Talk:Introduction to general relativity

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Contents

[edit] From special to general relativity

Moving on with the step-by-step discussion from the lead to the next section, more specifically its first subsection:

[edit] Introductory subsection (untitled)

  • I would like to shorten the part about action at a distance. As I've said in our earlier discussion, this is not something that was central to Einstein's way to go from special to general rt - he chose a different starting point, namely the (mistaken) assumption that special relativity wasn't compatible with the universality of free fall. Thence to the equivalence principle, the question of a "general relativity principle", and the chain of thought followed in the rest of the section. We can try to find a short version that mentions action-at-a-distance, but I would like to get rid of the rather long version we have now, which, I think, sends the wrong signal (making it seem that this question was much more important for the transition from sr to gr than it really was). --Markus Poessel 06:58, 20 July 2007 (UTC)
    You may have a point, but I disagree with the reasoning: this article is not called Introduction to the development of general relativity, and we already have History of general relativity. I've noticed that the article is a bit Einstein-centric. Obviously that is justified to some extent, but we do not have to do everything "Einstein's way", because we are introducing the reader to the subject, not to Einstein's role in developing it. Action-at-a-distance is an easy way to see the incompatibility between Newtonian gravity and SR. If this sends the wrong signal, it could be the Einstein-centric approach that needs tweaking, not the good pedagogy. We can be guided by the many excellent secondary sources.
    Having said that, I suggest you just go ahead and make an edit so that others can see what you have in mind. The ample discussion thus far shows to me at least that the excellent editors working on the article are all basically pulling in the same direction, so lets edit! Geometry guy 13:55, 20 July 2007 (UTC)
  • Note: When I read this article, I definitely came away from it with the idea that Einstein did practically everyting (but perhaps that is correct). I agree with Geometry guy that focusing too much on the history distracts readers from the concepts. At times, I started asking all sorts of historical questions about the development of general relativity that were not answered here (rightly so) rather than focusing on learning the concepts at hand. This may be my own bias, though; I have a strong interest in the history of science. Awadewit | talk 14:36, 20 July 2007 (UTC)
  • A general remark ahead: The history of general relativity (from the beginning to 1915/16) is pretty Einstein-centric (much more so than that of special relativity, with Poincare and Lorentz). I think the present version is rather OK as a history (even though that's not what it's meant to be) - we have Minkowski; we might add a sentence about Hilbert. That said, my reasoning is strictly pedagogical. For me, the main function of "From SR to GR" is to develop the structure of gr in a way the reader can follow. Choosing Einstein's own path, telling those part of it that follow logically from each other (equivalence, tidal forces, geometry) and summarizing the others (search for the field equations) seems to work. The "action-at-a-distance" doesn't really add anything to the arguments developed here - it doesn't tell us why we might want to look at the equivalence principle, it isn't used in the later text. If you look closely, it doesn't really help the reader to understand why sr and gravity are incompatible (or else, it gives a false sense of understanding - see the argument I made earlier on this page, the analogy with Coulomb's law). My proposal would be to avoid all the pitfalls associated with a too-simple version of the action-at-a-distance argument, keep it short and write something like (not brilliant prose yet, I know, more for the sake of the flow of argument):
"In 1905, Einstein published his theory of special relativity, which included radically new concepts of space and time. Special relativity reconciles electrodynamics (the interaction of objects with electric charge) with Newton's laws of motion. At first glance, it looked as if there should be a straightforward way to incorporate Newton's theory of gravity (which has formal analogies with parts of the theory of electrodynamics) into the framework as well; however, attempts by Henri Poincare and others to do so failed.(Reference here would be Pauli, Theory of Relativity, section 50.)
Einstein himself started in 1907 to devote serious attention to this problem. Over the following eight years, his thinking led him from a simple thought experiment involving an observer in free fall (the "Equivalence Principle") to a fully geometric theory of gravity.[1]"
Howzat? --Markus Poessel 20:18, 20 July 2007 (UTC)
Sorry I've been slow in responding, I got a little distracted! :) I agree that the paragraph explaining the inconsistency between SR and Newton's law of universal gravitation is maybe labored and long. On the other hand, it would be nice if we could explain the history a little deeply and set up the rest of the article. How about something vaguely like this?
“ Beginning in the later 19th century, physicists such as James Clerk Maxwell and Oliver Heaviside began to consider whether gravity could be described by laws similar to those of electromagnetic field. The two types of forces are similar in several ways, but early theories led to clearly wrong predictions, such as that planets could not orbit stably around the Sun. The search for a better gravitational law took on new urgency when it was realized that Einstein's 1905 theory of special relativity was inconsistent with Newton's law of universal gravitation. Despite the similarity of the two forces (electromagnetism and gravity), and despite the fact that special relativity is already consistent with electromagnetism, it proved tricky to reconcile special relativity and gravity; provisional theories by Albert Einstein, Max Abraham, and Gustav Mie either failed to reconcile the two or predicted effects that had not been seen experimentally. The only theory of gravity that maintained special relativity intact was Gunnar Nordström's 1913 theory of gravitation. However, his theory predicted that the path of light would not be bent by gravity, which Einstein had hypothesized in 1907. The decisive test disproving Nordström's theory came in 1919, when experiments showed that gravity bends light.

