Talk:Introduction to general relativity/Archive 04

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[edit] Style suggestions and main concepts

Unresolved.

I like Awadewit's suggestion that we clarify for ourselves what points we're trying to get across to our readers, and maybe decide on what liberties we'll allow ourselves in writing. At the same time, we shouldn't get bogged down in process; we should stay focused on improving the article. Here are two lists that anyone is free to ignore, use or add to.

[edit] Style suggestions

  • We should try to avoid unfamiliar technical terms and concepts. Instead, we should prefer familiar, everyday ones or at least ones that are easily visualized or commonly found in the popular press, such as black hole and Big Bang.
  • Ideally, each section would be linked conceptually to the one following it, so that the reader has the sense of flow and building on their earlier work.
  • We should not ask the reader to absorb too much in any one sentence. Brevity can be sacrificed in favor of clarity and a slower pacing.
  • Our watchword should be : as long as necessary; as short as possible. It's easy to get carried away adding more and more details; let's leave out what we can leave out without distorting our account of general relativity. -- Markus Poessel 07:23, 19 July 2007 (UTC)
  • Vague formulations should be avoided in favor of concrete, easily visualizable ones, even if some generality known to experts is lost.

[edit] Main concepts

Organized along the lines of the present article:

  • 1. Why Newton's theory of gravity is inconsistent with special relativity; search for a relativistic theory of gravity
  • You have focused on Einstein in articulating this concept ("Einstein felt"); I think Einstein is less important the move from special to general - do you want to reader to understand Einstein's motivations or the connection between the two theories? Awadewit | talk 07:35, 19 July 2007 (UTC)
  • Your insights are great! I'd like to convey the idea that the Newton's theory of gravity needed to be fixed, because it was inconsistent with the theory of special relativity. Several people tried to fix it in the early 20th century, but only Einstein arrived at a theory that has stood the test of time.
  • 2. Equivalence principle (EP) and its predictions (1907)
  • 3. Why the EP doesn't suffice, why Einstein made the transition to geometry (1913)
Perhaps "why geometry is necessary to GR"? Awadewit | talk 16:21, 20 July 2007 (UTC)
    • Key idea? Because of the gravitational dependence of time (EP), special relativity fails on finite scales. SR describes space-time geometry; need to extend that geometry to account for finite scales. This corresponds (sort of) to the present "tidal effects" section.
      • Agree with the "Why the EP doesn't...", but have trouble understanding what your explanatory paragraph means. Anyway, that is what the current tidal effects section is meant to convey. --Markus Poessel 07:29, 19 July 2007 (UTC)
    • Sorry, I'm still struggling to understand it myself. I think it's an important transition to convey to our readers because they'll naturally want to know, "why did Einstein feel it necessary to bring in all this curved space-time stuff?" My impression was that Einstein realized that SR could hold for infinitesimal displacements in space time (or, rather, that a local inertial frame could be defined in which)
c2dτ2 = c2dt2 − dx2 − dy2 − dz2
but not for finite displacements (no global inertial frame could be defined)
c^{2} \Delta \tau^{2} \neq c^{2} \Delta t^{2} - \Delta x^{2} - \Delta y^{2} - \Delta z^{2}
because he saw time should flow at different rates at different gravitational potentials. But my impression could be very wrong, indeed. :( Willow 18:28, 19 July 2007 (UTC)
Time flowing at different rates is already true in a homogeneous gravitational field; there, the transition to a freely falling frame will still get you sr (even with finite differences). The problems start with varying gravity (tidal effects, as described in the article), when a freely falling frame will only give you sr in an infinitesimal region. --Markus Poessel 06:23, 20 July 2007 (UTC)
It all came into focus with your pithy explanation; thank you so much! :D I think I was trying to understand it differently, sort of: "SR predicts that two reference frames at rest with respect to one another should see the same phenomena in the same way. But that's not true for two reference frames at rest at different heights in a homogeneous gravitational field; their clocks tick differently. Ergo, SR doesn't hold globally." But your way of getting to the idea "SR holds only locally" is much better. :) Willow 17:58, 25 July 2007 (UTC)
  • 4. Space-time is a player in its own right, and can convey waves independently of matter
  • 5. Understanding curvature of space-time
  • 6. Matter curves space-time, space-time affects material motion (Wheeler quote); field equations and their solutions (1915)
  • I would list the field equations separately. Some people simply won't understand the equation. Awadewit | talk 07:35, 19 July 2007 (UTC)
  • Written out, the field equations get a little repetitive
  • G_{00}=\frac{8\pi G}{c^4} T_{00},
  • G_{01}=\frac{8\pi G}{c^4} T_{01},
  • G_{02}=\frac{8\pi G}{c^4} T_{02},
  • G_{03}=\frac{8\pi G}{c^4} T_{03},
