Phys 325: General Relativity

"... until at last it came to me that time was suspect!" - A. Einstein (Shankland interview 1950)

"... the concept of time is nothing more than a convenient, although potentially treacherous, device for summarizing compactly all the relationships holding between clocks." - N. D. Mermin It's About Time

"...the Einsteinian view [of space-time] is the most comprehensive, the most profound, and the most accurate."- R. Penrose, Adam's Prize Essay 1965.

"Grossmann is getting his doctorate on a topic that is connected with fiddling around and non-Euclidean geometry. I don't know exactly what it is."
- A. Einstein to Mileva Maric, 1902

"We should take comfort in two conjoined features of nature: first, that our world is incredibly strange and therefore supremely fascinating. . . second, that however bizarre and arcane our world might be, nature remains comprehensible to the human mind." - Stephen Jay Gould

Links:

SR: A translation of "Electrodynamics of Moving Bodies", Einstein's original 1905 paper on special relativity. Here's a pdf of the original article in German pubished in Annalen der Physik.

SR: The first principle of relativity is Galileo's. Here's the quote from Galileo on the ship's cabin in the Dialog.

MATH: A handy listing of hyperbolic trig function identities.

GR: A piece by Dennis Overbye on the second image of M87 by the Event Horizon Telescope. The newly released image is on the top right of the page.

SR: Beautiful animations of the apparent geometry of relativistically moving objects. The dice and the ride down Marktgasse in Tuebingen are particularly good. Note, however, that red/blueshift is not accounted for.

GR: A short popular science piece on the equivalence principle.

GR: A demonstration of the parallel transport on a sphere (uses Mathematica).

GR: A link to the paper (pdf) by Baez and Bunn on the meaning of the Einstein equations. For an older published version see Amer. Jour. Phys. 73 (2005) 644-652.

GR: There are recent results on exploring spacetime with light and black holes. See the piece by Denis Overbye in the NYTimes. The movie of null geodesics is absolutely amazing! The original article (pdf).

GR: About the stunning visualizations of black holes in Interstellar.

GR: Wee, light cones! Lillie found this link to some visualizations, including of the warp drive light cone structure.

GR: Tensor computation! The pdf of the mathematica introduction.

GR: k=0 Roberston-Walker in native mathematica, html, and text forms.

GR: Here's the html version of the "einstein.nb" Mathematica notebook.

There is the python implementation of tensor calculations as well.

GR: The GW discovery paper on GW 150914 from LIGO and a simulation of the event. The video I showing a simulation of the event GW190412 observed a year ago, but just annouced during the virtual APS April meeting.

GR: A piece by Cliff Will on the Gravity Probe B experiment.

GR: Notes (8.5 MB) on cosmology used in our last class.

GR: A text version of mathematica curvature notebook.

Additional Reading:

Jim Hartle, Gravity: An Introduction to Einsetin's General Relativity

Dan Styer, Relativity for the Questioning Mind

Elis and Williams, Flat and Curved Spacetimes

Kip Thorne, The Science of Interstellar

Kip Thorne, Black Holes, Warp Drives, and Einstein's Outrageous Leagacy

Dennis Overbye, Einstein in Love (A wonderful ``1st half" biography of Einstein. It ends in 1919.)

Abraham Pais, Subtile is the Lord (A full biography of Einstein with a careful treatment of the science.)

(For fun) Paul Krugman's The Theory of Intersellar Trade written many years ago.

Last modified 22 May 2024

General Relativity

News:

Course Info:

Problem Sets (pdf):

Links:

Additional Reading: