Talk:General relativity/Archive 11

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Archive 10 Archive 11 Archive 12

Error about the curvature of spacetime

There is a false statement in the main article: General relativity further calls for the curvature of space-time.

The general relativity doesn't call for the curvature of spacetime. Besides, the spacetime has to be flat if the 4-momentum of a particle is to be uniquely determined after its parallel transport to another event in spacetime which seems to be indispensable for a magic free physics. Jim 22:11, 16 October 2007 (UTC)

You transport that vector along the world-line (path) which the particle actually follows. This removes any ambiguity. Flatness is not required. JRSpriggs 00:09, 17 October 2007 (UTC)

WikiProject Relativity

I've finally decided to introduce Wikipedia:WikiProject Relativity. I've included it as a subproject of Wikipedia:WikiProject Physics. Please note in particular the 'Miising articles' section. Thanks. MP (talkcontribs) 11:34, 24 October 2007 (UTC)

references section

I've attempted to organise the refs. a little better. I've just made a division into BOOKS and JOURNALS , but there are some refs in the latter subdivision that are not quite journals (lecture notes on Arxiv) and hence a finer subdivision may be given. Also, the names of authors are repeated links; this superfluousness should be sorted too. MP (talkcontribs) 20:15, 10 November 2007 (UTC)

Still much too long

This article is still much too long — at least twice its maximum acceptable length. It takes forever to down-load even now that I have a fiber-optic connection. Trying to go through the revision history to make sure that no vandalism or other errors have been introduced is torture. JRSpriggs 08:24, 12 November 2007 (UTC)

I wouldn't say much too long - the text part is currently 63kB, which is acceptable as per WP:SIZE, especially seeing that the article covers a complex topic with many ramifications. That said, I am all for streamlining the article further - I just haven't gotten around to it recently as I'm in the process of moving house. On my to-do list, I have:
  • streamline the first three sections, possibly merging them into one, resulting in a concise description of the core of the theory; add references
  • streamline the "Relationship with quantum mechanics" sections (although I don't think that one is going to get much shorter); add references
  • merge the "Alternative theories" section into the basic description (when describing how one obtains gr from basic principles, there are opportunities to say "but if you do it differently in this way, you'll end up with that alternative theory")
  • propose deletion of "Quotes" section (I remember reading they are discouraged)
As for the page taking forever to download - I'm currently online via DSL using a standard copper phone line. Page download time is 5 seconds if it's the first WP page I load after clearing the cache, 2 seconds if I've visited other WP pages before. Sounds acceptable to me. --Markus Poessel 09:32, 12 November 2007 (UTC)

Gravitational lensing as means to look into Earth's past (Mirror by Gravity)

my hypotesis needs following elements to work:

  • discovery of a massive gravitational lensing effect in our proximity (10-5000 l.y.)
  • this lensing needs to be particulary lucky oriented such that light emited from Earth in the past is now emitted

towards the path our solar system is moving to.

Taking in account a slight time diltation given to Earth by its movement through space (as part of rotation of the galaxy arm) it would be possible to observe same light emited in the past by Earth by just passing through the beam of light diverted from the straight line that light takes by the gravity that caused the above lensing

  • Another hypotesis would work just by observing every close lensing and trying to catch a glimpse at the light emitted by Earth in the past .. that has has been curved 180 degrees and slinged back at us although im unsure if the said movement by the galactic arm would not move Earth too far and thus prevent us from observing our own reflection.


As a 'Quotations section' is now deprecated at Wikipedia, perhaps the Wheeler quote Spacetime grips mass, telling it how to move, and mass grips spacetime, telling it how to curve can be incorporated into the Einstein field equations section. If there are no objections to this, I'd like to try this. Thanks. MP (talkcontribs) 17:59, 18 November 2007 (UTC)

I've incorporated the Wheeler quote into the Einstein field equations section. I'd like to kill the Quotes section altogether, but out of courtesy to the editor who inserted the other quote, I've left it in for now. MP (talkcontribs) 19:24, 19 November 2007 (UTC)

Quotes section removed. MP (talkcontribs) 19:04, 24 November 2007 (UTC)

Alternative theories

I'm not sure exactly what the 'Alternative theories' section should really be about. Is it to only describe alternatives to GR without quantum mechanics ? If so, the main article link to Alternatives to general relativity seems to be inconsistent with this rationale, as it appears to describe all possible alternatives to GR. I've added an introductory sentence to the section that I think should set the scene for the section. In consequence, I think that the 'Relationship to Quantum mechanics' section be placed after the 'Alternative theories' section. MP (talkcontribs) 18:34, 18 November 2007 (UTC)

Regarding Markus' suggestion of incorporating the Alternatives section into the Basic description, I still think that the Alternatives should remain, as they are historically important. Also, the basic description is of GR; incorporating the various alternatives into the main text would make the description not so basic. MP (talkcontribs) 18:38, 18 November 2007 (UTC)

Perhaps it would be better to divide the section into subsections: (1) pre-GTR alternatives, i.e. those which do not go as far as GTR; (2) alternatives which try to build on GTR, but do not comply with QM; (3) attempts to modify GTR (or its alternatives) to be consistent with QM, and (4) inherently QM alternatives for explaining gravitation, e.g. string theory. JRSpriggs (talk) 22:59, 18 November 2007 (UTC)
Sounds like a good idea. The section may become quite large if all the theories are mentioned explicitly, however. Perhaps you mean that a brief description of each type of theory (the 4 types you mentioned above) should be given and that this should, and hopefully will, be shorter than the present large list of theories. MP (talkcontribs) 19:28, 19 November 2007 (UTC)
Yes. In the interest of shortening the article, the actual lists should be put into another article(s) such as Alternatives to general relativity. However, I just noticed that that article divides the theories into four subsets which are different from the four which I suggested. JRSpriggs (talk) 01:58, 20 November 2007 (UTC)
I'm working on the section at Talk:General relativity/WIP. Any comments/suggestions are welcome. MP (talkcontribs) 21:48, 28 November 2007 (UTC)

Streamlining first 3 paragraphs

I'm not sure about Markus' 1st suggestion that the first 3 sections should be merged. Perhaps the first 3 paragraphs (maybe this is what Markus meant?) can be merged or shortened with less technical details. Here is my latest attempt (it takes out about 220 bytes):

General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16.[1] It unifies special relativity, Newton's law of universal gravitation, and the insight that gravitational acceleration can be described by the curvature of space and time, this latter being produced by the mass-energy and momentum content of the matter in spacetime.

General relativity is distinguished from other metric theories of gravitation by its use of the Einstein field equations to relate spacetime content and spacetime curvature.[2][3] The field equations are a system of partial differential equations whose solution gives the metric tensor of spacetime, describing its "shape". In the resulting geometry, an object moving inertially in a gravitational field is viewed as following a geodesic path that may be found using the Christoffel symbols of the metric. Solutions of the Einstein field equations model gravitating systems, especially important ones exhibiting spherical symmetry, notable examples being the Schwarzschild solution, the Reissner-Nordström solution and the Kerr metric.

General relativity is currently the most successful gravitational theory, being almost universally accepted and well-supported by observations.[citation needed] General relativity's first success was in explaining the anomalous perihelion precession of Mercury. In 1919, Sir Arthur Stanley Eddington announced that observations of stars near the eclipsed Sun confirmed general relativity's prediction that massive objects bend light. Other observations and experiments have since confirmed many of the predictions of general relativity, including gravitational time dilation, the gravitational redshift of light, signal delay, and gravitational radiation. Numerous observations are also interpreted as confirming one of general relativity's most mysterious and exotic predictions, the existence of black holes.

