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Introduction to general relativity

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Introduction to general relativity has recently been overhauled, streamlined, and given a fair number of references and images, with the aim of eventually bringing it to featured article status. In preparation for that process, I would appreciate feedback especially on the following:

  • Is anything missing? Since this is only an introduction (there is a main article general relativity), it doesn't need to provide all the details, but it should still cover all important points.
  • Previous versions of this article were deemed too technical (see the discussion page). Is the present version accessible enough, and if not, what could be improved? I haven't participated in this kind of review process before, but I understand that the review request will also be posted to the standard WP:Peer review - since this article is meant to be accessible for everybody, feedback from non-scientists would be very helpful.

Of course, any suggestions on how to improve presentation, style, grammar etc. are welcome as well. Many thanks in advance! Markus Poessel 08:46, 14 June 2007 (UTC)[reply]

I have also transcluded this into WP:PR. --Bduke 12:33, 14 June 2007 (UTC)[reply]

Review by Awadewit

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I am an English graduate student who is an avid reader of popular science books, so my review will focus on accessibility and prose. I found this article to be, in general, remarkably clear and easy to follow. I am curious as to who you believe your audience will be. My roommate, who is an undergraduate physics major, learned nothing from this page, so I am assuming that you are aiming exclusively for lay readers?

Sentences and sections that may be too technical:

  • General relativity (GR) is Albert Einstein's theory of gravitation, first published in 1916. It is based on Einstein's earlier theory of special relativity and the equivalence principle, and utilizes the mathematics of Riemannian geometry. - not clear to a non-scientist - Don't scare readers away with the first sentence!
  • The image in the "Physical consequences" section could be explained better. When I first looked at it, I dumbly thought "that wave isn't going up or down, it is going straight."
  • "Physical consequences" section - explain "downward" and "upward" more clearly as "down" and "up" into the gravitational field (this is done better later in the section, but should be done the first time such terms are mentioned).
  • I found the "From acceleration to gravity" section a bit technical and hard to follow.
  • But in relativity, mass and energy are equivalent (expressed by the famous formula E = mc²), and energy is intertwined with momentum (just as space is intertwined with time). - Explain equation and subsequent claims more clearly.
  • In the section on "Einstein's field equation", the phrases "right-hand" and "left-hand" are confusing when you don't have the equation.
  • The section on "Einstein's field equation" is a bit confusing overall.
  • I'm still working on that one - but I need to make an image for it, and that takes a bit of time. Note that I only said I had addressed all your prose/minor style issues; I know very well that there's still this issue from the "Too technical" list I haven't solved yet. Markus Poessel 08:34, 4 July 2007 (UTC)[reply]
  • The anomalous precession of the orbit of Mercury and other planets (anomalous perihelion shift) has been measured using VLBI observations. - Readers can't click on everything - any terms that are crucial to sentences, such as "precession," should be quickly defined.

Other concerns:

  • The lead lacks enough detail to be a standalone summary of the article as required by WP:LEAD.
  • In the "Gravity and acceleration" section, the numbered list is oddly positioned next to the picture. It is hard to see the numbers at a glance.
  • So far, general relativity is consistent with all available measurements of large-scale phenomena. - What does large-scale mean? What about small-scale? Does "quantum gravity" apply at that scale?

Prose:

