Experiment 13: Relativity of Time and Length

Relativity of Time

Question 1: How does the distance traveled by the light pulse on the moving light clock compare to the distance traveled by the light pulse on the stationary light clock?

1. The distance is different by a factor of gamma.

Question 2: Given that the speed of the light pulse is independent of the speed of the light clock, how does the time interval for the light pulse to travel to the top mirror and back on the moving light clock compare to on the stationary light clock?

The time is different by a value of 2.73 microseconds.

Question 3: Imagine yourself riding on the light clock. In your frame of reference, does the light pulse travel a larger distance when the clock is moving, and hence require a larger time interval to complete a single round trip?

As a person riding on the light clock frame, there is no difference in the time interval.

Question 4: Will the difference  in the light pulse travel time between the earth's timers and the light clock's timers increase, decrease, or stay the same as the velocity of the light clock is decreased?

When the velocity is decreased, the system will become more classical and the difference between the timers will decrease.

Question 5: Using the time dilation formula, predict how long it will take for the light pulse to travel back and forth between mirrors, as measured by an earth-bound observer, when the light clock has a Lorentz factor of 1.2.

Time = 8.004 microseconds

Question 6: If the time interval between departure and return of the light pulse is measured to be 7.45 microseconds by an earth-bound observer, what is the Lorentz factor of the light clock as it moves relative to the earth?

Lorentz factor value = 1.12

Relativity of Length

Question 1: Imagine riding on the left end of the light clock. A pulse of light departs the left end, travels to the right end, reflects, and returns to the left end of the light clock. Does your measurement of this round-trip time interval depend on whether the light clock is moving or stationary relative to the earth?

Yes, the light clock that is moving will experience a longer time interval than the light clock that is stationary relative to the earth.

Question 2: Will the round-trip time interval for the light pulse as measured on the earth be longer, shorter, or the same as the time interval measured on the light clock?

The round-trip time interval for the light pulse will be longer by a factor of gamma.

Question 3: You have probably noticed that the length of the moving light clock is smaller than the length of the stationary light clock. Could the round-trip time interval as measured on the earth be equal to the product of the Lorentz factor and the proper time interval if the moving light clock were the same size as the stationary light clock?

Yes, the round-trip time interval could be equal due to the Lorentz factor of the length contraction equaling 1.

Question 4: A light clock is 1000 m long when measured at rest. How long would earth-bound observer's measure the clock to be if it had a Lorentz factor of 1.3 relative to the earth? 

The observers would measure a length of 769.2 meters.