Comments welcome. MP (talkcontribs) 19:34, 19 November 2007 (UTC)

Is the word 'metric' in para 2 (other metric theories of gravitation) really needed this early on ? MP (talkcontribs) 19:38, 19 November 2007 (UTC)

Oh, sorry. Maybe I should have looked here before changing the lede on the page. Meh... call me bold. Anyways, I made two substantial changes. First, I swapped the second and third paragraph. I think it's always good to ramp up complexity in an intro. A lot of people would never get to the section on what GR has done, if they had to wade through talk of tensors and partial differential equations first. Second, I added a note about the expansion of the Universe. Maybe it's not a great sentence, but I think it's an important point. (Also, I really don't think "aka" belonged there.) -- (talk) 00:17, 20 November 2007 (UTC) P.S. Sorry about the inaccurate edit summary. I didn't actually swap the first two paragraphs.

I actually did mean the first three sections - I think they can be replaced by a more concise description of the theory (which would automatically include the motivation, and mention the mathematics), similar in style to the way the Consequences and Astrophysical Applications sections are written now. I've got a rough draft and a list of references I want to include, but it's going to be a few weeks before I can get down to do some actual re-writing — the re-writing itself, of course, depending on how the article looks then! As for the lede — is it customary to include references there? Since it's merely a summary of the main, ideally well-referenced text, it's probably unnecessary, and I've seen featured articles without (which I, personally, find neater). --Markus Poessel (talk) 13:14, 20 November 2007 (UTC)
I don't think it's customary to include references at the start, but personally, I think it looks more respectable - I'm not going to quibble over this issue; do as you see fit regarding refs. I've included my version of the intro. (above) into the article for now. We'll see how it develops until your rewrite. MP (talkcontribs) 20:29, 20 November 2007 (UTC)
I just realised that by 'first 3 sections' you meant, 'first 3 after the intro.' (initally, I thought you meant the intro. + the next 2 sections). I'm sure you can conjure up a condensed version. Good luck! MP (talkcontribs) 20:39, 20 November 2007 (UTC)
Yes, sorry, may be that wasn't clear. I meant the first three as per the table of contents. We'll see how it goes with the condensed version. --Markus Poessel (talk) 22:56, 21 November 2007 (UTC)
Markus - Go for it. There is a slightly complex history to the evolution of those sections after I did the initial rewrite, and I can see where it has left those sections with a less-than-unified focus and message. So let's see what you can do with them. --EMS | Talk 04:20, 22 November 2007 (UTC)
Just a brief heads-up that I've started on streamlining the first three sections; the result is also likely to include what is currently the "Alternative theories" section. I'm currently working in my own sandbox, and will move the results to the WIP once they're a bit more presentable. Markus Poessel (talk) 19:47, 27 February 2008 (UTC)


Perhaps there should be a catchy image at the start of the article, like the one in Introduction to general relativity. That article has some good images etc. MP (talkcontribs) 19:02, 24 November 2007 (UTC)


The section General relativity#Cosmic segregation: Horizons uses the word "segregation" in a way which seems inappropriate to me. It could be interpreted as suggesting that an entity in either one of the two parts of spacetime cannot cross to the other. Actually, you can cross in one direction (indeed it may be difficult to avoid crossing), but not in the other. There is no physical barrier. It is like the Red Queen's race. JRSpriggs (talk) 04:55, 25 November 2007 (UTC)

Agreed. I suggest we look for more appropriate words or descriptions for the section title and the section itself. MP (talkcontribs) 16:55, 25 November 2007 (UTC)

Incentive to improve article

Check this out: Wikipedia:The Core Contest. GR, amongst many other articles, is listed in the contest. MP (talkcontribs) 20:11, 25 November 2007 (UTC)

Citation Needed? As if

"General relativity is currently the most successful gravitational theory, being almost universally accepted and well-supported by observations.[citation needed]"

I removed the citation warning. That's like asking for a citation when someone makes the claim that if you drop an apple it will fall to the ground. Come on, people. —Preceding unsigned comment added by (talkcontribs)

Avoid {{weasel}} words?

"Weasel words" are weasel words. If a statement is true, it is true. If it is false, it is false. If it is meaningless, it is meaningless. We should remove statements which are false or meaningless from Wikipedia. "Weasel words" imply that there is some hidden agenda behind a statement without saying what that hidden agenda might be, or suggesting a statement which is either more explicit or avoids the alleged hidden implication. Thus we should not use the

template nor the [weasel words] template. JRSpriggs (talk) 06:25, 14 January 2008 (UTC)

Annoying picture

there is an annoying moving picture on the page..... can we please get it deleted is keeps distracting me, and might distract others as well

Hello, anonymous person. Could you please state which picture you are referring to? There are two; the current intro picture and the gravitational wave animation. I am responsible for introducing the latter; I tried to keep it as unobtrusive as possible (choosing light colors, a smallish amplitude, and low frequency), but I think it is so much more helpful in illustrating what a gravitational wave does than a series of still images that it's worth keeping. Markus Poessel (talk) 13:10, 24 February 2008 (UTC)

I inserted the intro picture but won't object to removing it if someone else finds it annoying and finds a better picture to replace it. Also, Image:Light reflection.png seems to be a dead link. --Lantonov (talk) 06:57, 25 February 2008 (UTC)

In my subjective opinion, a moving intro picture might not be such a good idea. Many people object to the distraction caused by moving pictures in general, and while I do think they have their place whenever what they show is crucial for the understanding of an important concept, that is arguably not the case for an intro picture.
As you mention, there is a problem with Image:Light deflection.png - as far as I can see, that is one that I put on Wikimedia Commons, but where there was a problem with the license (I didn't state the license properly or something). I will see that I find the original and repost it. --Markus Poessel (talk) 15:06, 25 February 2008 (UTC)

Point well taken. I put the picture as an answer to the request for a "catchy image" in the intro Talk:General_relativity#Images. Maybe this is a wee too catchy. Anyone welcome for replacing the intro picture with a non-annoying one. --Lantonov (talk) 15:19, 25 February 2008 (UTC)

We've had a number of different pictures in previous versions, but nothing that made everybody happy, as far as I can see. Personally, I like the one we used for Introduction to general relativity, although I can see why we wouldn't want to re-use that one here. How about this one, which is a static version of the one we have there now? Markus Poessel (talk) 15:13, 26 February 2008 (UTC)

Not bad. I saw a number of good pictures on the APOD site. I know that NASA pictures from telescopes can be used freely but the situation with those that say "This is an artist's impression on ... " is different and one must ask permission from the author to use them. I chose several of them that I liked but all are artist's impressions. The picture that you propose is taken originally from the APOD site, I think, and the question of permissions is resolved somehow as it is already loaded in commons. --Lantonov (talk) 15:33, 26 February 2008 (UTC)

In fact, it's not an "artist's impression". The brief summary is misleading - on the commons page, there is a more accurate description. It's a simulation of what a black hole would look like if it were placed between the observer and the Milky Way (the background image being based on astronomical observations). Permissions aren't a problem - it was uploaded to Wikimedia Commons by one of the people who have run this simulation (Corvin Zahn). Markus Poessel (talk) 20:28, 26 February 2008 (UTC)

This is right, seems permission is ok here. So it is for now either this, or the one in Introduction to general relativity. Both are fine. This one is less catching (obtrusive, annoying, whatever) because it has less colors. But somehow it's more on topic (describing the movement of objects in the Solar system is principally on Newtonian mechanics, and makes less use of GR while black holes are GR throughout). --Lantonov (talk) 06:25, 27 February 2008 (UTC)

Actually, I think they're equally on-topic, but, as I noted above, I think it's good if the two articles (main and intro to) do not have the same lead pictures, so I would vote for the black hole, as well. Will you do the honours? Markus Poessel (talk) 13:43, 27 February 2008 (UTC)

Sure, with pleasure. Done. --Lantonov (talk) 13:59, 27 February 2008 (UTC)

Streamlining and referencing the first sections

I've finally managed to do what I promised back in November (now that my books have finally caught up with me after the move). So please find a new version of what are currently still the sections "Justification", "Fundamental principles" and "Mathematical framework", on Talk:General_relativity/WIP. I have brought the arguments contained therein into a form that, I think, is more suitable for a modern presentation of the theory, added some information that I thought was sorely missing (the concept of a solution, for example), and also added suitable references (on the WIP page, the references are only those not yet contained in the main article). The new version also makes the current "Alternatives theories" section redundant - it mentions the important metric alternatives at the point where it is logical to do so, namely where the field equations are addressed, and the PPN formalism has found a new home in the model-building section (the KK and supergravity bit should go into the current Quantum section). All in all, the new version is somewhat shorter than what's currently there, though not by as much as I had hoped it would be; still, given that the main text of the article is still on the long side, every bit helps. Oh, and the bit in the "Status" section about the additional assumptions about matter that need to be added is now also in the description of the concept of solution, where I think it belongs.

