trc (08/21/82)
My physics book seems to say that light appears to travel at the same velocity, regardless of the reference frame that it originates in, and regardless of the frame it is taken in reference to. I think it argues that this is because there is no prefered inertial reference frame. 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
JWJ@MIT-MC@sri-unix (08/21/82)
From: Joseph W. Johnson <JWJ at MIT-MC>
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