Tag Archives: Relativistic gravitational field equation

General relativity at last

I’ve finally arrived at the relativistic gravitational field equation which includes mass, doing ALL the math and understanding the huge amount of mathematical work it took to get there:  Chistoffel symbols (first and second kind), tensors, Fermi coordinates, the Minkowski metric, the Riemann curvature tensor (https://luysii.wordpress.com/2020/02/03/the-reimann-curvature-tensor/) geodesics, matrices, transformation laws, divergence of tensors, the list goes on.  It’s all covered in a tidy 379 pages of a wonderful book I used — “The Geometry of Spacetime” by James J. Callahan, professor emeritus of mathematics at Smith college.  Even better I got to ask him questions by eMail when I got stuck, and a few times we drank beer and listened to Irish music at a dive bar north of Amherst.

Why relativity? The following was written 8 years ago.  Relativity is something I’ve always wanted to understand at a deeper level than the popularizations of it (reading the sacred texts in the original so to speak).  I may have enough background in math, to understand how to study it.  Topology is something I started looking at years ago as a chief neurology resident, to get my mind off the ghastly cases I was seeing.

I’d forgotten about it, but a fellow ancient alum, mentioned our college president’s speech to us on opening day some 55 years ago.  All the high school guys were nervously looking at our neighbors and wondering if we really belonged there.  The prez told us that if they accepted us that they were sure we could do the work, and that although there were a few geniuses in the entering class, there were many more people in the class who thought they were.

Which brings me to our class relativist (Jim Hartle).  I knew a lot of the physics majors as an undergrad, but not this guy.  The index of the new book on Hawking by Ferguson has multiple entries about his work with Hawking (which is ongoing).  Another physicist (now a semi-famous historian) felt validated when the guy asked him for help with a problem.  He never tooted his own horn, and seemed quite modest at the 50th reunion.  As far as I know, one physics self-proclaimed genius (and class valedictorian) has done little work of any significance.  Maybe at the end of the year I’ll be able to read the relativist’s textbook on the subject.  Who knows?  It’s certainly a personal reason for studying relativity.  Maybe at the end of the year I’ll be able to ask him a sensible question.

Well that took 6 years or so.

Well as the years passed, Hartle was close enough to Hawking that he was chosen to speak at Hawking’s funeral.

We really don’t know why we like things and I’ve always like math.  As I went on in medicine, I liked math more and more because it could be completely understood (unlike medicine) –Why is the appendix on the right and the spleen on the left — dunno but you’d best remember it.

Coming to medicine from organic chemistry, the contrast was striking.  Experiments just refined our understanding, and one can look at organic synthesis as proving a theorem with the target compound as statement and the synthesis as proof.

Even now, wrestling with the final few pages of Callahan today took my mind off the Wuhan flu and my kids in Hong Kong just as topology took my mind off various neurologic disasters 50 years ago.

What’s next?  Well I’m just beginning to study the implications of the relativistic field equation, so it’s time to read other books about black holes, and gravity.  I’ve browsed in a few — Zee, Wheeler in particular are written in an extremely nonstuffy manner, unlike medical and molecular biological writing today (except the blogs). Hopefully the flu will blow over, and Jim and I will be at our 60th Princeton reunion at the end of May.  I better get started on his book “Gravity”

One point not clear presently.  If mass bends space which tells mass how to move, when mass moves it bends space — so it’s chicken and the egg.  Are the equations even soluble.