35.5 - Interactive problem: Conduct Einstein's simultaneity experiment
There are two simulations to the right. In the first, the professor, Katherine and the
train are all stationary. In the second, the professor and the train move.
As discussed before, lightning bolts strike each lightning rod. These lightning strikes
cause flashes of light that will be visible to the observers. Photons í packets of light
í move from the position of each lightning rod toward them. Each lightning strike
counts as one of the two spatially separated events we are analyzing. We draw the
photons from one rod in blue, and the photons from the other rod in red, so that you
can easily distinguish them.
The lightning bolts also scorch the sides of the train as they hit the rods. The
professor can use these scorch marks to confirm that the two events are equidistant
from the train’s center where he is standing.
Press GO to launch the lightning strikes. The simulations run in extreme slow
motion. We have slowed time down by a factor of more than fifty million to clearly
show what is happening.
The first simulation is in Katherine’s reference frame. The second simulation starts
in Katherine’s reference frame. You can view the same events in the professor’s
reference frame by pressing the “Professor’s reference frame” tab.
Try each simulation. Do Katherine and the professor observe the lightning bolts as
striking the lightning rods simultaneously when the train is stationary? When the
train is moving?
In order to let you experiment further with this thought experiment, both simulations
contain a feature on the control panel that allows you to adjust the interval of time
that Katherine observes between the lightning strikes. You can use this controller to
see how she and the professor observe the events as this interval changes. For
instance, you can cause there to be a five-nanosecond interval of time between
when one photon reaches her and the next photon reaches her. This lets you go
beyond Einstein’s thought experiment, where the time interval in Katherine’s
reference frame was always zero and she observed the lightning strikes as
occurring simultaneously.
In the second simulation, can you adjust the time interval in Katherine’s reference
frame to cause the photons to arrive at the same instant at the professor’s location?
If you cause this to happen, what does Katherine now observe? Can you cause them to both believe the strikes occurred simultaneously when
the train is moving? (Hint: Do not spend too much time trying!).
35.6 - Time dilation
Time dilation: A clock moving relative to an
observer runs more slowly, measuring longer
time intervals, than clocks at rest relative to the
observer.
Einstein pondered: If the speed of light is constant, what does this imply? He concluded
that it means that things we think of as absolute í like the time interval between events
í must be “relative.”
Consider the professor and the student, Katherine, in the diagrams above and on the
right. The professor moves rapidly through the classroom on his skateboard. He throws
and catches the ball, using his stopwatch to measure the time interval between the
throw and the catch. You see this illustrated in Concept 1.
Proper time
Clock is at same location as events
Time dilation
Observers differ on how much time
passes between events