From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3132 Path: news.gmane.org!not-for-mail From: jim stasheff Newsgroups: gmane.science.mathematics.categories Subject: Re: cracks and pots Date: Fri, 17 Mar 2006 09:25:09 -0500 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019112 7373 80.91.229.2 (29 Apr 2009 15:31:52 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:31:52 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Mar 17 23:20:11 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 17 Mar 2006 23:20:11 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FKRvu-0003bf-43 for categories-list@mta.ca; Fri, 17 Mar 2006 23:16:50 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 78 Original-Lines: 74 Xref: news.gmane.org gmane.science.mathematics.categories:3132 Archived-At: Robert J. MacG. Dawson wrote: And, as you know, there are still scales, almost a century later, on which its predictions are unsatisfactory. For us ignorant of these, please explicate. thanks jim > Eduardo Dubuc wrote: >> Well Robert, >> >> 1) >> >> >>> Well, Einstein was not "trying to"; he was using it, and presented this >>> use as an accomplished fact. > > ... > >> General relativity was born with differential geometry; it has no meaning >> without differential geometry. String theory was already there when a >> category theory approach began. > > Sorry, Eduardo! That's a little oversimplified. See, for instance, > section 17.7 of Misner, Thorne, and Wheeler's "Gravitation", among other > references. > > General relativity (though of course not in its modern form) goes back > to Einstein's formulation of the equivalence principle in 1907 (only two > years after special relativity), and the prediction of the gravitational > red shift. In 1911 Einstein also predicted the bending of light by > massive bodies; this too is intrinsically part of GR. > > But it was only in 1912 that he realized that Euclidean geometry awas > not compatible with this, and (encouraged by Grossmann and Levi-Civita) > started looking at differential geometry as a way to handle > non-Euclidean spacetime. Einstein and Grossmann's 1913 attempt at a > general relativity theory was wrong; it did not transform correctly. > Some time after this, Planck specifically warned him that the > differential geometry approach would not work and would not be believed > if it did. > > In November 1915 Einstein submitted two papers. The first of these > explained some observations such as the precession of the perihelion of > Mercury, but in other ways made wildly nonphysical predictions > (essentially ignoring many of the effects of mass -though this > "linearized theory" does have some uses as an approximation) He > corrected this soon with a second paper in which he finally got it > right. Sort of. > > In 1917 Einstein introduced a cosmological constant into his field > equations to account for the "fact" that the universe wasn't expanding. > In the 1920's he took it out again when it turned out that the universe > *was* expanding. Now astronomers think there ought to be one, but with > a value very different from what Einstein originally put forward. > > So GR got by without differential geometry for five years; and it was > another decade or so before it was a mature theory with enough of the > bugs out to do what was expected of it. And, as you know, there are > still scales, almost a century later, on which its predictions are > unsatisfactory. > > -Robert > > > >