Demystifying The Metric Tensor in General Relativity

The path to understanding General Relativity starts at the Metric Tensor. But this mathematical tool is so deeply entrenched in esoteric symbolism and complex mathematics that its simplistic, intuitive purpose often goes neglected. Here we attempt to expose the basic principles behind the Metric Tensor -- and investigate how they tie into General Relativity -- in as simplistic a manner as possible. Do we succeed? Feel free to let us know in the comments!

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Contents:

00:00 - Intro
00:54 - The Equations of General Relativity
01:33 - The Metric as a Bar Scale
02:45 - Reading Topography on a Map
04:53 - Coordinate Distance vs. Real World Distance
05:35 - Components of the Metric Tensor
08:50 - Mapping the Earth
09:48 - Stretching and Skewing / Law of Cosines
11:37 - Geometrical Interpretation of the Metric Tensor
12:37 - Coordinate Systems vs. Manifolds
13:39 - Conclusions