Relativity of Length Activity

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?

The light pulse takes longer if the light clocks are in motion. However, the path is shortened on the way back in the situation where both clocks are moving. With the stationary light clock, the displacement of the pulse is the same. 

 

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?

It takes longer for the pulse to make a roundtrip when it is measured on 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?

For the times to be the same, the moving light clock should be adjusted so there will be a smaller distance for the light clock to travel. 

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?

Δx = γΔx_proper;                                    1000 = 1.3 Δx_proper;                           Δx_proper = 769.23 m