Unless there are objections, I will move the WIP version onto the main article page in a few days or so. Markus Poessel (talk) 03:52, 29 February 2008 (UTC)

The references in the last section became a little too much (5 already) but you can move them to other sections as you see fit. I think that the article is overeferenced if there is such an animal. --Lantonov (talk) 11:22, 29 February 2008 (UTC)
I think that, all in all, the article isn't over-referenced by Wikipedia FA standards – each statement has one or more references, and when they are multiple references, they often complement each other (some more, some less technical; different references for different aspects of a statement etc.) so no, I think we're in good shape there. You might want to put the five references in the last section into the same endnote, though, and include brief comments of what they are ("For information on the 6pN, see..." or similar. Markus Poessel (talk) 12:53, 29 February 2008 (UTC)
Nice work. I just have one suggestion to make: keep the quote, If all accelerated systems are equivalent, then Euclidean geometry cannot hold in all of them., as I think that it illustrates a very important aspect of the development of GR. If you believe that it shouldn't remain, then it should go somewhere else in the article. I was thinking it would fit in nicely into your relativistic generalistaion section, though. Thanks. MP (talkcontribs) 19:21, 1 March 2008 (UTC)
Hi MP, thanks for the positive feedback. I didn't manage to fit the quote in there literally, but I've reformulated the last paragraph of the section "Relativistic generalization" in a way that reflects more closely what the quote appears to say. I hope that addresses your concerns. Markus Poessel (talk) 21:29, 6 March 2008 (UTC)
OK, given that there are no additional comments, I will now make preparations for moving everything in. I'll try to get everything done by this evening (EST). Markus Poessel (talk) 16:11, 7 March 2008 (UTC)
Main move accomplished; some clean-up work remains. On a positive note, we're now at 60 kB, which, according to WP:SIZE, means we're no longer in the "Probably should be divided (although the scope of a topic can sometimes justify the added reading time)", but down to "May eventually need to be divided (likelihood goes up with size)". Given the complexity and scope of this article, I would say the streamlining goal has now been reached. Markus Poessel (talk) 19:36, 7 March 2008 (UTC)

Do we really need a split of references...

...into books and journals? I am dealing with the references section right now, reverting the expanded-template entries that I made back when the template engine had a limit that made those expansions necessary, and I notice that some articles are in the book section, and the other way around, which made me think: Why do we have this split in the first place? I'm all for putting the references section back into alphabetical order, with no subdivisions. My reasons:

  • At what point is that split going to benefit a user? As far as I can see, the only reason to look at the references directly (that is, not while following an end-note link from the article) is that you're looking for something specific by author. In that case, splitting the reference section can actually be confusing: you might be looking for some entry that you don't find because you're in the wrong subsection. Conversely, I can't think of a realistic scenario in which the split would be helpful
  • To be consistent, we would need to decide how to make the split. Do contributions to books count as articles? Should the book contributed to show up in the books section for completeness? Splitting seems to lead to unnecessary complications.
  • At least in the physics literature, it's not as if this split is common. So we cannot just say "Well, it's of no practical use, but we're conforming to general usage here"
  • The relevant section of the MOS (as far as I can see, the one I linked to is the relevant one, that is) just mentions listing all the articles, usually in alphabetical order.

Markus Poessel (talk) 17:44, 7 March 2008 (UTC)

Since nobody said otherwise, I've now brought the references back into alphabetical order. Markus Poessel (talk) 20:34, 4 April 2008 (UTC)

Missing paragraph from Status section

Any Lorentzian manifold is a solution of the Einstein field equation for some conceivable stress-energy tensor. Thus one must add auxiliary assumptions about the kinds of energy, momentum, and stress in the universe to make any inferences from GTR, e.g. about cosmology.

Why was the foregoing paragraph removed from the "Status" section? Surely this is essential to understanding that Einstein's theory cannot be tested in isolation from other physical theories. JRSpriggs (talk) 07:53, 8 March 2008 (UTC)

Precisely because it is so fundamental, the information on how to build models - including the information that additional matter laws need to be imposed - and what a solution of Einstein's equation is in the first place has moved up in the world, to the Model building section. Markus Poessel (talk) 19:16, 8 March 2008 (UTC)

Towards FA candidacy

I've just made the next-to-last of the major content changes and reference-adding that I had planned for this article: replacing the old quantum theory section, which had a lot on effective field theory and non-renormalizability, but very little on the other aspects of both the motivation of quantum gravity theories and on the different candidates with a text that is more inclusive but also, since our article is already very long, summary style. (I'm still in the process of adding the new references to the bibliography.)

Next, I would like to:

  • Revise the "Status" section – I propose that it be merged with the current history section, as the current state is very much a natural end-point for any account of what went on before
  • Revert the bibliography to simple alphabetical format, with no sub-division in books and articles (see my arguments two sections back, in Talk:General relativity#Do we really need a split of references... )

...and then starts the clean-up phase:

  • Some bibliography entries need re-formatting
  • Weed out (and remove to the Gr resources page) whatever is in the bibliography, but not referred to from the text
  • There are still some red-links for which I'd at least start stubs.

At that point, I'd figure we're ready for a peer review. Markus Poessel (talk) 18:57, 16 March 2008 (UTC)

Additional things to do:
  • Edit lead
  • Better images?
  • Some references have missing doi info
Markus Poessel (talk) 19:26, 16 March 2008 (UTC)
Have now gone through all the references, adding doi and some missing details where I could find them, and put everything into Citation templates that wasn't. Markus Poessel (talk) 17:54, 30 March 2008 (UTC)
I'm now done with the changes I wanted to make: status section is now merged with history, and I like the result; bibliography is now back to alphabetical, and I went through the entries to provide missing doi and other information; I created stubs for the last three red-links; I've replaced one image, and written a new lead that better reflects the article's current content (drawing both upon the existing version and the lead for Introduction to general relativity). Looking at the current version, I think it's time for the next step, namely getting a peer review. Which is what I'm going to initiate now. Markus Poessel (talk) 17:40, 6 April 2008 (UTC)
I'm going to try to talk my roommate into reviewing this page for you. He's only taken one general relativity class, but he's brilliant and loves to learn (he's also very good at explaining difficult concepts). I keep telling him he'd learn a lot from the article. I'm going to try RelHistBuff, too. I can say the page looks pretty. By the way, I've read Einstein's Relativity now and I've been watching the MIT online physics lectures. Go me - the autodidact. Awadewit (talk) 16:42, 10 April 2008 (UTC)
Great, thanks! The more eyes, the better (as the famous last words before many an edit war go). And I do applaud your autodidacticism (or would, if I knew how to spell it). Markus Poessel (talk) 17:42, 10 April 2008 (UTC)

Newly uploaded image

I'm not sure if the editors here are interested in fluffy historical images, but I have recently uploaded Image:GeneralRelativityTheoryManuscript.jpg. :) Awadewit (talk) 18:00, 29 March 2008 (UTC)

