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9. LIGO The Laser Interferometer Gravitational-Wave Observatory (LIGO) was designed to detect gravitational waves predicted by Einstein's general theory of relativity. The theory predicts that certain cosmic events will cause ripples of spatial distortion. LIGO made global news in 2015 when it detected the gravitational waves generated by a pair of colliding black holes 1.3 billion light-years away, and since then many more detections have been made. The fundamental structure of LIGO is closely modeled on Michelson's work (Figure 2.26). A laser travels along two perpendicular arms, bounces off mirrors, and merges back. (Just like Michelson's device, LIGO bounces the light back and forth many times to elongate its path length. But the scale is quite different: LIGO bounces 400 times along arms 4 km long!) Of course we know that the speed of the light along the two paths is the same; LIGO is looking for changes in the distance. A gravitational wave will elongate one arm and shrink the other arm slightly, changing the interference of the two beams. Figure 2.26 Figure 2.26 The laser beam that LIGO uses has a frequency of $2.8 \times 10^{14}$ Hz. (a) How much would one arm have to grow relative to the other to cause the phase difference to shift by 10% of a period? (Remember that each arm has an effective length 400 times its actual length, and if one grows a bit its effective length grows by 400 times that much.) (b) In the first gravity wave ever detected, the interferometer arms grew and shrank by approximately $2 \times 10^{-17}$ m. What phase shift would that cause in the interference pattern? You should find that LIGO's measuring devices are capable of detecting shifts a whole lot smaller than Michelson and Morley could have detected by eye.

9. LIGO
The Laser Interferometer Gravitational-Wave Observatory (LIGO) was designed to detect gravitational
waves predicted by Einstein's general theory of relativity. The theory predicts that certain cosmic events
will cause ripples of spatial distortion. LIGO made global news in 2015 when it detected the
gravitational waves generated by a pair of colliding black holes 1.3 billion light-years away, and since
then many more detections have been made.
The fundamental structure of LIGO is closely modeled on Michelson's work (Figure 2.26). A laser
travels along two perpendicular arms, bounces off mirrors, and merges back. (Just like Michelson's
device, LIGO bounces the light back and forth many times to elongate its path length. But the scale is
quite different: LIGO bounces 400 times along arms 4 km long!) Of course we know that the speed of
the light along the two paths is the same; LIGO is looking for changes in the distance. A gravitational
wave will elongate one arm and shrink the other arm slightly, changing the interference of the two
beams.
Figure 2.26
Figure 2.26
The laser beam that LIGO uses has a frequency of $2.8 \times 10^{14}$ Hz.
(a) How much would one arm have to grow relative to the other to cause the phase difference to shift
by 10% of a period? (Remember that each arm has an effective length 400 times its actual length, and
if one grows a bit its effective length grows by 400 times that much.)
(b) In the first gravity wave ever detected, the interferometer arms grew and shrank by
approximately $2 \times 10^{-17}$ m. What phase shift would that cause in the interference pattern? You
should find that LIGO's measuring devices are capable of detecting shifts a whole lot smaller than
Michelson and Morley could have detected by eye.

Added by Olga L.

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