  • G_{11}=\frac{8\pi G}{c^4} T_{11},
  • G_{12}=\frac{8\pi G}{c^4} T_{12},
  • G_{13}=\frac{8\pi G}{c^4} T_{13},
  • G_{22}=\frac{8\pi G}{c^4} T_{22},
  • G_{23}=\frac{8\pi G}{c^4} T_{23},
  • G_{33}=\frac{8\pi G}{c^4} T_{33},
It's good to help people understand that multiple equations can be packed into one, but we should then probably explain how T00 differs from T01, etc. But that might take us into deeper waters. Willow 19:22, 19 July 2007 (UTC)
  • The imprecision of language! I did not mean "the equations should all be spelled out on the page in mathematical terms", I meant that "matter curves spacetime, spacetime affects material motion" should be listed as a separate concept from "field equations and their solutions" here on this page and that the two should have separate sections in the article, since many readers will simply skip anything with equations. Awadewit | talk 16:21, 20 July 2007 (UTC)
blush Sorry about that; I was just a little dim. I totally agree with you on the separation! Willow 17:58, 25 July 2007 (UTC)
Personally, I wonder if the field equations need to be brought up at all here. In an introduction inteded for a more-or-less general audience, they are little more that a bunch of fancy gobbledygook. For the main general relativity article (which I edit) they are obviously essential, but you are under no constraint to cover the same material as the main article does. --EMS | Talk 00:48, 10 August 2007 (UTC)
  • 7. Careful experimental tests have been done to discern GR from Newton's theory and some other relativistic theories; GR has passed them all (so far) but its competitors have failed
  • More of a focus on GR's completeness than on the scientific process, perhaps? I realize you are trying to get at the scientific method here, but the method is another concept! Awadewit | talk 07:35, 19 July 2007 (UTC)
  • Good point; here's a rewording. Does it read better? Willow 19:24, 19 July 2007 (UTC)
  • OR "GR is the only theory of gravity to have passed rigorous experimental tests." Awadewit | talk 16:21, 20 July 2007 (UTC)
  • I think Markus' version is more accurate, "GR is the simplest theory of gravity to have passed rigorous experimental tests."
  • What is their relationship to GR specifically? Awadewit | talk 07:35, 19 July 2007 (UTC)
  • There's a plausible solution of Einstein's equations that predicts that an object of sufficient density has a special radius; any light ray or matter passing within this radius, even tangentially, is not allowed to continue, but is sucked inexorably inwards, towards the center. Therefore, such objects appear as perfectly black spheres. In the Newtonian model, there is no such radius; indeed, a light ray or matter cannot strike the center unless it is aimed exactly at it. Also, mention other astrophysics: Other types of stars are not as dense as black holes (such as neutron stars) but general relativity can have significant effects there as well.
  • "GR helps to explain black holes while Newtonian gravity does not." Awadewit | talk 16:21, 20 July 2007 (UTC)
  • This point might be a little finicky. How about, "GR predicts that black holes can exist and describes their properties in detail. Objects passing within a certain distance of such black holes are sucked inexorably inwards, regardless of their initial velocity. Astrophysical calculations suggest that any star having more than roughly three times the mass of the Sun is likely to collapse into a black hole once its fuel runs out, which seems consistent with observations. A black-hole-like object is also possible in the Newtonian theory, if it is assumed that Newtonian gravity affects light. However, the properties of such Newtonian black holes differ from those predicted by GR; for example, an object can always escape the pull of a Newtonian black hole, if it moves with sufficiently high speed." Willow 17:58, 25 July 2007 (UTC)
  • 9. Combined with the assumptions of isotropy and homogeneity of the universe on large length scales (1010 light years), GR yields predictions for physical cosmology that have been verified.
  • Second part of sentence only, perhaps? Awadewit | talk 07:35, 19 July 2007 (UTC)
  • I wanted to convey the idea that, by itself, GR is not enough to describe cosmology. It requires some kind of additional assumptions, such as isotropy and homogeneity. These assumptions seem to be justified from experimental data, however. Willow 19:03, 19 July 2007 (UTC)
  • Yes, but this is supposed to be a list of the most important or fundamental concepts you want the reader to learn. I would say that with regards to cosmology, you have to pick one idea. (Remember the reader has just learned what GR is and now they are trying to understand its application to numerous topics!) Awadewit | talk 16:21, 20 July 2007 (UTC)
  • OK, that makes sense. :) Willow 17:58, 25 July 2007 (UTC)
  • 10. Outstanding questions being addressed in modern research
  • That is three things! :) Awadewit | talk 07:35, 19 July 2007 (UTC)
  • Better wording now? Willow 19:22, 19 July 2007 (UTC)

Perhaps these are too many concepts to hope to convey in an introductory article, but it'd be great if we could. Alternatively, some of them can be stricken. Willow 21:36, 18 July 2007 (UTC)

  • I've tried to focus them more with my questions. I don't know if that will help anyone. Awadewit | talk 07:35, 19 July 2007 (UTC)