Issues of Simultaneity
Answer questions on a separate piece of paper. Attach this paper and the graphs.
Alan, Andy, Alex, and the usual bunch of guys are riding on Spaceship Alpha. Beth, Beatrix, Betsy, and the rest of
the ladies ride on Spaceship Beta. (Will they ever meet?) Alan and Beth stand at the center of their respective ships.
The spaceships may or may not be the same length—you will find out shortly.
Event 1: When the front end of Alan’s ship is at the same location as the rear of Beth’s ship, a spark jumps between
them and light waves spread out. Char marks from the spark are left on both spaceships.
Event 2: Likewise when the rear of Alan’s ship and the front of Beth’s ship pass, a spark jumps between them
emitting a light pulse, and leaving char marks.
Event 3: Alan is equidistant from the char marks on his spaceship, and receives the pulses of light from both sparks
at the same time (simultaneously). The diagram represents this, showing wavefronts arriving at Alan.
Beth
Char marks from Event 2
Char marks from Event 1
Alan
Event 3
NOT to scale!
A. 1. In Alan’s frame, does spark 1 (from Event 1) jump before, after, or at the same time as spark 2 (from Event
2)? Explain your reasoning.
2. Alan’s friend Andy stands near Char mark 2 (in their ship). According to Andy, does spark 1 jump before,
after, or at the same time as spark 2 (on the left of picture)? Explain your reasoning.
3. What does the distance between the char marks in Alan’s ship tell you about Beth’s ship? Explain your
reasoning.
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4. The diagram below represents the situation in Andy’s frame a short time after the sparks. Show the
wavefronts at this time.
Beth
Char marks from Event 2
Char marks from Event 1
Alan
B.
On gridded paper, draw the spacetime diagram as seen by Alan. Time and distance will be measured in the
same units, “squares.” Assume that Alan measures the length of Spaceship Alpha to be 20 squares. Alan sees
Beth move to the right at β = 0.50. On your diagram identify the following events (some may occur
simultaneously):
Event 1 Spark 1 occurs
Event 3 Light waves reach Alan
Event 2 Spark 2 occurs
Event 4 Alan and Beth are exactly opposite each other.
Draw the world lines for the char marks and for the wavefronts.
Use the diagram to give the time separation, as measured by Alan, in squares, between
Event 1 and Event 2
Event 1 and Event 4
Event 1 and Event 3
C. Proper lengths. We will now identify the relative speeds of the spaceships be β = 0.50.
1. Who measures the proper length of Spaceship Alpha, Alan, Beth, both, or neither. Explain
2. Who measures the proper length of Spaceship Beta, Alan, Beth, both, or neither. Explain
3. Alan measures the length of Spaceship Alpha to be 20 squares. What does Alan measure for the length of
Spaceship Beta? Explain.
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4. What does Beth measure for the lengths of Spaceship Alpha, and for Spaceship Beta? Explain.
D. Spacetime Diagram for Beth.
At the top of gridded paper, draw boxes representing the lengths of the two spaceships as seen by Beth. This
is just for reference.
Start about 10 squares up from the bottom of the paper, and draw the diagram corresponding to Event 4. Show
the locations of the front, back, and center of both ships, and draw world lines for the front, back, and center
of both ships. Also show the world lines of the light emitted from the sparks. Extend the lines as necessary
and determine the times and locations of the other three events. Mark the events on the diagram.
Use the diagram to determine the time separation, in squares, between
Event 1 and Event 2
Event 1 and Event 4
Event 1 and Event 3
E.
Carefully draw an event diagram as seen by Beth—that is draw pictoral diagrams like those on the first page.
Time is positive upwards. Show all 4 events, as well as the spaceships and the wavefronts.
III.
Does Lack of Simultaneity Make Sense? (Well probably it won’t make “sense” to you, but at least, can it be
consistent?)
A. A CD burner sits at Beth’s feet. In Alan’s frame, when the wavefront from spark 2 reaches the burner, it
starts to burn a legal copy of a Green Day CD. When the wavefront from 1 reaches the burner it shuts off.
If the wavefronts reach the burner at the same time, or the wavefront from 1 reaches the burner first, no
music is recorded.
In Alan’s frame, is there any music burned onto the CD? In Beth’s frame, is there any music burned onto
the CD? Explain how your spacetime diagrams are consistent with this.
Is your answer consistent with your answers to the following question?
Later in the day the CD is removed from the burner, and Beth travels with it via courier rocket to Alan.
They play the CD. Will they hear Green Day or not?
B. Alan also has a CD burner that operates just like Beth’s. In Alan’s frame, is there any music burned onto
the CD? In Beth’s frame, is there any music burned onto the CD? Explain how your spacetime diagrams
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are consistent with this.
Is your answer consistent with your answers to the following question?
Later in the day when Beth has traveled via courier rocket to Alan, they play Alan’s CD. Will they hear
Green Day or not?
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