Purpose: to use computational models at near light speed scenarios to analyze relativity and time.
Part A) 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 light in the moving car travels a longer distance than
its stationary counterpart as displayed in the animation.
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?
The observable light in the moving car is relatively faster
by a factor of 1.41 compared to the stationary counterpart.
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?
No, time appears to run at the proper time.
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?
In decreasing the speed, the distance is decreased and the
difference in time therefore decreases.
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.
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?
Part B) 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?
Time does not depend on whether the light clock is moving or
stationary relative to the earth.
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 time interval will be longer as viewed on earth on the
moving frame because there was a relative longer distance traveled by the
light.
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?
No it is not equal because the length has decreased and the
time has increased on earth(observer).
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?