here - Department of Physics, HKU
here - Department of Physics, HKU
here - Department of Physics, HKU
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
CHAPTER 2. SPECIAL RELATIVITY 9<br />
l 2<br />
glass<br />
l 1<br />
Figure 2.1: Michelson-Morley experiment.<br />
glass<br />
vt 2<br />
l 2<br />
v<br />
Figure 2.2: The whole experiment is moving to the right with speed v.<br />
distance vt 2 , Fig. 2.2. Hence, we have<br />
( ) 1/2<br />
2 l2 2 + (vt 2<br />
2 )2 = ct 2<br />
t 2 = 2l 2<br />
c<br />
1<br />
√1 − v 2 /c 2 . (2.2)<br />
Let β = v/c. The time difference between them is<br />
∆t = t 2 − t 1 = 2 (<br />
l<br />
√ 2<br />
c<br />
)<br />
1<br />
1 − β<br />
2 1 − β 2 . (2.3)<br />
To simplify this expression, notice that for small β,<br />
1<br />
√ 1 − β<br />
2<br />
= 1 + β2<br />
2 + 3β4<br />
8 + · · · (2.4)
Change language