Relativity: The Special and General Theory |
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acceleration according æther body of reference Cartesian co-ordinates chest classical mechanics co-ordinate system consideration corresponding definition disc distance earth eclipse electrodynamics embankment energy equations Euclidean continuum Euclidean geometry experience expression finite fixed stars fundamental Galilei transformation Galileian reference-body Galileian system Gaussian co-ordinates gravitational field gravitational mass hold hypotheses imagine inertial mass laws of nature length light in vacuo little rods Lorentz transformation magnitudes manner marble slab material points matter means measured measuring-rods and clocks ment mollusk motion observer obtain orbit perihelion phenomena physical physicists plane position postulate of relativity principle of relativity propagation of light propositions radius railway carriage ray of light regard rela RELATIVITY OF SIMULTANEITY result rigid body rotation satisfied Section simultaneous space co-ordinates space-time continuum special theory spectral lines square straight line surface system of co-ordinates theoretical theory of relativity tion transmission of light universe validity velocity of light velocity of propagation x-axis
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Page v - THE present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus
Page 63 - of the theory of relativity this solution of the difficulty was the right one. But on the basis of the theory of relativity the method of interpretation is incomparably more satisfactory. According to this theory there is no such thing as a "specially favoured" (unique) co-ordinate system to occasion the introduction of the
Page 31 - the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative. When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and
Page 145 - world" by Minkowski, who also termed a point-event a "world-point." From a "happening" in threedimensional space, physics becomes, as it were, an "existence" in the four-dimensional "world." This four-dimensional "world" bears a close similarity to the three-dimensional "space" of (Euclidean) analytical geometry. If we introduce into the latter a new Cartesian co-ordinate system (x\,
Page 22 - c — v. The velocity of propagation of a ray of light relative to the carriage thus comes out smaller than c. But this result comes into conflict with the principle of relativity set forth in Section V. For, like every other general law of nature, the law of the transmission of light in
Page 42 - 2 of a metre. The rigid rod is thus shorter when in motion than when at rest, and the more quickly it is moving, the shorter is the rod. For the velocity v - c we should have
Page 119 - its beauty; nor in removing the defect attaching to classical mechanics which was brought to light in Section XXI; nor in interpreting the empirical law of the equality of inertial and gravitational mass; but it has also already explained a result of observation in astronomy, against which classical mechanics is powerless.
Page 112 - description resolves itself into a number of statements, each of which refers to the spacetime coincidence of two events A and B. In terms of Gaussian co-ordinates, every such statement is expressed by the agreement of their four co-ordinates
Page 71 - motion with respect to K; all these bodies of reference are to be regarded as Galileian reference-bodies. The validity of the principle of relativity was assumed only for these reference-bodies, but not for others (eg those possessing motion of a different kind). In this sense we speak of the special principle of relativity, or special theory of relativity.
Page v - of theoretical physics. The work presumes a standard of education corresponding to that of a university matriculation examination, and, despite the shortness of the book, a fair amount of patience and force of will on the part of the reader. The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the