Show from Einstein’s postulates that two events measured as simultaneous in one inertial frame are not necessarily simultaneous in all inertial frames.
Describe how simultaneity is a relative concept for observers in different inertial frames in relative motion.
Galilean Transformation
Relativity of Simultaneity
Practice!
Practice 1.2.1
Consider Alice’s spaceship with the paintball apparatus that shoots two paintballs towards clocks at opposite ends of her ship, each with speed S relative to the apparatus. Assume that Alice has properly synchronized her clocks, that her spaceship is moving with speed V to the right (+x direction) relative to Bob, and that S is greater than V. According to Alice, in her frame of reference, what will be the speed of the paintball that is moving to the right?
A. V
B. S + V
C. S
D. S – V
Check your answer: C
Practice 1.2.2
Consider the same situation as in question 1.2.1. According to Alice, what will be the speed of the paintball that is moving to the left? (We’re interested in the speed as the magnitude of the velocity, so don’t worry about the direction.)
A. V
B. S
C. S + V
D. S – V
Check your answer: B
Practice 1.2.3
Consider the same situations as in questions 1.2.1 and 1.2.2. True or False: In Alice’s frame of reference, the two paintballs will hit the clocks simultaneously.
A. True
B. False
Check your answer: A. True
Practice 1.2.4
Consider the same situations as in the previous questions. According to Bob’s observations of Alice’s spaceship (and clocks and paintballs) flying by, what will be the speed of the paintball that is moving to the right?
A. V
B. S – V
C. S + V
D. S
Check your answer: C
Practice 1.2.5
According to Bob’s observation from his frame of reference, what will be the speed of the paintball that is moving to the left?
A. S – V
B. V
C. S
D. S + V
Check your answer: A
Practice 1.2.6
True or False: In Bob’s frame of reference, the two paintballs will hit Alice’s clocks simultaneously.
A. True
B. False
Check your answer: A. True
Practice 1.2.7
Consider Alice’s spaceship with the light pulse apparatus that shoots two light pulses towards clocks at opposite ends of her ship, each with speed c relative to the apparatus. Assume that Alice has properly synchronized her clocks, that her spaceship is moving with speed V to the right (+x direction) relative to Bob, and that c is greater than V. According to Alice, in her frame of reference, what will be the speed of the light pulse that is moving to the right?
A. c – V
B. c
C. V
D. c + V
Check your answer: B
Practice 1.2.8
Consider the same situation as in question 1.2.7. According to Alice, what will be the speed of the light pulse that is moving to the left? (We’re interested in the speed as the magnitude of the velocity, so don’t worry about the direction.)
A. V
B. c
C. c + V
D. c – V
Check your answer: B
Practice 1.2.9
Consider the same situations as in questions 1.2.7 and 1.2.8. True or False: In Alice’s frame of reference, the two light pulses will hit the clocks simultaneously.
A. True
B. False
Check your answer: A
Practice 1.2.10
Consider the same situations as in the previous questions. According to Bob’s observations of Alice’s spaceship (and clocks and light pulses) flying by, what will be the speed of the light pulse that is moving to the right?
A. c
B. c – V
C. c + V
D. V
Check your answer: A
Practice 1.2.11
According to Bob’s observation from his frame of reference, what will be the speed of the light pulse that is moving to the left?
A. c – V
B. V
C. c
D. c + V
Check your answer: C
Practice 1.2.12
True or False: In Bob’s frame of reference, the two light pulses will hit Alice’s clocks simultaneously.
A. True
B. False
Check your answer: B. False
Discuss!
Bob is standing at the center of his railroad car as it passes Alice on the ground. Firecrackers attached to the ends of the car explode. A short time later, the flashes from the two explosions arrive at Bob at the same time.
Were the explosions simultaneous in Bobs reference frame? If not, which exploded first? Explain.
Were the explosions simultaneous in Alice’s frame? If not, which exploded first? Explain.
Physics Education Research at UNG 