Looks good. I'm sure we'll find a place for it. Are there other pages where you found this one? Something with Einstein's equations perhaps? This looks like it has possibilities. Markus Poessel (talk) 13:29, 30 March 2008 (UTC)
I hope this is helpful! Awadewit (talk) 16:25, 30 March 2008 (UTC)
Ah, OK, you just took them from the regular archives. I thought those had a pretty rigorous copyright policy, which is why I didn't use their photos, but I admit I'm not an expert – when a photo is taken of a manuscript, does the photo automatically become public domain if the manuscript is old enough? I know that there is something like that for two-dimensional works of art; just not sure about manuscripts. Markus Poessel (talk) 17:53, 30 March 2008 (UTC)
I thought that if the manuscript was old enough, it was in the PD. Sometimes archives try to claim copyright they do not have. However, I am no expert, either. We could ask Lquilter - she is. Awadewit (talk) 18:02, 30 March 2008 (UTC)
I responded on my page at greater length, but in brief my take on it is: As a text, a work that is in public domain is fair game. As an image of a text, Bridgeman Art Library v. Corel Corp. suggests that photo-duplications of 2d images have no originality that would create a copyright. That the duplicated source image is a handwritten text, as opposed to an oil painting or a watercolor, would not add any originality to the photoduplication. --Lquilter (talk) 14:32, 2 April 2008 (UTC)
Great, thanks - and I meant to reply to you on your page, as well, but haven't gotten around to it. Looks like we're all set then. I was even thinking we might want to make one of these images the lead image. Markus Poessel (talk) 18:13, 2 April 2008 (UTC)
I've put the image into the history section. Markus Poessel (talk) 14:08, 6 April 2008 (UTC)
Glad it worked out! Awadewit (talk) 15:50, 9 April 2008 (UTC)

Source of the gravitational field

As you know, the source of the gravitational field is the stress-energy tensor: the energy density, momentum density, and flux of momentum (i.e. stress, including pressure & shear). It is reasonable to summarize this as the four-momentum (energy and linear momentum) which is the conserved quantity whose density/flux is the stress-energy tensor. However, referring to it as just "mass" is a dumbing down. Mass is not the point. Light has no mass, but it does generate gravity. Adding "(and further properties such as the momentum)" leaves one unclear. What are the further properties? Which other ones besides momentum are included?

I interpret Chrislintott (talk · contribs)'s comment in the review as simply suggesting that we link to mass-energy rather have two links to mass and energy (in addition to the link to (3D) momentum). JRSpriggs (talk) 11:38, 9 April 2008 (UTC)

In the Newtonian limit (which is the starting point for most readers), mass is indeed the point. I agree it would have been a dumbing-down without the remark about additional quantities, but since those quantities were mentioned, I think your judgment is too harsh in this particular case. Also, I don't think that "four-momentum" is much help – most of those readers who have a vague idea about momentum are not going to realize that, when looking at a star, it's not only the overall, center-of-mass four-momentum that is important – pressure/internal stress contribute as well (and, sometimes, tip the scale).
As for adding radiation, that opens up another can of conceptual worms. In general relativity-speak, radiation is a form of matter, after all. But I suppose we can leave that as it is in the lead. Markus Poessel (talk) 14:46, 9 April 2008 (UTC)

spacetime vs. space-time

The article uses both alternative spellings for spacetime. Consensus should be reached regarding a preferred spelling. I personally prefer spacetime. space-time suggests that time and space are two separate things combined in one object, while the essence of the notion is that the two are inseparable. (TimothyRias (talk) 12:58, 28 April 2008 (UTC))

Unfortunately, my spelling checker chokes on "spacetime" or "timespace", but it has no problem with "space-time" or "time-space". Having too many false positives in the spelling checker obscures the really misspelled words. Thus I prefer the hyphenated spelling. I would not put any philosophical significance on the hyphen. JRSpriggs (talk) 14:43, 28 April 2008 (UTC)

That is simply because space and time are in its dictionary, hence putting a hyphen in between yields a correct word in its logic. I just checked the Oxford dictionary it contains neither space-time of spacetime. That your spell-checker does not recognize spacetime is easy to fix, just add it to the dictionary. (That is what its for.) As arguments for using spacetime over space-time I would like to add:

  1. The main wikipedia article is spacetime. (space-time redirects there.)
  2. A quick search on titles in the arxiv yields 1000+ vs 23 in the favor of spacetime. Spacetime is the professionally accepted spelling.
  3. Spacetime is a word, while space-time is a combination of individual words.

(TimothyRias (talk) 15:07, 28 April 2008 (UTC))

I also prefer spacetime, one word, and I find the arguments you make quite convincing. I'll wait for JRSpriggs to respond, though, before making the changes. BTW, there is currently a peer review of this article going on. If you have the time, please contribute! Markus Poessel (talk) 18:30, 28 April 2008 (UTC)

I changed all occurances of space-time with spacetime. (TimothyRias (talk) 10:30, 6 May 2008 (UTC))

Symmetry group

The article says "In the language of symmetry: where gravity can be neglected, physics is Lorentz invariant (the defining symmetry of special relativity), not Galilei invariant (the defining symmetry of classical mechanics).". Actually, the symmetry of special relativity is the Poincaré group, not just the Lorentz group. In addition to Lorentz boosts, one should include translations and rotations (and, possibly, inversions and reflections). A similar change should be made for classical physics. JRSpriggs (talk) 15:44, 2 May 2008 (UTC)

This was meant to be about the defining symmetries, in the sense of what distinguishes these theories from each other. Both special relativity and classical have translational symmetry, so that doesn't help in distinguishing them. Should we call it "characteristic" instead? Markus Poessel (talk) 01:41, 7 June 2008 (UTC)

Recent edit by

I have no idea what this edit was about - according to diff, many text sections (but by no means all, and with gaps in between) were taken out and put back in, seemingly unchanged. By an anonymous user, and with no explanation given. The end result were 125 characters less than before. Since I've come across an increased number of subtle vandalism lately (small changes meant to confuse the patrolling robots), I am suspicious, and have reverted. If there was some meaning behind these edits, it would be great if they could be explained here. Markus Poessel (talk) 12:05, 10 May 2008 (UTC)

Probably he has used the auto mode of WikEd. This removes white spaces and Wikifies the article, leaving it, generally, with less bytes than before. --Lantonov (talk) 12:26, 10 May 2008 (UTC)
In some cases, he seems to have removed a blank at the beginning of a line (in citations). He also added a link to the images about general relativity in the wiki-commons. JRSpriggs (talk) 21:41, 10 May 2008 (UTC)

Gravitational energy-momentum

At its core are Einstein's equations, which link the geometry of a four-dimensional, semi-Riemannian manifold representing spacetime with the energy-momentum contained in that spacetime.

This sentence, as it is now, is slightly misleading. Not the sentence itself, but the link energy-momentum. It points to the energy-momentum in special relativity, and that is not Riemannian metric. Could it be made to point to Stress-energy-momentum pseudotensor? I know that the pseudotensor article is in a terrible shape but hope that it will be improved some day. --Lantonov (talk) 05:50, 30 May 2008 (UTC)

To Lantonov: You have it all backwards.
(1) The total stress-energy is the sum of the gravitational stress-energy-momentum pseudotensor plus the non-gravitational stress-energy tensor. The source term on the right hand side of the Einstein field equations is the non-gravitational stress-energy tensor. So those equations relate gravity to non-gravity. Thus you are referring to the wrong part of the stress-energy.
(2) To give a basic explanation of something one must describe it in terms of concepts which are simpler (e.g. four-momentum), not concepts which are more difficult (e.g. gravitational stress-energy-momentum pseudotensor). JRSpriggs (talk) 07:31, 30 May 2008 (UTC)

I somehow got confused by the fact that the pseudotensor is derived from Einstein equations, and also that in empty space the Ricci tensor is 0 but the Riemann tensor is not 0 so the space is still curved. But of course, if Rik = 0 then Gik is also 0, and you are right, Tik is only matter + radiation. --Lantonov (talk) 08:47, 30 May 2008 (UTC)

Peer review almost over

As far as I can see, all comments at the peer review have now been addressed. I will wait a few days and, if there are no further comments, move the article to FA candidacy. So if anybody reading this has comments that should be addressed before we present this article to the critical eyes of the FAC reviewers, please post them either here or on the peer review page! Many thanks in advance, Markus Poessel (talk) 01:43, 7 June 2008 (UTC)

Suggestion for "General Relativity for Dummies" section.

