Talk:Introduction to general relativity/Archive 2

Feedback on new version of article wanted
I have now added all suitable images I could think of, including a lead image, and all statements should now be properly referenced. Regarding the references, I have given preference to texts accessible to the target audience of this article (namely readers who are interested in an introduction, but do not have sufficient background knowledge to read the technical literature). As far as I can tell, the article should now meet all the FA criteria. For anyone who might have this on their watchlist, I'd appreciate any polishing, feedback etc. - my plan is to let the article sit for a few days while polishing it a bit, and then (unless there turns out to be need for major revisions) propose it as an FAC. Markus Poessel 15:48, 13 June 2007 (UTC)

OK, as you can see, the article went through a peer review first (see this page), and a good thing, too - it wasn't quite as ready for FA as I thought back then, and it has improved a lot thanks to a very thorough review by User:Awadewit. Now I'm quite confident it's ready, though, so I'm proposing it as a featured article candidate. Markus Poessel 13:34, 9 July 2007 (UTC)

Merge
See draft page at User:Madcoverboy/Sandbox/General relativity for example of the merged article at General relativity. Madcoverboy 18:09, 16 July 2007 (UTC)


 * Let's have the discussion for both candidates on the talk page of general relativity and not on two talk pages at once. --Markus Poessel 19:23, 16 July 2007 (UTC)

Reliability of the results of Eddington's eclipse experiments
I'm having trouble finding reliable sources on this. They do exist cos I read them (a few years ago)! But they easily get swamped by the crackpot websites holding this up as a bad thing. Do the main books say anything on this? Carcharoth 22:40, 16 July 2007 (UTC)
 * I tell a lie. I found something reasonably objective here. Have a read of the whole page and let me know what you think. Carcharoth 22:44, 16 July 2007 (UTC)
 * Possibly less objective (see the URL title and their main page) is this one. But the previous one I mentioned above is a fascinating look at some of the history. Carcharoth 22:51, 16 July 2007 (UTC)
 * Do you mind if I come back to this later? Too many balls in the air at the moment. --Markus Poessel 06:29, 17 July 2007 (UTC)
 * Not at all, but do read the first source I provided in full. The history of science is a fascinating topic, and too often skipped in science textbooks. Of course, the real home for this is History of general relativity, but the mention of the experiment here should be as accurate as possible. Carcharoth 10:01, 17 July 2007 (UTC)

Or maybe just look at the final paragraph which sums things up as follows:"'Because of the euphoric veneration of Einstein and relativity in November 1919, the objectivity with which science is supposed to act has been compromised, and the search for better theories has been inhibited. Canonization, deification, and claims of personal communication from Nature, should have no place in science. If the findings of the eclipse expeditions had been announced as being inconclusive instead of decisive in 1919, general relativity would have had to compete with other possible theories, such as Gerber's, to explain certain astronomical observations, and a better theory might eventually have been found. In the author's opinion, the confident announcement of the decisive confirmation of Einstein's general theory in November 1919 was not a triumph of science, as it is often portrayed, but one of the most unfortunate events in the history of 20th-century science.' Anomalies in the History of Relativity - Ian McCausland" In essence, the perspective on the history of general relativity is still in flux. The textbooks present the 1919 results as a great success, but the real story is not so clear. The results since 1990, by all accounts, are much clearer. Carcharoth 10:19, 17 July 2007 (UTC)

Technical level
I am rereading the article, at the request of Willow, and I have found to my dismay that it is growing increasingly technical (and getting longer). In the previous incarnation of the article, I did not feel that I had to work as hard to read it. Please consider us lay readers who come to the article knowing very little or nothing. Remember that every time a new term is introduced and used, we have to keep reminding ourselves of what it means when we see it again (if we even bother to do that!). Too many new terms makes an article impenetrable. Also, please remember to explain rather than state conclusions (they may seem obvious to you!). Awadewit | talk  23:41, 16 July 2007 (UTC)
 * Could you give specific examples of what has dismayed you? Personally, I'm still enjoying the plethora of articles on general relativity. It is the first article I have come across that has spun out its "external links/further reading" section, in the form of General relativity resources. Amazing. Carcharoth 00:20, 17 July 2007 (UTC)
 * Ignore that, I've just found your "internal comments", my responses to which range from "good point" to "the article can't explain everything"! :-) I'm educated to science undergraduate level, so maybe my take on this is less relevant than yours. It is difficult to gauge the response of an arts graduate until you force them to read the article. Carcharoth 00:29, 17 July 2007 (UTC)
 * I am planning on going through the rest of the article later today (Willow asked me to). I liked the "resources" section, too. Please note that I am not against the plethora of articles on general relativity - I am very much for them. I just want one to be accessible; something entitled "Introduction to general relativity" seems like the perfect choice. I also thought that the article was surprisingly accessible back when I peer-reviewed it, but I think that in the efforts to add accuracy, that accessibility has been lost a bit. There are no "accurate" explanations of general relativity without math, so I don't think that "accuracy" is really the standard the article should be set to achieve, precisely. Remember how the first atomic model everyone learns in the planetary model and then the shell model (apparently the shell model is wrong, but I never got beyond that). I think that the editors should think in terms of those kinds of heuristics: helpful, but, in the end, not really correct. It is incredibly difficult to place yourself in the shoes of a reader so differently-informed than yourself. I have trouble with that all of the time. That's why it's nice that so many science-y people read the literature articles I edit. They can say, "no one knows what subjectivity means!" :) Awadewit | talk  00:40, 17 July 2007 (UTC)
 * Hi Awadewit, I'm of course dismayed to find that the article has lost in accessibility. I had hoped that I might be able to strike a balance between addressing the detailed suggestions made in FAC and still keeping it accessible (e.g., I thought that Einstein's equation, with the nice way in which the constants parallel the theory's development, might actually be a nice addition).  Please be sure to mention this at the FAC if you haven't already, in response to calls for even further math to be added to the article (may be you have already done so; I'll be heading over there in a minute).  If you have concrete suggestions of how to restore accessibility with the least amount of loss of comment-addressing additions, please tell. --Markus Poessel 06:27, 17 July 2007 (UTC)
 * OK, I admit to being a bit gobsmacked at the moment. As far as I can see, a number of the changes made since yesterday have made parts of the article markedly worse.  I don't know if I have the time to do it all today, but I'll try to repair things by and by, and try to address your internal comments at the same time.  After that, I would be interested in hearing your opinion no the current state of the article once more (if you can stand reading it yet another time. --Markus Poessel 08:07, 17 July 2007 (UTC)
 * I sympathize. How about this time around I summarize what I learned from reading the article for you? This will take me longer but might, in the end, be more useful to you. You can find out what I missed and what I absorbed. Let me know. (I shudder to think what your opinion of me will be, though, after you read it.) Awadewit | talk  11:25, 17 July 2007 (UTC)
 * I think that will be useful information indeed, but if you don't mind, I think we should wait a bit. My hope is that, instead of the current fluid state (in which I feel I am putting out one brush fire while two more spring up elsewhere), I will eventually reach consensus with Willow on the changes made so far, and on some further changes (a general streamlining of the article included) that I think are necessary; then would be a good time for the summarizing experiment.  In the meantime, I would appreciate if you could mediate on issues of accessibility - there are now some very specific cases where I claim one way is more accessible, while Willow favours another; your input would be greatly appreciated. --Markus Poessel 09:06, 18 July 2007 (UTC)
 * Just let me know when the storm has quieted enough. Awadewit | talk  10:21, 18 July 2007 (UTC)

