Talk:General relativity/Archive 13

Black Holes
These were considered before General Relativity, using Newton's Law. A complete gravitational collapse was possible, although problematic. They didn't call it a " Black Hole", but that statement in an early paragraph is misleading, and implies that gravitational collapse had never occurred to anyone before GR. — Preceding unsigned comment added by 184.147.125.176 (talk) 06:15, 3 December 2013 (UTC) 77Mike77 (talk) 12:17, 3 December 2013 (UTC)


 * Do you have a reference to gravitational collapse being considered before GR? Martin Hogbin (talk) 09:12, 3 December 2013 (UTC)

I couldn't find what I was looking for, but found this http://www.amnh.org/education/resources/rfl/web/essaybooks/cosmic/cs_michell.html, which has the idea of a "black hole" in all but name. 1783, hypothetical star so massive that the escape velocity exceeds the speed of light, so it is, effectively, black.77Mike77 (talk) 12:17, 3 December 2013 (UTC)


 * Are you referring to, '...it implies the existence of black holes...'? I do not think that this statement can be taken to imply that Newtonian gravitation could not have had black holes.  Do you have any suggestions as to how the text might be made clearer? Martin Hogbin (talk) 09:18, 3 December 2013 (UTC)

Did I suggest that? I thought I was suggesting that BHs are possible with Newtonian gravity. Once the field is stronger than the material's ability to resist, the object has to collapse. The only problem is that of the infinities at the centre point. In GR, time slows to a stop at the event horizon, when viewed from the universe outside, so the singularity at the centre only exists for someone who falls through; for those outside, the BH is hollow, and the central singularity only exists in a hypothetical infinite distance into the future. I'll think about how to make it clearer with minimal change, and get back.77Mike77 (talk) 12:17, 3 December 2013 (UTC)

I'm thinking of replacing these two sentences, "Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not even light, can escape—as an end-state for massive stars."...with this: "Einstein's theory has important astrophysical applications. For example, the mystery of what happens when a star undergoes catastrophic gravitational collapse was explained, leading to the modern concept of black holes—regions of space in which space and time suffer such extreme gravitational distortion that nothing, not even light, can escape—as an end-state for massive stars." Does anybody object to this, or have any suggestions to make it better?77Mike77 (talk) 23:30, 4 December 2013 (UTC)


 * Your language is perhaps a bit too flowery for my taste, and somewhat inaccurate in what it implies about the historical sequence of events. See Chandrasekhar limit. However, I won't be the person to revert it if you make the change. I suspect somebody else would, however. Stigmatella aurantiaca (talk) 01:27, 5 December 2013 (UTC)

The only "flowery" word I can see is "mystery". Let me know if you can think of a non-flowery synonym. I was trying to keep the flow of the article intact, and not turn it into another edit disaster where a huge paragraph of dull prose replaces a sentence. It's just plain wrong the way it is. If this is like most other articles, someone will revert it back to its current incorrect version once people have spent a few hours straightening it out, so I'll probably just leave it wrong if there is no simple synonym for "mystery".77Mike77 (talk) 22:18, 5 December 2013 (UTC)

How about this? "Einstein's theory has important astrophysical applications. For example, the problems involved in trying to find a Newtonian description of what happens when a star undergoes catastrophic gravitational collapse were resolved, leading to the modern concept of black holes—regions of space in which space and time exhibit such extreme gravitational distortion that nothing, not even light, can escape—as an end-state for massive stars."77Mike77 (talk) 02:22, 6 December 2013 (UTC)


 * The language is improved, but your statement still has inaccuracies. Please bear in mind that although theorists such as John Michell predicted that massive bodies could exist exhibiting gravitational forces sufficiently great that light would not escape, no physicist working with Newtonian concepts EVER anticipated the possibility of gravitational collapse. The implicit assumption was always that, although a mass might be squeezed down to something incredibly dense, it would nevertheless remain a finite sized body. It was the 19-year-old Chandrasekhar who showed that general relativity predicted a runaway collapse of the mass into a point singularity. Eddington was perfectly aware of older work predicting the possibility of dark stars. But the idea of a mass collapsing into a point singularity was something that he simply could not accept.


 * Therefore, when you write that the "problems involved in trying to find a Newtonian description of what happens when a star undergoes catastrophic gravitational collapse were resolved", you are writing about things that never occurred. Stigmatella aurantiaca (talk) 03:16, 6 December 2013 (UTC)

I give up then. The original sentence is still wrong, because it gives the false impression that nobody had previously thought of a situation where light could not escape because of gravity, when this clearly had been thought of (Mitchell, and those who commented on Mitchell), and so I guess that the article will simply remain with this serious flaw, since any attempt to correct that error will be rejected. Despite the subtle inaccuracies in my statement, it is still an improvement on the existing mistake. Unfortunately, the mistakes in the article itself do not come under as much scrutiny as attempts to rectify those mistakes. Oh well, another defective Wikipedia article remains defective...what else is new?77Mike77 (talk) 15:27, 6 December 2013 (UTC)


 * No need to give up. It is extremely difficult to tell the entire story without going into WP:Undue detail. Yes, it is true that certain properties of what we know of as "black holes" could have been, and were, anticipated by theorists working exclusively within a Newtonian framework. But gravitational collapse was not one of them. "Escape velocity greater than the speed of light" is not "gravitational collapse." We need to be careful not to conflate these distinct concepts. Stigmatella aurantiaca (talk) 19:49, 6 December 2013 (UTC)

