Predicted by general relativity in 1916, then experimentally confirmed in 2015, gravitational waves have allowed astrophysics to enter a new era of observation of the cosmos. Instruments like LIGO, Virgo and soon KAGRA and IndIGO, constantly scan the sky in search of these space-time ripples. But how do they detect them?
In 1916, Albert Einstein demonstrated that when two massive bodies accelerate, this results in disturbances of space-time which propagate within it in the form of waves. It was not until September 14, 2015 that gravitational waves, produced by the coalescence of two black holes located 1.3 billion light-years away, were detected by the LIGO collaboration. A second detection took place in December 2015, this time carried out jointly by LIGO and Virgo.
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To detect gravitational waves, astrophysicists use specific instruments using the principle of interferometry. This method exploits the interference patterns created by coherent waves. The interferometers used by scientists, such as LIGO and Virgo, are Michelson interferometers.
An interferometer like LIGO is composed of two arms of identical lengths and exact multiple of a particular wavelength. A high vacuum is created within these arms. A laser beam (coherent light) of the same wavelength is split by a beam splitter into two perpendicular components, each sent into an arm whose end includes a mirror. The light is therefore reflected many times and then recombined to form an interference pattern.
If this interference pattern remains perfectly constant in the absence of gravitational waves, then the interferometer is correctly configured. For about 40 years, scientists in the LIGO collaboration worked to properly calibrate the interferometer to achieve a sensitivity to detect true gravitational signals. The amplitude of the latter is extremely low, which is why the calibration required several decades.
Gravitational waves are different from all other known waves propagating in the Universe. Instead of signatures detectable through interactions between particles (electromagnetic radiation, for example), gravitational waves are ripples in the very fabric of space-time.
Instead of monopolar waves (carrying charges) or dipolar waves (oscillating fields), gravitational waves are a quadrupole waveform. And instead of electric and magnetic fields perpendicular to the direction of wave propagation, gravitational waves alternately stretch and contract the space they pass through in mutually perpendicular directions, depending on the polarization of the wave.
When a gravitational wave passes through an interferometer like LIGO, one of the arms contracts while the other stretches, and vice versa, creating a characteristic pattern of oscillations.
LIGO detectors are deliberately placed at opposite angles and in different locations on the Earth's surface, so that regardless of the orientation of the wave, at least one of the sensors will detect it. Thus, astrophysicists make sure to always have a detector placed in an optimal way, according to the orientation of the gravitational wave.
Inside the arms, in a vacuum, the light (the laser beam) travels at 299,792,458 m/s. When a gravitational wave passes through the detector, the contraction and stretching of the arms also causes the contraction and stretching of the wavelength of light.
Instinctively, one would think that if the light wavelength is contracted and stretched along with the arms, then the total interference pattern remains unchanged. However, the operation of the detector is different. In reality, the wavelength of light, which strongly depends on how space is changed as the gravitational wave passes, is not important in the interference scheme. Indeed, what is important is the duration of propagation of the light in the arm.
When a gravitational wave passes through an arm, it temporarily changes the effective length of the arm, and therefore the time it takes each laser beam to cross it. One arm is stretched, lengthening the propagation time; while another is contracted, reducing the spread time.
As the relative time of arrival changes between the two arms, an oscillatory pattern appears following the reconstruction of the interference pattern. In other words, when the two beams recombine, there is a difference in their propagation time, and therefore a characteristic shift in the final interference pattern.
It is true that the wavelength of light changes when a gravitational wave passes:when space is stretched, so is the wavelength, and the light is red-shifted; when space is contracted, the light is blue shifted. However, regardless of its wavelength, light will always travel at ~300,000 km/s in vacuum. The speed of light in vacuum is a constant that does not depend on wavelength. The only significant parameter is therefore the time it takes for the light to pass through the arms.
