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, 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 that 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 line 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
ten nonlinear differential equations [2nd order] 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 just energy and matter and spacetime around the earth or sun – they can be used on the
universe as a whole to describe and understand the past and 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+1 dimensional universe, the predictions generated by this idea
have been experimentally verified by many many incredibly precise observations, ranging from
the precession of the orbit of Mercury, to the slight drift of the moon’s orbit away from the
earth, 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 polarization 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.
Wait but how does general relativity explain the everyday “force” of gravity we experience
on earth? Well, you know how when a vehicle turns but your body’s inertia makes you want
to go straight 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 the earth
accelerates us away from that straight-line path, we feel that acceleration as a weight or force
that we call gravity [equivalence principle]. If you’re in free fall (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 “0 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! It’s hard. 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
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