I was just posting an edit to my comment, but got a posting conflict. I wanted to say that you had a valid point re Mitchell's "Dark Star" not collapsing to a point, and that you are right that the light not escaping is a distinct concept from gravitational collapse. I had somehow got the idea from something I read, that the idea (that a gravitational field could be stronger than the material's ability to resist gravitational collapse) was first thought of in Newtonian terms, where the star would collapse to a point with infinite density and infinite gravitational field strength, and that those infinities were part of the problem. I think what I read must have been hypothetical, i.e. the author was posing a Newtonian "solution" to contrast it with the Relativistic one. I have a B.Sc. with a physics major, and am an "avid amateur" in following physics, so I understand Special Relativity very well, but never took post-grad courses in General Relativity, just a little tensor analysis in final year, and so I am certainly no "expert" on any formal treatment of GR. There is an important role to play in translating the abstract into terms understandable to the average reader, which I think is part of what wikipedia is supposed to do, even thought that goal is too often lost here. Anyway, I'll have another go at it and post it soon. Thanks for your "colourful" comment.77Mike77 (talk) 20:04, 6 December 2013 (UTC)

Okay, this is a new attempt. "For example, the topic of extremely strong gravitational fields, and their effect on light, was clarified. In 1783, John Mitchell hypothesized that light might interact with gravity, and suggested the possible existence of "Dark Stars", which were massive stars with gravitational fields so strong that light could not escape. His analysis was based on the Newtonian view that light consisted of "pellets" traveling at a certain speed, and that if the gravitational field of the star were strong enough, the "escape velocity" would exceed the speed of light, so that the light could not escape. General Relativity generated a completely different analysis of this problem, which took into account the wave nature of light, and the possibility of a catastrophic gravitational collapse in which the massive star would collapse down to a point, leading to the modern concept of black holes—regions of space in which space and time exhibit such extreme gravitational distortion that nothing, not even light, can escape—as an end-state for massive stars." I've tried to keep the "flow" of the original statement, even though I've lengthened this part. There is a wikipedia entry for "Dark Star", which I can link to that phrase. I used the word "point" instead of "singularity", because the lay reader won't know what a singularity is (I could link the word "point" to the article https://en.wikipedia.org/wiki/Gravitational_singularity). What do you think? — Preceding unsigned comment added by 77Mike77 (talk • contribs) 20:32, 6 December 2013 (UTC)


 * If a black hole is defined as "regions of space in which space and time exhibit such extreme gravitational distortion that nothing, not even light, can escape", then they were hypothesized back in 1783 and general relativity has very little to do with their existence. Relativity sheds some light on properties of black holes, but not existence. So I agree that the sentence is wrong but so are your fixes. Roger (talk) 21:28, 6 December 2013 (UTC)


 * I think your current attempt is well-reasoned enough to try out in the article. Just be sure to reference this Talk section discussion, remember that John Michell has no "t", and don't take it too hard if somebody immediately objects to something or other and rewords it. Popular articles such as this one are heavily monitored by lots of cooks. Good luck! Stigmatella aurantiaca (talk) 21:42, 6 December 2013 (UTC)

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Why is there a qualitative statement about the Wheeler-DeWitt equation in this article?
Hello, I've just read in section "Quantum Gravity" the following:

"Another approach starts with the canonical quantization procedures of quantum theory. Using the initial-value-formulation of general relativity (cf. evolution equations above), the result is the Wheeler–DeWitt equation (an analogue of the Schrödinger equation) which, regrettably, turns out to be ill-defined.[177] " The source given is the only one: Kuchař, Karel (1973), "Canonical Quantization of Gravity", in Israel, Werner, Relativity, Astrophysics and Cosmology, D. Reidel, pp. 237–288, ISBN 90-277-0369-8

Wheeler-DeWitt equation is pretty much out there influencing physics research, and it is extremely strange that here it is called "ill-defined" and only one reference dated 1973 is given.

There has been recent experimental research confirming the absence of time for an external observer of a universe: http://arxiv.org/pdf/1310.4691v1.pdf

It's highly ridiculous for a Wikipedia article to have qualitative statements about theories unless they have completely been dismissed by the entire scientific community through numerous failed attempts to verify them. — Preceding unsigned comment added by Whitely3000 (talk • contribs) 17:35, 24 February 2014 (UTC)

Expected domain of validity
I think there should be a (sub)section on the expected domain of validity of GR in the article. When reading about GR (whether popular or real thing), one is always fed the message that "most physicists expect..." and hence quantization is necessary. (The breakdown is just around the corner...) From the little I know myself, the circumstances are pretty extreme when one can surely expect GR to break down (giving incorrect predictions). Note: This is not something that can be disposed of by saying GR has already broken down because black holes exist and singularities don't. I think it would be interesting for the reader to get "pretty extreme" quantified in terms of, say, distance from the singularity of a really nasty black hole, or anything else suitable.

Also, provided GR is correct (within its expected domain of validity), can we ever expect to experimentally verify a quantum theory of gravity? Sure, such a theory might predict other things that can be detected, but I personally doubt that we will be able to produce graviton showers (instead of gravitational waves or whatever) at CERN. I understand I'm being vague here, but some skilled and knowledgeable editor might have an idea about good stuff to spice up the article with. YohanN7 (talk) 02:58, 4 July 2014 (UTC)

Objects do not follow the geodesic
Objects do not follow the geodesic because the gravitational field is in non-inertial motion. If there are two objects under their mutual gravitational field, both will be accelerated and follow a non-inertial motion. If one is a photon, the other will still follow non-inertial motion. Saying the object follow the geodesic is an approximation but not their true path. Shawn H Corey (talk) 14:05, 21 August 2014 (UTC)

Outstanding challenges
I feel it may be beneficial to include some discussion of the outstanding challenges encountered by the theory, and preferably in its own section. Certainly, the notion of singularities is one where most physicists are uncomfortable to the point where I really can't understand why it seems to be so universally espoused. Then of course there are the broader cosmological observations of dark matter and dark energy, which are almost beyond direct measurement despite comprising 95% of the universe. On top of that, we have inflation, and the elephant in the room - the fact the big bang could occur at all given that it should have by all rights gravitationally collapsed on itself.

