined with a speech defect and shyness, led to a lonely existence at school, where he was the constant object of torment by his classmates. His stout resistance to this persecution was leavened by an irrepressible sense of humor. He survived and flowered. Later in life he remarked sadly, "They never understood me, but I understood them."
The early death of his mother, at age forty-eight, had put the boy's education into his father's hands. Although the doting father, John Clerk Maxwell, blundered badly in his initial choice of a tutor, who turned out to be brutal, James's later successes at school led John to take the boy to meetings of the Royal Society of Edinburgh. Results were not long in coming.
His first scientific paper, written when he was fourteen, was read for him before the Royal Society and published by that institution in 1846. In it he gives a method for constructing curves that are known as Cartesian ovals. It generalizes the way that an ellipse can be traced with a pencil by keeping taut a piece of string attached at two fixed points (the foci of the ellipse).
In 1855, when Maxwell was twenty-four, a competition was announced at Cambridge, where Maxwell was a Fellow of Trinity College. (Newton had also been there, almost two centuries before.) The prize was to be awarded for the best study of the rings of Saturn, focusing particularly on the question of their stability. Some seventy years earlier, the French astronomer Pierre Simon Laplace (1749–1827) had asserted that the rings are irregular solid bodies. After showing that a solid structure was either inherently impossible or contrary to observation, Maxwell demonstrated that the rings must be composed of very many small bodies. Happily, he won the prize.
Maxwell's work on Saturn's rings eventually directed his attention to another subject dealing with myriad small bodies: the molecular theory of gases. According to this theory, the pressure of a gas is produced by the collisions of the many tiny molecules against the walls that confine the gas. But molecules also collide with each other. One consequence of this is a resistance to flow, which is called viscosity. Maxwell proceeded to show that molecular viscosity would be independent of pressure. Then, as he was one of that rare breed of scientist—outstanding theorist and outstanding experimenter—Maxwell set out to prove this prediction by experiment. For two years, in the mid-1860s, Maxwell and his wife, Katherine Mary Dewar, made measurements of gaseous viscosities at different pressures. In the course of these experiments, carried out in their London home, they had to maintain various constant temperatures in their work room, sometimes with roaring fires, sometimes with a vast amount of ice—a far cry from today's multimillion dollar laboratories. The results vindicated Maxwell's molecular theory.
Maxwell's crowning achievement was his unification of electricity and magnetism in the electromagnetic theory of light. To understand this accomplishment, it will be helpful to review some of the experimental and theoretical developments after the time of Newton.
LIGHT
Newton had shown that the gravitational force of attraction between two massive bodies, at a distance apart that is large compared with their individual sizes, is directed along the straight line connecting the bodies with a strength that varies in inverse proportion to the square of that distance. This inverse-square law of force asserts, for example, that halving the distance quadruples the strength. The experimental investigations of Charles Augustin Coulomb (1736–1806) and of Henry Cavendish (1731–1810), in the second half of the eighteenth century, revealed that the electrical force between charged bodies also has these characteristics, except that the force can be either repulsive or attractive: like electric charges repel, unlike charges attract. Magnetism behaves similarly, with North and South poles playing the roles of positive and negative electric charge. Therefore, early in the nineteenth century, there was no reason to question the universality of the Newtonian pattern of forces.
Then, in 1820, the Danish physicist Hans Christian Oersted (1777–1851) broke the news that a magnetic compass needle, placed near a wire carrying a current (i.e., a flow of electric charge), is influenced by that proximity. Electricity and magnetism are related! But the compass needle was neither attracted nor repelled; rather, the needle aligned itself perpendicularly to the current. Here was something new.
And yet, this new force could be squeezed into the Newtonian pattern. Almost immediately (1820), the French physicist André Marie Ampère (1775–1836) discovered that two wires carrying currents also exert forces on each other (which led him to the hypothesis that all magnetism is attributable to the flow of electric charge). As a simple example of such forces, consider the currents carried by two long parallel wires: if the currents flow in the same direction, there is an attractive force between the wires; opposite flows produce a repulsion. This force varies inversely with the distance between the wires. That is not a contradiction: the lengths of the wires are not small compared with the distance between them. Indeed, Ampère was able to show that in general such forces can be considered to be built up from elements of force between small segments of wire. These elements of force are directed along the straight lines between the segments and vary in inverse proportion to the square of the distance between segments. Apart from the added complication that the elements of force also depend on various angles—that between the directions of the segments and those made with the lines connecting them—this is fully in the Newtonian spirit.
