Tag Archives: Stephen Hawking

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.

Relativity becomes less comprehensible

“To get Hawking radiation we have to give up on the idea that spacetime always had 3 space dimensions and one time dimension to get a quantum theory of the big bang.”  I’ve been studying relativity for some years now in the hopes of saying something intelligent to the author (Jim Hartle), if we’re both lucky enough to make it to our 60th college reunion in 2 years.  Hartle majored in physics under John Wheeler who essentially revived relativity from obscurity during the years when quantum mechanics was all the rage. Jim worked with Hawking for years, spoke at his funeral and wrote this in an appreciation of Hawking’s work [ Proc.Natl. Acad. Sci. vol. 115 pp. 5309 – 5310 ’18 ].

I find the above incomprehensible.  Could anyone out there enlighten me?  Just write a comment.  I’m not going to bother Hartle

Addendum 25 May

From a retired math professor friend —

I’ve never studied this stuff, but here is one way to get more actual dimensions without increasing the number of apparent dimensions:
Start with a 1-dimensional line, R^1 and now consider a 2-dimensional cylinder S^1 x R^1.  (S^1 is the circle, of course.)  If the radius of the circle is small, then the cylinder looks like a narrow tube.  Make the radius even smaller–lsay, ess than the radius of an atomic nucleus.  Then the actual 2-dimensional cylinder appears to be a 1-dimensional line.
The next step is to rethink S^1 as a line interval with ends identified (but not actually glued together.  Then S^1 x R^1 looks like a long ribbon with its two edges identified.  If the width of the ribbon–the length of the line interval–is less, say, than the radius of an atom, the actual 2-dimensional “ribbon with edges identified” appears to be just a 1-dimensional line.
Okay, now we can carry all these notions to R^2.  Take S^1 X R^2, and treat S^1 as a line interval with ends identified.  Then S^1 x R^2 looks like a (3-dimensional) stack of planes with the top plane identified, point by point, with the bottom plane.  (This is the analog of the ribbon.)  If the length of the line interval is less, say, than the radius of an atom, then the actual 3-dimensional s! x R^2 appears to be a 2-dimensional plane.
That’s it.  In general, the actual n+1-dimensional S^1 x R^n appears to be just n-space R^n when the radius of S^1 is sufficiently small.
All this can be done with a sphere S^2, S^3, … of any dimension, so that the actual k+n-dimensional manifold S^k x R^n appears to be just the n-space R^n when the radius of S^k is sufficiently small.  Moreover, if M^k is any compact manifold whose physical size is sufficiently small, then the actual k+n-dimensional manifold M^k x R^n appears to be just the n-plane R^n.
That’s one way to get “hidden” dimensions, I think. “

Stephen Hawking R. I. P.

Stephen Hawking, brilliant mathematician and physicist has died.  Forget all that. He did something for my patients with motor neuron disease that I, as a neurologist, could not do.  He gave them hope.

What has chemistry done for them?  Quite a bit, but there’s so much left.

Chemistry, when successful, just becomes part of the wallpaper and ignored. All genome sequencing depends on what some chemist did.

For one spectacular example of what, without chemistry, would be impossible is Infantile Spinal Muscular Atrophy (Werdnig Hoffmann disease).  For the actual molecular biology behind it — please see — https://luysii.wordpress.com/2016/12/25/tidings-of-great-joy/.   Knowing the cause has led to not one but two specific therapies — an antisense oligonucleotide and a virus which infects neurons and actually changes the gene.

So knowing what the cause of a disease is should lead to a treatment, shouldn’t it?  Hold that thought.  Sometimes one form of motor neuron disease (amyotrophic lateral sclerosis or ALS) can be hereditary.  Find out what is being inherited to find how ALS is caused.

Well, the first protein in which a mutation is associated with familial ALS (FALS) was found exactly 25 years ago.  It is called superoxide dismutase (SOD1).  Over 150 mutations have been found in the protein associated with FALS, and yet despite literally thousands of papers on the subject we don’t know if the mutations cause a loss of function, a gain of function (and if so what that function is), an increased tendency to fold incorrectly, and on and on and on.  It’s a fascinating puzzle for the protein chemist and over the years my notes on the papers I’ve read about SOD1 have ballooned to some 25,000 words.

If you’re tired of working on SOD1, try a few of the other proteins in which mutations have been associated with FALS — Alsin, TAF15, Ubiquilin, Optineurin, TBK1 etc. etc.  The list is long.

Now it’s biology’s turn.  Motor neurons go from the spinal cord (mostly) and brain to produce muscle contraction.  Why should only this tiny (but crucial) minority of cells be affected.  The nerve fibers leave the spinal cord and travel to muscle in nerves which contain sensory nerve fibers making the same long trip, yet somehow these nerves are spared.

More than that, why should these mutations affect only these neurons, and that often after decades.  Also why should great athletes (Lou Gehrig, Ezzard Charles, etc. etc. ) get the disease.

One closing point.  Hawking shows why, in any disease median survival (when 50% of those afflicted die) is much a more meaningful statistic than average duration of survival.  Although he gave my patients great hope, they all died within a few years even as he mightily extended average survival.