Talk:General theory of relativity

Higher math template?

Question: I know we have this template for sections that get into early-undergrad math:

This article/section deals with mathematical concepts appropriate for late high school or early college.

But the quantitative section is going to make (gentle) reference to tensor algebra and some aspects of differential geometry. Do we have a template that somehow conveys "this section is hard-core math, but don't be scared?" Or maybe something that gets across the idea that you don't have to follow everything in this section to understand this article?

Proofread?

I'm going to leave this page half-done for tonight and pick it up tomorrow. Anybody available to give what's there right now a proofread? I'd love any and all feedback. --KSorenson 18:45, 13 November 2009 (EST)

The math is way out of my depth, but I tried clarifying the section about Eddington's experiment. It now says what I think it said - if I'm way off-base, please correct me. -- EvanW 19:01, 13 November 2009 (EST)

Yep, everything in there seems okay. Can't wait to read the rest of the article.--DanHutchin 19:14, 13 November 2009 (EST)

Yeah, I'm struggling with the math. The math of general relativity is hellishly complex, to the point where only a small number of exact solutions have been found in nearly a century. But I think examining the mathematics, even if it's in a superficial way, could really help the motivated student understand what the theory means, and to understand what it does and doesn't predict. I'm not planning to dive into covariant and contravariant tensor transformations or the expansion of the Christoffel symbols, but I'm trying to provide a sort of nickel tour of the equations. To your right, we see the stress-energy tensor; it's like mass. To your left, we see the Ricci tensor; it's a contraction of one of the vector fields of the Riemann with its dual, leaving the fully traceless Weyl tensor to describe gravitational radiation and yeah, I think you see my point. It's challenging.

But the math is so pretty. Really, it's like a jigsaw puzzle, and every piece has a really clear physical interpretation. This piece describes how the volume of a sphere in curved spacetime differs from the volume of a sphere in flat spacetime; it's a direct representation of the shape of spacetime in a gravitational field. This piece represents the plain, old, warm-and-friendly Pythagorean theorem; it's really no more complicated than that! This slot here is where you put the energy of the vacuum in order to model a vacuum-dominant expanding universe. The math is gorgeous, and I want to find a way to share that with kids without boring them or scaring them off.

Anyway, the Mercury thing really deserves its own section under tests of general relativity, I think. It's such an important prediction from the points of view of astronomy, theoretical physics and the modern history of science. I'll turn my attention to it after I finish the quantitative section, unless somebody wants to dive into it.

Thanks for the feedback, you guys! Enjoy your Friday night. --KSorenson 19:25, 13 November 2009 (EST)

The templates are math-e, math-m, math-h, and math-a, for elementary, middle-school, high-school, and advanced. But the detailed content suggests some overlap. (By the way, I made them, based on earlier work by, I think, DanielB.) If anything deserves a "math-a", it's this! Math-a was intended for discussion of things like topology, the axiom of choice, the Riemann hypothesis, etc. That is, stuff really at the outer edges of CP's mission.

I know a fair amount about this subject, and about presenting it in a palatable way. I will look at the page over the weekend. There are many other things on my plate, but this has just gone to the top of the list. I'll deal with the Peano postulates later.

Kate: I will send you the paper on tensor calculus that we discussed.

PatrickD 20:31, 13 November 2009 (EST)