  • I do not mind "essay style" (e.g. So much for the effects of curved spacetime, but what causes the curvature in the first place?) but some editors at FA do.
  • Still, a number of open questions remain, notably the question of how the theory can be reconciled with quantum theory, resulting in a theory of quantum gravity. - repetition of the word "theory"
  • This gave Einstein a first clue about the nature of gravity - Don't begin a paragraph with "this" - it is not always clear what the referent is.
  • Effects of this type, which are due to the differences in strength and direction of gravitational forces felt by different bodies, are called tidal effects - another example of the problem - we lose what the "effects" are Awadewit | talk 08:09, 4 July 2007 (UTC)[reply]
  • Following earlier ideas by Ernst Mach, Einstein also explored centrifugal forces and their gravitational analogue. - This statement could be clearer and more precise.
  • Using the analogy between gravitational and inertial effects, as well as the insight that, for an observer in free fall, the laws of physics are approximately those of special relativity, Einstein was able to derive a number of interesting consequences of the new approach to gravity. - unclear and long
  • In his considerations, Einstein had come across - Considerations of what? Always be absolutely clear at the beginning of a paragraph or section to what you are referring.
  • Going from an inertial to a rotating reference frame is analogous to going from a Cartesian to a curved coordinate system. - "Going" is colloquial and imprecise.
  • While the geometric analogy had set Einstein onto the right track - colloquial language
  • The analogue of the curved, two-dimensional surface is four-dimensional spacetime, a geometric entity that had been introduced in 1907 by Hermann Minkowski as part of a geometric formulation of special relativity in which it unifies and replaces the separate entities space and time. - Too long
  • In the third paragraph of "From acceleration to gravity" "Einstein" is used repetitiously.
  • Paraphrasing John Wheeler - Who is he? Why should we care what he said? At least say something like "Paraphrasing the physicist John Wheeler" or "Paraphrasing the great physicist..." or "Paraphrasing an expert in general relativity..."
Nice use of the word "doyen." :) Awadewit | talk 08:09, 4 July 2007 (UTC)[reply]
  • For comparatively low-mass objects such as those we know from everyday life (such as our own bodies) - Two "such as" constructions in a row - perhaps eliminate the "everyday life" part and just use "our own bodies"?
Mountain is a nice touch. Awadewit | talk 08:09, 4 July 2007 (UTC)[reply]
  • In Newtonian gravity, the gravitation force is caused by matter, more precisely - Should that be "gravitational"?
  • The key part of general relativity are Einstein's equations - verb tense - should be "is" since "part" is the subject of the sentence
  • These equations are formulated using Riemannian geometry, where the geometry of spacetime is defined by an object called the metric. - "in which" instead of "where" - Riemannian geometry is not a place
  • the crucial observations that justified the adoption of general relativity over Newtonian gravity - awkward - perhaps "justified replacing Newtonian gravity with general relativity"?
  • notably VLBI observations of the deflection of the light of distant quasars by the sun, have confirmed Eddington's results with significantly higher accuracy - Do not use abbreviations without explanation
  • To this day, scientists try to challenge general relativity with more and more precise experiments and observations - Why are they still testing it? Also, "challenge" is not the best word - for lay readers it sounds like they want to overturn all of realativity theory (creationists challenge evolution, for example).
  • and the success of these models is further indirect evidence of the theory's validity - Just how "indirect" is it? Reading this sentence as a lay person, I think to myself - only indirect? Pshaw - they have nothing.
  • such as quasars and other types of active galactic nucleus - "nucleus" should be plural
  • The current cosmological models, the Big Bang models which postulate the emergence of our present expanding universe - repetition of "model"
  • It is a longstanding hope that the theory of quantum gravity would also do away with a rather disturbing feature of general relativity: The presence of spacetime singularities – spacetime boundaries at which geometry becomes ill-defined – in the interior of black holes and at the beginning of the universe (the big bang) that general relativity predicts via the so-called singularity theorems. - too long

Minor style details:

  • It is traditional to use a lower-case letter after a colon. This article sometimes uses upper-case letters (there is no pattern to the choice, either). Find a style and stick to it.
  • The "See also" section should not include articles that have already been linked.
  • Make it clear if the online tutorials are for a lay audience or not.

Two suggestions from my live-in physics expert:

  • Perhaps the page should recommend that users read the Introduction to special relativity article before reading this one?
  • Would a paragraph on GPS be helpful here? It would give readers a real-world example of the usefulness of general relativity. Astrophysics is fascinating to some (myself included) and I don't think that section should be deleted or cut down, but many more people know what GPS is and would be intrigued to know more about how it works. Awadewit | talk 01:21, 28 June 2007 (UTC)[reply]
  • I do think that this is a good idea. It brings scientific knowledge to the everyday level. That is a necessity for many people. Also, they may vote to fund it, if they think that it helps them. :) Awadewit | talk 08:09, 4 July 2007 (UTC)[reply]


