Tag Archives: Stephen Hawking

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. “
Advertisements

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.