Riemann's Tensor Analysis for Curved Surfaces

4min Snip

00:00

Play full episode

Summary

Transcript

Episode notes

In Riemann's way of thinking about it, you need nine numbers to specify it in a three dimensional space. The metric by itself could be any numbers that just depends on the coordinate system. And so we want to take that metric, which depends on what coordinates you use. Maybe not XYZ, maybe R theta phi, if you have spherical coordinates or something like that. We want to extract from that metric what the curvature is. You're measuring how long things are, and tensor because it is a generalization of a vector.

My little pandemic-lockdown contribution to the world was a series of videos called The Biggest Ideas in the Universe. The idea was to explain physics in a pedagogical way, concentrating on established ideas rather than speculations, with the twist that I tried to include and explain any equations that seemed useful, even though no prior mathematical knowledge was presumed. I’m in the process of writing a series of three books inspired by those videos, and the first one is coming out now: The Biggest Ideas In The Universe: Space, Time, and Motion. For this solo episode I go through one of the highlights from the book: explaining the mathematical and physical basis of Einstein’s equation of general relativity, relating mass and energy to the curvature of spacetime. Hope it works!

Support Mindscape on Patreon.

See Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.