Part 1
(Introduced sections merely for editing convenience; having part 2 doesn't mean we're done with part 1. Markus Poessel 18:29, 17 July 2007 (UTC))

Here are some comments on recent changes to the article (one, I have changed back; the others are, I think, in dire need of change). --Markus Poessel 08:07, 17 July 2007 (UTC)
 * Forgive me, but I think several of the things you mention here and below are "too much, too soon" for the lay-person. I understand that you want to keep everything scrupulously correct, but we also need to show some gentleness with the reader who won't appreciate these subtleties.  Another problem was that I tried to keep as much of your writing as possible, which resulted in unfortunate chimeras.  I'm not at all attached to my changes, and I won't be offended if you change them back; but I do think many of them may help the complete newbie to understand GR. Please try to read your paragraphs with fresh eyes and try to see how some changes might have helped others to get your main points. Willow 12:04, 17 July 2007 (UTC)

Nothing to forgive, although I would like to point out that the things I mention there and below are aimed at you and the other editors. All I wrote was, hopefully, in compliance with the golden "two in one" principle of accessible science texts: write the text in a way that the specialist notices that everything is scrupulously correct, but that the reader who is not aware of the underlying issues does not even notice all that's behind the chosen formulation - but that reader should notice that the text is accessible! I don't propose stubborn "changing back, thank you very much", but I do think we can find a consensus that is better than both the versions that went into it. --Markus Poessel 14:21, 17 July 2007 (UTC)


 * Great! :) That's exactly how I feel. As Big Bird says, "Let's co-oporate...umm...coopidate...umm...work together to make the article better!" :) I'm going to set to work trying to address Awadewit's wonderful and painfully justified suggestions. ;) I'm not sure how many hours I'll have to give today — I'm teaching a knitting class in a few hours — but I'll do my best in the time we have. :) Willow 14:29, 17 July 2007 (UTC)


 * "In contrast with Newton's law of universal gravitation, general relativity posits that gravitation is not a force between two objects in the usual sense; rather, it results from the two objects warping the geometry of space and time around them." - One key point is that, in Einstein's theory, gravity is more than just attraction between bodies.  There can be gravitational waves, for instance, independent of a body.  Newtonian gravity is only a subset of Einsteinian gravity; in the original formulation, while not explicitly making that point yet, I tried to lay the groundwork for not focusing the description too narrowly ("rather, it is closely linked to the geometry of space and time").  I think that subtlety has gotten lost now.
 * It's a subset? I totally missed that. :) Awadewit | talk  10:25, 17 July 2007 (UTC)
 * I didn't like "closely linked" since it conveys almost no information. I used the word "gravitation" to mean "gravitational phenomena", which for the lay-person means "two masses attract one another".  Perhaps a better wording might be

In contrast with Newton's law of universal gravitation, general relativity posits that the apparent gravitational attraction between masses does not result from a force, but rather from those masses warping the geometry of space and time around them.


 * We can tinker with it a bit longer if you don't like this version. Willow 12:04, 17 July 2007 (UTC)


 * I'd like to include at least some indication that Einstein's gravity is more than just Newton's attraction. After all, this is our initial one-sentence summary of the theory, and the current reformulation makes it encompass only the un-innovative parts of gr. Also, I'm not sure whether the attraction is "apparent" (except in the sense of "obviously true"). How about

According to Newton's theory of gravity, masses attract each other via a gravitational force. General relativity posits that, instead, they warp the geometry of space and time around them; one of the resulting effects is gravitational attraction.
 * --Markus Poessel 08:59, 18 July 2007 (UTC)
 * --changed that another bit. Markus Poessel 09:02, 18 July 2007 (UTC)


 * Dare I suggest a rewording? I'm sure this is wrong, but what I want to emphasize with my rewording is that "general relativity" should be placed in the strongest position in the definition (the beginning). Starting with a contrast is more difficult for the reader, I think. Try to state what general relativity is and then compare it. (I detest my syntax and wordiness in the suggestion below, but you get the idea.)

General relativity posits (proves?) that masses warp the geometry of space and time, thereby creating a gravitational attraction; this theory corrected Newton's law of universal gravitation, which states that masses attract each other via a gravitational force only.
 * -- Awadewit | talk  09:10, 18 July 2007 (UTC)


 * "It also makes several new predictions that have been confirmed experimentally, such as the bending of light by gravity, the slowing of time by gravitation and the expansion of the universe." - the latter is more of a postdiction, isn't it? Quite generally, I think the current paragraph about predictions is a bit clunky.
 * Clunky it may be, and we should work to help its flow. Strictly speaking, the theory predicts the expansion, even if Einstein didn't accept it.  To be more general, we could say "the possibility of an expanding universe". Willow 12:04, 17 July 2007 (UTC)


 * "anomalous rotation of the planet Mercury"? Ouch.
 * (sheepish) oops, my bad. But it's clarified by Cronholm's nice picture. Willow 12:04, 17 July 2007 (UTC)


 * Why are the neutron stars gone now? Those are the most significant tests of gr we have!
 * True, but explaining those tests to lay-people is hard. I found the previous sentence uninformative for the lay-person. Willow 12:04, 17 July 2007 (UTC)


 * "can be reconciled with the laws of quantum physics to produce a sensible theory of quantum gravity." - sounds colloquial, as if the theory has a 401(k) plan and looks left and right before crossing the road
 * It's "sensible" that is the problem; how about a "complete" or "more accurate"? Whichever is correct. Awadewit | talk  10:25, 17 July 2007 (UTC)
 * I was indeed going for a comfortable wording here, rather than the "shock and awe" type, for the lay-people. But it is uninformative, I agree; we'll need to fix this up. Willow 12:04, 17 July 2007 (UTC)


