ActivPhysics Lab - 17.1 Relativity of Time

ActivPhysics Lab

17.1 Relativity of Time
This activity was used to help us understand the basic concepts of relativity. In these problems we will explore how space and time are distorted as different frames approach the speed of light.

Question 1: Distance traveled by the light pulse
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?

Answer:
The distance traveled by the moving light clock is greater than the distance travel by the stationary light clock.


Question 2: Time interval required for light pulse travel, as measured on the earth
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?

Answer: Since the speed of light is constant, the moving light clock must travel a further distance and therefore must take more time to complete one cycle.


Question 3: Time interval required for light pulse travel, as measured on the light clockImagine 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?

Answer: In the moving frame of reference, the light pulse does not travel a greater distance, thus the time required for the light to make one cycle in the moving frame is the same time as the light to make one cycle in the stationary frame.


Question 4: The effect of velocity on time dilation
Will the difference in 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?

 Answer: If the velocity of the light clock is reduced, the difference of the distance also decreased. Therefore, the difference of earth's timer and the light clock's timers also decreases.

Question 5: The time dilation formula
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 (γ) of 1.2.

Set γ = 1.2 and run the simulation to check your prediction.

Answer: The time dilation of a moving clock with a Lorentz factor of 1.2 will have a time 1.2 times that of the original time.

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

Since the Lorentz factor is the ratio of the earth-bound observor's time interval measurement to the proper time interval. Then ratio is 7.45 µs / 6.67 µs = 1.12.