12 You can see the nose of Ali’s ship and the tail of Brenda’s ship at the same spacetime point. This is event #1 At this time t=0, the laser cannon at Ali’s tail is fired. This happens at a different point and is event #2
13 20012015010012050Event #1Event #250100150v = 3/5 c
14 You can’t show the path of the laser shot on the diagram because it moves too fasttoo slowparallel to the pageperpendicular to the page
15 You can’t show the path of the laser shot on the diagram because it moves into another dimension that is perpendicular to the page.tF’yFx
16 However, the ships are very close and the shot will cross the distance in almost no time. The important question is, is the nose of Brenda’s ship nearby when the shot is fired?
17 200120150100120This line marks all the positions ever occupied by the nose of Brenda’s ship.5050100150v = 3/5 c
18 At t = 0 ns, where does Ali see the nose of Brenda’s ship?
19 At t = 0 ns, Ali sees the nose of Brenda’s ship at x = 80 ns. 50 100 20012015010012050At t = 0 ns, Ali sees the nose of Brenda’s ship at x = 80 ns.50100150v = 3/5 c
20 At t’ = 0 ns, where does Brenda say her nose is?
21 At t’ = 0 ns, Brenda says her nose is at x’ = 100 ns. 50 200120150100120At t’ = 0 ns, Brenda says her nose is at x’ = 100 ns.5050100150v = 3/5 c
22 When does Brenda say that her nose was closest to the laser cannon?
23 20012015010012050At t’ = -32 ns, Brenda sees her nose beside the cannon, well before it is fired.50100150v = 3/5 c
24 Ali and Brenda disagree because of a difference in simultaneity Ali and Brenda disagree because of a difference in simultaneity. The simultaneity of two events depends on the frame of reference .
28 The two ships are in this position when the shot is fired. 200120150The shot does not occur at the same time as the tail and nose being lined up. The events are not simultaneous.At t’ = 0, the two ships are in this position, with the nose and tail lined up.1001205050100150The two ships are in this position when the shot is fired.v = 3/5 c
29 Not everything is relative. They both agree that the shot misses Not everything is relative. They both agree that the shot misses. They just don’t agree as to why.
30 Reality Check#6: Muons are formed at the top of the atmosphere by cosmic rays. Muons that are at rest have a half-life of 2.2 x 10-6 s.
31 However, when they are streaming toward the Earth at 0 However, when they are streaming toward the Earth at c, we see them live 10 times longer!
32 The muons would disagree. Their time feels completely normal. They would say that the muons at rest in the Earth lab were living 10 times longer.How could the muons explain the fact that they managed to make it through the kilometer thick atmosphere?
33 This diagram shows the problem with the speed slowed down. Event#2: Muon hits EarthThis diagram shows the problem with the speed slowed down.Event #1: Muon enters atmosphereAtmosphereEarth
34 The times between events are different. DtDt’The distances between events are also different.DxDx’
35 We measure the muons living ten times longer. DtDt’The muons measure an atmosphere that is ten times shorter.DxDx’
36 The Earth measurement of length is the largest any frame will measure. We and our ruler are at rest with both positions.This is called the ‘proper’ length.
37 The muon’s time interval is the shortest any frame will measure. They and their clock are at rest with both events.This is called the ‘proper’ time.Dt
38 Not everything is ‘relative’. We agree on our relative speeds and the speed of light.c = Dx’ /Dt’= Dx /DtDtDt’DxDx’
39 We also agree on the number of muons getting the Earth. We just don’t agree on the explanation of the two events.