 * "General relativity is also the basis of the standard model of cosmology, in which the present universe evolved out of a much more dense and energetic state in a Big Bang." - why "in a Big Bang"? The big bang is either the more dense and energetic state itself, or else the singularity at the ill-defined beginning of that state.
 * Don't define the Big Bang. Let it go. There are so many other things to do in the lead. Awadewit | talk  10:25, 17 July 2007 (UTC)
 * I agree with Awadewit; the present sentence is one of those chimaeras. Willow 12:04, 17 July 2007 (UTC)


 * "General relativity is the basis for much research in modern astrophysics." - the "much" sounds a bit awkward. What fault did you find with the "cornerstone"?
 * I liked "cornerstone", but is it inaccurate? It means something totally different from "much", obviously. Awadewit | talk  10:25, 17 July 2007 (UTC)
 * Much of astrophysics concerns the physics of stars, and much of that physics does not require GR.  To be sure, ultracompact stars and cosmology require GR, but how about everything else?  The word "cornerstone" seemed too strong for me. Willow 12:04, 17 July 2007 (UTC)


 * "this holds even if the acceleration and its corresponding gravitational field are not constant" - my impression is that this additional information will not help the typical reader, who probably has not thought about this restriction on his or her own, and thus will gain nothing (but might become confused) when it is lifted. I think the "Conversely..." is a valuable addition, though.
 * I agree - do not too many qualifications. That is where we lay people start to get lost! Awadewit | talk  10:25, 17 July 2007 (UTC)
 * I agree; I wrote that sentence thinking of a quibbly young student somewhere. Please remove as you will. :) Willow 12:04, 17 July 2007 (UTC)


 * "By design it was consistent with electrodynamics" - why is that? By design, it is based on the principle of relativity and the constancy of the speed of light.  If it had turned out that electrodynamics is not inherently Lorentz-invariant, then Einstein might have needed to find a generalized, relativistic theory of electrodynamics.
 * As I said in my internal comment, never use the word "design" in a science article. It reeks of intelligent design for a US reader. Awadewit | talk  10:25, 17 July 2007 (UTC)
 * I was trying to convey the idea that it was no accident that EM was already consistent with SR ("what are the odds of that?" an imaginary reader said); rather, Einstein arrived at SR by changing mechanics (well, space-time) to fit EM. Gravity was the odd one out because it wasn't Lorentz-covariant to begin with. Willow 12:04, 17 July 2007 (UTC)
 * But "changing mechanics to fit EM" isn't the whole story, either. People might get the wrong idea. It sounds like fudging; if you have something very changeable, you can make it fit anything you want; Einstein chose EM.  But there aren't really that many ways of "changing mechanics" - Einstein's took its cues from significant portions of EM (light propagation, early thoughts about magnets, Lorentz), but I don't see that he could have foretold in the beginning that this change would indeed take care of the whole problem.  For all he knew, it might be that he would need to modify mechanics, and modify EM a bit, as well.  I don't think he would have balked at modifying EM if necessary, as long as the principles he wanted to see satisfied (now the two axioms of sr) were indeed satisfied.  So no, it isn't surprising that EM and SR go together well, but it's not automatic (or at least, it wasn't before people knew a lot more about physics) that EM and SR not only are easy to bring into line, but that EM is completely SR-compatible in the form found by Maxwell, without any modifications. --Markus Poessel 16:56, 17 July 2007 (UTC)
 * I'd also give Einstein credit that he would've changed EM to suit his conceptions, had it proven necessary, although that's a hypothesis contra factum so we can't argue it here. And you're quite right that the Lorentz transformation is pretty unique if we require certain symmetry properties for the transformation.  Let's find a compromise wording that captures all of this. Willow 17:45, 17 July 2007 (UTC)


 * "but it was not consistent with gravity (the mutual attraction experienced by bodies due to their mass). A key contradiction lay in special relativity's prediction that nothing could travel faster than the speed of light." - I think that's simply wrong, and I would like to revert those changes. I know that's the way it's sometimes written up in the popular literature, but  the problem is quite different - try it on for size on electrostatics, and imagine that only Coulomb's law had been known when Einstein had found special relativity.  Would you argue that Coulomb's law was "inconsistent with sr, since it postulated instantaneous reaction of particles, etc., etc."? Yes and no.  But all that would have needed to happen was that Coulomb's law had to be supplemented, and you would have ended up with Maxwell and electromagnetism, but the point is: the electric force is still a force; Coulomb's law is still valid. No need for geometry, and no explanatory power for the special form of gr. The case of gr is different.  You can't just make a generalized "force theory" of gravity by analogy with electromagnetism (it leads to runaway instabilities, due to the one little sign difference), you need a non-scalar potential.  This is why I left out the "Newton is instantaneous!" argument deliberately; I'm dismayed to see it back.
 * I didn't understand the "contradiction", anyway. *sigh* Awadewit | talk  10:25, 17 July 2007 (UTC)
 * Pauli's review article of general relativity uses this "change gravity to reconcile with SR" argument. Your Coulomb example is a very good one.  To make the Coulomb force compatible with SR, you would be forced to introduce a magnetic force, and you would arrive at Maxwell's equations.  I recognize that GR is different, because Coulomb's law didn't need fixing, whereas Newton's did.  I did address the scalar and vector theory alternatives to GR lower down in the article. Willow 12:04, 17 July 2007 (UTC)
 * Rereading Pauli, he also says that those were earlier considerations. Then came Einstein and viewed matters from a completely different angle (equivalence principle etc.).  In the current version, it sounds as if the speed-of-interaction thingies were Einstein's considerations. I'd like to pretty much revert this change to the previous version; let's copy and store it for the history version of new-and-improved general relativity, though! Markus Poessel 14:55, 17 July 2007 (UTC)


 * "Einstein formulated the Equivalence Principle in 1907, but it required another eight years of difficult work to arrive at the final theory of general relativity." - I think it's misleading to recap that here in that way. The consequences described in this paragraph are already in the 1907 paper; at the end of this sentence, we're mentally in 1915.  I have reworded a bit.


