1. Muons are short-lived subatomic particles that can be produced in accelerators or when cosmic rays hit the upper atmosphere. A muon at rest has a lifetime of 2.2 microseconds. Muons produced in the upper atmosphere travel at nearly the speed of light, so they have a much longer lifetime. (Their clocks run slowly.)

2. Muons produced in the upper atmosphere travel at nearly the speed of light, so they have a much longer lifetime. (Their clocks run slowly.) Suppose we have synchronized clocks at the top and the bottom of the atmosphere. We start the clocks when the muon is created, and we stop them when it decays, which happens in this case to be at the bottom of the atmosphere. What does the muon see?

3. What does the muon see? A] Since it’s moving and our clocks are not, it sees our clocks running fast B] It sees our clocks running slowly, but it disagrees with us about the reading on the bottom clock (only) when it decays C] It sees our clocks running slowly, but it observes that the top clock is ahead of where it should be for proper calibration D] It sees our clocks running slowly, but it observes that the top clock is behind where it should be for proper calibration. E] It sees our clocks running slowly, but disagrees with us about the readings on both clocks as it passes/decays F] Muons don’t have eyes or brains, so it can’t see or think anything.

4. Signals can’t travel faster than c Calibration & Lorentz Transformation

5. Two supernovas A&B are equidistant from the earth in opposite directions, and stationary wrt earth. They explode at the same time, according to an earth observer. (She sees the flashes of light at the same time.) An observer in an airplane flying toward B will A] see the flash of light from A first B] see the flash of light from B first C] will see the flashes at the same time

6. C] The observer will ALSO see the flashes at the same time. These events all happen in the same place and at at same time, so they are simultaneous for all observers. To the observer on the airplane, how do the distances (at the moment the flashes are observed) compare? A] A is closer at this instant B] B is closer at this instant C] A&B are equidistant when the flashes are seen

7. The plane is flying toward B, away from A. C] The supernova are equidistant at the time the flashes are seen. (The distance to each is less than according to the earthbound observer, however.) Since the flashes are seen by the plane rider to be simultaneous, and the SN are equidistant at the time of observation, what does the plane rider conclude? A] SN A must have occurred earlier than SN B B] SN B must have occurred earlier than SN A C] The two SN were simultaneous.

8. The plane is flying toward B, away from A. Although the flashes are seen simultaneously, and the SNs were equidistant when the flashes were seen, the observer knows that, in the past, B was farther away than A. If B was farther away when it emitted its flash, it must have done so earlier in time. (That light had farther to go!) Let’s draw a Minkowski diagram.