When we say ‘speed of light’, what’s special is not the ‘light’, what’s special is the ‘speed’. ‘c’ is a more fundamental quantity than I ever thought. ‘c’ is the speed of massless-ness, it’s the speed of causality. Anything with zero mass, travels, and more accurately ‘will have to’ travel at c. And nothing can go faster than c. Light was just the first phenomenon that humans measured to be travelling at c, and hence the name.
Gravitational waves or disturbances in spacetime travel exactly at the speed of light. If the sun suddenly disappears right now🫥, it would take us 8 minutes 20 seconds to notice. And we would notice it in two ways. One, the sky will go dark, and second, we will stop orbiting the sun, both in the exact same amount of time, 8 minutes and 20 seconds, no joke. Mars will experience the same, 4 minutes 20 seconds after Earth. More on spacetime later.
Why do physicists treat gravity differently? What’s so different about gravity? A few things. Gravity treats everyone equally, even light, which has no mass at all. Gravitational redshift explains it – when light climbs out of a gravitational field, it loses energy, its frequency drops, shifting it towards red. There’s no hiding from gravity, no shield can block it. And it curves spacetime. Gravity has no working quantum theory, string theory might explain stuff, but that isn’t confirmed yet. For all these reasons gravity needs to be treated differently.
‘Higher the gravity, slower the time’. A simplified proof of gravitational time dilation is given here. Anything more will take time and I’ll go to that on a need basis.
💡Fun fact: September 2015 marked the first ever detection of a gravitational wave! It was observed at LIGOs in Livingston and Hanford. LIGO stands for Laser Interferometer Gravitational-wave Observatory. This gravitational wave was caused by two black holes, each 30 solar masses, merging 1.3 billion light years away (a solar mass is the mass of Sol, our sun). In the final fraction of a second before the merger, the power radiated was more than ALL the stars in the observable universe combined, and was released in the form of gravitational waves. On earth, the LIGOs detected a stretch and squeeze of 10^−18 metres (one thousandth the diameter of a proton) in their 4km long detectors!

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