Awadewit - many thanks for your very thorough review. This is exactly the kind of helpful and constructive reaction I was hoping for (OK, better than what I was hoping for, but then I'm relatively new to Wikipedia). I'll be addressing the different issues you have raised point by point as I make the appropriate changes to the article; for now let me just say that, yes, this article is intended for a lay audience. For everyone from knowledgeable undergraduate physics students on up, there is the main article general relativity. Markus Poessel 12:55, 29 June 2007 (UTC)[reply]
I'm glad that you didn't find it too overwhelming. If this article is exclusively for those unfamiliar with real science, there may be even more material that needs to be explained. If you are aiming for college-educated readers (which is almost what you have to do given the subject matter), you might consider exactly what type of college graduates you are thinking about. There is a huge variation. I teach freshmen composition and literature classes at a large state university and I am pretty sure that the majority of the students whom I have taught would not understand this page (sadly). I don't know how low you want to aim, but it is worth thinking quite a bit about what your audience knows. Have you read the NSF's report on the public understanding of science? It is quite enlightening. Only half of the US population knows that electrons are smaller than atoms, for example, and only 70% knew that the earth went around the sun (not the other way around). Awadewit | talk 21:06, 29 June 2007 (UTC)[reply]
I have read similar report, but not this particular one (thanks for the link!). On reflection, my intended reader is someone who is interested in understanding general relativity at the level of the first few chapters of The Elegant Universe or A Brief History of Time - someone who has a good idea of what a planet is, has heard the expressions "black hole" and "expanding universe" before, and is interested in understanding some of the connections between the physics of relativity and more familiar notions, albeit at a simple level. And I suppose that, yes, for that intended readership some of the sections (you have indicated a number in your review) are in need for a bit of further simplification. I'll have a go at it, starting with the sections you suggested. Markus Poessel 19:29, 30 June 2007 (UTC)[reply]
I think that that is a good way to think about the reader. From my perspective, this page seems much more sophisticated than the The Elegant Universe (that is not necessarily bad). I think that it is more along the lines of Deep Down Things. Awadewit | talk 20:54, 30 June 2007 (UTC)[reply]
  • Lead section: I have fleshed out this section, adding a bit more detail, changing the rather technical first sentence, and taking care of the prose issue raised for this section. Hopefully, it is now long enough for a proper stand-alone lead section. Markus Poessel 13:40, 29 June 2007 (UTC)[reply]
  • Yes, I think that it is better, although I feel that it might be too technical, especially for a lead. A lead should make people want to read the article. Looking at this lead, I would assume that the article was too advanced for me to understand when in fact it is not. Think of the lead as (horrifyingly, I know) yet another simplification of GR - it is a simplification of the already simplified article. Awadewit | talk 21:06, 29 June 2007 (UTC)[reply]
  • As for the proposed recommendation that users read the Introduction to special relativity article before reading this one, I think it's not a good idea. The level of presentation in that introduction is markedly higher than in this (the intro to gr makes no great use of formulae, the intro to sr does), and in fact most of the ideas presented there are not needed to understand the basics of general relativity as they are presented here. I did add a reference to the Introduction to special relativity to the first mention of the theory in the main text, but I think it's wrong to give readers the impression that they should read that text first.Markus Poessel 14:33, 29 June 2007 (UTC)[reply]
  • I have replaced the image in the "Physical consequences section" by one that is rotated by 90 degrees. Now, the directions in the image are the same that are associated with our everyday notions of "up" or "down". I have also added an explanation of "upward" and "downward", as you suggested, and changed the introductory sentence that was "unclear and long". Markus Poessel 18:48, 1 July 2007 (UTC)[reply]
  • an object that is less close to the massive body, and thus less strongly influenced by its gravity, is said to be "higher up" than an object that is closer to the massive body, and thus more strongly influenced by its gravity - Would "further away" be equivalent to "less close"? I found "less close" to be an awkward phrase. Awadewit | talk 08:09, 4 July 2007 (UTC)[reply]
  • I have no idea why the numbered list in "Gravity and acceleration" was shown in the way it was (with the numbers to the left of the main text). Anyway, I've moved the image to the right, and that appears to have fixed the layout. Markus Poessel 19:07, 1 July 2007 (UTC)[reply]
  • I've now explained the anomalous perihelion shift a bit better, adding an image. There was a bit of a chain reaction, though: I had to shift the Cassini image (which I would like to keep) towards the bottom, and I have added a bit more about binary pulsars (which should have gotten more coverage anyway) to re-balance the layout. Markus Poessel 19:42, 1 July 2007 (UTC)[reply]
  • In such a star system, two highly compact neutron stars orbit each other; at least one of them is a pulsar – an astronomical objects that appears to send a highly regular series of radio pulses towards earth. - Can you spot the grammar mistake? :) Awadewit | talk 08:09, 4 July 2007 (UTC)[reply]
