58 /,. Page — Fundamental Relations of Electrodynamics. 



the principle of relativity. As a mathematical consequence of 

 the fact that the velocity of light must be the same as observed 

 from different systems, Einstein, in his celebrated paper- in 

 the Annalen der Physik, has derived a set of space time trans- 

 formations, which, because they were first deduced by Lorentz 

 from entirely different considerations, usualty go by his name. 



Einstein starts off by a consideration of the meaning that can 

 be attached to time simultaneity at two different points in any 

 one system. Suppose A and B to be two widely separated 

 places in the same system. An observer at A is watching cer- 

 tain phenomena in his immediate neighborhood, while an 

 observer at B is watching certain other phenomena in his (B's) 

 immediate neighborhood. They wish to compare the times of 

 their observations. Obviously they must be provided with 

 sjmehronous clocks. How are these clocks to be set synchron- 

 ously ? Let A send a light wave toward B when A's clock 

 indicates the time t A . This light wave reaches B at a time t B on 

 B's clock, and. is returned to A by instantaneous reflection, 

 reaching A at the time t' A as indicated on A's clock. Since 

 the measured value of the velocity of light is the same in all 

 systems, and the same in all directions in any one system, the 

 clocks at A and B will be synchronous when, and only when, 

 t B = \(t A + t' A ). Applying this definition of synchronism to 

 two systems in motion relative to one another, Einstein is led 

 to a set of transformations which show that the time at a point 

 P in one system is a function not only of the time at a point Q' 

 in the other system, but also of the relative positions of the 

 points F and Q. 



When applied to the measurement of distances, these trans- 

 formations show that a bar which is fixed in the first system 

 with its axis parallel to the direction of relative motion of the 

 two systems, and which has a length I as measured by an 

 observer in the first system, will appear to have a shorter 

 length when measured by an observer in the second system. 

 This apparent shortening is not surprising when we consider 

 the method used in measuring a body which is in motion rela- 

 tive to the observer. Let AB be a bar which has a velocity 

 relative to the observer in the direction AB. In order to 

 measure the length of the bar, the observer must mark the 

 positions of the two ends of the bar at the same instant, and 

 then measure the distance between these two marks. If he 

 marks the position of the end B a little earlier than he marks 

 the position of the end A, his measurement will be too short. 

 Hence we see that space measurements as well as time meas- 

 urements on moving systems, depend on the definition of 

 simultaneity at different points of the same system. 

 * Annalen der Physik, xvii, 891, 1905. 



