22.3. Simultaneity http://www.ck12.org
22.3 Simultaneity
Objectives
The student will:
- Understand what is meant by simultaneous events.
- Understand the twin paradox.
Vocabulary
- proper time
- simultaneity:A thought experiment used to illustrate the relative nature of time.
Simultaneity
If the velocity of light is constant regardless of the motion of the source or observer, we can demonstrate that
Newton’s idea of absolute time cannot hold. Observers in different inertial frames will measure unequal time
intervals when observing the same event. The classic example of this is a “thought experiment” suggested by
Einstein. The example involves a railroad embankment and a very long train. The rails are attached to Earth, which
we assume represents an inertial frame, and the train moving with velocityvrelative to the rails is another inertial
frame.
We can define what we mean by simultaneous in this manner:
We mark pointsAandBon the rails and in the train as shown inFigure22.8. At the moment the train is coincident
withAandB, lightning strikes the rails atAandB. An observerOon the ground has positioned himself equidistant
fromAandB. He measures the arrival time of the two light flashes at his location, discovering that the times are
identical. Under such conditions we claim that the lightning strikes occurred simultaneously at pointsAandBwith
respect to the ground observer. The question, however, is: Will an observer on the train, moving with velocityv, as
shown, who is positioned exactly aboveO(in blue) at the instant of the lightning strikes, measure the arrival time of
the lightning to be identical?
As the train travels to the right inFigure22.9, we can see that the light moving fromBwill reach the observer
earlier than the light traveling fromA, since the train is moving towardBand awayA. The light fromBhas less
distance to cover than the light fromA. The observer in the train will, therefore, claim that the lightning strikes are
not simultaneous. Thus, the Newtonian idea of an absolute and unchanging time will not hold if the velocity of light
is independent of the source and the observer.
http://demonstrations.wolfram.com/RelativityOfSimultaneity/
Let us compare the “classical” Newtonian explanation of the above situation with the modern explanation.