As Lord Kelvin would no doubt attest, we still have a few clouds on the horizon. I fear I do not share his optimism, however. 150.203.179.56 (talk) 03:49, 8 September 2014 (UTC)
 * The statement about "the elephant in the room" is simply false whether or not the Big Bang should (have) collapse(d) back on it self is simply the old question of whether we live in an open or closed universe. Depending on the initial conditions both are valid outcomes.
 * Nonetheless, a section on "open challenges" is probably a good idea, as long as it is sourced by reliable sources. Given the upcoming centenary, I suspect we should be getting a few of those soon.TR 08:48, 8 September 2014 (UTC)


 * If the universe began with no matter or radiation (only the cosmological constant &Lambda;), then the Friedmann equations which incorporate the Einstein field equations reduce to:
 * $$ \frac{\dot{a}^2 + kc^2}{a^2} = \frac{\Lambda c^2}{3} $$
 * $$\frac{\ddot{a}}{a} = \frac{\Lambda c^2}{3} $$
 * which can be satisfied by:
 * $$ a = \sinh \left( c \, t \, \sqrt{\frac{\Lambda}{3}} \right) $$
 * $$ k = - \frac{\Lambda}{3} \,.$$
 * At time t=0, the universe was already expanding so fast that it could not collapse on itself. JRSpriggs (talk) 15:26, 8 September 2014 (UTC)

Another note on style
Not being a physicist, I would like to throw another note on style. We have two articles, one for the general theory of space (general relativity theory, this article), the other for an introduction into it. However, the physical section in this article starts by a phrase: "General relativity can be understood by examining..." I think that this (technical) article should, like all other articles on other subjects, state what the subject of the article is, while the introductory article should contain the opinionated discussion of how the subject can be best understood; we need to separate the concerns and get two essentially different articles. I do not negate that this section may be potentially applicable into the article, but I think that in any case it should go after an essential presentation of the subject (what does it consist of, into where are applied its parts in the process of cognition, how is it used in real-life cognition, what most discussed&weighted properties does it have), if it should go at all in this article, and not say, in the historic article or in the introductory article, or even in a wikibook. - Evgeniy E. (talk) 13:19, 1 January 2015 (UTC)

A note on style
«In 1917, Einstein applied his theory to the universe as a whole, initiating the field of relativistic cosmology. In line with contemporary thinking, he assumed a static universe, adding a new parameter to his original field equations—the cosmological constant—to reproduce that "observation".» Irony is out of place here; we know very well that that was not an observation, so let us not "affect ignorance" for no purpose. I think we need a different word. - Evgeniy E. (talk) 12:30, 1 January 2015 (UTC)
 * Edited for "assumption" - Evgeniy E. (talk) 12:37, 1 January 2015 (UTC)
 * I agree. Isn't it the case that a static solution is impossible without the cosmological constant? The wording is still not good. Something along "to make the assumption possible at all" might me better. (But I still don't like it.) YohanN7 (talk) 13:13, 1 January 2015 (UTC)
 * You are a native speaker here (are you? ;) ), so it is up to you to decide, or to other people who would have better versions. Indeed, a static solution is impossible without the cosmological constant. - Evgeniy E. (talk) 13:19, 1 January 2015 (UTC)
 * Even with the cosmological constant, a "static solution" would still be unstable.
 * Actually, that the universe is static is an observation, just not a very good observation. When we look at the sky we do not see stars, nebulas and galaxies visibly rushing towards us, nor away from us. That is, their angular diameter does not visibly change. So the Hubble constant is close to zero, just not close enough to justify what Einstein did. JRSpriggs (talk) 22:02, 1 January 2015 (UTC)
 * Certainly a valid point. But "observation" (with quotes and all) is just derogatory. I think Q's attempt is best so far, not perfect though. Something longer could be put in an "nb" (footnote with a suitable name to catch the readers attention). YohanN7 (talk) 23:00, 1 January 2015 (UTC)

Image from Interstellar
This added image]: I think the license description and caption needs modification if the image is to be retained. —Quondum 16:39, 16 February 2015 (UTC)
 * needs its licensing description tweaked (according to the source: "This image may be used under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 (CC BY-NC-ND 3.0) license. Any further distribution of these images must maintain attribution to the author(s) and the title of the work, journal citation and DOI. You may not use the images for commercial purposes and if you remix, transform or build upon the images, you may not distribute the modified images.")
 * has a caption that is somewhat misleading, in that it makes a general statement about the appearance of a black hole, but the image relates to a very specific configuration (high rate of spin, specific assumptions about light source; if this is an accretion disk, this is curiously (or should I say unrealiscally?) transparent
 * is unrealistic for the encyclopaedic context due to, as the source puts it: "(no colour or brightness shifts) with lens flare added". Or: certain cinematographic choices were made to meet the perceived expectations (or familiarity) of the viewers, deliberately changing it from what an observer would see directly with their eyes, possibly the most "realistic" content.


 * If the image is retained, then its caption should be enhanced to explain the three bands of light seen. And if the black hole is rotating, which way is it rotating? Is the axis of rotation pointed at the observer or slightly below the observer? Is the light emitted by an accretion disk or does it come from objects behind the black hole? JRSpriggs (talk) 06:14, 17 February 2015 (UTC)

fermions and the need for the tetrad formulation over the metric formulation
The formulation of GR in terms of a metric cannot be fundamentally correct, because it does not allow coupling to fermions, and fermions exist. We need the tetradic formulation to couple to fermions, see spin connection.

Need a section on the tetradic formulation and links to spin connection and Tetradic Palatini action? Ibayn T 15:01, 31 December 2014‎ (UTC)


 * This article is about general relativity as it is usually understood and described in most reliable sources, i.e. the metric version. Variations can be described in separate articles and/or summarized in alternatives to general relativity.
 * Do you know of a conclusive proof that coupling to electrons is not possible? Please give a link or citation to that effect.
 * Perhaps fermions (such as electrons) do not exist as fundamental particles, but instead they are emergent phenomena (such as holes in semiconductor crystals, or wormholes in a higher-dimensional bulk M-theory) who's apparent existence depends on the fact that the metric here is nearly Minkowskian (flat). JRSpriggs (talk) 06:28, 1 January 2015 (UTC)

On point 2...In "Quantum field theory" by Michio Kaku:

"However, the coupling of gravity to spinor fields leads to an immediate difficulty: There are no finite dimensional spinorial representations of the group GL(4). This prevents a naive incorporation of spinors into general relativity. There is, fortunately, a trick that we may use to circumvent this problem. Although spinor representations do not exist for general covariance, there are, of course, spinorial representations of the Lorentz group. We utilize this fact and construct a flat tangent space at every point in the space."

