Talk:General relativity/Archive 2

message: The best way so far as I know to grasp the connection is to understand that a GR spacetime consists of a patching-together of a continuum of inifintesimal local Lorentzian (SR) pieces.  Think of a soccer ball with those little pentagons.  Make them smaller and smaller, and as they are so small that they approach flatness, extend each patch as a small section of an infinite plane.  When you apply the Equivalence Principle all you are doing is saying that, in principle, if you could live in that (tangent) plane, you would be in Minkowski (SR) spacetime and everything would be as usual in SR. (Be careful on notation - "tangent space" is a mathematical construct that includes, as I understand it, lots of other vectors besided displacements and velocities - I think it has E&M vectors in it, too.)  Of course, all these vectors can be imagined to lie in that extended plane I just described, too.
How is this conceptualization applied to some poor chap standing in Dallas, TX and feeling the force of gravity pulling him downwards?  Well, this discussion is all in four dimensions, and those little soccer ball patches all exist in a sequence of spacetime sections falling, in free fall, past this person. The patches have an inclination of their time axes to his that can be zero, if we make them by dropping them just like a lead sinker that he drops from rest, because if at rest when they meet him, the time axes are (instantaneously) aligned.  If you want to extend these little patches above his head, I think you have to use ones with the time axes slanted, as if he threw up a sinker (or a clock) and then it passed by him again on the way down.  But the point is that he is accelerated in regards to any of these coordinate patches that slip past him, and that is why he feels gravity.
If you could extend the little patches to mate smoothly over a region larger than first order in the differentials, you would have found a local Minkowski space - hard to do in GR. It would exist inside a massive spherical shell, but not in very many other places I can think of, if matter is present.  OK, nested shells, hollow at the center, that works.  The patches can be just bent into a curved surface, or they can be more like vanes on a windmill, not mating smoothly.  That is what happens in rotating systems; the patches that represent, for example, small regions on the Earth's surface are set up like vanes on a centrifugal fan.  see: "Cylindrical Cardboard Model for a Rotating System in Special Relativity," Amer. J. Phys., 47, pp. 218‑223 . That's for special relativity, not GR, but it carries over to GR for rotating systems.
Pdn 16:19, 23 Apr 2005 (UTC)
thread_title: GR SR connection

message: Easier to move the history chunk to the article The development of general relativity (which I've done) and make modifications to that article (and the GR article) as appropriate. Mpatel 15:46, 30 May 2005 (UTC)
replies: text: You didn't do the second half of that job, namely cutting the fat out of the GR article's history section.  I have now done that.  The new article also could use some elaboration and expansion, but that job I will leave mostly to others. --EMS | Talk 00:05, 31 May 2005 (UTC)
thread_title:  History of GR 

message: Hi, EMS and MP, thanks for the kind words.  I am very glad to see you are both doing your bit (or more) to upgrade the gr articles here!  I already have compiled a long list of articles I want to (re)-write here on gr topics.  While, I haven't yet found the energy/time/courage to start in on the gr article itself,  I -did- rewrite the article on Brans/Dicke theory! :-/
Looks like we all agree that ideally the main gr article should feature the briefest possible summaries of various broad topics, including
* the dramatic players (gravitation, matter) and the stage (spacetime) as a player,
* Einstein's motivation, desiderata, and heroic search for GR,
* role of diffeomorphism covariance,
* equivalence principle,
* Newtonian limit,
* geometric/physical meaning of the EFE, nonlinearity,
* global versus local distinction,
* conformal/causal structure, horizons,
* role of boundary conditions, smoothness,
* role of approximations (linearization/weak-field, far-field, slow motion),
* gravitational radiation,
* reformulations of GTR (ADM, Regge),
* relationship to other gravitation theories, PPN parameters,
* tests of GTR (past, present, future).
At the end of each brief summary, a link could point interested readers to a longer article devoted to this particular aspect, which can be written from scratch, perhaps using the best of what is already present in various Wikipedia articles.  Right now, the only one of these topics which appeals to me is the meaning of the EFE.  
As things stand, I think that even the list of references which I entered is fairly unwieldy.  Is there any wikiprecedent for putting a list of printed refrences in a separate page?  Maybe only the two on-line tutorial articles should be in the gr article itself--- maybe a very brief reference section could include these two and then link to a longer page containing all the other references? 
FWIW, some much easier projects I'd like to carry out include:
* add suitable references to all the longer articles, and put any existing references into a uniform (wikitemplated) format,
* improve various of the less unwieldy articles,
* add suitable figures (e.g. to the Regge calculus and Penrose diagram articles).
In the near future, I'd like to rewrite the weak-field theory article, add an article on multipole moments, add more pp-wave related articles, add an article on the Neugebauer/Meinel disk solution, and write articles on the Weyl and Ernst families of vacuum solutions.  We'll see.
--Chris Hillman
: Chris -
: First of all, thanks for the outline.  This is something that people can and may well work towards.  I myself a few months ago mentioned a set of principles that the article of the time did not address.  Now they are addressed, mostly due to the work of others.  If you feel comfortable with addressing the physical meaning of the EFE, then go ahead and write it up.  Just be aware that the EFE has its own article, and that much the same (but in more detail) should also be there.
: As for moving the full list of references to another page:  I know of no precedent, but an article on the available printed and web resources on GR is not inappropriate.  Normally there is not such a wealth of resources available on a topic such that a special page is needed.  I don't know that I would remove all references from the GR page itself.  Instead I would keep 4-6 (including the web tutorials) and then have a prominent link ("For addition references ... " perhaps) to the full bibliography/references page.
: Beyond that I repeat my prior advice:  Choose your battles.  There is so much that can and needs to be done, including fixing up many of the existing articles.  As you already see, Wikipedia is living growing resource that over time is constantly improving due to the efforts of its contributors.  That does not mean that you are not needed.  In fact part of what is happenning is that as Wikipedia improves so does the quality of the contributors.  So hopefully in a few more years the GR part of Wikipedia will be high quality text guarded and maintained by some of the better people in the field.  For now we are a band of mostly dedicated amateurs with a few professionals in the mix, but your presense is a sign that the mix is changing.
: --EMS | Talk 15:42, 8 Jun 2005 (UTC)
thread_title:  Resolved 

message: What is this supposed to mean? Why is it important to non-logged-in editor 81.218.238.113 to have this particular language? This editor keeps reverting to this with no explanation. WCFrancis 17:09, 10 Jun 2005 (UTC)
thread_title: Geometric physical theory