 * Description of acceleration/redshift: I'm unhappy with the current version as it is a strange hybrid. It attempts to give something like a derivation (by starting with acceleration and going to gravity - something I had avoided since I felt the article was getting too long as it was), but then is strangely silent on some points.  How does the acceleration cause the redshift?  There's the central point, and it's not explained. Even worse, readers might think that there is some strange direct way in which acceleration generally causes redshift.  If you want to explain the physics, you have to do it the usual way - introduce a freely falling comparison frame, for instance, and then apply Doppler effect.  My feeling is that, properly done, this would a) blow the whole section up out of proportion to the rest, and b) still lose a great number of potential readers (although Loom 91 would disagree here).
 * readers might think that there is some strange direct way in which acceleration generally causes redshift - I can definitely see this problem arising. Awadewit | talk  10:25, 17 July 2007 (UTC)
 * I definitely don't want to include the derivation, but we're faced with a dilemma. Either we say "Einstein concluded that gravitation causes redshift" without explaining why; or we say, "Acceleration causes redshift" (again without explaining why) and use the just-introduced equivalence of acceleration and gravity to arrive at "gravity causes redshift".  I prefer the second way, since it connects with the previous section and is more physics-based. Willow 12:04, 17 July 2007 (UTC)
 * If we don't include a derivation, why mention the acceleration analogue at all? In this case, I would propose going back to something not unlike the previous version, which didn't try to start the derivation, just stated the facts (with apologies to Loom91). --Markus Poessel 14:55, 17 July 2007 (UTC)
 * If we're going to appeal to authority and tell the reader to just swallow something, I'd personally prefer that we appeal to physical authority ("acceleration does X") rather than personal authority ("Einstein says that X must happen."). Willow 17:45, 17 July 2007 (UTC)
 * Pop psychology: "Einstein says X" carries a lot more weight than "acceleration does X"; sadly, people are more likely to accept the Einstein formulation, however logically flawed. Remember that the average reader isn't going to ponder each sentence carefully (they won't even do it in English classes!). If you want them to accept this and move on, choose Einstein. Awadewit | talk  10:35, 18 July 2007 (UTC)


 * "According to Newtonian gravity, a massless particle such as photon should not be deflected; however, a particle with infinitesimal mass will be deflected by an amount half of that predicted by Einstein, as noted first in 1804." - Again, that changes carefully chosen wording to something more concrete, but questionable. Why shouldn't a massless particle be reflected?  It all depends on what you regard as more fundamental, force (if you're after a unified description matching with that of other forces) or acceleration (which is the more natural thing to do for gravity).  But it's too strong to say that a massless particle should not be deflected.  The reason why I called the derivation "heuristic" is that it is a tad half-baked.  If we do look at a ballistic theory of light, why do we at the same time suppose that all the light particles are travelling at speed c?  They should be slowed down a bit escaping their source star; their velocities should follow a distribution derived from the velocity distribution of the atoms that sent them out.  Starlight should have a velocity distribution, and be smeared out when deflected by mass.
 * Date is confusing, too, as I mentioned in my comments. Why are we back in 1800? Who did this? Awadewit | talk  10:25, 17 July 2007 (UTC)
 * Here I fell prey to trying to be scrupulously correct while actually making things more obscure. The 1804 reference was to von Soldner, who assumed that light was made of massive particles; taking the limit as m goes to zero gives the "half" prediction.  But my impression is that most classical physicists of that era did not expect light to be deflected at all; having no mass, it should feel no gravitational force. I agree, we should simplify this. Willow 12:25, 17 July 2007 (UTC)
 * I saw the Soldner reference, but I have seen no indication that the fact that physicists of that era, and certainly of later eras, did not expect light to be deflected at all had to do with the reasoning you mention. After all, they all knew about the universality of free fall. The real reason seems pretty clear to me: We're way past the point where Young had made his refraction experiments, and the wave theory of light was gaining ground.  For light that isn't corpuscular, Newtonian theory really doesn't tell us anything, so the question of gravitational deflection of light couldn't really be solved theoretically.  Certainly after Maxwell, it is misleading to simply state "Newtonian gravity predicted light deflection by half the amount" - in 1915, it was Newtonian gravity, plus a naive interpretation of the long-abandoned and not-at-all clear interpretation of the recently quantum mechanically revived corpuscular theory of light that predicted this value, or equivalently, Newtonian gravity plus the equivalence principle plus special relativity.  As far as I know, only gr brought the question of light bending back onto the table; let's not make it sound as if the very fact of light bending was widely accepted, and only the exact value controversial. --Markus Poessel 14:55, 17 July 2007 (UTC)
 * I think we agree here? Namely, that most classical physicists of that era did not expect light to bend? Willow 17:45, 17 July 2007 (UTC)


 * Separation into early and later tests: Why? There is no strict chronological separation.  The first Shapiro effect measurements where undertaken in 1966, before the first direct time delay measurements.  All tests have continued, and I have included references to more modern observations.  I think the separation simply sends the wrong message.
 * I would've fixed that myself, but I had to run off to work. I was trying to break up a long section, and thought to distinguish the "classic" tests proposed by Einstein (which may be easily visualized) from the later tests that are obscure to laypeople.  Willow 12:25, 17 July 2007 (UTC)
 * OK, if we're in agreement, I'm removing the section headers now. Let's focus on an alternative strategy, and see if we can streamline that section a bit!  (I hope Carcharoth will keep monitoring this; he can object if he thinks any of the streamlining undoes the revisions that were made in reaction to his suggestions.) --Markus Poessel 14:55, 17 July 2007 (UTC)


 * "Of these tests, only the perihelion advance of Mercury was known prior to Einstein's final publication of general relativity in 1916." - hey, I've even cited Pais: Einstein was still groping around for the field equations, not quite sure about what their final form should be (he had changed them around quite a bit). The fact that, with this version, the anomaly comes out right was the key moment: Einstein writes that he was "beside [him]self with joyous excitement", he tells Fokker that the discovery gave him "heart palpitation", he told de Hass that something at that moment actually snapped within him.  That's the key moment when Einstein realizes that, finally, he's on the right track. "Einstein had used as a guidepost during his search for the final form of his theory"
 * Why aren't those quotes in the article! They're great! They get across the excitement of discovery, as requested by someone somewhere in that hideously long FAC. Awadewit | talk  10:25, 17 July 2007 (UTC)
 * Those are excellent quotes, I agree. I was trying to avoid giving the impression that Einstein fudged the laws just to get one observation correct.  But surely he used other criteria as well?  Bending of light, red-shift, absence of negative-energy waves, and probably many others, right? Willow 12:25, 17 July 2007 (UTC)
 * Don't forget that he didn't have any data on bending of light and red-shift, so no, that wasn't a criterion. Einstein was guided more by principles (covariance, which he didn't distinguish background independence; the equivalence principle; in between some determinant condition for the metric - later abandoned).  But he knew, of course, that he had to get Newton as a limiting case, and later on (I don't know how early) he used the perihelion anomaly as a test criterion. And, yes, general sanity checks like energy conservation/stability.  It's not a matter of fudging - it's not as if there were many parameters to adjust. --Markus Poessel 14:55, 17 July 2007 (UTC)
 * The difference between "guidepost" and "sanity check" is probably semantic, so either way is fine with me. If I'm not mistaken, though, Einstein was looking for a theory that produced bending of light and the red shift, based on his 1907 thought experiments. Willow 17:45, 17 July 2007 (UTC)
 * As for "looking for a theory that produced bending of light and the red shift" - that is true only in the sense that he was looking for a theory that satisfied the equivalence principle, which didn't help him with the main problem of finding the correct field equations. The perihelion advance, on the other hand, was a guiding post for progress beyond the EP; the fact that his "Entwurf theory" failed this sanity check was an important step. We can discuss this, though, when we've come to that section in our step-by-step discussion; I, for one, am glad that we're now proceeding a bit more systematically. --Markus Poessel 13:53, 18 July 2007 (UTC)


