Episode 136: Introduction to General Relativity

The Science of Everything Podcast

James Fodor

Natural Sciences, Science, Social Sciences

4.8 • 750 Ratings

🗓️ 11 May 2023

⏱️ 85 minutes

🔗️ Recording | iTunes | RSS

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Summary

An introduction to the conceptual and mathematical framework of Einstein's General Theory of Relativity. We begin by considering the key insight of gravity as a geometric phenomenon, and how the curvature of spacetime by matter explains the equality of inertial and gravitational mass. We then discuss the mathematics of general relativity, including geodesics, differential manifolds, covariant derivatives, the metric tensor, Christoffel symbols, the Riemann curvature tensor, the Ricci tensor, and the energy-momentum tensor. The episode concludes with a derivation and explanation of the significance of Einstein's Field Equations. Recommended pre-listening is Episodes 114 and 115: Special Relativity 1 and 2. If you enjoyed the podcast please consider supporting the show by making a PayPal donation or becoming a Patreon supporter. https://www.patreon.com/jamesfodor https://www.paypal.me/ScienceofEverything

Transcript

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0:00.0	Oh, wow, oh, oh, wow, oh, wow, oh, wow.
0:13.0	Oh, wow.
0:15.0	Oh, my. Hello, you're listening to the Science of Everything podcast episode 136.
0:39.8	Introduction to General Relativity.
0:42.5	I'm your host, James Fodor.
0:44.4	Now, this is an episode that has been requested for a very long time, and I have been meaning
0:49.2	to do for a very long time, but it is a very complex and difficult topic, and I've had to do quite a lot of additional
0:55.0	research, so it's been a while in the making, but here we are. So in this episode, we're going
1:00.4	to talk about the science and mathematics behind Einstein's theory of general relativity. In particular,
1:07.2	we're going to talk about the notion of space-time and how we can represent
1:10.9	the curvature of space-time using differential manifolds.
1:14.6	We're going to talk about some of the mathematics behind covariant derivatives, Christophil
1:18.6	symbols, the metric tensor and the Riemann curvature tensor and the Ritchie tensor,
1:23.6	all of that building up to a discussion of Einstein's field equations in general
1:29.0	relativity. Because of this background that needs to be given, we're not going to get much of a
1:33.9	chance in this episode to talk about the solutions to Einstein's equations, experimental evidence,
1:39.1	and other scientific aspects of general relativity. That will be deferred to a future episode.
1:45.6	So this is really an introduction and an overview to the mathematics and conceptual underpinnings of general relativity.
1:51.5	Recommended pretty listening for this episode is episodes 114 and 115 on special relativity.
1:57.5	This episode also is a bit mathematical. So if you have even a small background in calculus,
2:04.4	that will be helpful, although I don't want to say that that's essential. Of course, the purpose of
2:08.0	these episodes is conceptual, not in doing calculations, but I will be referring to concepts
	...

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