Experiment: Time and Length Relativity

Relativity of Time:



 

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 travels a longer distance by the factor of gamma in the moving frame than the stationary frame.

 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 clock in the moving frame is 2.73 micro second longer than that of the stationary frame.

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?

-No, there wont be a larger distance, nor longer time interval.

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?

- As the velocity id slowed down, the difference in the timers will decrease because they will be less relativistic and more classical.

 

 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 = γ*Δt(proper)

   Δt = (1.2)(6.67 µs) = 8.00 µs

 

6. If the time interval between departure and return of the light pulse is measured to be 7.45 microseconds by an earth-bound observer, what is the Lorentz factor of the light clock as it moves relative to the earth?

-  Δt = γ*Δt(proper)

   7.45µs = (γ)(6.67 µs) 

   γ = 1.12 

 

Relativity of Length

 

 

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?

- The clock that is moving relative to earth will measure a longer time for the round trip distance than then the one stationary relative to earth.

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 time interval for the light pulse will be longer by a factor of gamma.

 

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?

- It could be the equal if the Lorentz factor is equal to one, which means that they would be traveling at non-relativistic speeds.

 

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?  

- L = Lp / γ

  L = (1000m) / 1.3 = 769.2 m