 * "These tests not only refuted the Newtonian model of gravity, but also other relativistic theories of gravity, such as scalar and vector models that did not exhibit light deflection or perihelion advance; some of these other models also exhibited anomalous features such as waves that carry negative energy." - that's either too much or too little. We haven't really mentioned alternatives so far; the typical reader doesn't know what "scalar and vector models" are, or what is meant by the waves.  I think that all the paragraph does at the moment is make things a bit harder for the average reader, without conveying crucial information; I would propose to either condense it and make it more general (other people had derived alternatives; the test serve to refute them), or leave it out.
 * I vote for leaving them out. As I said in my internal comment, the lay reader is still trying to grasp the right model - don't introduce incorrect ones! Awadewit | talk  10:25, 17 July 2007 (UTC)
 * OK. My own feeling is that we should mention that GR is not the only conceivable theory, but that the others have been eliminated by experiment.  That's a teaching moment: that's how science works.  GR stands on its experimental verification, not because Einstein came down like Moses and everyone agreed that his laws were beautiful and correct. Willow 12:25, 17 July 2007 (UTC)
 * Can we go for a brief version: "Three of them were derived by Einstein himself and have led to what are now known as the classical tests of the theory – the crucial observations that justified adopting general relativity over Newton's description of gravity (and, incidentally, over a number of alternative theories of gravity that had been proposed in the meantime):" - is that short enough not to be distracting, yet mentions those other theories? -- Markus Poessel 14:55, 17 July 2007 (UTC)
 * Close but no cigar - should be alternative theories of relativistic gravity, since those theories we're talking about here were formulated when there was no such thing as gr. Markus Poessel 17:16, 17 July 2007 (UTC)
 * Not sure if I understand your point here; isn't that link what we have now? Willow 17:45, 17 July 2007 (UTC)
 * The compactness! Give us ignorant readers some breathing room to absorb each sentence. Also, I think you have to be willing to lose precision and accuracy to some extent in this article; without clear markers of what is important, the reader will inevitably become confused. Also, try to explain a bit more--add in the links. How about something like this: "Three of them were derived by Einstein himself and are now known as the classical tests of the theory: 1, 2, and 3 [whatever they are]. These observations, because they exactly matched Einstein's predictions, justified replacing Newton's description of gravity with general relativity." Awadewit | talk  10:35, 18 July 2007 (UTC)


 * "In such a star system, two highly compact neutron stars orbit each other, of which one is a pulsar – an astronomical object that sends radio pulses that strike the Earth at very regular intervals." - that's exactly what I was trying to avoid. Now readers are bound to think that the pulsar indeed sends out radio pulses: Sending - pause - sending - pause, and that there are indeed separate pulses flying through space and striking the Earth. On a sidenote, the "at least one" got lost, but is hugely important.  Double pulsars provide the most stringent tests to date.
 * They don't? That's what I got from that - star sends radio signals to earth. I am apparently the most idiotic reader of all time. Awadewit | talk  10:25, 17 July 2007 (UTC)
 * I think we're both trying to avoid the same mis-conception and failing. ;) Maybe we could include a pulsar image and clarify matters in the caption to it? Willow 12:25, 17 July 2007 (UTC)
 * You're in very good company, Awadewit, don't worry. It's our fault for trying to cram the description into half a sentence.  How about "In such a star system, two highly compact neutron stars orbit each other, of which at least one is a pulsar.  Pulsars are cosmic lighthouses; they rotate while sending out beams of radio waves; as those beams brush over the Earth again and again, astronomers measure radio pulses that arrive at very regular intervals." Or something along those lines? -- Markus Poessel 14:55, 17 July 2007 (UTC)
 * How about: "In such a star system, two highly compact neutron stars, one a pulsar, orbit each other. Pulsars are cosmic lighthouses: they rotate while sending out radio waves. Astronomers can measure these radio pulses as they repeatedly strike the Earth in order to...." It has lost nuance, I know, but sometimes simpler is better. What is the the most important idea here? Focus on that somehow. Awadewit | talk  09:43, 18 July 2007 (UTC)

This needs more consideration. --Markus Poessel 08:07, 17 July 2007 (UTC)


 * Dear Markus,


 * I hope you'll forgive my good-faith but sometimes clumsy efforts. But I somehow sense that you will, and that we'll be able to work together in a friendly way for our readers' benefit.  :) Willow 12:25, 17 July 2007 (UTC)

Um, much of the above is great, but I couldn't let Willow's comment here pass: "GR stands on its experimental verification, not because Einstein came down like Moses and everyone agreed that his laws were beautiful and correct." - the history does indicate that Einstein was deified, and on rather dodgy experimental ground. The accurate measurements were not made until much later. Have a look at this account. Carcharoth 12:59, 17 July 2007 (UTC)


 * I would dispute that version of events - you should distinguish between the reception in the scientific community and public perception. For the latter, the Eddington measurements (as for dodgy, as I said, I'm willing do discuss that later) were certainly the flashpoint, justified or not – although I would argue that the general public was not impressed with the accuracy of the results, but with the grand consequences, the fact that something as everyday as space was suddenly completely different, and also the sensational fact that, shortly after WWI, an English expedition had managed to prove the revolutionary predictions of a German.  The scientific community was much more cautious - case in point: The official reasoning for giving Einstein the Nobel prize (no, not relativity; not even the special theory was sufficiently accepted at that time).  Many regarded the theory as beautiful and elegant, but were skeptical as long as there were just scattered measurements and no real applications (astrophysical or otherwise).  As far as I can see, that only changed in the Golden age of general relativity, when better measurements were performed, and exciting new applications (black holes as engines for active galactic nuclei) discovered. --Markus Poessel 15:52, 17 July 2007 (UTC)