This is intended to give those with only high-school math the best insight possible into Einstein’s theory of General relativity, including why it was such a startling idea. Obviously not all aspects of the theory can be made accessible to everyone, but I tried to give a taste..........(I also notice in the preview that superscripts have been squashed, so Dsquared comes out as Dtwo.)

In 1905, Einstein had published his Special Relativity theory. The central idea of Special Relativity is that that if you play table tennis on a steadily moving ship, the ball will bounce exactly as it would if the ship was not moving. This had actually been stated centuries before by Galileo, but since then a major problem had arisen. In air of a given temperature and composition, sound travels at a known speed relative to the air. Sounds travel more slowly upwind than down, and this fact can be used to measure the wind velocity (though there are better ways). It was assumed that light waves behaved the same, traveling at a particular speed relative to some universal “air” called the aether which was believed to fill the universe. In the nineteenth century, two American scientists, Michelson and Morley, tried to measure the speed of the aether, but always got the result that the aether was not moving relative to their apparatus, no matter how the earth was moving the apparatus around the sun. Einstein managed to combine this result with Galileo’s principle. To do so, he had to introduce the idea that if one ship was moving East at speed v, and another ship was moving West at speed V, then someone on board one ship measured the speed of the other, the result would not be v+V, as common sense might suggest, but (v+V)/√(1+vV/c2) where c is the speed of light. Because speeds we encounter in everyday life are so much smaller that c, we never noticed the difference until Einstein suggested looking for it. This change messed up many other laws of physics, so Einstein had to make many other adjustments before he had a self-consistent theory. In our discussion, we will be particularly interested in the fact that he had to assume that if an object weighed M when it was at rest, it would weigh M/√(1-V2/c2) when it was moving at speed V. Again, the result is normally too small to measure, but it, and many other startling predictions of the theory, have been dramatically confirmed by experiment, and have proved crucial to our understanding of the world.

Special Relativity took care of the fact that playing table tennis was unaffected by the ship moving in a straight line, but did not address what happened if the ship was spinning around. Obviously, one cannot play table tennis on a carrousel without being aware that it is spinning. This does not seem puzzling until one asks oneself “If I was the only object in the universe, could I tell if I was spinning? If I could, what would I be spinning relative to? If not, how does the existence of the rest of the universe create the sensations of spinning? For example, if I stand on the center of a carrousel with my arms out, I feel the centrifugal force in my hands.” General Relativity tells us that we feel the centrifugal force because we are spinning relative to distant stars and galaxies. But how do they exert this effect?

To set the stage, let us go back to Newton’s understanding of gravity. One of his results was that if the Earth was a uniform hollow shell, someone inside the earth would feel no gravitational field. The only way I can explain this without calculus is to point out that to “escape” from the interior in a straight line from whatever was your initial position, you would have to pass through the same thickness of rock as someone escaping in exactly the opposite direction, and the fact that there’s more area of rock on the more distant side exactly cancels the fact that the distance decreases the effect, so the two pulls balance. The result is that if you and a friend were floating together inside a hollow earth, attached to each other by a rope, there would be no tension on the rope. If you and your friend were spinning around each other, then “centrifugal force” would put tension on the rope. But if you and your friend were stationary, and the hollow earth around you began to spin, that would not put tension on the rope. Or would it? If you two and the earth made up the entire universe, how could there be a difference according to which was doing the spinning?

To simplify the math, let’s replace the hollow earth with six equal weights, equally spaced around you (one in front, one behind, one above, one below, one left, and one right). These are truly massive weights - let’s call them stars - so they each pull on you gravitationally, but because they are in three opposing pairs, the forces balance out, and you stay still. Still doing everything we can to simplify the math, let’s say each star is one unit of distance (light year?) away from you, and pulls on you with one unit of force. Your friend is again floating in front of you at a small distance D, attached by a rope. Will there be tension on the rope? (If there is, our approximation of the universe is clearly not up to my hopes!)

Lets see, the star in front of you is only 1-D from your friend, so the pull on him is now 1/(1-D)2 by the inverse square law of gravitation. If you remember your math this is approximately 1+2D for small D. Similarly, the star behind you is 1+D from your friend, pulling him 1/(1+D)2 or approximately 1-2D, so there seems to be a net force of 4D on your friend away from you. But wait! There are four other stars. Because the small distance from you to your friend is perpendicular to the distance from you to these stars, his distance from them is still 1, but he is not exactly between these pairs as you are, so the pulls do not exactly cancel. The star above you is pulling him up with a force of 1/(1+D)2 and toward you with a force of D. So the net force from these four stars exactly cancels the one from the first two stars (for small D), so there is no tension on the rope. Our approximation of the universe by six stars is successful!

Now let’s start the universe spinning around an axis passing through you and the stars above and below you. We’ll spin it fast enough so that the four stars away from the axis are moving at c√3/2, where c is the speed of light. This would not make any difference according to Newton, so there would still be no tension on the rope. But according to Special Relativity, the moving stars now weigh exactly twice as much, so they are each pulling with twice the gravitational force. You are not affected, since the stars are still symetrically placed about you, but what happens to your friend?

The stars in front and behind are now twice as heavy, so the net force from them is now 8D instead of 4D away from you. The left and right stars are also twice as heavy, so the net force from them is now 4D instead of 2D toward you. The up and down stars are on the axis and not moving, so the net force from them is still 2D toward you. Therefore your friend is feeling a net force away from you of 8D-4D-2D=2D. Because the universe consists only of two people and six stars, it will seem more reasonable to describe the stars as stationary, and your friend as spinning around you. The 2D force on him will therefore be described as centrifugal. Note that centrifugal forces are indeed proportional to the distance from the center of rotation.

The first amazing thing about this idea is that when you feel a centrifugal force, you are directly detecting the most distant galaxies in the universe. The second amazing thing is that if there was twice as much matter in the universe, it would seem that the centrifugal force would be doubled. But the centrifugal force is also defined purely by geometry – it must cause unconstrained objects to move in straight lines relative to an inertial frame of reference. Therefore gravity is absolutely necessary for the universe to behave self-consistently! Even more amazing, there is only one possible average density for the universe for the measured gravitational constant.

The average density of the universe has been estimated by counting stars, galaxies, etc. and making reasonable estimates of the amount of hydrogen floating about in intergalactic space. It turns out that this “observed” density is about 4% of the density which General Relativity seems to predict. This may seem like a large error, but it’s very small compared to the minimum (one hydrogen atom in the observable universe) and maximum (neutron star? black hole?) densities the universe could have, so this is actually encouraging. Various theories of "dark matter" have been thought up to try to explain the “missing mass”.

John Blackwell (talk) 04:06, 8 June 2008 (UTC)

I am afraid that your suggestion is too dumbed down even for Introduction to general relativity let alone for this article. Also the style is not encyclopedic. Sorry. JRSpriggs (talk) 11:37, 8 June 2008 (UTC)

I don't see a link to the introductory article you mention within this article. Would one be a good idea?

Within the introductory article, there seems no way that someone without a degree in math or physics could read it and, with a bit of work, say "I see. It makes sense. Maybe if I put some work in I could understand more." This is what I tried to provide. There is an article on solving cubic equations in my Brittanica that illustrates my purpose perfectly. Any high-school graduate with an interest in math could use the article to learn to solve cubic equations, though he would have some real work to do, such as learning to calculate cube roots of a complex number.

As for the style, I tried to model it on Feynman's QED, since his purpose was similar, though obviously that was a book, not an article.

I don't claim I succeeded, but I wonder whether you think my purpose has value, and whether it is possible.

