From: utzoo!decvax!cca!JWJ@MIT-MC@sri-unix
Newsgroups: net.physics
Title: train - light race
Article-I.D.: sri-unix.2819
Posted: Sat Aug 21 05:52:42 1982
Received: Sun Aug 22 02:19:16 1982

From: Joseph W. Johnson 
Subject: train - light race
    In the classic thought experiment with a train and light flashes, suppose 4
    lights are used - two on *stationary* poles, two on board the train.
    They will be set off at the instant that the train and stationary lights
    are adjacent - since they are the same distance apart (in appearance to
    both frames - so that any relativistic effects on length can be ignored),
    this should be an acceptable means of getting simultaneity.

    >From the stationary point of view, all light flashes should arrive
    simultaneously at the center of the two stationary flashes.
    >From the trains inertial frame, they should all meet at the center
    of the two train lights.
    Unfortunately, the centers will not be the same, by the time the light
    arrives, since the centers will have moved apart. This effect should
    be apparent to both the train and stationary observer, as the position
    at which the flashes meet can be determined regardless of time dilation
    or length shortening.

    Where does the problem lie here?  Is one of my inital assumptions
    false?

	 			Tom Craver
				houti!trc

I believe part of the problem here is that length contraction does play an
important role in this problem. In the stationary frame, all of the light 
flashes will arrive simultaneously at the center, if we assume that the
distance between the stationary lights is the same as the contracted length
of the train. Thus the proper length of the train is longer than the distance
between the stationary lights. From the perspective of the observer at the center
of the train, it is the distance between the stationary lights that is contracted.
The front of the train will be adjacent to the forward light before the rear of
the train is coincident with the rear stationary light, so from the train's
frame, the forward flash of light will arrive first.

The distinction between the flashes of light which originate on the train and
those which come from the stationary lights is unimportant because the velocity
of light is independent of frame.

There is a pretty good discussion of simultaneity (and other aspects of
special relativity) in Tipler's Foundations of Modern Physics.

                                Joe Johnson