Comments on: Lecture One http://asymptotia.com/2008/01/15/lecture-one/ Sun, 06 Jul 2008 05:43:54 +0000 http://wordpress.org/?v=2.5.1 By: Thane Plambeck http://asymptotia.com/2008/01/15/lecture-one/#comment-105228 Thane Plambeck Sat, 19 Jan 2008 03:51:02 +0000 http://asymptotia.com/2008/01/15/lecture-one/#comment-105228 I liked Bernard F Schutz's A first course in general relativity, from which I was able to learn both special and general relativity with what seemed to be an absolute minimum of fuss. I don't see many people talking about that book, however. I liked Bernard F Schutz’s A first course in general relativity, from which I was able to learn both special and general relativity with what seemed to be an absolute minimum of fuss.

I don’t see many people talking about that book, however.

]]> By: pedant http://asymptotia.com/2008/01/15/lecture-one/#comment-104927 pedant Thu, 17 Jan 2008 13:02:50 +0000 http://asymptotia.com/2008/01/15/lecture-one/#comment-104927 It is the lot of the old to envy the young. I first encountered General Relativity when I came upon a copy of Weyl's 'Space Time Matter', owned and autographed by A.S. Ramsey, and defaced by his son (Frank Plumpton): the blighter injected a 'badly' in front of "translated from the German by Henry L. Bose". But, hey, it was nonetheless a blast, as we used to say. Frank's marginalia could yet inspire a Ph.D, or two (the defaced translation still lies in the library of Magdalene College, Cambridge.) Nonetheless: your route to the essentials of GR does seem to rock. Put the course notes on-line, so that an old fart can read them. It is the lot of the old to envy the young. I first encountered General Relativity when I came upon a copy of Weyl’s ‘Space Time Matter’, owned and autographed by A.S. Ramsey, and defaced by his son (Frank Plumpton): the blighter injected a ‘badly’ in front of “translated from the German by Henry L. Bose”. But, hey, it was nonetheless a blast, as we used to say. Frank’s marginalia could yet inspire a Ph.D, or two (the defaced translation still lies in the library of Magdalene College, Cambridge.) Nonetheless: your route to the essentials of GR does seem to rock. Put the course notes on-line, so that an old fart can read them.

]]> By: Clifford http://asymptotia.com/2008/01/15/lecture-one/#comment-104810 Clifford Wed, 16 Jan 2008 18:08:02 +0000 http://asymptotia.com/2008/01/15/lecture-one/#comment-104810 See the class schedules online. Best, -cvj See the class schedules online.

Best,

-cvj

]]> By: Bilal http://asymptotia.com/2008/01/15/lecture-one/#comment-104809 Bilal Wed, 16 Jan 2008 18:03:41 +0000 http://asymptotia.com/2008/01/15/lecture-one/#comment-104809 Hi Clifford! When and where are you teaching GR? I'd love to sit in on a few lectures. Hi Clifford! When and where are you teaching GR? I’d love to sit in on a few lectures.

]]> By: Francis Caestecker http://asymptotia.com/2008/01/15/lecture-one/#comment-104772 Francis Caestecker Wed, 16 Jan 2008 13:04:17 +0000 http://asymptotia.com/2008/01/15/lecture-one/#comment-104772 Sounds like a great class indeed. In my course, relativity only comes in the third year of bachelor. Elektromagnetism is coming up in my second year. Why is all the great stuff so far off? Sounds like a great class indeed. In my course, relativity only comes in the third year of bachelor. Elektromagnetism is coming up in my second year.

Why is all the great stuff so far off?

]]> By: candace http://asymptotia.com/2008/01/15/lecture-one/#comment-104770 candace Wed, 16 Jan 2008 12:23:38 +0000 http://asymptotia.com/2008/01/15/lecture-one/#comment-104770 Right, I'll be acquiring that book, then, and adding it to the growing stack. Sounds like a lovely class -- wish I could take it! Right, I’ll be acquiring that book, then, and adding it to the growing stack. Sounds like a lovely class — wish I could take it!

]]> By: Clifford http://asymptotia.com/2008/01/15/lecture-one/#comment-104725 Clifford Wed, 16 Jan 2008 06:36:15 +0000 http://asymptotia.com/2008/01/15/lecture-one/#comment-104725 Carl, yes. Have a look at Jim's book. Your applets sound like fun. Will look. Thanks! -cvj Carl, yes. Have a look at Jim’s book. Your applets sound like fun. Will look. Thanks!