  • The section "From acceleration to geometry" (apparently what is meant by "From acceleration to gravity" in the review) has now been re-written. I have added some more information on the analogies in the first paragraph, as well as a more elementary description of spacetime, fixing a number of prose issues along the way. Markus Poessel 16:26, 2 July 2007 (UTC)[reply]
  • Sorry about the confusing with titles. It is much better. What do you think about including this image in that section (click to enlarge)?
  • I think it would be confusing in several respects: It mixes the two- and three-dimensional views (in the curved surface, the third - embedding - dimension is only a mathematical artefact, but the inclusion of the three-dimensional globe makes it seem like a real space dimension), and it suggests that space curvature is the important effect (for near-Newtonian gravity, the distortion of time is much more important). All in all, I feel that if that picture were included, one would need to include so many qualifications the the text would become not simpler, but more complicated. Markus Poessel 11:28, 5 July 2007 (UTC)[reply]
  • as well as the binding energy of bound systems such as nuclei or molecules - Could you just say "the binding energy of systems such as nuclei or molecules"? Having the word "bind" in the sentence twice is inelegant.
  • Consequently, in general relativity, all the different forms of energy are on an equal footing as sources of gravity. - Hmm. A little colloquial, perhaps? Also, not particularly clear. Awadewit | talk 08:09, 4 July 2007 (UTC)[reply]
  • However, already in special relativity, energy is closely connected to another physical quantity, namely to momentum. - This sounds slightly odd; with "already," the sentence suggests a chronological progression of some kind. Do you want to suggest that? Awadewit | talk 08:09, 4 July 2007 (UTC)[reply]
  • If a system has a certain energy, then for some observers (relative to which the system is in motion), it will also have a certain momentum. - Would this also be accurate? "If a system has energy, then for some observers (relative to which it is in motion), it will also have a momentum." - Yours is a bit wordy and vague. (I realize x's and y's would be preferable.) Awadewit | talk 08:09, 4 July 2007 (UTC)[reply]
*Except for one small change (...it will also have non-zero momentum), I have now used the simplified form you suggested. Markus Poessel 11:28, 5 July 2007 (UTC)[reply]
  • I don't understand what "four-momentum" is. (I clicked, but then I saw all of the equations that I know I can't understand, and I returned to your page. Anything you want readers without a strong mathematical background to understand must be explained on your page.) Awadewit | talk 08:09, 4 July 2007 (UTC)[reply]
  • Tthe statement was meant to be that a) energy and momentum are part of one unified quantity, and b) physicists have taken to calling that quantity "four-momentum". I've tried to make it clearer in the new version. Markus Poessel 11:28, 5 July 2007 (UTC)[reply]
  • Fixed use of upper-/lower-case letters after each colon. There had, in fact, been a system at least to the colons written by me (upper-case if what follows could serve as a stand-alone sentence, lower-case otherwise), but it's now all changed to conform to the more traditional way. Markus Poessel 12:35, 3 July 2007 (UTC)[reply]
I looked for just such a system, but didn't see one. I wonder if someone else messed up your system. :) Awadewit | talk 08:09, 4 July 2007 (UTC)[reply]
  • Going by my annotated printout of your review, the changes I made should now address all the prose issues you raised as well as the three minor style details you remarked upon. What I don't understand is why you marked the first paragraph of the section "Beyond general relativity?" with "citation needed". That paragraph is merely an introductory sentence; the next three paragraph raise the three main issues on which the conclusion that "the theory is very likely incomplete" is based. Markus Poessel 16:14, 3 July 2007 (UTC)[reply]
  • Since you said that you wanted to bring the article to FA (which I think will be no problem), you should probably just slap a citation on there. FAC seems to have a rule of thumb of at least one citation per paragraph. I have found, at least, that if you have one for each paragraph, you are less likely to have the citation police breathing down your neck. But I write literature and history articles; perhaps the rules are somewhat different for science articles. Awadewit | talk 08:09, 4 July 2007 (UTC)[reply]
  • In principle, I would have said that since "details follow", a reference for the first paragraph would be overdoing it, but in fact, I've found two references presenting some aspects that are not covered in the following paragraphs, so I've added those. Markus Poessel 14:55, 4 July 2007 (UTC)[reply]
  • Having revised the "Einstein's equations" section, and having added a paragraph on GPS in the "General relativity and observation" section, it appears to me that I have now addressed all the issues you raised. Markus Poessel 17:18, 6 July 2007 (UTC)[reply]

This is an excellent piece of work! Before submitting it to FAC, you might want to look carefully at the manual of style and be sure that your article adheres to all of its guidelines. I am currently going through an FAC that seems to be hung up on those issues. Awadewit | talk 01:34, 6 July 2007 (UTC)[reply]

Coming from someone with such a keen eye for a text's weaknesses, that is welcome praise indeed. Thanks for the suggestion regarding the manual of style; I'll certainly do that. All in all, many thanks for your very thorough, constructive, and helpful review! Markus Poessel 17:18, 6 July 2007 (UTC)[reply]

You are welcome. If you want me to review another "introductory" article, let me know. I had a lot of fun doing this one and learned a lot. That is the best kind of reviewing. Awadewit | talk 09:06, 7 July 2007 (UTC)[reply]
I'll be sure to take you up on that offer the next time I do a similar article! Markus Poessel 18:23, 7 July 2007 (UTC)[reply]
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