John Blackwell (talk) 18:39, 8 June 2008 (UTC)

The very first line in the article says
For a generally accessible and less technical introduction to the topic, see Introduction to general relativity.
General relativity is an inherently difficult topic. It is unreasonable for someone without an advanced education to expect to understand it. JRSpriggs (talk) 04:05, 9 June 2008 (UTC)

That depends what you mean by "understand". To have a respected opinion on the relative usefulness of GR vs. (say) MOND, certainly one needs considerable study of the underlying mathematics, as well as the observational evidence. It does seem to me that the kind of semi-understanding that Feynman accomplished with QED also has value. In RPF's collected letters, one scientist wrote that QED had led him to an understanding of Hanbury-Brown-Twiss, which had previously defeated him. I suspect that many people have been encouraged to study QFT by reading QED, but I have never seen anything analogous about GR. —Preceding unsigned comment added by Johnblackwell (talkcontribs) 15:17, 9 June 2008 (UTC)

I would agree that a certain degree of understanding is possible with general relativity, using high-school math. It's not uncommon for semi-popular accounts of special relativity (Born, Einstein's theory of relativity, Mermin, About time etc.) to include some heuristic material on general relativity, as well. I just don't think that's what an encyclopedic article about gr should be like. Markus Poessel (talk) 16:11, 11 June 2008 (UTC)

I know this piece will not be added to the article, but I would like to thank John Blackwell anyway for providing it. It proved the most comprehensible explanation of rotation I have yet seen, and I enjoyed the enthusiastic yet unpatronising style. Thank you again. (talk) 01:30, 1 August 2008 (UTC)

Status update

The recent peer review which, thanks to Mike Peel, Chris Lintott, RJHall, RelHistBuff, Timothy Rias and Ealdgyth, led to significant improvements, is now completed. Having had a look at recent discussions on WP:FAC, it seems to me that some sections can still be improved by simplifying and shortening sentences, so I've started to work on that. Once I'm done, I intend to put the article up as an FAC. Markus Poessel (talk) 13:35, 11 June 2008 (UTC)

Motivated by Eleassar's recent flagging of broken citations, I have now gone through all the footnotes and fixed an embarrassing amount of small mistakes and omissions. Markus Poessel (talk) 23:32, 15 June 2008 (UTC)

FA Candidacy

After a last run-through, mainly adding author-wikilinks to the references, I think the article is now ready, and have put it up for FA candidacy. Markus Poessel (talk) 01:59, 19 June 2008 (UTC)

A few questions from Willow

  • When did general relativity begin to be applied in stellar physics? My impression was that that happened well before 1960. If that's true, then we should soften the wording on "GR entered the mainstream of theoretical physics and astrophysics only with the developments between approximately 1960 and 1975." Willow (talk) 06:39, 23 June 2008 (UTC) See next section.
Oppenheimer-Volkov was earlier than the 1960s, and obviously some of the cosmology, too. Where do you want to insert the sentence? Markus Poessel (talk) 00:31, 25 June 2008 (UTC)
We could put in a new sentence, or just soften the old one? Perhaps something like: "GR was responsible for the birth of physical cosmology, and allowed for more accurate models of the physics of stars; it also played a minor role in establishing the uncertainty principle for quantum mechanics. However, in other respects, GR entered the mainstream..." Willow (talk) 01:13, 25 June 2008 (UTC)
Which sentence and which work on stellar physics to you refer to? And no, I think the "uncertainty principle" bit isn't important enough. Also, I don't think it's correct the way you wrote it: for most people, the experimental evidence for qm was perfectly sufficient to establish the uncertainty principle, and for Einstein, I would say it was more a matter of what the uncertainty principle meant (a limit to finding out what's there, or an indication that there's no there there) rather than the principle itself. Markus Poessel (talk) 02:28, 25 June 2008 (UTC)
  • Sorry, what does semi-Riemannian mean? I've heard of Riemannian. Is there something we can link to; could somebody write an article or give a quick, referenced definition? Willow (talk) 06:50, 23 June 2008 (UTC)
    • See semi-Riemannian manifold. Basically, in a Riemannian manifold distances are always positive while in a semi-Riemannian manifold distances can also be negative. -- Jitse Niesen (talk) 09:59, 23 June 2008 (UTC)
  • I think I remember hearing about an experiment by Clifford Shull in which a beam of neutrons was split and then re-combined to interfere with itself. By rotating the apparatus in a gravitational field, the phase change along the lower path could be made different than that of the upper path, with a detectable change in the interference pattern. In the quantum mechanical/GR section (say, QM in curved spacetime), maybe it might be nice to reference something like this? My interpretation is that some simple effects of GR on QM can be accounted for by taking gravitational time dilation and the like into account. There's also the example of Einstein's thought experiment with Bohr, where a box is weighed on a spring and allows a single photon to escape through a shutter that opens at a precise time. Willow (talk) 21:31, 24 June 2008 (UTC) See two sections ahead.
    • Do you mean this? I don't see where this can even distinguish between Newton and Einstein. The Einstein thought experiment is a cute application of time dilation to the quantum mechanics debate, but I don't think it's important enough to include here. Seeing how short the shrift we've given to so many other topics. Markus Poessel (talk) 00:31, 25 June 2008 (UTC)
The point here was not to distinguish Newtonian from GR. but rather to show that GR could be reconciled with QM in simple cases. I suspect that only 1% of your readers will get the present QFT stuff, but maybe 2% might get the QM illustration? I'll understand, though, if there's not enough space. Willow (talk) 01:13, 25 June 2008 (UTC)
But with an example that cannot distinguish between Newton and Einstein, it's no surprise there's no problem. After all, Newtonian mechanics is the basis for classical quantum mechanics. Claiming this shows that GR is compatible with QM, while the experiment isn't sensitive enough to "see" what makes GR different from Newton, doesn't quite work, I think. Markus Poessel (talk) 15:45, 25 June 2008 (UTC)
  • I'm wondering how the causal-structure assumption is reconciled with the closed, time-like world-lines seen in the Kerr metric? They seem to be contradictory to the lay-reader. Willow (talk) 21:35, 24 June 2008 (UTC)
    • The "causal-structure assumption" being...? Markus Poessel (talk) 00:31, 25 June 2008 (UTC)
Sorry, maybe I misunderstood your section on "Causal structure", but it seemed to be saying that closed, time-like loops were impossible. If not, then maybe that section should be clarified for dimwits like me. ;) Willow (talk) 01:13, 25 June 2008 (UTC)
I thought I was pretty careful in formulating it – where does it exclude closed time-like curves? Markus Poessel (talk) 02:28, 25 June 2008 (UTC)
  • Mention the role of general relativity in actual astrophysics, i.e., in calculating the properties of stars? Willow (talk) 21:40, 24 June 2008 (UTC) See next section.
    • I'm pretty sure that many astrophysicists will be shocked to hear that what they're doing with cosmology, black holes, gravitational lenses etc. doesn't count as actual astrophysics. Which calculations are you referring to, though? Gravitational redshift and mass? Markus Poessel (talk) 00:31, 25 June 2008 (UTC)
I'm mortified, I meant no slight, I was just making a pun on the Greek, "astrophysics = nature of stars", i.e., purely stellar physics. Willow (talk) 01:13, 25 June 2008 (UTC)
They will probably still be shocked. Markus Poessel (talk) 02:28, 25 June 2008 (UTC)
I'm surprised, too; who knew that physicists could be shocked by an innocent mistake? ;) Willow (talk) 19:41, 25 June 2008 (UTC)
  • In the section on orbital mechanics, is it worth mentioning that all geodesic orbits of the Schwarzschild metric (and I guess a few others?) can be classified into a few basic types? Maybe that's a technicality, though. The photon sphere thing is pretty cool, though; photons moving in a circular orbit might inspire the imaginations of some readers! :) Willow (talk) 21:40, 24 June 2008 (UTC)
    • I don't think so. Given the overall length of the article, remarked upon previously to and during the review, those sections were very much converted to summary style. For details like the classification of orbits, the reader will need to read the other articles. And the photon sphere is, I think, too problematic to mention briefly (you would need to say what it is, but also instability). Compared to what little space, say, the much more important ergosphere gets, that would be inappropriate. Markus Poessel (talk) 00:31, 25 June 2008 (UTC)
Sure, that makes sense. :) Willow (talk) 01:13, 25 June 2008 (UTC)
  • My understanding was that some numerical simulations had provided evidence for naked singularities and against the cosmic censorship hypothesis. Is that true? If so, the article doesn't quite say that. Willow (talk) 21:47, 24 June 2008 (UTC)
    • Only with fine-tuned initial conditions. That's exactly why the "realistic" is in that sentence. Details should be in Berger 2002, which is cited. Markus Poessel (talk) 00:40, 25 June 2008 (UTC)
Some little proviso might be more scientifically scrupulous. Right now, the article seems to say that there's universal agreement that naked singularities cannot exist. Willow (talk) 01:13, 25 June 2008 (UTC)
I thought the "realistic" was that little proviso. There's pretty universal agreement that realistic (generic initial condition, future) naked singularities don't exist. Markus Poessel (talk) 02:28, 25 June 2008 (UTC)
I'll confess, I find the "realistically" a little unsatisfying. There's a fundamental difference between things that can't exist and those that don't often exist. Even if the probability p of finding a naked singularity is 10-100000 per cubic lightyear, surely there's a finite chance of finding one somewhere in the infinity of space? But perhaps I'm not understanding the situation correctly? Perhaps the requirements are so strict that p is effectively zero? But then I don't understand how they could've produced on in a computer simulation. Willow (talk) 19:41, 25 June 2008 (UTC)
  • Perhaps this article should mention the problem of motion in general relativity? If I've understood that correctly, some theoretical analyses by Einstein, Infeld and others suggest that the geodesic equation of motion is not an axiom independent of the Einstein field equations, but rather the consequence of assuming that the curvature tensor is continuous across spacetime? Willow (talk) 21:51, 24 June 2008 (UTC)
    • That's the reason for what is currently footnote 32. Markus Poessel (talk) 00:40, 25 June 2008 (UTC)
Footnote 32 and its precursor sentence seem to say something different. Rather than saying that geodesic paths depend on the local geometry, which is determined by the field equations, I mean to say that the geodesic law can be dispensed with entirely, in favour of only Einstein's field equations. A minor point, and I understand the argument that the geodesic law is implicit in saying that spacetime is locally flat, but I mention it because it seemed significant to Einstein, based on his multiple publications on the subject. Willow (talk) 01:13, 25 June 2008 (UTC)
OK, you mean something analogous to the current footnote 58 then? Markus Poessel (talk) 02:28, 25 June 2008 (UTC)
Not exactly, although that's closer. Specifically, I'm referring to this, this, and this publication of Einstein and coworkers, plus the analogous work published by Hermann Weyl and others. It's described on pages 288–291 of the Abraham Pais biography under the sub-heading "Singularities; the Problem of Motion". Maybe it's overly technical for this article, but we are trying to be encyclopedic, so I thought it might be worth mentioning. Willow (talk) 19:50, 25 June 2008 (UTC)
As I said at the last paragraph of Wikipedia talk:WikiProject Relativity#How to improve relativity-related articles:
The principle that a particle (which is not affected by forces other than gravity) follows a geodesic through space-time is a consequence of the field equations, i.e. it is the only way that the metric of the surrounding vacuum can be matched to the Schwarzschild metric generated by the particle. So the action of mass upon the geometry produces the reaction of geometry upon mass.
This leads me to the conclusion that electromagnetic forces act on charges via changing the geometry — the charge is deflected, not directly by the electric field, but by the gravitational effect of the cross-term in the stress-energy tensor between the particle's field and the ambient field. JRSpriggs (talk) 04:06, 25 June 2008 (UTC)
  • Speaking for myself, I'd appreciate a clearer explanation of the "formal and conceptual" problems faced by quantum field theories of general relativity. Is the main problem that the theories all predict infinity for certain numbers, in a way that can't be renormalized? Feynman gives a nice lay-person's understanding of non-renormalizability. Or is there more to it than that? Willow (talk) 22:04, 24 June 2008 (UTC) See two sections ahead.
    • If, by "quantum field theories" of general relativity, you mean quantum gravity models in general, then yes, there's much more. The problem of time, the problem of what parts of geometry should be quantized, and so on. The Isham article I quote gives a good overview. But again, this section has been severely summary-stylized, and I don't quite see how to incorporate it into that section. Markus Poessel (talk) 00:40, 25 June 2008 (UTC)
Check, got it, boss. :) Willow (talk) 01:13, 25 June 2008 (UTC)
Sorry, don't mean to sound bossy. But am trying to be brief (both in the article and in the substantial FAC-related discussion). Markus Poessel (talk) 02:28, 25 June 2008 (UTC)
  • Oh, one more thing. Do the various competing theories of quantum gravity differ in their predictions? Or are they just formally different ways of saying the same thing? If they are different, it'd be nice for the reader to understand the experimental ways in which the theories might be distinguished from one another. Willow (talk) 22:04, 24 June 2008 (UTC) See two sections ahead.
    • Some have (not very firm) predictions that others haven't, yes. I've put an addition in parentheses in the last sentence of the quantum gravity section. Markus Poessel (talk) 00:40, 25 June 2008 (UTC)
Can you give at least a hint in what respects they vary? Or is it too various? Willow (talk) 01:13, 25 June 2008 (UTC)
Not too various, but rather subtle, and with the needs for lots of extra explanations. For instance, if supersymmetry is found, many will see that as indirect evidence for string theory. It is in a sense, as string theory needs supersymmetry, so it's great if some form of susy is actually discovered, but susy breaking isn't all that well understood in string theory so as to make this an actual prediction. There were some hints about frequency-dependent light speed derived from loop quantum gravity, but that has problems of its own. And there are a number of different predictions for gravitational waves in the CMB, but those aren't all that firm and specific, either. My fear is that going into this, there will be no way of giving examples, while still staying accurate, reasonably readable, and reasonably short. Markus Poessel (talk) 02:28, 25 June 2008 (UTC)