Einstein took a different route to a gravitational theory. In 1907, he hypothesized the Equivalence Principle, which states that a free-falling observer inside a small box (say, an elevator) cannot tell that he is falling by any experiment carried out within the box. In other words, every effect of gravity within the box disappears if the elevator is free-falling. This principle — which can be tested experimentally — led Einstein to predict that gravity would bend light and cause time to flow at different rates, depending on the clock's position in a gravitational field. This warping of time due to gravity then forced him to consider the warping of space, since the two share the same nature according to special relativity. Rather than introducing a new physical field to describe gravity, Einstein proposed that the quantities used to describe the warping of space and time could themselves be taken as the gravitational fields. In 1915, after exploring many equations to describe these fields, Einstein hit upon a simple equation that reproduced Newton's laws (with small corrections) and made several testable predictions that have been verified experimentally. This equation represents the general theory of relativity.

 ”
Welcome back - an impressive list of poems! I think the text you propose is problematic, though. Why does it need to mention so many concepts already, especially in a form much too brief for most readers to understand? Why, for instance, does the bending of light need to be mentioned in such historical detail, when we only explain how light bending even works and what it is later on? Why does there need to be a rushed description of the equivalence principle, when the equivalence principle itself will be explained in the following paragraph? Why the mention of geometry - again so briefly that the reader cannot be expected to understand it from this part of the text alone (and when there already has been a brief mention in the lead)?
I am open to suggestions when it comes to including more history, but I don't think there's a point in making the opening paragraphs of "From special to general relativity" a compressed version of that history. Our introduction is, overall, not that long – the section "From SR to GR" is probably pretty much the minimum length for developing the ideas of GR, yet presenting them in an accessible way; as such, it would be overkill to insert yet another level of summary – the opening paragraphs should set up what follows directly, namely the equivalence principle, but I think it makes the text less readable if we try to get them to do more. Also, the section is currently named "From SR to GR", and I think that makes sense. If we start too far back (Maxwell etc.), we would need to include even more – and, as Geometry guy, this is not the "Introduction to the development of GR". In my original draft, the somewhat historical approach was mainly used as an ordering scheme for the physical concepts that need to be introduced - equivalence principle, tidal acceleration, and so on. We can mention a bit of history, but it definitely should not overwhelm the physics! All that said, I would like to keep up my previous proposal. May be there is a way of working Maxwell in (please provide a reference for that), but not using the "planetary orbits wouldn't be stable" argument – planetary orbits aren't stable after all; an orbiting planet radiates gravitational waves and will eventually plunge into the Sun! Mie, Abraham and Nordström could come later, when the text has progressed to 1912 or so, but again I think putting them into the opening and then backtracking interrupts the flow of the text. Also, I'd be interested to hear why you left Poincare out – I'd be in favor of mentioning him, but again, if there are reasons to leave him out, I'm open to compromise. --Markus Poessel 14:36, 4 August 2007 (UTC)

[edit] Topics to cover here?

