Relativity of Time/Length

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 distance traveled by the moving clock is greater than the distance traveled by the stationary clock




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 interval for the stationary clock is slower than the time interval for the moving clock.






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 distance would appear to be the same.






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?

y = 1/(sqrt [1+(v^2/c^2)]), as velocity decreases the difference in time 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 (y) of 1.2.

Using the dilation formula, the predicted time is about 8 e-6 seconds.





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

Using the dilation formula, the Lorentz factor is about 1.12.




The effect happening in theses situations are know as "Time dilation." This effect happens when an event occurs and the event is viewed at two frame of references. One reference is at the same space point where the event occurs, this frame of reference is moving with a constant velocity relative to the a second frame of reference. The time interval from the second frame of reference is larger than the time interval from the frame of reference where the event occurred.



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?


No, it does not matter. 









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 product of the measured time interval on the light clock and the Lorentz factor is equal to the time inteval on earth. The time intervals will be the same as long as you take time dialation into account.










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?

 Only if the Lorentz factor is equal to 1, this can happen if the velocity of the the moving light clock is relatively small compared to c.

4)A light clock is 1000m 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?

The earth-bound observer will measure a lenght of 769 meters.

The effect happening in this situations is know as "Length Contraction." This effect happens when a distance between two points is measured in the rest frame of reference, known as proper length, is moving at a constant velocity relative to a second frame of reference. The length of the two points measured at the second frame of reference is shorter than the proper length.