Part 2
Next batch of comments
 * Binary star image is nice, but messes up the lay-out (section is too short; second image can slip into next section, dislocating section title...) - which is why I confined myself to one image per subsection. Which can we do without - LISA or the binaries? --Markus Poessel 17:12, 17 July 2007 (UTC)
 * Too much, too much. Please take out the animated image. It is hard to read with that swirling text to the next, at least when you have to concentrate on the material. Also, I would assume that people with reading disorders wouldn't appreciate it, either. Awadewit | talk  09:18, 18 July 2007 (UTC)
 * It's gone; the text is probably clear enough so that people will understand what a binary star is without an animation. Willow


 * "This equation is usually referred to in the plural as Einstein's equations, since the mathematical objects on both sides have sixteen components." - sounds a tiny little bit as if we would have to use a different numerus if it were only fifteen components. I think this addition isn't helpful at all - why should the reader now have to worry about what redundant means here, and keep count?  The physics is that there are ten independent conditions, why can we not just write that? --Markus Poessel 17:12, 17 July 2007 (UTC)
 * The logic is a tiny bit flawed, anyway; it is not plural because there are sixteen, but because there is more than one, right? Awadewit | talk  09:20, 18 July 2007 (UTC)
 * I agree with Awadewit, I'm not sure if I understand your idea here? I clarified the "mathematical objects" as G and T, lest people think it might involve those constants in front of T. Willow 20:25, 18 July 2007 (UTC)


 * "A solution of these equations describes a particular geometry of space and time; for example, one solution describes the geometry around a stationary black hole, whereas another describes a rotating black hole." - ouch! ouch! Schwarzschild is static, not merely stationary.  And a solution doesn't just need to describe the geometry, it needs to specify compatible matter properties as well - otherwise, it's just half a solution.  Also, in your change the important fact gets lost (which was implied in "model universe") that you cannot, in gr, restrict yourself to isolated systems (only by the artificial trick to have a completely empty universe around them). I think the model universe is a good way of saying that; may be we should add one more sentence of explanation.  Where did the dates for the solutions go?  That was added as part of my effort to satisfy Carcharoth's objections (which had led to him withholding support).  Why are you reverting this? --Markus Poessel 17:12, 17 July 2007 (UTC)


 * As I wrote before, I'm very sorry for messing things up. However, my own feeling is that, in an introductory article like this one, we needn't be so scrupulous about dating everything explicitly, although we should include the dates in the inlined references.  In my opinion, working the publication dates into the sentence with the Schwarzschild and Kerr solutions hampers its flow and focus.  I'd like to keep the flow and focus strong, since we're demanding a lot of our readers even without asking them to absorb all of the history.  Carcharoth, what do you think? Can we let interested readers pursue the history through the references, or through the main article, general relativity? Willow 20:43, 18 July 2007 (UTC)


 * For the other point, I think we can get away with discussing isolated systems in an introductory article. To my mind, qualifying the boundary conditions as a "model universe" seems likely to confuse the readers, although you may be able to find a deft way of explaining them.  Do you really think that experts will object if we leave out the boundary condition issue?  The Schwarzschild solution is still a solution of the field equations, which is all that we're claiming for it.  Willow 20:43, 18 July 2007 (UTC)


 * "GR is also used to model gravitational lensing, in which the appearance of distant objects is distorted by gravity; on their way to Earth, light rays from the distant object are bent by the gravity of an intervening object, much as a lens does." - the point that is crucial for astronomy (multiple images) has gotten lost. --Markus Poessel 17:16, 17 July 2007 (UTC)
 * "This curvature is visualized here as blue circles, although no "dip" in the signal's path would be visible." - the circles are not really the curvature, right? As for the dip not being visible, well, the whole signal wouldn't be visible, strictly speaking.  I think this doesn't add anything helpful (and might even serve to confuse); could we just change "Illustration" to "Artist's impression" (indicating creative licence), and leave it at that? --Markus Poessel 17:19, 17 July 2007 (UTC)
 * "Although general relativity is not the only relativistic theory of gravity, it is the only one consistent with the experimental data." - yes and no; how about "it is the simplest theory that is consistent with the available experimental data."? Markus Poessel 18:29, 17 July 2007 (UTC)
 * Great! that's much better than my version, thank you. Willow 20:59, 18 July 2007 (UTC)


 * "This is not true for all types of acceleration; for example, a person enclosed in a uniformly rotating room could tell that the room was being rotated." - Why are you inserting statements that are in direct contradiction to the way Einstein developed general relativity? He included that kind of rotation, introduced gravitomagnetism to account for it, and thought he was completing the program of Mach.  It used to be in a footnote in a previous version; I'm too disheartened to look whether it is still there or has become a victim of the ongoing change-fest.  --Markus Poessel 07:29, 18 July 2007 (UTC)
 * I'm sorry, but this point seems too elevated for an introductory article. Don't you agree that absolute rotation is detectable in a closed room, whereas free fall acceleration is not?  I was trying to describe how gravitational free-fall is different from other forms of accelerated reference frames, which produce other fictitious forces besides gravity. Let's work on this section as we come to it.  Willow 20:59, 18 July 2007 (UTC)


 * "General relativity predicts the correct anomalous perihelion shift for all planets where this can be measured accurately (Mercury, Venus and the Earth)." - this sounds a bit off, as if there are inaccurate measurements that are in disagreement with gr. There aren't (even for an inaccurate measurement, namely one with a large error, we can tell whether it agrees or not, i.e. whether the prediction is inside the error range or not). I'm dismayed that your changes are introducing really a lot of slightly sloppy formulations like that.  Could we please switch to a discussion where you first propose changes here, then we reach consensus, then we make the changes to the article itself?  The way it's going now is very frustrating to me. --Markus Poessel 07:35, 18 July 2007 (UTC)
 * We've already agreed to this, and I hope that our work together will soon become less frustrating. Please consider, though, that I'm your target audience, or at least I was a few months ago.  I'm honestly not trying to dishearten you, but rather to clarify sections that would've frustrated me a few months ago.  Please try to see the world through my eyes; can you see that I'm sincerely trying to be helpful?  I know that you've put tremendous work into this article and are approaching it with a generous spirit; please try to hear my ideas, even if my words are going askew.  You'll find that I accept correction very readily, and gladly learn better. Willow 20:59, 18 July 2007 (UTC)


 * "Just as most effects of gravity can be made to vanish by observing them in a co-moving free fall, the same effects can be produced by observing objects in an accelerated frame of reference." - I think "co-moving" is not only something that will sound unduly technical to the average reader, it also doesn't really scan, does it? Or do you mean, even more technically, "observing them in a co-moving reference frame that is in free fall"?  You can be in free fall; free fall is not a container ("observing them in free fall" is not "observing them while in free fall").  Also, making the effects vanish by observing them (quantum mechanics?) is just not right.  You make a transition into free fall (that is an action - you let yourself fall) and the effects vanish.  I think this is exactly what the reviewer who just withdrew his support was objecting to. --Markus Poessel 07:39, 18 July 2007 (UTC)
 * I was trying to say "observing them in a co-moving reference frame that is in free fall" while still being picturesque. The problem I saw with the old way — which did not specify "co-moving" — is that there are many different free-falling reference frames, as you point out in the "Tidal" section.  Only in one, the co-moving frame, do the effects of gravity vanish.  Therefore, the phrase "the most obvious effect of gravity – things falling down – can be eliminated by making the transition to a reference frame that is in free fall" seemed a little ambiguous. Willow 21:13, 18 July 2007 (UTC)


