Relativity of Simultaneity and Distance
Section Nine and Ten
Given the preceding analysis of time, what new insights can we get? Einstein now points out the relativity of simultaneity (hence of time) and of distance (hence of space). The two notions may vary depending on which coordinate system you are referring to.
First, the relativity of simultaneity, and see the following figure. The two flashes simultaneous in the embankment system are not simultaneous in the train system!
From this figure, it is obvious that for the observer at M' on the train, the flash from B comes earlier than that from A; thus the two events, simultaneous in the embankment system, are not simultaneous seen from the train.
A similar consideration applies to the notion of distance too. What is important here is that you've got to "freeze" time, so to speak, in order to obtain the notion of distance. Thus the notion of simultaneity (time) affects the notion of distance (space). The distance between two points can be easily measured wthin a given system, by using the standard rod. But if you want to measure the "same distance" from another system in relative motion to the original, that is quite another question! The following figure summarizes the problem.
The relationship between d and d' is determined by the Lorentz transformation, but it also depends on the (relative) velocity of one system to the other; in our case, that is the velocity of the train. To make things easier (or harder, for some of you?), just imagine the train goes with the velocity of light!
Last modified, April 23, 2002. (c) Soshichi Uchii
suchii@bun.kyoto-u.ac.jp