General relativity and stellar physics

Separated off from previous section for clarity

I should say up front, both that I like the article as is, and that I'm no expert in any of this, so you don't need to change anything to win my Support at the FAC. But I do want to help out as best I can to improve the article, so I would be remiss if I didn't mention things that I thought could bear improving. Willow (talk) 19:17, 25 June 2008 (UTC)

Revise sentence on "mainstreamness" of GR?

The sentence that seems inaccurate to me is this one: "Yet the theory entered the mainstream of theoretical physics and astrophysics only with the developments between approximately 1960 and 1975" Somehow the sentence leaves me, as a naive reader, with the impression that physicists didn't accept or use GR until around 1960. My impression is that GR was generally accepted, but used only infrequently, since the regimes in which Newtonian gravity fails to be adequate are rather extreme.

I remember reading about this when I was writing up the equipartition theorem, so I rummaged through my notes to remind myself of something concrete. The earliest reference I could find was in the 1926 book, The Internal Constitution of Stars by Arthur Eddington, where he uses GR to establish that Betelgeuse must have a density at least a thousand-fold smaller than that of the sun. As an aside, Eddington also alludes to the possibility of a black hole: "the mass would produce so much curvature of the space-time metric that space would close up round the star, leaving us outside" (p. 6).

The next set of references I found are dated from the late 1930s, from Tolman, Oppenheimer, Volkoff and Snyder on the possibility of collapse into a neutron star or black hole. These studies seem to have been made in response to the 1931 publication of the Chandrasekhar limit, which naturally begs the question of what happens when a star exceeds that limit.

The third set of references I found were by Subrahmanyan Chandrasekhar, and date from the early 1960s. While I was trying to read up on the equipartition theorem and the virial theorem, I discovered his 1963 paper on the latter's generalization to GR, and his subsequent papers incorporating GR into stellar physics, esp. on pulsations, stability criteria and interactions with gravitational radiation. The present article does not seem to do justice to this body of work? Of course, black holes, quasars, cosmology and quantum gravity are cool, but maybe there's space to slip in a phrase or two about more ordinary stars?

Returning to the original question of how to re-write that paragraph, whose purpose is to summarize the history from roughly 1920 to the present, perhaps you can extract some useful elements from this draft?