The need for tetrads to couple fermions to gravity is quoted in many other places.

I would say that point 3 is not how fermions are "usually understood and described in most reliable sources".

Ibayn T 15:01, 1 January 20145 (UTC) — Preceding unsigned comment added by 86.152.185.4 (talk)


 * In any case, fermions only arise in the context of quantum mechanics which has yet to be reconciled completely with general relativity. After that reconciliation, we will be in a better position to see whether GR needs to be changed to accommodate fermions. JRSpriggs (talk) 18:34, 4 January 2015 (UTC)


 * I concur with JRSpriggs that this topic is too obscure to include this, or even draw attention to it specifically. It is too harsh to point out such an obscure point in a theory that is known to be incompatible with QFT. This is an obscure aspect of the incompatibility, in the sense that it is poorly developed, at least in WP. To call it the "tetrad formulation" is also a misnomer, and it seems to relate to the relaxing of an assumption and has nothing to do with tetrads: in particular, it relates to the coupling between the metric and the affine connection, if the article Tetradic Palatini action is to be taken literally.  Even Kiku's quoted claim about the nonexistence of a finite spinoral representation of GL(4) also seems in need of confirmation or scrutiny, and even if valid, is not necessarily an inherent obstacle to the "naïve incorporation of spinors into general relativity". This article is about general relativity, not about finer points of QFT. —Quondum 19:05, 4 January 2015 (UTC)


 * GR in not known to be incompatible with QFT. YohanN7 (talk) 20:30, 4 January 2015 (UTC)


 * This hardly seems worth arguing about. My statement may need qualification, but suffice it to say that combining GR and QFT seems to be a thorny problem, and that one or both seem to be in need of tweaking for a successful unification. My point remains. —Quondum 22:43, 4 January 2015 (UTC)
 * It was not a personal attack. For years I thought it was a proven fact that GR is incompatible with QFT. It isn't. Just saying. YohanN7 (talk) 01:58, 5 January 2015 (UTC)

Not sure what

"To call it the "tetrad formulation" is also a misnomer, and it seems to relate to the relaxing of an assumption and has nothing to do with tetrads: in particular, it relates to the coupling between the metric and the affine connection, if the article Tetradic Palatini action is to be taken literally."

means. Possibly you have missed the point of what a first order formulation of the action principle is about? Perhaps I need to explain it better in the article? The general idea of first order formulations is introduced, for example, in Ray D'Inverno there in the context where you take the metric $$g_{\mu \nu}$$ and affine connection $$\Gamma^\sigma_{\mu \nu}$$ as independent variables both to be varied over. There it is explained that this first order formulation is a more elegant way of proceeding...

With the Tetradic Palatini action we take the tetrad $$e^I_\mu$$ and the spin-connection $$\omega^{IJ}_\mu$$ as independent variables. This independent spin-connection defines a "new" curvature tensor yep. Variation of the action due to variation of the teterad field $$e^I_\mu$$ only directly gives Einstein's equations all be it involving this "new" curvature tensor (and the tetrad). Variation with respect to the spin-connection implies the "compatibility condition" $$D_{[\mu} e^I_{\nu]} = 0$$ which uniquely gives the spin connection in terms of the tetrad - it also allows this "new" curvature tensor to be identified with usual curvature tensor written in terms of tetrads (so end result is all written in terms of tetrads!)...What this all tells you is that if you had written the action solely in terms of tetrads in the first place (and never introduced the spin-connection as an independent variable - given it in terms of these tetrads. This is the second order formulism and probably what you would call the tetradic action), varying the action with respect to tetrads you would have got out Einstein's equations written in terms of tetrads - the first order formulation is just a more elegant way of arriving at this result.

Ibayn T 8 January 2015.


 * I am not objecting to, nor do I even understand the Palatini action. My point was simply that the use of tetrads is inherently non-essential to any result, although a treatment of the subject may find such a set of basis fields convenient. The statements "We need the tetradic formulation ..." and "The need for tetrads to couple fermions to gravity is quoted in many other places" seem to imply that they are essential. —Quondum 21:54, 8 January 2015 (UTC)


 * Tetrads are essential if spinor fields are to be consistent with general relativity. This article is about the classical General Relativity of Einstein so I don’t think much should be said about spinors and tetrads here. But they should certainly be mentioned and links provided. There is a very extensive and important body of literature on “Gauge Theories of Gravity” which extend General Relativity by taking the tetrad rather than the metric as fundamental. For a comprehensive survey of the field, see for example http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=gauge+theories+of+gravity+hehl . Unfortunately Wikipedia does not yet have any authoritative article on this topic (Gauge_theory_gravity and Frame fields in general relativity are still minimal and inadequate). I’m too lazy to write one myself but I hope somebody will    (-:  Ericlord (talk) 16:53, 21 February 2015 (UTC)


 * Unlike the metric, there is no evidence that tetrads exist in physical reality. So it is questionable to call that subject "important". JRSpriggs (talk) 17:11, 22 February 2015 (UTC)

Information unsourced
Good evening. I hereby inform you that this this article - a featured article - possess many sections and information on any source (see the link to my edition). Someone who understands the subject, or that is "responsible" for its quality, or know how to do it could add sources? I really appreciate it. --Zoldyick (talk) 07:22, 30 June 2015 (UTC)
 * You tagged the opening sentence of several sections. If you read the corresponding sections you will see that they are all sourced. Reverted! Coldcreation (talk) 07:43, 30 June 2015 (UTC)

''Kurt Gödel showed that closed timelike curve solutions to Einstein's equations exist which allow for loops in time. The solutions require extreme physical conditions unlikely ever to occur in practice, and it remains an open question whether further laws of physics will eliminate them completely. Since then other—similarly impractical—GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes.''