You're right, Markus; I was experimenting with providing the reader with a roadmap of the article after the lead but, as you say, that may be too much too soon. The references can be found in the Pais biography of Einstein, where he discusses the Nordström theory, and in the Pauli encyclopedia article from Dover Press. I left out Poincaré (1905) because it wasn't a field theory and H. A. Lorentz (1900) because I was forgetful. ;) Perhaps it'd be good to agree on the points that we'd like to cover in this subsection? Willow 12:07, 7 August 2007 (UTC)

Yes, we can do that. The main points I would like to put into this subsection (that is, between the section header "From special to general relativity" and the subsection header "Equivalence principle") is:
  • Einstein's SR revolutionized the concepts of space and time
  • When Einstein had finished SR, he started to look for ways of incorporating gravity
  • He started with a simple thought experiment.
Since this is probably too Einstein-centric, we could follow Pauli's lead and at least mention briefly that others (Poincare) were looking for a relativistic theory of gravity as well; if we do, it would be good to stress that Einstein's perspective (to be explored in the following sections) was radically different from those people's starting point. I'm very reluctant to put in much more than that. It's not meant to be anything like a complete history; the sort-of-historical order is only chosen as it allows us to develop the physical ideas gradually, and in a way most readers will hopefully be able to follow. --Markus Poessel 15:39, 7 August 2007 (UTC)

I agree with all those points, especially the last one, since we should definitely provide a strong lead into the next section on the Equivalence Principle.

The Einstein-centricity doesn't bother me that much, although I worry that people's strong feelings about him might prevent them from really seeing the strengths of his theory. It does him and everyone a disservice to paint him as a Moses descending from Sinai with the Tablets of Obvious Truth, rather than as a bold theorist who made a really good theory that has weathered many experimental tests. So I'm not really concerned with historical accuracy or giving the also-rans like Poincaré their due, as much as explaining that alternative theories are possible and that GR is not apodictic, even classically.

I'd also like to explain why people started tinkering with alternative theories of gravity after SR was published; do you think we can explain the present long middle paragraph in a shorter way?

I'd also like to avoid words like "fail" or "revolutionize" in favor of words that convey more concrete meaning, such as "is logically inconsistent", "failed experimental tests", "failed thought experiments", or "makes false predictions". Do you agree? I see the danger of burdening the reader with too much to digest, but I think we aren't being helpful by using vague wordings. Willow 12:42, 8 August 2007 (UTC)

PS. By instability, I meant that the Solar System would fly apart. A system of two bodies that converge to a single point is indeed "stable", no? :)

Sorry for the delay. In view of our goals for this part of the text, here's another attempt that hopefully makes clearer what the whole section is about:
"In 1905, Einstein published his theory of special relativity, which reconciles electrodynamics (the interaction of objects with electric charge) with Newton's laws of motion. Special relativity re-defined the foundations for all of physics by introducing radically new concepts of space and time, but, as it turned out, not all of physics could be readily made to fit into the new framework. The notable exception was Newton's theory of gravity, which describes the mutual attraction experienced by bodies due to their mass.
"Of the various attempts to find a relativistic description of gravity, the one that was ultimately successful was Albert Einstein's development of what is now known as the general theory of relativity. In order to understand the theory's basic ideas, it is instructive to retrace a simplified version of Einstein's own research between 1907 and 1915, which led him from a simple thought experiment involving an observer in free fall (the "Equivalence Principle") to a fully geometric theory of gravity.[2]"
- that way, we would make clear that the purpose of this section is indeed not a full historical account, rather a historically-inspired presentation of the main ideas. As for stability: I'm not aware of any model that would make the Solar System fly apart. Where is the energy supposed to come from? As far as I know, the instability is always orbital decay. --Markus Poessel 19:52, 16 August 2007 (UTC)

