I had the opportunity to attend a LIGO conference at Pune university in 2018 along with a ThoughtWorks team working on Engineering for Research (E4R - PDF alert).
LIGO or the Laser Interferometer Gravitational-wave Observatory is a super awesome, science fiction like (but really existing & operational) instrument that detects Gravitational waves (GWs, not to be confused with Gravity Waves). Think of LIGO like a telescope for Gravitational waves, and because GWs are so different than the light waves that optical telescopes can detect, LIGO itself does not even closely resemble a telescope.
Crash course on Gravitational Waves
The 'empty' space between planets, stars, galaxies or between two atoms that we perceive as void is actually a 3D malleable membrane. The interaction of this membrane with mass (Higg's particles) causes it to warp, and just like throwing a stone in still water, creates ripples. Especially, a jiggling heavy mass (black holes or neutron stars) in this membrane causes waves (literally). These waves travel at the speed of light in all directions and stretch the very fabric of Spacetime, i.e. it changes the dimensions of distance measurement. LIGO basically detects these waves.
Physicists and engineers employed an ingenious trick to detect the GWs. As the GWs pass through earth, they cause a subtle (quantum level) change in the dimensions of the Spacetime. LIGO consists of two long arms (4 km each!) that use interference patterns (hence the 'I' in LIGO) to detect the the stretching and squeezing of the fabric (more details here).
LIGO is like re-inventing the telescope, but for a different kind of medium. It's like developing a sixth sense, and being able to detect properties of the universe that light cannot. It's like seeing through walls, all across the universe.
LIGO India official statement
The scientific benefits of LIGO-India are enormous. Adding a new detector to the existing network will increase the expected event rates, and will boost the detection confidence of new sources (by increasing the sensitivity, sky coverage and duty cycle of the network). But the dramatic improvement from LIGO-India would come in the ability of localizing GW sources in the sky. Sky-location of the GW sources is computed by combining data from geographically separated detectors ('aperture synthesis'). Adding a new detector in India, geographically well separated from the existing LIGO-Virgo detector array, will dramatically improve the source-localization accuracies (5 to 10 times), thus enabling us to use GW observations as an excellent astronomical tool.
A LIGO project is proposed in India at a site near Hingoli District in Maharashtra. Once successful by 2024, it will be the fourth such detector, and will add to the accuracy of measuring events such as black hole or neutron star mergers in early universe.
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