9.1.2 The Relativity of Simultaneity Flashcards
The Relativity of Simultaneity
• Einstein’s postulates for his special theory of relativity:
- The laws of physics are the same in every inertial reference frame.
- The speed of light (in vacuum) is the same for all observers in inertial reference frames regardless of their motion or the motion of the light source.
• Events occur at a particular place and time. Two events are simultaneous if they occur at the same time.
• Simultaneity is relative. Events that are simultaneous in one reference frame may not be simultaneous in another reference frame.
P and Q are traveling in the boxcars of two trains that are moving parallel and opposite to each other with relative speed v. Both observers are standing in the middle of their boxcars. As the observers pass each other, as shown in the figure, each turns on a light bulb and the light signal strikes the respective walls on each boxcar. Which of the following statements is not correct?
P notes that the light signal strikes the two ends simultaneously in Q’s car.
An observer O, at rest in an inertial frame, notes the clock readings of two events, A and B, located at positions as shown in the figure. O witnesses event A at time tA = t0 and event B at tB = t0 = 1/c. Which of the following is the correct order of occurrence of A and B according to observer O?
A and B occur at the same time.
True or false?
Suppose two events, A and B, occur at fixed positions and are simultaneous in an inertial frame S. Based on Newton’s laws, an observer in a moving reference frame relative to S will not observe A and B as simultaneous events.
false
Two ticket conductors on a train moving to the right with velocity v notice a person on the platform. One conductor remarks that the person is standing at rest while the other insists that the person is moving. Who is correct?
Both conductors are correct
Which of the following condition(s) must be satisfied for two events to be simultaneous in an inertial reference frame?
The two events occur at the same time.
Tow observers, P and Q, witness a light flash as shown in the figure. They are in the same reference frame and at rest relative to the light source. Suppose a clock is palced at the location of the light flash and the clock reads time t0 at the time of the flash. If P and Q have their own clocks, when will they see the flash? Let dP be the distance from the light flash to P, dQ be the distance from the light flash to Q, and dP
P witnesses the flash at tP = t0 + dP/c and Q witnesses the flash at tQ = t0 + dQ/c
Consider an observer P in a boxcar and another observer Q who sees the boxcar move to the right with speed v. A light flash goes off when P and Q pass each other. According to Q, because the boxcar is moving to the right, light has more to travel tot he right end than the left end. Also, the left end gets closer to the light signal. Based on newton’s laws, calculate the times tL and tR to reach the left end and the right end of the train. The length of the boxcar is L.
tL = (L/2 - vtL)/(c-v) -> tL = L/2c tR = (L/2 = vtR)/(c+v) -> tR = L/2c
Two events, separated by distance d in the same reference frame, occur at the same time if they have the same clock reading. Imagine that every position in a reference frame is fixed with a clock, and each clock should read the same time at any given instant. But because light signals take a finite amount of time to travel, it is necessary to compensate for this time to synchronize the clocks.
Consider a master clock located at O and another clock located at position P at a distance of d meters. Suppose a light signal is sent from O at time 0. The goal is to synchronize the two clocks, that is, the two clocks should read the same time at any given instant. At which of the following times should the clock C 1 start running when the signal reaches there?
d/c
True or false?
An observer O standing in the middle of a train boxcar turns on a light bulb. Light travels to both ends and strikes the walls. Based on the special theory of relativity, the two events are simultaneous for the observer.
true
