22.2. Time Dilation and Length Contraction http://www.ck12.org
FIGURE 22.7
Clocks moving relative to an observer run more slowly compared to the clocks that are at rest relative to the
observer. This slowing down of time called time dilation.For example, Earth-bound observers will measure time moving more slowly (than their own time) when observing
a space ship moving with velocityv.
The situation is symmetric, with each inertial frame seeing the other’s time as slower. We will shortly see, however,
that the symmetry is not preserved if the space ship returns to earth.
http://demonstrations.wolfram.com/LightClocksAndTimeDilation/
We will see in this chapter that the postulates of special relativity suggest that space and time are not independent of
each other, but are interdependent. We refer to this interdependence, today, as space-time.
Illustrative Example 1
a. A futuristic space ship leaves the Earth traveling at a speed 0. 75 c. A clock on board the ship reads an elapsed
time of 1. 00 hsince the take-off. What time interval does an Earth-bound observer measure at that instant?
Solution:
Proper time is measured in the space ship, thustp= 1. 00 h.
t=√tp
1 −vc^22
=√^1.^00 h
1 −(^0.^75 c) 22 c^2=√^1.^00 h
1 −(^0.^751 )^2= 1. 51 hb. The ship slows to a speed of 100, 000 kmh. Again, if the clock on board the ship measures 1. 00 h, what is the
amount of time measured on Earth?