...making Einstein instantly famous. The experimental confirmation of these predictions and the astronomical evidence for an expanding universe caused general relativity to be accepted. However, for roughly forty years, few physicists besides Einstein applied the theory, since the traditional Newtonian theory of gravitation fails only under extreme conditions of density, scale or velocity. General relativity was instrumental in the 1920s and 30s in predicting neutron stars and black holes, and the alternative steady-state cosmology was introduced in the late 1940s. Beginning in roughly 1960, however, general relativity came to the forefront of astrophysics, in the so-called golden age of general relativity (1960–1975). General relativity was applied to understand quasars, black holes, the stability and pulsations of stars, and general theorems of spacetime structure. New astronomical objects such as pulsars, gravitational lenses and the cosmic background radiation were discovered that gave strong support for classical general relativity, in particular, for gravitational waves and the Big Bang theory of cosmology. Alternatives to general relativity such as the Brans-Dicke theory were also developed. Since 1975, blah blah blah...

We can certainly incorporate some changes. Several issues, though. First of all, what does "accepted" mean? Up until the golden age, astrophysicists and relativists were pretty much separate communities, some early and important exceptions (De Sitter, Eddington) aside. That's one of the things that changed in the Golden Age. Even Werner Israel by his own account (Dark stars article in the biography, p. 245) didn't hear about Oppenheimer-Volkoff until the 1963 Texas meeting. I'm especially concerned with the statement that general relativity "was instrumental in the 1920s and 30s in predicting neutron stars and black holes". In Israels's account (cited above, sections 7.4 and 7.5) it seems that astronomers had pretty much come to the conclusion that larger stars somehow shed their excess mass to end as White Dwarfs, before speculations about neutron stars (from 1934 on) opened up other possibilities. So the "1920s" in the statement do not sound quite right. As for neutron stars themselves - was gr "instrumental"? The original short Zwicky/Baader article doesn't mention the theory at all. Israel states that Zwicky was aware that gr would be needed to understand the structure of neutron stars, but didn't manage to formulate a general-relativistic theory until Oppenheimer/Volkoff came at the problem from a different angle. So even the "1930s" would seem to be a bit misleading. And after Oppenheimer/Volkoff, the subject entered a "dark age" (says Israel), only to be reviewed in the late 1950s, when Wheeler revisited the question in the run-up to the Golden Age – when physicist would finally get their minds around the idea of a black hole. Markus Poessel (talk) 18:00, 27 June 2008 (UTC)

General relativity and quantum mechanics

Separated off from two sections ago for clarity

Einstein's 1930 thought experiment and the uncertainty principle

My memory was that GR played a role in establishing the uncertainty principle. That's not exactly true, but here's the story, for completeness. It's true that Heisenberg and Pauli didn't care what objections Einstein made, but I believe that Bohr took them seriously, since it takes only one solid counter-example to place limits on a "fundamental" principle.

At the 6th Solvay conference, Einstein proposed to defeat the ΔEΔt uncertainty principle by allowing a single photon to escape at a predetermined time from a box, which could then be weighed to determine the energy of the photon with arbitrary precision. As Leon Rosenfeld describes the situation,

During the whole evening, [Bohr] was extremely unhappy, going from one to the other and trying to persuade them that it couldn't be true, that it would be the end of physics if Einstein were right;...the next morning came Bohr's triumph.

Bohr saved the uncertainty principle by appealing to gravitational redshift formula, which does not require general relativity per se, but only the equivalence principle and the time dilation of special relativity. Following this refutation, Einstein accepted quantum mechanics as a theory containing "a piece of ultimate truth", and nominated Heisenberg and Schroedinger for the 1931 Nobel prize.

The article's treatment of quantum gravity

I'm afraid that I'm left unsatisfied by the article's present treatment of quantum gravity. I see the need for brevity and generality, but frankly the whole section seems so vague that very little information seems to be communicated. Speaking just for myself, I feel as though I don't know what the issues are, where the theories succeed or fail, in what regimes a quantum theory of gravity is necessary or even observable, and how they can be discerned experimentally. If the various theories are still undeveloped — so that they haven't yet made any predictions that can be tested empirically, even in principle — then the article should say that, no? If on the other hand they have made concrete predictions, e.g., the speed of light varies slightly with frequency, then the readers should be filled in, at least for a few major cases. I'm not asking that one go into the details of the theories, but a hint or two about the axes along which the controversies and problems are playing out would be very welcome.

My comments about the neutron diffraction experiment was just trying to suggest that the article mention that GR can be reconciled with QM in "ordinary" situations; it just seems to hit problems under super extreme situations, e.g., the Big Bang. For example, the article might mention that QM is usually observable only with very light (low mass) or very small things, whereas GR is usually observable only with very heavy (high mass) and very large things, so that it's very rare to find a situation in which both types of effects are significant. Maybe something like that? Willow (talk) 20:20, 25 June 2008 (UTC)

Questions from Tolkien_Fan

In section 1, paragraph 3, there is a statement that reads "Einstein's theory has important astrophysical applications. It points towards the existence of black holes..." I think this should be thought through. The Theory of General Relativity is so named because it is a generalization of Einstein's Theory of Special Relativity. So the two theories should live in harmony with each other, right? Wrong! The theory of the black hole violates the theory of Special Relativity. Let me give a simple explanation. According to the Theory of Special Relativity, infinite mass is forbidden because it requires infinite energy. Therefore, the Theory of Special Relativity (and thus also General Relativity) actually defies the existence of black holes amd does not "point towards" their existence. My point is, that perhaps the clause about black holes should be removed or revised. Does anyone else see this contradiction? —Preceding unsigned comment added by Tolkien fan (talkcontribs) 16:54, 30 June 2008 (UTC)

Where to start? As explained in the article, the connection between the two theories is the equivalence principle. No further "harmony" required. Also, you seem to assume that black holes have "infinite mass", which is simply wrong. As for black holes themselves: again, the basics are in the article. The Schwarzschild solution describes the simplest form of black hole, is a bona fide vacuum solution of Einstein's field equations, and the basis of our current understanding of astrophysical black holes. Markus Poessel (talk) 18:30, 30 June 2008 (UTC)

Whither Cosmological Constant?

In simple-minded engineering terms, the Cosmological Constant term is a "fudge factor" used to make theory match observations. Einstein put it in to make GR match the static universe model then in vogue. When Hubble's results came in, Einstein disavowed it. Now some Cosmologists are saying that the Cosmological Constant is in fact non-zero. If their observations prove true, that would mean that GR is missing something now being approximated by the CC term. Has this been noted by anyone in the field and should it be discussed in the Cosmology section? Virgil H. Soule (talk) 07:24, 8 September 2008 (UTC)

See Quintessence (physics), dark energy, and dark matter. JRSpriggs (talk) 12:07, 9 September 2008 (UTC)

Reversion, perhaps temporary

At the risk of making a fool of myself, I have reverted an addition by User:Delaszk which seems radically at variance with my understanding (which is admittedly not comprehensive) of relativity. Essentially the same section was added to Special relativity, which I have also reverted, but I saved the material on the discussion page there until its correctness can be verified by other editors. Wwheaton (talk) 09:40, 30 October 2008 (UTC)

Well I don't see the addition being notable, so this was probably the right call. (TimothyRias (talk) 10:55, 30 October 2008 (UTC))

I think the concept that special relativity can be derived without recourse to Einstein's second postulate and also that the expansion of the universe does not need dark energy or any other mechanism is definitely notable, and was not adequately covered in wikipedia prior to the addition of this material. Delaszk (talk) 11:48, 30 October 2008 (UTC)

The material is now only in the article Galilean invariance and is pointed to from other articles with:

Maximum speed limit and other consequences of Gallileo's principle of relativity

It has been shown that special relativity and the accelerating expansion of the universe are just consequences of Gallileo's principle of relativity, requiring no further postulates or data. See Galilean invariance#Maximum speed limit and other consequences of Gallileo's principle of relativity. Delaszk (talk) 15:51, 30 October 2008 (UTC)

This is a fallacy which has been repeatedly discussed and exploded at Talk:Special relativity. I see no reason to go over it again. JRSpriggs (talk) 17:37, 30 October 2008 (UTC)