On stability, I should say that I haven't studied this, nor can I claim any expertise. But I remember reading somewhere that vector theories of gravitation can produce runaway conditions. It had something to do with vector gravitational radiation carrying negative energy; perhaps the energy of what's left behind grows without bounds? There was a paper by Abraham in 1912 or so about it, I remember that much. Anyway, it's probably a bad idea to include something so strange in this article, even if it's just to disprove a faulty theory, so we should probably just forget it. :( Willow 11:53, 20 August 2007 (UTC)

On language: I'm a little bit worried about the use of the following phrases: "not all of physics could be readily made to fit" and "the one that was ultimately successful". They suggest invention rather than discovery to me. Awadewit | talk 01:59, 17 August 2007 (UTC)
I agree that "made to fit" sounds as if there was some underhand manipulation involved ("if it don't fit, we'll make it fit!"). On the other hand, we're talking about models, which are human inventions. How about "not all of physics could be readily made to fit into the new framework" -> "some previously formulated physical laws did appear to be at odds with the new framework"? I'm less worried about your second example: in "the one that was ultimately successful", the "one" refers to attempts to find a relativistic description of gravity. Several attempts were made; all but one of these attempts did not succeed; one was successful. --Markus Poessel 07:40, 17 August 2007 (UTC)

I like your new section! But I also agree with Awadewit that we need to clarify words like "succeed" for lay-people. Here are a few other small tweaks to the writing that I hope you might like as well:

"In 1905, Einstein published his theory of special relativity, which reconciles Newton's laws of motion with electrodynamics (the interaction between objects with electric charge). Special relativity provided a new framework for all of physics by introducing radically new concepts of space and time. However, some then-accepted physical theories were inconsistent with that framework; a key example was Newton's theory of gravity, which describes the mutual attraction experienced by bodies due to their mass.
"Several physicists, including Albert Einstein, proposed modifications to Newton's law of gravity to make it consistent with special relativity. However, only Einstein's 1915 theory of general relativity has proved to be consistent with experiments. To understand its basic ideas, it is instructive to follow Einstein's thinking from 1907 and 1915, which led him from a simple thought experiment involving an observer in free fall (the "Equivalence Principle") to a fully geometric theory of gravity.[3]" Willow 12:11, 17 August 2007 (UTC)
Great, I like the modified version. There's something I'd like to change in the second paragraph, though. It wasn't just about modifying Newtonian gravity to make it consistent with sr, it was about modifying sr as well. So how about:
"Several physicists, including Albert Einstein, proposed ways of constructing a relativistic theory of gravity that would encompass key features of both Newton's law of gravity and special relativity; of these, however, only Einstein's theory of general relativity proved to be consistent with experiments and observations. To understand that theory's basic ideas, it is instructive to follow the rough outline of Einstein's thinking from 1907 to 1915, which led him from a simple thought experiment involving an observer in free fall (the "Equivalence Principle") to a fully geometric theory of gravity.[4]"
(Oh, and I've changed "1907 and 1915" to "1907 to 1915", and I've omitted the year in "Einstein's theory of general relativity" - the year is mentioned in the lead, and later in this section; no need to overdo it; also, we're not following Einstein's thinking, only a simplified version of it. I've tried to express this by "rough outline" which sounds somewhat awkward in conjunction with "thinking", so I'd appreciate if one of you were to come up with a more elegant way of putting this.) --Markus Poessel 07:50, 18 August 2007 (UTC)
Uninformed editor's suggestion: "Several physicists, including Albert Einstein, attempted to find a theory of relativity that accounted for both Newton's law of gravity and special relativity; however, only Einstein's theory proved to be consistent with experiments and observations. To understand the theory's basic ideas, it is instructive [best?] to follow the trajectory [path?] of Einstein's thinking between 1907 and 1915, from his simple thought experiment involving an observer in free fall (the "Equivalence Principle") to his fully geometric theory of gravity." - Trying to reduce wordage, too. Awadewit | talk 15:16, 18 August 2007 (UTC)
Except for two little details ("find a theory of relativity", better: "find a theory"; I'd like an "ultimately" in there), I like your re-write - in context, the sub-section would now read:
"In 1905, Einstein published his theory of special relativity, which reconciles Newton's laws of motion with electrodynamics (the interaction between objects with electric charge). Special relativity provided a new framework for all of physics by introducing radically new concepts of space and time. However, some then-accepted physical theories were inconsistent with that framework; a key example was Newton's theory of gravity, which describes the mutual attraction experienced by bodies due to their mass.
"Several physicists, including Albert Einstein, attempted to find a theory that would account for both Newton's law of gravity and special relativity; however, only Einstein's theory ultimately proved to be consistent with experiments and observations. To understand the theory's basic ideas, it is instructive to follow the trajectory of Einstein's thinking between 1907 and 1915, from his simple thought experiment involving an observer in free fall (the "Equivalence Principle") to his fully geometric theory of gravity.[5]"
Sounds good to me. --Markus Poessel 06:51, 19 August 2007 (UTC)
This sounds good to me as well, although I'd replace "account for" in the first sentence of Paragraph #2 with "reconcile"; the verb "account for" is usually used with experimental data rather than theories, no? Other than that, I think we're ready to move on, does everyone agree? Willow 11:39, 20 August 2007 (UTC)
I agree we should move on (thanks to all for being so patient), unless there are objections. I'm opening up the next section, and if no-one has objected after a few days, I'll implement the last version we agreed upon here (with "reconcile" instead of "account for"). --Markus Poessel 08:41, 21 August 2007 (UTC)
I concur - this is good. Let us move on. Awadewit | talk 14:46, 21 August 2007 (UTC)
OK, I've put our consensus version into the article. --Markus Poessel 12:47, 27 August 2007 (UTC)

