ActivPhysics Lab- 17.2 Relativity of Length

17.2 Relativity of Length
In this activity we will learned how relativity distorts the length of objects as they approach the speed of light.

Question 1: Round-trip time interval, as measured on the light clock
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?

Answer:  If you are riding on the light clock, then in your frame of reference the light clock is not moving. If the light clock is stationary in your frame of reference, then the round-trip time interval is always the same. So the round trip time depends on whether the clock is stationary or moving.


Question 2: Round-trip time interval, as measured on the earth
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?

Answer:  The round-trip time interval as measured by a timer on the light clock is the proper time interval between the departure and arrival of the light pulse. Therefore, the round-trip time will be measured to be shorter than the time measured relative to the earth.

Question 3: Why does the moving light clock shrink?
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?

Answer: Yes, in order to for the time intervals to obey the time-dilation relation, the length of moving light clock had to be small. And if the loreanzt factor is known and the time required for a moving clock to travel a given distance we can use the formula stated at the beginning of the activity to calculate the time required to reach the same distance relative to the stationary frame.

Question 4: The length contraction formula
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?
Set the Lorentz factor to 1.3 and run the simulation to check your prediction.

Answer: The length of the light clock in the frame of reference of someone riding on the clock is termed the proper length of the clock. So we use the length is given by the proper length divided by the Lorentz factor. We obtain 1000/1.3 = 769 meters.