Derive the time dilation equation found in Section 15.4 of the text. Explain each step of the derivation.
Einstein proposed that time can be stretched depending on the
motion between the observer and the events being observed. The
stretching of time is time dilation. Time dilation occurs ever so
slightly for everyday speeds, but significantly for speeds approach-
ing the speed of light.
We measure time with a clock

Question

Derive the time dilation equation found in Section 15.4 of the text. Explain each step of the derivation.
Einstein proposed that time can be stretched depending on the 
motion between the observer and the events being observed. The 
stretching of time is  time dilation.  Time dilation occurs ever so 
slightly for everyday speeds, but significantly for speeds approach-
ing the speed of light.
We measure time with a clock

anonymous · Answer

Imagine an empty tube with a mirror at 
each end as shown in Figure 15.8. A flash of light bounces back and 
forth between the parallel mirrors. The mirrors are perfect reflectors, 
so the flash bounces indefinitely. If the tube is 300,000 km in length, 
each bounce will take 1 s in the frame of reference of the light clock. 
If the tube is 3 km long, each bounce will take 0.00001 s.
Suppose we view the light clock as it whizzes past us in a high-
speed spaceship as shown in Figure 15.9. We see the light flash 
bouncing up and down along a longer diagonal path.

anonymous · Answer

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