[edit] Equivalence principle

The only thing I would like to change in this section is the reference to rotation (currently the last sentence). Rotation is a bit tricky - it is not different from linear acceleration (as a reader might infer from the last sentence) in that you can always make the transition to a non-rotating frame of reference; also, Einstein thought that rotation would be on an equal footing with linear acceleration (hence gravitomagnetism). Also, the sentence itself reads a bit off - the fact that the person is in a uniformly rotating room doesn't make much of a difference - does the person him- or herself (i.e. the observer) rotate or not? I would simply leave this sentence out. --Markus Poessel 09:15, 21 August 2007 (UTC)

  • Just to let you know, I am here - watching. :) I'll wait until the pronoun issue is paramount to say anything. Awadewit | talk 17:15, 27 August 2007 (UTC)
  • It's good to know you're still here - I greatly value your input in this discussion (or is that "I value...greatly"?). I'm quite in favour of the slow pace of the current revamping, as long as neither you nor Willow get bored and leave this discussion altogether (but with the "watch" feature, a slow pace should probably not a problem). All the best, Markus Poessel 20:23, 27 August 2007 (UTC)
I'm really glad to hear you say that, Markus, since I've been feeling lame about my glacial pace in replying; it's not for any, ummm, frostiness towards the article, but rather because I've had family visiting and it's anyway a very busy time of year for me. I'll try to keep up! :)
I'm thinking that we might do better with this section, but first I'd like to understand what's going on — always a good desideratum. ;) With the "rotation" sentence, I was trying to clarify the equivalence principle (gravity cannot be detected by a free-falling observer) by contrasting it with other types of acceleration that can be detected by a co-moving observer. I haven't read Einstein's old paper on gravitomagnetism; but as anyone knows who's ridden a Tilt-A-Whirl, you can detect when your surroundings are rotating even if your eyes are closed. Isn't there a qualitative difference between rotational motion and free fall? For one thing, fictitious forces such as the centrifugal and Coriolis forces appear in a uniformly rotating frame, which aren't seen in an infinitesimal free-falling frame, are they? Confused Willow 20:19, 28 August 2007 (UTC)