-cvj

]]> By: Carl Brannen http://asymptotia.com/2008/01/15/lecture-one/#comment-104719 Carl Brannen Wed, 16 Jan 2008 06:24:35 +0000 http://asymptotia.com/2008/01/15/lecture-one/#comment-104719 Clifford, this is the way it should always be taught. I'm guessing that you introduce the Schwarzschild metric and how to make calculations with it, before you show that the metric satisfies Einstein's equations for a point mass. One normally takes the metric and derives the equations of motion for orbits using an affine parameter so you have 4 differential equations, three for spatial coordinates and one for the time coordinate. An alternative method to calculate the orbits that is painfully obvious and requires less fancy math (and so is very suited for undergraduates) is to write down the elapsed proper time for a path, i.e. integral of (ds/dt) dt, and use the calculus of variations to determine the orbit (since the orbits extremize proper time s). The result is a much more difficult calculation than usual, but it's just basic undergraduate crank turning rather than tensor magic. And instead of ending up with differential equations in the affine parameter, <a href="http://carlbrannen.wordpress.com/2007/12/30/the-painleve-equations-of-motion/" rel="nofollow">you end up with differential equations</a> with the derivatives taken with respect to coordinate time. I did this for Schwarazchild and Painleve coordinates and turned it into a <a href="http://www.gravitysimulation.com/" rel="nofollow">java applet</a> that a professor at MIT intends on using in his class the next time he teaches GR. The applet is set up so that it automatically sequences through a series of gravity demonstrations. But you can stop it and modify the initial conditions and start it up again. My favorite demonstration is the circular orbits near the accretion radius, where they start spiralling into the hole. A demonstration that I don't have is one that shows frame dragging. I think it's possible for the applet to do this. If you or one of your students figures out a set of initial conditions that will do this, take a "print screen" of your display (which will show the initial conditions) and email it to me and I'll add it to the demonstrations. Clifford, this is the way it should always be taught. I’m guessing that you introduce the Schwarzschild metric and how to make calculations with it, before you show that the metric satisfies Einstein’s equations for a point mass.

One normally takes the metric and derives the equations of motion for orbits using an affine parameter so you have 4 differential equations, three for spatial coordinates and one for the time coordinate.

An alternative method to calculate the orbits that is painfully obvious and requires less fancy math (and so is very suited for undergraduates) is to write down the elapsed proper time for a path, i.e. integral of (ds/dt) dt, and use the calculus of variations to determine the orbit (since the orbits extremize proper time s). The result is a much more difficult calculation than usual, but it’s just basic undergraduate crank turning rather than tensor magic. And instead of ending up with differential equations in the affine parameter, you end up with differential equations with the derivatives taken with respect to coordinate time.

I did this for Schwarazchild and Painleve coordinates and turned it into a java applet that a professor at MIT intends on using in his class the next time he teaches GR. The applet is set up so that it automatically sequences through a series of gravity demonstrations. But you can stop it and modify the initial conditions and start it up again. My favorite demonstration is the circular orbits near the accretion radius, where they start spiralling into the hole.

A demonstration that I don’t have is one that shows frame dragging. I think it’s possible for the applet to do this. If you or one of your students figures out a set of initial conditions that will do this, take a “print screen” of your display (which will show the initial conditions) and email it to me and I’ll add it to the demonstrations.

]]> By: Clifford http://asymptotia.com/2008/01/15/lecture-one/#comment-104713 Clifford Wed, 16 Jan 2008 05:29:22 +0000 http://asymptotia.com/2008/01/15/lecture-one/#comment-104713 Hey, fly over and sit in. It will be good to see you - it's been a while! You'll love Jim's book by the way... -cvj Hey, fly over and sit in. It will be good to see you - it’s been a while!

You’ll love Jim’s book by the way…

-cvj

]]> By: Amara http://asymptotia.com/2008/01/15/lecture-one/#comment-104707 Amara Wed, 16 Jan 2008 04:49:50 +0000 http://asymptotia.com/2008/01/15/lecture-one/#comment-104707 You make me want to take your course, Clifford! But I put Hartle's book on my Amazon wish list, instead. ;-) You make me want to take your course, Clifford! But I put Hartle’s book on my Amazon wish list, instead. ;-)

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