Where is the source for all that text? I am exercising my right player and checker. I want to check the source. Where / what is the source? --Zoldyick (talk) 08:18, 30 June 2015 (UTC)


 * Without commenting on the sourcing issue, the quoted sentences make a judgement of "unlikely to appear in practice" and "similarly impractical". These phrases do not belong in a WP article on this subject as exppressing bias.  —Quondum 13:24, 30 June 2015 (UTC)


 * Noncontroversial sentences that discuss common well-known facts do not always have to be backed up by citations. Many, but not all, of the sentences that you tagged were of that category. The citation needed template indicated that you found the material doubtful, although not harmful enough to actually require removal. Is this what you believe? See WP:NOCITE for discussion of these points. Stigmatella aurantiaca (talk) 16:08, 30 June 2015 (UTC)


 * There are essentially no sentences (or not very many at all) in this article that constitute common knowledge or well known facts as described by WP policy. The sky is blue is common knowledge; "Kurt Gödel showed that closed timelike curve solutions to Einstein's equations exist which allow for loops in time" bloody well is not.


 * I am a former professor of chemistry at a major institution, with years of teaching and research experience at the interface between the fields of chemistry, physics, and other fields (and doctoral training done at a premier institution known for its physics and physical chemistry, with graduate coursework with the likes of Steven Berry et al.). I want citations to these sentences, (a) to check and convince myself that they reflect the preponderance of expert opinion on the subject of each section, and/or (b) to do further reading to learn what is needed when the text alone is insufficient to convey understanding. This is what encyclopedic writing her,e in the sciences, especially, is intended to allow. And if I desire clear unequivocal sourcing, lessor trained individuals need and deserve them.


 * Stop arguing 's point and start sourcing unsourced sections and sentences. This is the main article space, and not someone's sandbox. The articles factual content should be sourced, per WP:VERIFY, from good secondary scientific sources.


 * I am placing a tag indicating the need for better sourcing. And by the by, having black hole as opening image is as pedagogically nonsensical as the argument for common knowledge.


 * Le Prof Leprof 7272 (talk) 02:49, 26 November 2015 (UTC)


 * An article of moderate size having 200 incline citations is not, in general, lacking inline citations. Making the article look like a junkyard (by splattering tags) is not an improvement, nor beneficial. If you feel a sentence needs a citation, well, then add a citation. If you are an experienced professor, you should know how to find (even have access to) the relevant publications. (Even I can do that, and I do it a lot when I am in the right mood, including in subjects I know little about.) That is the way to improve the article. For instance, if you fail to find Gödel's original paper or secondary sources (having both is preferable), then you can place a tag at the relevant sentence.


 * Stepping in here giving others orders to "fix the bloody article" will not have the desired effect. Fix things yourself since you very obviously could. YohanN7 (talk) 10:57, 26 November 2015 (UTC)


 * As för Gödel's timelike curves, it took me ten seconds to find Closed timelike curve, and a bunch of papers/PDF's via Google (I'm a slow typist.) The wiki article contains references. YohanN7 (talk) 11:04, 26 November 2015 (UTC)

So, I added a primary source on the closed timelike curve (CTS). It remains to find a second source, and I think this, Closed Timelike Curves by Kip Thorne should suffice. I don't have time a t m to fill out all details about the publication (presumably conference proceedings), but CiteSeer says it is cited, hence published. (The link is to a preprint.)

Interestingly, according to Thorne, Gödel wasn't first to find a CTC. YohanN7 (talk) 12:18, 26 November 2015 (UTC)

600 kilometers
In the summery of the image featuring a simulated black hole, it says a "distance of 600 kilometers" - should this really be light years? It seems like 600 kilometers is really close in astronomical units
 * A simulated black hole of 10 solar masses within the Milky Way, seen from a distance of 600 kilometers. -- 19:00, 26 January 2016‎ UTC


 * A black hole of ten solar masses would be rather small (in radius) compared to the Sun. Thus at a distance of light years, it would be invisible. I think the caption is correct as is. JRSpriggs (talk) 22:42, 26 January 2016 (UTC)

Tentative removal of "new era" quote, pending at least acceptable revision of it
Tossing in "thus opens new beginning of gravitational wave astronomy" at as the end of an otherwise coherent sentence was an insignificant improvement and part of an overall damaging edit. Mansi Kasliwal (who is one of the authors of a paper we cite elsewhere  an earlier paper we cite elsewhere) is an astro PhD & visiting assoc. prof. at the institution and may even be the best qualified source we can quickly quote, b ''. But the butchery into word-salad of whatever she said, and the lack of info about how close to the work she is, make that edit a very definite minus in the form that i found and removed''. -- Jerzy•t 10:15 & 10:45, 16 February 2016 (UTC)

Problem with vacuum Einstein equations
Re quote: the results are the vacuum Einstein equations, R_{\mu\nu}=0.\ This implies that away from sources (matter and energy), the Ricci curvature is zero. Clearly, spacetime is curved near but outside the sun. Further explanation is needed. — Preceding unsigned comment added by Ian R Bryce (talk • contribs) 07:11, 25 March 2016 (UTC)


 * The Ricci curvature tensor is merely the trace of the Riemann curvature tensor. The Riemann curvature tensor would only be zero, if one were in flat (Minkowski) space. The Ricci curvature tensor can be zero even when the Riemann curvature tensor is not zero. That is what happens just outside a star.
 * What this means is that the tidal forces in a vacuum (where Ricci is zero) must add up to zero. In Earth orbit, for example, gravity stretches things vertically and compresses them horizontally. The total change in volume resulting from this is zero. Within the Earth (where Ricci is positive) the compression effect is greater than the stretching. JRSpriggs (talk) 11:43, 25 March 2016 (UTC)

Qualitative animation of 3D space + time
People have suggested me to create an animation of a 3D cubical grid getting distorted by a spherical mass. Along the points where the grid crosses, tiny clocks would be added with hands spinning at different rates, with slower clocks near the mass. The idea is to have it as a looped GIF or a small video.

