Relativity: the special and general theory 
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accelerated according behaviour of measuringrods body of reference Cartesian coordinates centre chest classical mechanics coordinate system coordinates x1 consideration corresponding deductions definition density of matter disc displacement distance ellipse embankment equations Euclidean geometry existence experience expression finite fixed stars formulation fundamental Galileian referencebody Galileian system Gauss coordinate gravitational field homogeneous functions imagine inertial mass infinite large number laws of nature light in vacuo Lorentz transformation manner marble slab material points means measured measuringrods and clocks ment Mercury Minkowski mollusk motion Newton’s law observation obtain orbit perihelion physical physicists plane position postulate of relativity principle of relativity propagation of light radius ray of light regard result rigid body rotation satisfy seconds of arc Section simultaneous space coordinates spacetime continuum special theory spectral lines spherical space square straight line system of coordinates theory of Newton theory of relativity threedimensional tion tional field universe validity values velocity of light xaxis
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Page 32  B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their referencebody must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result: Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and...
Page 27  M is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity.
Page 26  After thinking the matter over for some time you then offer the following suggestion with which to test simultaneity. By measuring along the rails, the connecting line AB should be measured up and an observer placed at the midpoint M of the distance AB. This observer should be supplied with an arrangement (eg two mirrors inclined at 90°) which allows him visually to observe both places A and B at the same time. If the observer perceives the two flashes of lightning at the same time, then they are...
Page 10  body of reference" we insert "system of coordinates," which is a useful idea for mathematical description, we are in a position to say: The stone traverses a straight line relative to a system of coordinates rigidly attached to the carriage, but relative to a system of coordinates...
Page 32  every reference body (or coordinate system) has its own particular time; unless we are told the referencebody to which the statement of time refers, there is no meaning in a statement of the time of an event.
Page 31  Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.
Page 159  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.
Page 31  B) which are simultaneous with reference to so 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 B, where the lightning occurs, meet each other at the midpoint M of the length A > B of the embankment. But the events A and B also correspond to positions A and B on the train....
Page 135  ACCORDING to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter. Thus we can draw conclusions about the geometrical structure of the universe only if we base our considerations on the state of the matter as being something that is known.
Page 15  If, relative to K, K' is a uniformly moving coordinate system devoid of rotation, then natural phenomena run their course with respect to K' according to exactly the same general laws as with respect to K.