Enter Michael Faraday (see Box 1.3). After ten years of investigations, he discovered in 1831 that electric currents are induced in a conducting circuit by changes in a nearby magnet, whether produced by moving it or by altering its strength, which is easily done with an electromagnet. However, what is important here is not this discovery in itself—indeed, Ampère's force could be used to describe this phenomenon of current induction—but the way in which it turned Faraday's thoughts toward a new and ultimately revolutionary direction.
Strangely enough, the ground had already been prepared by Isaac Newton, playing an unfamiliar role. The well-known Newton is the one who insisted that a description of the phenomena must precede speculative inquiry about causes.
... to derive two or three general Principles of Motion from Phaenomena, and afterwards to tell us how the Properties and Actions of all corporeal Things follow from those manifest Principles, would be a very great step in Philosophy, though the Causes of those Principles were not yet discover' d.
This is the Newton of the motto Hypotheses non fingo [I feign no hypotheses]. The other, less well known, speculative Newton is the one who wrote the following to the classics scholar Richard Bentley:
That gravity should be inate, inherent, and essential to matter so that one body may act upon another at a distance through a vacuum and without the mediation of anything else ... is to me so great an absurdity that I believe that no man who has in philosophical matters a competent faculty of thinking can ever fall into it.
Having been influenced by this passage (Newton's letters to Bentley were published in 1756), Faraday was predisposed to seek an understanding of the magnet's influence in some intervening medium. The way that iron filings, sprinkled on a card held near a magnet, arranged themselves in curved lines supplied him with a visual manifestation of just such a physical influence permeating the space around the magnet. This led him to replace the notion of forces acting across finite distances with that of lines of force filling all of space. The seed was thus planted in the field that Maxwell would reap.
Maxwell's electromagnetic investigations began in his undergraduate days at Cambridge, where he
... resolved to read no mathematics on the subject till I had first read through Faraday's Experimental Researches in Electricity. I was aware that there was supposed to be a difference between Faraday's way of conceiving phenomena and that of the mathematicians.... For instance, Faraday, in his mind's eye, saw lines of force traversing all space where the mathematicians saw centres of force attracting at a distance: Faraday saw a medium where they saw nothing but distance.... As I proceeded with the study of Faraday, I perceived that his method ... [was] capable of being expressed in ordinary mathematical forms.
Maxwell's first paper on this subject (1855), written largely in that Cambridge period, is called "On Faraday's Lines of Force." In this, and in several subsequent papers, Maxwell made speculative analogies with fluid motion. Ten years later, with the publication of "A Dynamical Theory of the Electromagnetic Field," the analogies disappeared; this definitive paper is firmly grounded in experiment and in general dynamical principles. Like Newton, Maxwell succeeded by insisting on an economical description of the phenomena.
Following Faraday, Maxwell used the term "field" to describe the physical state of affairs in a region of space that can manifest a certain kind of force: the gravitational field of the Earth; the electric field of a charge; the magnetic field of an electric current. These terms also relate the various kinds of fields to their sources. In essence, Maxwell extended Faraday's induction discovery—that, as shown by the flow of electric charge, a changing magnetic field creates an electric field—to the reciprocal statement, that a changing electric field generates a magnetic field. Here is the unification of electric and magnetic fields in the electromagnetic field.
Suppose that at a point out in otherwise empty space—a vacuum—a magnetic field changes. (It changes because, somewhere else, at an earlier time, an electric current changed; but that is not the significant point here.) The changing magnetic field creates a changing electric field, which in turn regenerates a magnetic field. That is, as time elapses, at that point there is an oscillation between the two kinds of fields. In addition, the fields vary from one point of space to another. All this is reminiscent of a more familiar phenomenon, the motion of waves. For example, if you are floating in a boat on the ocean surface, the passage of ocean waves by that point in space is experienced in the course of time as a rhythmic up and down motion of the boat—it oscillates (see next page). And, at a given instant, if you look out, there in the distance—removed in space—are the successive troughs and crests of the advancing waves. In short, Maxwell's unification of electricity and magnetism led to his prediction of electromagnetic waves.
(Continues...)
Excerpted from Einstein's Legacy by Julian Schwinger. Copyright © 1986 Clarice Schwinger. Excerpted by permission of Dover Publications, Inc..
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Table of Contents
Contents
Title Page,Copyright Page,
Dedication,
PREFACE,
1 - A CONFLICT BROUGHT TO LIGHT,
2 - MARKING TIME,
3 - E = mc2,
4 - A MATTER OF GRAVITY,
5 - GEOMETRY AND PHYSICS,
6 - AT THE FRONTIER,
INDEX,