 * "This converse principle allowed Einstein to predict several novel effects of gravity in 1907, as explained in the next section." - that's overstating the case - making it sound as if the converse actually qualifies as a separate principle.  It doesn't, it's all still only one principle. --Markus Poessel 07:51, 18 July 2007 (UTC)
 * I agree. I only wanted to prime the reader for understanding how Einstein predicted the three effects in the next section.  Einstein predicted gravitational effects from thinking about acceleration, rather than the other way around.

Replies from Willow
I'm very sorry to have thrown a monkey wrench into your compromise with Carcharoth, which I missed; this discussion is getting long and I'm not always a careful reader. As for the other points, please be understanding:
 * Both images are great; maybe we can shuffle things around? I do think that lay-people need to see a picture of a binary star, ideally an animation, although maybe the present one is too coarse.  We might put the LISA image in the lead and restore the Cassini image in the main article.  It might help if we numbered the Figures, so that we could refer to them in the text, even at a distance.
 * Hm. I like the change with Cassini; it means putting our best foot forward (my impression is that, graphically, the image is more appealing to the general reader than the somewhat darker LISA picture. Where do you see the need to refer to figures at a distance?  I think that actually would make the text less readable.  The reader would still need to jump back and forth to see the figure; we should arrange matters so that all the figures that need to be viewed are visible when the text mentions them. --Markus Poessel 07:22, 18 July 2007 (UTC)
 * Ah! The "Cassini illustration" next to the lead has the longest caption of all time! :) We need an illustration with a very short or very easy caption. Perhaps even Einstein. You want the reader to focus on the lead; with all of that other text, one gets distracted. Awadewit | talk  09:16, 18 July 2007 (UTC)
 * Sorry for the disorganized state of this discussion. I'm addressing the tape worm caption below. Markus Poessel 09:19, 18 July 2007 (UTC)


 * The Schwarzschild metric and Kerr metric are empty-space solutions of the field equations, so "matter properties" embodied in T are irrelevant, aren't they? Or perhaps I've misunderstood your "half solution" comment?  Perhaps you meant that we have to describe the geodesic equation for motion in the Schwarzschild solution metric?
 * Even specifying "T=0" is a way of specifying matter properties, albeit very simple ones. There's no way around it: You need to specify matter properties if you want to have a solution; that's part of the definition.  And note that we are not trying to define "vacuum solution" - we want to define "solution", and of course we have FLRW as an example of non-vacuum! --Markus Poessel 07:22, 18 July 2007 (UTC)


 * Awadewit objected to the usage of "model universe" as unintelligible to the lay-reader, and I have to agree with her. I understand what you're driving at, but I think that experts won't object and lay-people will only be confused by this subtle point.
 * Oh, experts will definitely object if you leave out half the definition. As for "model universe", I still think that one explanatory sentence would make this intelligible. --Markus Poessel 07:29, 18 July 2007 (UTC)
 * I don't believe I "objected" (did I?) - I believe I asked what a model universe is exactly. An explanation would be fine. Awadewit | talk  09:32, 18 July 2007 (UTC)


 * We can change "stationary" to "static" if you like; my only aim was to contrast that solution with the rotating solution.
 * If I'm not mistaken, there are only six physical equations in GR, not 10. Of the sixteen components, 6 are redundant by the index symmetry, Gμν = Gνμ, leaving ten (16-6=10).  Of those, four are irrelevant by the arbitrariness of choosing coordinates, leaving six  physical equations (10-4=6).
 * Correct. I wasn't thinking. (The 10 stem from the earliest version of the article I know, and you're right, they're the number of components, not the independent equations.) 6 it is, then.


 * I think that many lay-people might expect that they would actually see the signal dip in space, as it's depicted now, so I thought we should forestall this misconception. Such a signal could be visualized if it were a laser pointer shining through dust, no?
 * I still think it would be best to go with "artist's conception". It's just meant to be a nice starting picture, we don't want people to feel like they need to decipher it before they can move on to the text.  When the caption takes half as much space as the image itself, it not only looks like bad layout, it also looks like the picture is bad. --Markus Poessel 07:46, 18 July 2007 (UTC)
 * OK, new compromise proposal that is hopefully brief enough not to look unprofessional (from a lay-out point of view) and still conveys what you felt needed to be included about the dip: "Artists impression of precision tests of general relativity undertaken with the Cassini space probe: warped space (blue lines) and its effects on radio signals (green line) exchanged between the probe and Earth." --Markus Poessel 09:18, 18 July 2007 (UTC)
 * (Another daring suggestion): "This image is an artist's impression of the Cassini space probe's precision tests of general relativity..." See, I can't even redo the last part it's so confusing. What is being exchanged? The phrase should read "X or (X and Y are) is exchanged with Z..." or some such formulation. Awadewit | talk  09:32, 18 July 2007 (UTC)


 * I understand the importance of multiple images in astronomy, but we're not writing for professional astronomers, but for complete newbies, who may have little experience with normal lenses causing multiple images, but who will likely have seen distorted images through a magnifying glass. Perhaps we can confine the multiple images to the caption of the image?
 * But we're trying to tell people what gravitational lenses do! The important thing they do is produce multiple images.  That was the key prediction, that's how they were discovered, that's what you see with (almost all) current observations.  The distortions are secondary.  The effect is also not hard to describe:  If I say "you see multiple images of the same object in the night sky", I would expect the average reader to understand what is meant - it's even more simple than talking about optical lenses (which only need to be mentioned if you want to explain the name). --Markus Poessel 07:29, 18 July 2007 (UTC)
 * What is wrong with the image which I thought was a kind of "multiple exposure" of the star? That was cool - I thought I understood it (it's pretty, too). Awadewit | talk  09:32, 18 July 2007 (UTC)

I have to run soon, so please don't wonder if I can't reply immediately. Willow 17:32, 17 July 2007 (UTC)


 * I'm still reading, but don't have much to say yet. Except please keep the dates, obviously! :-) Carcharoth 19:55, 17 July 2007 (UTC)

