Episode 136: Introduction to General Relativity
The Science of Everything Podcast
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The Curvature of Space Time
In general relativity we're interested in four dimensional manifolds because there are four dimensions, three of space in one of time. A manifold is a topological space so think of it like a sheet but in more dimensions which can be bent and warped and curved globally but if you zoom in close and close enough it looks flat. The reason we need it to be locally flat is so we can apply some of the tools of mathematics and calculus and things like that. So basically the idea is I want to be able to describe curved geometries but I want to ensure that locally like if I get near enough to each point it look flat.
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