Hi Willow, it's good that we are in agreement about the pace (and implicitly about the time-scale of this reworking), then. The point is that you can make all the local effects of linear acceleration vanish by changing the reference frame. The same is true for gravity. Also, you can make centrifugal and Coriolis forces vanish by changing the reference frame, so the analogy is between "going into free fall" and "going from a rotating to a non-rotating reference frame", not between "going into free fall and feeling no acceleration" and "remaining in a rotating reference frame and feeling inertial forces". In practical terms, it is admittedly easier to make the transition for linear acceleration (just let yourself fall) than for rotation (you need to get rid of that pesky angular momentum first), but the important thing is that a transition to suitable reference frames will get rid of the inertial forces in both cases. --Markus Poessel 07:25, 29 August 2007 (UTC)

Yeay! I think I get it. :) Let me check with you whether my understanding is OK. Two sisters go to the carnival, and one rides the merry-go-round; sister A is standing on the ground and sees no fictitious forces whereas sister B on the merry-go-round sees several. Likewise, two other sisters are in a gravitational field, with sister P free-falling and sister Q standing on the ground watching her fall. Then sisters A and P are similar, by being both in the privileged reference frame where no faux forces are observed, nor do they feel unusual forces on their bodies. Likewise, sisters B and Q are similar in that they both observe fictitious forces and can feel forces on their bodies: sister B feels the force from her horse holding her on the ride and sister Q feels an upward force on the soles of her feet.
I was mistakenly trying to equate sisters A and Q, since they're both just "standing on the ground", rather than sisters A and P, the proper pairing. Do you see how someone might make that mistake? That's why I think we need to clear up this section a little more. I also think we might emphasize a little more strongly that the Equivalence Principle agrees with our intuitive understanding of gravity, but that it's only a hypothesis and could be disproven someday by sensitive experiments. What do you all think of this? Willow 20:15, 29 August 2007 (UTC)
Yep, that's it. My next question would be: If we leave rotation out altogether, is the typical reader still going to be confused? In other words: without our prompting, will he or she actually think of rotation by themselves, and make the same mistake you did? I'd still guess it might be best to leave rotation out altogether, and focus on linear acceleration only. That's what we need for the following argument, anyway (I think that, at Awadewit's behest during the peer review, I banished another rotation reference to the footnotes, for similar reasons; it was making matters more complicated without helping with the main argument). --Markus Poessel 06:22, 30 August 2007 (UTC)
Yeay, thank you, Markus! :) I deleted the sentence, now that I understand it, but I still think we can do better in explaining the Equivalence Principle for lay-people. I need to think more about how to do that, but it seems like there are two possible levels, one simpler and one more complicated. In the first, we could just not mention "acceleration" , "inertial observers", "reference frame" or "fictitious forces" and just say that Einstein's principle hypothesizes that gravity affects everything (all matter and energy) exactly the same, and therefore a person can't tell whether they're free-falling in a (uniform) gravitational field by any experiment. This principle has been tested experimentally and so far seems to be valid, within the sensitivity limits of our experiments. In the second level, which might correspond to a second paragraph, we could try to explain the "fictitious force" aspect of gravity and try to build a nice bridge to the next section, in which Einstein hypothesized that an accelerated reference frame will mimic every effect of gravity.
I do think that if we mention acceleration or accelerated observers or fictitious forces, people who have had a little physics will naturally gravitate (sorry, ;) to the closest related concepts that they've learned, which may involve circular motion, and perhaps be led astray as I was. I do agree, though, that linear acceleration is simpler than circular motion, and that should be our first choice in explaining fictitious forces, especially since we use linear acceleration in the next section. Willow 22:14, 30 August 2007 (UTC)
What you call the first level (all matter and energy affected in the same way) mostly isn't due to Einstein - it's the universality of free fall, going back as least as far as Galilei's experiments on different kinds of falling bodies, and it's not sufficient to ensure that no experiments can tell someone in free fall that they are falling (that last one is indeed Einstein). Hmmm. May be that's how first/second level/paragraph suggestion could work, though: mechanics first, Einstein equivalence second. How about this:
