ActivPhysics(Relativity)

In this ActivPhysics lab  we answered various questions regarding relativity. These questions concentrated on time dilation and length contraction.

Time Dilation

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?
The light on the moving clock traveled a longer distance so it will have a longer time on it. The stationary clock travels a shorter distance.

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 on the light moving in a diagonal will have a a longer time on it because it is traveling a longer distance. The clock on the stationary platform will have a shorter time because it is traveling a shorter distance. 

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?

The light pulse on the moving platform does travel a longer distance, however, in my frame of reference it takes me the same amount of time as the stationary clock. The light appears to be moving stationary to me so the time is same. Relative to the stationary clock, it will record a longer time.

Question 4: 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?

The difference in the timers will increase if the length of the light pulse traveled increases and decrease if the path traveled is decreased. 

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 (γ) of 1.2.

The normal time that it takes to travel is 6.67μs, with Lorentz factor at 1.2 it will take 1.2* 6.67μs to travel the distance. This results in 8.00μs. 

Question 6: 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?

γ*6.67μ = 7.45μs -> 7.45μs/6.67μs = γ Gamma results in 1.116 which is approximately 1.12.

Length Contraction

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?
If I am on the moving clock, the recorded time will be the same to me as the stationary clock. The light will appear to move the same distance that  I do. In my frame of reference, The clock doesn't move. 

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 will be longer because it travels a longer distance. The time observed on both frames will be the same. The time measured on the moving frame relative to the earth will be longer.

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?

The length traveled is shorter than the stationary frame, if it were not the same then the length would increase along with the time and the Lorentz factor would not correct it. 

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? 1000m = l_pγ -> 1000/γ = l_p l_p = 769m