LIGO_casebook

quantify the movement l. This quantity is related to the phase shift by l = (φ/4π)
λ laser . Here λ laser is the wavelength of the laser light used.
All this happens at one instant of time. At the next instant, the quantity l will
change as the gravitational wave moves a tiny bit further past the instrument. Now
it will be determined again. In this way l (plotted against the time t) will trace out
the passage of the wave, essentially mimicking the waveform.
The longer the arms are, the larger is l and hence the larger the phase shift and
the larger amount of light that arises at the photodetector. More light here means
better and more accurate measurement and better threshold of detection. This is the
incentive for making the arms AB and CD as long as practical.
The arms of LIGO are 1.2 m-diameter steel tubing sealed at the ends. The space
inside the tubing is evacuated to a high degree in order to prevent gas molecules from
degrading the laser beam and causing unwanted vibrations of the mirrors.
There are here two types of mirror movement one is concerned with:
(1). The mirror moves because of natural (e.g., seismic tremors) or man-made
vibrations (e.g., a heavy vehicle driving by), or because of the effect of currents
generated in the metal structures due to geomagnetic disturbances.
(2). The mirror “moves” because of the passage of a gravitational wave. This is not
a conventional movement or displacement. It is the space itself that is expanding and
contracting along with everything that is in it. So, the mirrors A and B for example
will be closer together sometime and farther apart sometime compared to where they
were before the arrival of the wave. The same is true of the mirrors C and D. This
closer-farther sequence is what is loosely described as ‘movement’.
LIGO reports its measurements in terms of strain which is the fractional change in
length of a LIGO arm (strain h = l /l ). A typical black hole merger event has been
estimated theoretically to produce a strain of 1 part in 10 21 . This degree of smallness
of the signal has been communicated to the general public by the LIGO scientists as
follows: The LIGO instrument needs to be able to measure a mirror movement that is
less than 1/10,000th the diameter of a proton. While the diameter of a proton is a
complex concept, for our purposes here it is about 1.6 x 10 −15 m. It is important to bear
in mind that we are speaking here of macroscopic movement of a large and heavy
object, and not movement in subnuclear quantum physics, for example. So, this
ability of LIGO to function as a “proton yardstick” is truly an astounding feat. LIGO
has in fact been described as the most precision scientific measurement instrument
ever built.
The instrument as described cannot however directly measure a strain this small.
To remedy this situation, the laser beam is made to bounce back and forth between
two mirrors (A and B; and C and D) some 300 times before arriving at the
photodetector. This effectively enlarges the 4 km arm to 1200 km. The bouncing laser
beam accumulates the displacements l three hundred times, bringing this amplified
displacement within the range of measurability.
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