4/17 Relativity of time and length

Purpose
The purpose of this experiment was to gain knowledge of relativity and understand how choosing different reference fram can cause the time dilation and length contraction by running the simulation.

Time dilution

     1. The distance traveled by the light pulse on the moving light clock is longer than the distance traveled by the light pulse on the stationary light clock.

     2. The time interval for the light pulse to travel to the top mirror and back on the moving light clock is longer than the interval on the stationary light clock because the distance is longer in the moving clock and speed of light is constant.

 

     3. 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 minimum time interval between events is referred to as the proper time.



     4. As the speed of the light clock is reduced, the difference between the distance traveled by the light pulse and the distance between the mirrors decreases. As this distance difference decreases, the time difference also decreases. Comparing the images below and above, the time difference decreases as the gamma value decreases. When gamma value decreases, the velocity of the traveling light clock decreases, and the time difference decreases.

     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.

Δt = γΔt_{proper =} 1.2(6.67 µs) = 8.004 µs predicted

actual Δt= 8.00µs very close to the predicted, 8.004s.

     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?
 

Δt = γΔt_proper  

Δt = 7.45 µs; Δt_proper  = 6.67 µs

γ =1.12

proved!

 

Length contraction
     1. The measurement of this round-trip time interval depend on whether the light clock is moving or stationary relative to the earth.

     2. The round-trip time interval for the light pulse as measured on the earth be longer than the time interval measured on the light clock.

 

     3. In order for the time intervals to obey this law, the length of the moving light clock had to be made smaller.
     4. Lp = 1000m, γ =1.3. L=?
         L= Lp/γ = 769m

proved!

 

Conclusion

When one event occurs, people in different frames observed it at different times. People who are in a relative stationary fram will observe a longer time than people who are in a moving frame, and the proper time means the time interval measure on a clock located at the events. However, people who are in the relative stationary fram will observe a shorter length, and the proper length is the length of an object measured in the reference fram in which the object is at rest.