Relativity: The Special and General Theory |
Common terms and phrases
accelerated according æther body of reference centre chest classical mechanics consideration corresponding definition disc distance domain ds² dx² earth electrodynamics ellipse 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 H. A. Lorentz hold imagine inertial mass laws of nature light in vacuo little rods Lorentz transformation magnitudes manner marble slab material points matter means measured measuring-rods and clocks Minkowski mollusk moving uniformly observer obtain perihelion physical physicists plane position postulate of relativity principle of relativity propagation of light radius railway carriage ray of light regard rela RELATIVITY OF SIMULTANEITY rest with respect result rigid body rotating 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 x-axis
Popular passages
Page 32 - Every reference-body (coordinate 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.
Page 10 - In the first place, we entirely shun the vague word "space," of which, we must honestly acknowledge, we cannot form the slightest conception, and we replace it by "motion relative to a practically rigid body of reference.
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 reference-body 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 free-will in order to arrive at a definition of simultaneity.
Page 30 - People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system): they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises: Are two events (eg, the two strokes of...
Page 15 - If, relative to K, K' is a uniformly moving co-ordinate 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.
Page 155 - 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 9 - I stand at the window of a railway carriage which is travelling uniformly, and drop a stone on the embankment, without throwing it. Then, disregarding the influence of the air resistance, I see the stone descend in a straight line. A pedestrian who observes the misdeed from the footpath notices that the stone falls to earth in a parabolic curve. I now ask: Do the "positions" traversed by the stone lie "in reality" on a straight line or on a parabola?
Page 31 - A and 5) 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 mid-point M of the length A > B of the embankment. But the events A and B also correspond to positions A and B on...
Page 78 - Relying on his knowledge of the gravitational field (as it was discussed in the preceding section), the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time. Of course he will be puzzled for a moment as to why the chest does not fall in this gravitational field. Just then, however, he discovers the hook in the middle of the lid of the chest and the rope which is attached to it, and he consequently comes to the conclusion...