Five-minute digest
Relativity: The Special and General Theory
Summary
Relativity: The Special and General Theory is Albert Einstein's own explanation of his two theories of relativity for readers who know no higher mathematics. He dated the preface December 1916, and the book appeared in German in 1917 as Über die spezielle und die allgemeine Relativitätstheorie (gemeinverständlich), published by Vieweg in Braunschweig. The library text is the authorised English translation by Robert W. Lawson, published in 1920, shortly after the eclipse observations of 1919 had made Einstein famous. In the preface he promises to repeat himself rather than seek elegance, following Boltzmann's advice that elegance belongs to the tailor and the cobbler. Part I, on the special theory, has seventeen short sections built on homely examples, above all a railway train running along an embankment. Einstein begins with what geometrical propositions mean physically, and with co-ordinates and time in classical mechanics. He states the principle of relativity, that the laws of nature are the same for bodies of reference in uniform motion, and shows its apparent conflict with the constant velocity of light. In Section VIII he asks what it means for two lightning strokes at points A and B on the line to be simultaneous, and in Section IX shows that strokes simultaneous for the embankment are not simultaneous for the train. Every body of reference has its own time. From this follow the Lorentz transformation, the contraction of moving rods and slowing of moving clocks, the relativistic addition of velocities confirmed by Fizeau's experiment, the equivalence of mass and energy, the evidence of the Michelson-Morley experiment, and Minkowski's four-dimensional space-time. Part II extends relativity to accelerated motion. Einstein imagines a man in a large chest far out in space, drawn upward by a rope at constant acceleration: the man would feel himself in a gravitational field, so that the equality of inertial and gravitational mass becomes the basis of a general principle of relativity. The theory predicts that light bends in a gravitational field and that clocks and rods on a rotating disc depart from Euclidean geometry. Einstein explains Gaussian co-ordinates and non-Euclidean continua, states the general principle, and shows how the theory accounts for the motion of Mercury's perihelion. Part III considers the universe as a whole, the difficulties of Newton's infinite universe, and the possibility of a space that is finite and yet unbounded. The appendices give a simple derivation of the Lorentz transformation, a note on Minkowski's world, the experimental tests of the general theory (perihelion of Mercury, deflection of light, red shift), and a later note on expanding space. The file notes that a fifth appendix, added to a much later printing, is omitted for copyright reasons.
Top Lessons
A concept must be tied to a test
Einstein refuses to accept that simultaneity means anything until we say how it could be checked. By asking how an observer would actually decide whether two lightning strokes were simultaneous, he finds that the answer depends on the body of reference. Clear thinking often begins by asking what a word means in practice.
Old theories live on inside new ones
Einstein does not say Newton was simply wrong. Classical mechanics remains valid for velocities small compared with light, and Newton's law of gravitation follows from the general theory as an approximation. He calls it the fairest destiny of a theory to point the way to a more comprehensive one in which it survives as a limiting case.
Imagination disciplined by experiment
The book's arguments rest on thought experiments, the train and the chest, but Einstein insists that the theory must be compared with reality. He points to Fizeau's experiment, the Michelson-Morley experiment, Mercury's perihelion and the bending of starlight, and states that if the predicted red shift were not found the general theory would be untenable.
Writing hard ideas plainly
Einstein wrote for readers with a school education and a fair amount of patience. He uses trains, embankments, clocks and rods, repeats himself deliberately, and prefers clearness to elegance. The book shows that even the most difficult ideas can be made accessible without being falsified.
Verified Quotes
“I adhered scrupulously to the precept of that brilliant theoretical physicist L. Boltzmann, according to whom matters of elegance ought to be left to the tailor and to the cobbler.”
“we entirely shun the vague word “space,” of which, we must honestly acknowledge, we cannot form the slightest conception”
“Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.”
“the inertial mass of a body is not a constant but varies according to the change in the energy of the body.”
“No fairer destiny could be allotted to any physical theory, than that it should of itself point out the way to the introduction of a more comprehensive theory, in which it lives on as a limiting case.”
“If the displacement of spectral lines towards the red by the gravitational potential does not exist, then the general theory of relativity will be untenable.”
“May the book bring some one a few happy hours of suggestive thought!”
Medical Lens
A work of physics with no medical content.