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Einstein A. Relativity.. the special and general theory(85s).pdf

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Relativity: The Special and General Theory possible relative position of practically rigid bodies.1) Geometry which has been supplemented in this way is then to be treated as a branch of physics. We can now legitimately ask as to the "truth" of geometrical propositions interpreted in this way, since we are justified in asking whether these propositions are satisfied for those real things we have associated with the geometrical ideas. In less exact terms we can express this by saying that by the "truth" of a geometrical proposition in this sense we understand its validity for a construction with rule and compasses. Of course the conviction of the "truth" of geometrical propositions in this sense is founded exclusively on rather incomplete experience. For the present we shall assume the "truth" of the geometrical propositions, then at a later stage (in the general theory of relativity) we shall see that this "truth" is limited, and we shall consider the extent of its limitation....

Relativity: The Special and General Theory three perpendiculars can be determined by a series of manipulations with rigid measuring−rods performed according to the rules and methods laid down by Euclidean geometry. In practice, the rigid surfaces which constitute the system of co−ordinates are generally not available ; furthermore, the magnitudes of the co−ordinates are not actually determined by constructions with rigid rods, but by indirect means. If the results of physics and astronomy are to maintain their clearness, the physical meaning of specifications of position must always be sought in accordance with the above considerations. 3) We thus obtain the following result: Every description of events in space involves the use of a rigid body to which such events have to be referred. The resulting relationship takes for granted that the laws of Euclidean geometry hold for "distances;" the "distance" being represented physically by means of the convention of two marks on a rigid body....

Relativity: The Special and General Theory from amongst all possible Galileian co−ordinate systems, we should have chosen one (K0) of a particular state of motion as our body of reference. We should then be justified (because of its merits for the description of natural phenomena) in calling this system " absolutely at rest," and all other Galileian systems K " in motion." If, for instance, our embankment were the system K0 then our railway carriage would be a system K, relative to which less simple laws would hold than with respect to K0. This diminished simplicity would be due to the fact that the carriage K would be in motion (i.e."really")with respect to K0. In the general laws of nature which have been formulated with reference to K, the magnitude and direction of the velocity of the carriage would necessarily play a part. We should expect, for instance, that the note emitted by an organpipe placed with its axis parallel to the direction of travel would be different from that emitted if the axis of the pipe were placed perpendicular to this direction. Now in virtue of its motion in an orbit round the sun, our earth is comparable with a railway carriage travelling with a velocity of about 30 kilometres per second. If the principle of relativity were not valid we should therefore expect that the direction of motion of the earth at any moment would enter into the laws of nature, and also that physical systems in their behaviour would be dependent on the orientation in space with respect to the earth. For owing to the alteration in direction of the velocity of revolution of the earth in the course of a year, the earth cannot be at rest relative to the hypothetical system K0 throughout the whole year. However, the most careful observations have never revealed such anisotropic properties in terrestrial physical space, i.e. a physical non−equivalence of different directions. This is very powerful argument in favour of the principle of relativity....

Next: The Apparent Incompatability of the Law of Propagation of Light with the Principle of Relativity...

Relativity: The Special and General Theory relativity, which appeals so convincingly to the intellect because it is so natural and simple. The law of the propagation of light in vacuo would then have to be replaced by a more complicated law conformable to the principle of relativity. The development of theoretical physics shows, however, that we cannot pursue this course. The epoch−making theoretical investigations of H. A. Lorentz on the electrodynamical and optical phenomena connected with moving bodies show that experience in this domain leads conclusively to a theory of electromagnetic phenomena, of which the law of the constancy of the velocity of light in vacuo is a necessary conse. quence. Prominent theoretical physicists were theref ore more inclined to reject the principle of relativity, in spite of the fact that no empirical data had been found which were contradictory to this principle. At this juncture the theory of relativity entered the arena. As a result of an analysis of the physical conceptions of time and space, it became evident that in realily there is not the least incompatibilitiy between the principle of relativity and the law of propagation of light, and that by systematically holding fast to both these laws a logically rigid theory could be arrived at. This theory has been called the special theory of relativity to distinguish it from the extended theory, with which we shall deal later. In the following pages we shall present the fundamental ideas of the special theory of relativity....

be continued across the whole of space, so that every event, no matter how far off it may be, could also be localised with respect to the second framework. Without committing any fundamental error, 21...

Relativity: The Special and General Theory obtained a contraction of the rod as a consequence of its motion. Let us now consider a seconds−clock which is permanently situated at the origin (x1=0) of K1. t1=0 and t1=I are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks : t=0 and...

But we can carry out this consideration just as well on the basis of the theory of relativity. In the equation x1 = wt1 B)...

This, hypothesis, which is not justifiable by any electrodynamical facts, supplies us then with that 34...

Moreover, according to this equation the time difference ”t1 of two events with respect to K1 does not in general vanish, even when the time difference ”t1 of the same events with reference to K vanishes. Pure " space−distance " of two events with respect to K results in " time−distance " of the same events with respect to K. But the discovery of Minkowski, which was of importance for the formal development of the theory of relativity, does not lie here. It is to be found rather in the fact of his recognition that the four−dimensional space−time continuum of the theory of relativity, in its most essential formal properties, shows a pronounced relationship to the three−dimensional 37...