This would be created in order to better convey the distortion of 3D space and time, and to avoid the rubber sheet model.

I'm not really formally well-versed in GR, and at this point what I have is merely qualitative. I think it is fine since the exact details won't work well in a diagram anyway. However, I'm wondering if there's a specific way to distort the grid that would be more accurate. For instance, should the distortion to the grid be conformal? Can we convey some useful information with colors on the grid?

At the moment, I'm not using an infinite grid as that looks really messy. I'm restricting myself to a 3x3x3 grid, as it conveys the idea just fine without clutter.

I'd love if someone could pitch in to help. Cheers! &mdash; LucasVB | Talk 05:26, 10 April 2016 (UTC)


 * Well, I went ahead and did it anyway. Feel free to include in the article if you guys think it's good. &mdash; LucasVB | Talk 02:04, 11 April 2016 (UTC)


 * Hi, I like your animation, but 21 MB is altogether too big, besides which, I can't play it on my mobile phone. So I took the liberty of extracting a few frames from it and making an animated GIF and a non-animated "cover letter", since I don't want to force people (especially mobile users) to download a 3.4 MB GIF unless they really intend to play the file. I'll shortly be using it in the article Spacetime, where the thumbnail is going to look like the one I've copied here. Stigmatella aurantiaca (talk) 20:42, 11 June 2017 (UTC)


 * It's there right now, the next to last figure. Stigmatella aurantiaca (talk) 09:43, 12 June 2017 (UTC)


 * Hello! Extracting frames from the video is probably not ideal, but will do for now. I'll see if I can generate the frames again soon and create an optimized GIF that's sharper. The reason I went for video was because the animation required too many colors between the stresses and distance fade out. I'll see what I can do about it. Cheers! &mdash; LucasVB | Talk 17:30, 20 June 2017 (UTC)
 * Much appreciate it. Just remember that not everybody using a cell phone has a 20 gazillion byte data plan. If you have kids on a family plan, you know the expense associated with them going "over" on the account! Frowny.svg Stigmatella aurantiaca (talk) 17:52, 20 June 2017 (UTC)

Overlinking
Does anyone else think we should examine the sea of blue in this article and reduce the amount of overlinking? Tayste (edits) 03:31, 26 July 2017 (UTC)
 * I undid some wp:repeatlinking starting wth the lead and the 1 - History section: . I might continue later... - DVdm (talk) 10:24, 26 July 2017 (UTC)
 * Some more in sections 2 - From classical mechanics to general relativity and 3 - Definition and basic applications, and their subsections: - DVdm (talk) 11:57, 26 July 2017 (UTC)
 * All remaining sections are now "de-repeatlinked": . There might still be some overlinking, but afaiac not much. - DVdm (talk) 13:28, 26 July 2017 (UTC)

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How important is it that general relativity is a beautiful theory?
Several editors disagree on the importance of the statement that general relativity is a beautiful theory. Is this an important point to make, and if so, where in the article should this statement go? A statement to this effect has been in the article (with some discussion on its precise wording) since this version from May 22, 2017. (See discussion and consensus above.) Entire books have been written on the importance of beauty in physics. One recent collection of papers flatly states in its title that general relativity is the most beautiful of theories. Do we remove this statement from the article because a few editors do not feel awed by general relativity and don't agree with previous consensus?

General relativity is universally acknowledged as a theory of extraordinary beauty, such that it has often been described as the most beautiful of all existing physical theories.

Prokaryotic Caspase Homolog (talk) 06:16, 7 May 2018 (UTC)


 * I repeat from my summary: Beauty is in the eye of the beholder. This article is about a beautiful(imho) physical theory. In itself it has no intention to be beautiful, it is -maybe universally- perceived as such, but as theory it is there to give a model of physical reality. This is the core topic. Of course, an article about a theory of this deepness and importance may also deal with its acceptance, but its degree of being worshiped, as is sourced by abundant eulogies, or combated by more rare theorists, considered partly as cranks, does not belong in the leade, rather to History, or -considering the fundamental importance- in a new section "Acceptance/Valuation". I do not want the part of WP, considered as floridly formulated, to grow, and I would not bold the consensus from the above thread, but rather scare it. Purgy (talk) 07:18, 7 May 2018 (UTC)


 * I think the remark should stay where it was. We don't say that GR is beautiful. We say that it is acknowledged as such, with sufficient sources, so I think we can safely undo the most recent removal. - DVdm (talk) 09:20, 7 May 2018 (UTC)
 * Agree, beauty should remain in the article, per Prokaryotic Caspase Homolog, DVdm, and per sources. Coldcreation (talk) 10:38, 7 May 2018 (UTC)
 * The sourced material has been restored to the lead, but it should also be mentioned in the article somewhere. Where? Coldcreation (talk) 11:11, 7 May 2018 (UTC)
 * Possibly there should be a short historical section on the scientific community's reaction to general relativity which refers to History of general relativity as the main article? However, History of general relativity at present does not have any discussion of beauty or the scientific reaction to GR. This gets all tied up into the story behind GR's creation and Einstein's motivations driving its creation. Fortunately, the genesis of GR is extremely well documented. I would see about editing the History first. I am extremely hesitant about digging in and making major changes to a featured article without having the groundwork prepared first. Prokaryotic Caspase Homolog (talk) 11:32, 7 May 2018 (UTC)