How to make this work

 * General remark: I think that many of the changes have made matters harder to understand. You cannot just insert something like "Fictitious forces are always proportional to the inertial mass on which they act; thus, an object in a gravitational field should feel a force proportional to its inertial mass, as is observed and embodied in Newton's law of gravitation." and expect the average reader to say "Oh, yes, right-ho, that's what it is."  At least one reviewer has now withdrawn support due to what he calls a marked decrease in the quality of the writing.  Could we please, please change gears here - first propose and discuss changes on this talk page, and only afterwards insert them into the article? --Markus Poessel 07:22, 18 July 2007 (UTC)


 * Yes, let's do that. Again, I'm no expert, as I conceded, but I do have some sense of what it's  like to be a newbie.  I've sincerely tried to clarify the article and make it more informative for the beginning student, although my skills sometimes fall short.  I'm really, really sorry if you think that I've just ruined the article. :( Willow 13:17, 18 July 2007 (UTC)


 * Also, could we please slow down a bit? There are now enough points of discussion on the table without the introduction of additional changes every new day; could we please first clear up the changes we have now, checking that all comments have been addressed, before further widening the field of issues that need to be discussed? --Markus Poessel 08:39, 18 July 2007 (UTC)


 * Striking out sentences and issues that have been addressed would help us all, I think. Awadewit | talk  09:32, 18 July 2007 (UTC)


 * A good point, too. I've started; hope to have occasion to make progress on this soon. --89.50.45.2 11:27, 18 July 2007 (UTC)


 * Still thinking about the best way of doing this. Perhaps we could go section by section?  For each section, we could discuss changes, refer back to the comments already exchanged, hopefully find consensus, and then move on to the next section.  I find that one of the more frustrating aspects of this process is constantly having to keep track of all the changes happening, commenting on some and finding that others have happened while I turned my back.  That way, we would proceed step by step, and minimize the risk of missing anything. --Markus Poessel 09:09, 18 July 2007 (UTC)


 * After having taught writing for a few years now, I can offer one tiny suggestion. It might be useful for the editors to make a list of the three or five most important concepts that they want the reader to know after reading this article. It is easier to make editing decisions when you all know what the goal is: communicate 1, 2, 3, 4 and 5. Everything in the article should then work in some way towards explaining those five concepts. Also, realize that five major concepts will be stretching it for most people. Typical essays have one thesis, or one idea that they want to communicate, even if they have subpoints; essays usually return to the same argument over and over again (think five-paragraph essay style, that tired but useful model). (Please do not respond and say "we are communicating only one idea, "general relativity""; think of the parts that make up this explanation.) I hope this helps a little. Awadewit | talk  10:45, 18 July 2007 (UTC)


 * Hm. I don't know.  My impression is that, at this point, it should still work to "argue locally" about changes, without introducing the additional structure of the most important concepts.  I also think that the most pressing problem at the moment is how many things are going on in parallel; going section by section would, in my opinion, make the process much, much more efficient and less stressful for all concerned. --89.50.45.2 11:27, 18 July 2007 (UTC)


 * Just a suggestion. It often helps students (and myself) to articulate the essence of an essay or argument in a few sentences; it focuses the writing process and the revision process. But perhaps that works better when only a single author is involved. :) Awadewit | talk  11:44, 18 July 2007 (UTC)

Did someone forget to sign in?--Cronholm144 11:34, 18 July 2007 (UTC)


 * Damn, you're just too fast. I was just about to fix the mistake; once I'd done it, I got an "edit conflict".  So yes, the above comment was by me. --Markus Poessel 11:40, 18 July 2007 (UTC)

Copyediting and other changes
Hi, I came here from the FAC mostly to do some copyediting, but I saw the discussion here and Awadawit's internal comments in the article, so I have been attempting to fix some other things as I went along. I have quite a bit of expertise in GR, but also a lot of my work on WP concerns making math more accessible and general copyediting (e.g. for encyclopedic tone) so I figured I might have a good chance to find the right balance between the readability and accuracy concerns. I don't know if I succeeded, but I made the edits in small batches, section by section, so I hope it is easy to see what I have done, and easy to correct or undo where appropriate.

A lot of the edits concern finding the right subject for a sentence to avoid the first and second persons and reduce the use of the passive tense, perfect tense, and sentences without subjects ("It can be shown..." and similar constructions). I think I've addressed many of Awadawit's comments (e.g. about wordiness) and have removed some of them, but I have also left a few in place with additional remarks for others to check.

I have made more substantial changes to sections involving geometry:
 * From acceleration to geometry. I've shortened this by some restructuring, and tried to draw out the analogies more clearly.
 * Probing the gravitational field. I reworked the introduction to geodesics. I also (sadly) rewrote the highly enjoyable but unencyclopedic approach to the force exerted by a chair on a backside :-)
 * Einstein's equations: quite a lot of changes here. They reflect my approach to dealing with the fact that mathematics can be difficult to understand: for instance, saying it is hard does not help, neither does it help to use words like "formalism", or give the impression that the reader is simply never going to understand it, even in outline. I believe that some readers will be able to see that there might be a relation between how a space is stretched and how it is curved. I also believe that many readers would like to know that there are quantities that describe these effects and that they have (wikilinked) names. The Einstein tensor was not pulled out of a hat. Other editors may not agree with all of these changes, and there is probably more to be done here in any case.
 * I also attempted to answer Awadawit's query about the constants appearing in the Einstein equation, although this may be too much detail, and reduced the components from 16 to 10: since we do not specify whether G and T are 2-tensors or symmetric 2-tensors, we might as well use the simpler point of view, and at least give the reader the idea that there are 6 physical equations because 6 = 10 - 4.

Finally I tried to clarify the von Soldner/eclipse issue, which has been discussed here quite a bit. I don't think I did a particularly good job: maybe some of the details can go in a footnote, with the von Soldner article itself as a genuine reference (in keeping with the notes and references style). Geometry guy 17:37, 19 July 2007 (UTC)

PS. I didn't touch the lead: that seems to be coming along very well, and I figured I could be one cook too many :-) Geometry guy 17:42, 19 July 2007 (UTC)


 * Hi, thanks for your support with the text. Please stick around; we're currently working our way through the whole article, section by section.  Eventually, we'll get to the sections you changed, and it would be great if you could then have an eye that we're not accidentally reverting any changes you thought important. (You're of course welcome to contribute to earlier parts of the discussion, as well!) --Markus Poessel 06:40, 20 July 2007 (UTC)


 * Sure. I also went through the whole thing section by section, so I know the article quite well now. Geometry guy 15:21, 20 July 2007 (UTC)
 * PS. By the way, your comment about introductions at Wikipedia talk:Featured article candidates/Introduction to general relativity was great. I also think you should consider making it into an essay.