Work and World

General Relativity Explained In 7 Levels Of Difficulty

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   video on Nebula, the Streamy-award-nominated 
independent streaming service that’s the   co-sponsor of this video. [short teaser of the 
extended video] Nebula was created by and for a   collection of educational video creators including 
Real Engineering, Mike Boyd, Up and Atom,   Jordan Harrod – and me – and Nebula has partnered 
with CuriosityStream, which offers thousands of   documentaries and nonfiction titles to give you 
access to both in one go! I recommend Vitamania,   about the history and science (or lack thereof, 
in some cases) of vitamins and supplements.   Sign up for CuriosityStream using the link in the 
description and you’ll also get access to Nebula,   including the extended version of this video as 
well as an ad-free viewing experience across the   site. Oh yeah, and you’ll also get 26% off 
an annual subscription to CuriosityStream.
Video source: https://www.youtube.com/watch?v=eNhJY-R3Gwg

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