General relativity is a physics theory invented by Albert Einstein. General relativity is just a fancy 20th century name for gravity, the force that pulls stuff to the ground and keeps the planets in orbit around the sun. General relativity is the idea that gravity happens because space is curved, like how when you walk along the surface of a ball, you end up curving downwards. Actually, general relativity is the idea that space and time aren't separate.
Time is a physical dimension, and together they form a single geometry called spacetime. And gravity is caused by curvature in spacetime. But spacetime can't be curved any which way. Just like how a ball looks flat when you're close enough, curved spacetime is locally flat, rather than crumpled or something. Of course, flat space makes sense, but what does it mean for spacetime to be flat?
That it obeys the rules of special relativity. Finite speed of light, time dilation and length contraction, relative addition of velocities, twin's paradox, and all that. Basically, if general relativity is like a globe, special relativity is being on the surface of the globe. and mathematicians call the globe a Pseudo-Riemannian Manifold with Lorentzian signature.
Except curvature in spacetime on its own doesn't explain gravity. I mean, just because you're on a curved ball doesn't mean you follow a specific path on the ball. General relativity is the combination of the ideas that spacetime is curved, and that stuff in spacetime obeys laws of motion.
An object in motion stays in motion along a straight path in curved spacetime. like following a straight path along the surface of a ball. Except we still haven't said anything about what determines the curviness or shape of spacetime in the first place, or why objects tend to follow straight paths in that spacetime.
General relativity is actually the idea that all the stuff in spacetime matter, radiation, pressure, energy, momentum, particles, and so on, all that together with spacetime itself obeys a set of equations called the Einstein field equations. These equations look simple if you write them in a clever way, but they're actually a very complicated set of 10 nonlinear differential equations that you have to solve in order to make predictions about how spacetime will curve, and how the stuff in it will move, depending on how spacetime is curving and how the stuff is moving. The solutions to the Einstein field equations of general relativity describe gravity around solitary objects like black holes or the sun or the earth, and they facilitate very accurate predictions of orbits around these objects.
But these equations aren't limited to describing the energy and matter in spacetime around the Earth or Sun. They can be used on the universe as a whole to describe and understand the past, present, and future of the cosmos. So... General relativity is the idea that the universe can be described by a pseudo-Riemannian manifold representing spacetime, and an energy-momentum tensor representing all matter and energy, which together obey the Einstein field equations. For our 3-plus-1-dimensional universe, the predictions generated by this idea have been experimentally verified by many, many incredibly precise observations, ranging from the slight drift of the moon's orbit away from the earth, to the precession of the orbit of Mercury, to the gravitational lensing and redshift of starlight, to time dilation of atomic clocks and precession of gyroscopes orbiting the earth, to observations of the cosmic microwave background radiation, to gravitational wave detections of black hole mergers, to direct imaging of the black hole at the center of the milky way.
That is general relativity. Wait, but how does general relativity explain the everyday force of gravity we experience here on earth? Well, you know how when a vehicle turns but your body's inertia makes you want to go in a straight line, and it feels like you're being pulled sideways because you're being accelerated away from your straight line path?
In general relativity, an object's straight line inertial path is actually to fall towards the center of the Earth. And since the surface of the Earth accelerates us away from that straight line path, we feel that acceleration as a weight, or a force, that we call gravity. If you're in freefall, or in orbit, then you are following a straight path through curved spacetime. that is, you're not accelerating in spacetime, so you feel like you're floating or experiencing zero-g.
And that explains gravity. Uh, yeah, general relativity doesn't explain quantum mechanical phenomena, and has problems jiving with the theory of quantum mechanics in certain extreme situations. Physicists have been working for over 90 years to reconcile general relativity and quantum mechanics in those situations, and while we've learned a lot, we still haven't come close to solving everything. General relativity works so well in most cases where we can test it, and quantum mechanics works so well in most cases where we can test it, and they're both so mathematically sophisticated and constrained and distinct from each other, that imagining a different mathematical model that encompasses both while being just as accurate where they're already accurate and better where they're in conflict is very high-level stuff.
If you want even more levels of general relativity, I have an extended version of this video on Nebula, the Streamy Award-nominated independent streaming service that's the co-sponsor of this video. One final nuance about general relativity. The concept of the shape of space actually has two different meanings.
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