I think the remark should stay, as above we are saying that people find it beautiful, not that it inherently is so. Absolutelypuremilk (talk) 12:58, 10 May 2018 (UTC)
 * I've added a paragraph explaining how, over the years, GR has acquired its reputation for beauty. Prokaryotic Caspase Homolog (talk) 23:29, 11 May 2018 (UTC)
 * Is its perceived beauty so absolutely integral to understanding general relativity that it should be the subject of the second sentence of the article? I think this material should remain, but not in the lead. 108.34.206.74 (talk) 22:01, 14 May 2018 (UTC)
 * I think that you make a good point. A general consensus indicates that it belongs in the lede, but its current position as the second sentence in the lede is perhaps too early. Personally, I see no problem with moving it to the last sentence of the lede. Prokaryotic Caspase Homolog (talk) 22:29, 14 May 2018 (UTC)
 * There being no objections expressed to my suggestion, I have moved the sentence to the end of the lede. Prokaryotic Caspase Homolog (talk) 04:55, 16 May 2018 (UTC)
 * Looks like a perfect location for that sentence. And nicely done on the follow-up paragraph on beauty in the main article. Coldcreation (talk) 05:59, 16 May 2018 (UTC)

Motivation for developing GR
The article says, "Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his new relativistic framework." Is this really true? My understanding is that Einstein wanted to include acceleration in relativity, to have all reference frames equivalent. He even says so in his book _Relativity: The special and general theory_. It was only when he realized that acceleration and a gravitational field are physically the same thing that gravity came into consideration. Betaneptune (talk) 16:37, 8 November 2018 (UTC)

Similarity of objects in accelerating elevator vs one at rest on the earth.
In the rocket figure it says, "According to general relativity, objects in a gravitational field behave similarly to objects within an accelerating enclosure. For example, an observer will see a ball fall the same way in a rocket (left) as it does on Earth (right), provided that the acceleration of the rocket is equal to 9.8 m/s2 (the acceleration due to gravity at the surface of the Earth)."

This is a _postulate_ of general relativity, not a result thereof, and was known by Galileo, although in a different form. Both imply the equivalence of inertial and gravitational mass.

Also, it is better to use a rope pulling a hook on top of the elevator car than a rocket engine. This is so the rider can look at the hook and rope and still have no way to conclude whether the elevator car is hanging or accelerating. From Einstein's book _Relativity: the special and general theory_: ". . . he discovers the hook in the middle of the lid of the chest and the rope which is attached to it, and he consequently comes to the conclusion that the chest [or our elevator car] is suspended at rest in the gravitation field." This is rather hard to do with a rocket instead of a rope and hook! Also, the elevator car would lose mass, requiring a changing force, and hence thrust, and would run out of fuel at some point. The rope and hook is a much better way to demonstrate the equivalence of acceleration and gravitation.

Additionally, they don't behave similarly; they behave identically, which is essential to the point. Betaneptune (talk) 16:58, 8 November 2018 (UTC)

"impossible to decide"?...
"for an observer in a small enclosed room, it is impossible to decide, by mapping the trajectory of bodies such as a dropped ball, whether the room is at rest in a gravitational field, or in free space aboard a rocket that is accelerating at a rate equal to that of the gravitational field"

I find this misleading because it seems to imply a constant acceleration for the rocket, but the gravitational field varies with 1/r2. So for this to be true mustn't the acceleration of the rocket vary according to the height of the ball above the floor? This seems impractical. (There are devices on earth that are capable of measuring the variation in the gravitational force over a distance as small as 1 metre, so this effect should be detectable.) Boardhead (talk) 14:00, 12 April 2019 (UTC)


 * See Rindler coordinates. The acceleration in a rocket does vary (slightly) depending on how high one is from the floor. Also the distribution of masses near the room affects the shape of the variation in the gravitational field so the 1/r2 (which assumes a spherically symmetric mass) may be modified. In other words, the equivalence principle is not just a first order approximation. By manipulating the gravitational sources and the rocket you can match them as closely as you need. JRSpriggs (talk) 06:34, 13 April 2019 (UTC)


 * Thanks for this explanation Boardhead (talk) 15:27, 26 April 2019 (UTC)

"General relativity is considered probably the most beautiful of all physical theories."
Finding the above sentence a bit awkward, I changed "probably" to "among", but my edit was reverted. While the cited source indeed says "probably", the encyclopedia does not need to parrot the sources' wording. To view something as "probably the most beautiful" is to consider it "among the most beautiful". The latter of the two isn't as specific, but the difference is minor, and thus the former isn't necessary when it makes the wording this way. AndrewOne (talk) 08:03, 8 August 2017 (UTC)


 * While the wording can be discussed, "among the most beautiful" does not capture what many sources say, namely that GR is the most beautiful theory. It really is. QM is fun (extremely interesting, ingenious, etc), but not pretty. YohanN7 (talk) 08:11, 8 August 2017 (UTC)


 * Perhaps, as this is not the first time the word "probably" gets removed or changed—see edit history—, in order to avoid this being changed again in the future, we can put the phrase in quotes. I don't think it is necessary now, but next time I'll do it anyway. - DVdm (talk) 08:18, 8 August 2017 (UTC)


 * Either that, or change the wording (so that it is not a literal quote) and supply a bunch of citations. They are easily found. YohanN7 (talk) 08:23, 8 August 2017 (UTC)


 * Somebody changed it to "one of the most important of all existing physical theories" and kept the reference. This is not what the reference says. It is weak, subjective and superfluous. Are we to rank physical theories by importance and mention it in the intro for all the others which are "one of the most important"? I removed it but it got reverted. Either it should be reverted to the original statement about beauty or removed altogether. If it is reverted the statement should be a quote as suggested above because it is too vague and subjective to stand as a verifiable claim. Weburbia (talk) 11:53, 20 August 2017 (UTC)
 * Oops, made a mistake. Corrected now: . The cited source says: "It was established by Einstein (and finally formulated by him in 1915), and represents probably the most beautiful of all existing physical theories." - DVdm (talk) 12:19, 20 August 2017 (UTC)
 * Thanks. How about "has been described as" rather than "is considered"? The text book was written a long time ago and I am not convinced that the quote establishes a current consensus as implied. Weburbia (talk) 12:29, 20 August 2017 (UTC)
 * Given the likely consensus on the value and the relevance of the source, I'd personally prefer to keep it, but not too big a deal... - DVdm (talk) 12:40, 20 August 2017 (UTC)

