Experiment 13: Relativity of Time and Length

Objective:
To observe the effects on time and length that occur as a result of traveling at high speeds.

Data/Calculations:
Relativity of Time

Question 1: Distance traveled by the light pulse

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 time of the stationary clock is longer by a factor of gamma=1.41

Question 2: Time interval required for light pulse travel, as measured on the earth

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?

(9.4 – 6.67)*10^-6 s = 2.73 *10^-6 s

The light pulse on the moving clock takes less time than the stationary clock.

Question 3: Time interval required for light pulse travel, as measured on the light clock

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?

You observe a smaller distance than the stationary observer, therefore, the time is also shorter.

Question 4: The effect of velocity on time dilation

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 between the clocks will decrease.

Question 5: The time dilation formula

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.

(6.67*10^-6)(1.2) = 8.004*10^-6s

Question 6: The time dilation formula, one more time

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?

7.45*10^-6 = (6.67*10^-6) γ

γ = 7.45/6.67

γ = 1.12

Relativity of Length 

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?

No. The light approaches both frames at the same speed.

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?

The round-trip time interval measured on the earth should be longer.

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?

The length has to be shorter to accommodate the time difference.

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?

l = lo/γ = 1000/1.3 = 769m

Conclusion:

From these simulations we can see that frames moving at high speeds will have slower times and shorter object lengths (length parallel to motion) when compared to stationary or relatively slow frames of references.