

Einstein for Everyone - Paananen
http://www.pitt.edu/~jdnorton/teaching/HPS_0410/

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orbifold
I briefly looked into the section on general relativity and did not find the
explanation particularly enlightening. A proper entirely geometrical
description of curvature can be found in Mathematical Methods of Classical
Mechanics (p. 301 ff.) by Arnold, although it is probably not accessible to a
lay person. Penrose's "The Road to Reality" should be more accessible and
seems to be of higher quality than the web site linked.

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nilkn
Somewhat on-topic, does anybody know of some decent and _accurate_ pictures of
what spacetime curvature actually looks like? No simplifications (other than
suppressing dimensions), no analogies -- the real deal.

Let me describe more accurately what I'm interested in. At least one spatial
dimension must be suppressed, maybe two. We're all familiar with the
"trampoline" picture of general relativity, but I don't think this is accurate
at all regarding the sort of curvature that actually occurs in general
relativity. In particular, it's spacetime, not space, which is curved, and the
trampoline picture almost invariably leaves that out.

Suppose space is one-dimensional. There's a great point-mass located somewhere
on this line. In space-time, this line sweeps out a plane and the point-mass
sweeps out a worldline trajectory along that plane. Now this plane must be
curved according to general relativity. This curvature is something that
should be fully visualizable by a human. What would it look like?

What if there were two great point-masses? Three? N, all equally spaced?

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quarterwave
Feynman-II has a nice chapter describing the idea of curved spaces:
[http://www.feynmanlectures.caltech.edu/II_42.html](http://www.feynmanlectures.caltech.edu/II_42.html)

The chapters on electromagnetism and special relativity are outstanding:
starting with why the magnetism we observe around a wire carrying current is a
v^2/c^2 effect, and proceeding all the way to how the electric and magnetic
field intensities are both part of an electromagnetic tensor. And then the
field-versus-potential question, leading to a discussion of the Aharanov-Bohm
effect, etc.

The discussion on the classical theories of the electromagnetic self-energy of
an electron is outstanding. It's in Vol.II that we really understand how much
this guy had _thought_ through the stuff, he wasn't just drawing squiggly
lines to calculate some numbers.

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elberto34
The problem is that this oversimplification is wrong. Curvature in general
relativity cannot be expressed merely with a 2-d matrix. It's actually a
hypermatrix a

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leni536
There is a small paragraph about the Riemann-tensor.