While that book was written long ago, it has been revised and brought up to date throughout the decades. That passage was kept. L&L did not splatter around assessments of theories (or their authors), but they made one exception, that for Einstein and his theory (throughout the whole L&L series). General relativity does have a status that no other theory has. The status is not so much about absolute fundamental correctness, but it is about its enormous predictive power and beauty. Like I said above, it is easy to find references in modern books by both mathematicians and physicists supporting this general observation. Its status didn't exactly diminish after the first observation of gravitational waves, and string theorists set out to prove GR (on all reasonable scales) right, not wrong. YohanN7 (talk) 10:56, 8 September 2017 (UTC)
 * One quote about its beauty does not warrant a general claim that it "is considered" beautiful, implying that everyone agrees. Maybe everyone does agree, but a single source (or even several sources) calling it beautiful doesn't show that. I think "has been described as" is closer to being neutral. KSFT (t&#124;c) 21:43, 18 October 2017 (UTC)
 * Here is another reference to beauty in this case, beautiful. There is also an exquisitely in there for good measure. Irondome (talk) 22:14, 18 October 2017 (UTC)

An subjective statement like "General relativity is considered probably the most beautiful of all existing physical theories" is almost impossible to properly source. No matter how well regarded the cited source, the authors clearly are expressing their opinion. As such the cited quote can only be used to verify the authors' opinion on the matter. To verify the statement including "is considered", you would need to cite a reliable source that establishes that this opinion is widely held (through sociological research or something). Lacking such a source a formulation involving "has been described as" comes much closer to be verifiable. (Don't get me wrong, personally I definitely share the opinion that GR is one of the most elegant theories out there, but I also recognize that that is my opinion.)TR 14:46, 19 October 2017 (UTC)
 * I agree and would see no issue with "has been described as", "is commonly described as", "often considered to be", etc. — Paleo  Neonate  – 16:30, 19 October 2017 (UTC)


 * I don't see the need to include any description of its beauty. Why is it included? You don't see the articles on quantum mechanics, evolution, germ, or other scientific theories described in an esthetic manner. MartinezMD (talk) 18:29, 29 May 2019 (UTC)


 * This is because none of the other theories that you mention have inspired multiple articles (and even an entire book) that describe the theory in terms of its beauty. In contrast, some other theories, such as the Standard Model, are consistently described as "ugly". I personally would consider the theory of Descent with modification by natural selection to be equally beautiful, but there are no articles (and certainly no book) that treat Natural Selection from an aesthetic point of view. Prokaryotic Caspase Homolog (talk) 19:16, 29 May 2019 (UTC)

A Commons file used on this page has been nominated for deletion
The following Wikimedia Commons file used on this page has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 07:36, 13 July 2019 (UTC)
 * Light deflection.png

refines / supersedes
To a third party observer like me who watches the page, this seems ridiculous (both are true). I suggest to form a consensus here for one or the other instead of constantly switching from one to another... Thanks, — Paleo Neonate  – 12:25, 23 July 2019 (UTC)

Well, or for an alternative that conveys more clearly the intended meaning, of course. — Paleo Neonate  – 12:25, 23 July 2019 (UTC)


 * Agreed. My take on it: as Newton's theory is still perfectly valid and useful in the low-gravity-low-speed limit, I think that "refines" is better (—even if perhaps just slightly—) than "supersedes". I don't think we need to worry about how flat-earthers might get confused by either alternative here. - DVdm (talk) 13:11, 23 July 2019 (UTC)


 * Likewise. There is no need to pay attention to the people who believe the Earth is flat. Such an idea is untenable even by the standards of 2000 years ago. Nerd271 (talk) 02:16, 24 July 2019 (UTC)

Short description
The original short description contradicts the article. It reads, "Theory by Albert Einstein, covering gravitation in curved spacetime." In reality, general relativity tells us that gravitation manifests itself as the curvature of spacetime. Again, that's not what the article says. My alternative is correct and does not contradict the article. Nerd271 (talk) 15:42, 22 June 2019 (UTC)
 * Then I propose "Theory by Albert Einstein, covering gravitation and curved spacetime", or better still, "Theory by Albert Einstein, covering gravitation as curved spacetime". Anyway, my main objection to your proposal was the somewhat accusing tone of the phrase "due to Albert Einstein", and the re-splitting of the essential concept of "spacetime" into "space and time". - DVdm (talk) 16:18, 22 June 2019 (UTC)
 * I went ahead. - DVdm (talk) 08:09, 23 June 2019 (UTC)
 * Thank you! That's much better. The word 'as' is the right one here. I think we should also add the adjective 'scientific' to emphasize the fact that general relativity is not a child of an idle mind or some crazy mathematics on a piece of paper but rather a proper scientific theory supported by mountains of empirical evidence. What do you think? Nerd271 (talk) 02:20, 24 July 2019 (UTC)
 * I don't think we need that, as the description is already significantly longer than its 40 recommended characters. In order to get closer to 40, perhaps we should amend it to "Einstein's theory of gravitation as curved spacetime".- DVdm (talk) 08:20, 24 July 2019 (UTC)
 * Fair enough. I think your new proposal is even better. Nerd271 (talk) 12:53, 24 July 2019 (UTC)
 * ✅: . - DVdm (talk) 13:14, 24 July 2019 (UTC)

A Commons file used on this page or its Wikidata item has been nominated for deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 23:37, 9 February 2020 (UTC)
 * Relativistic precession.svg

Books
Shall we create a separate page for the notable books on general relativity at various levels? This article is already long in its current state. We do have pages for lists of textbooks in classical mechanics and quantum mechanics, of thermodynamics and statistical mechanics, and in electromagnetism. Nerd271 (talk) 00:37, 14 June 2020 (UTC)

4D Spacetime: 3D Regular Space + 1D Time
Einstein recognized the 4 dimensions of spacetime: 3D regular space + 1D time. 2601:589:4800:9090:489:97E6:2CC8:D11E (talk) 13:01, 21 August 2020 (UTC)