"In a gravitational field, all objects, whatever their size or composition, fall at the same rate. Thus, leaving rotational motion aside, any person in a free falling elevator will experience weightlessness: objects will either float alongside, or drift at constant speed; since everything in the elevator is falling together, no gravitational effect can be observed. As far as the motions of objects are concerned, the experiences of such an observer in free fall will be similar to those of an observer freely adrift in deep space, far from any source of gravity.
"But for these latter observers, the laws of physics should be the same as for the privileged ("inertial") observers Einstein described in his theory of special relativity. In particular, they should find that light travels along straight lines at constant speed. Such observers feel no acceleration, and they need not introduce what physicists call fictitious forces (such as the force pressing the driver of an accelerating car into his or her seat) to explain what happens around them.[6] Einstein hypothesized that the similar experiences of weightless observers and inertial observers in special relativity represented a fundamental property of gravity: for an observer in free fall, all the physical laws of special relativity should hold. Not only is it impossible for any free-falling observer to tell by the motion of nearby objects whether or not they are in free fall. No other experiment involving electromagnetism, thermodynamics or any other physics within the realm of special relativity will tell them, either; every such experiment would give the same result in free fall and for an observer at rest (or moving uniformly) in deep space, far from all sources of gravity. This is the content of what is nowadays known as Einstein's equivalence principle, which Einstein chose as a cornerstone of his new theory of gravity.[7]"
It's not quite finished, but that could be the basic structure. Markus Poessel 21:43, 8 September 2007 (UTC)
Perhaps the sentence fragment could be fixed with a "not only...but also" construction? :)
I would also reduce This is the content of what is nowadays known as Einstein's equivalence principle" to "This is what is known as Einstein's equivalence principle".
Is "rotational motion" mentioned before this, because if it isn't, I would find myself asking "what rotational motion?" Awadewit | talk 18:16, 9 September 2007 (UTC)
OK, here's a slightly modified version:
"In a gravitational field, all objects, whatever their size or composition, fall at the same rate. A person in a freely falling elevator will experience weightlessness: objects will either float alongside, or drift at constant speed; since everything in the elevator is falling together, no gravitational effect can be observed. As far as the motions of objects are concerned, the experiences of such an observer in free fall will be similar to those of an observer freely adrift in deep space, far from any source of gravity.
"But for these latter observers, the laws of physics should be the same as for the privileged ("inertial") observers Einstein described in his theory of special relativity. In particular, they should find that light travels along straight lines at constant speed. Such observers feel no acceleration, and they need not introduce what physicists call fictitious forces (such as the force pressing the driver of an accelerating car into his or her seat) to explain what happens around them. (Similar fictitious forces occur when an observer is rotating; we have tacitly assumed that none of our observers are.)[8] Einstein hypothesized that the similar experiences of weightless and of inertial observers in special relativity represented a fundamental property of gravity: for an observer in free fall, all the physical laws of special relativity should hold. Not only is it impossible for any free-falling observer to tell by the motion of nearby objects whether or not they are in free fall, but also there will be no other experiment involving electromagnetism, thermodynamics or any other physics within the realm of special relativity which allows such a distinction; every such experiment would give the same result in free fall and for an observer at rest (or moving uniformly) in deep space, far from all sources of gravity. This is what is known as Einstein's equivalence principle, which he chose as a cornerstone of his new theory of gravity.[9]"
Oops, forgot to sign: Markus Poessel 19:25, 14 September 2007 (UTC)
Perhaps because I am reading this out of context, the sentence beginning "the "latter observers" was just a bit unclear to me. The latter are those "freely adrift in space", right? (That's the grammar of it.) And since I've been away for awhile, suddenly I wasn't sure anymore who the "privileged" observers were anymore (Sorry!). I feel adrift - or perhaps I'm in free fall? Sorry. I need to go read the article again.
Also, "This is what is known as Einstein's equivalence principle, which he chose as a cornerstone of his new theory of gravity." I dislike "chose". To a lay reader, it sounds as if this is not "true" but "subjective". Einstein could have chosen any principle, you know - everyone is entitled to their own opinion. :) Awadewit | talk 00:58, 18 September 2007 (UTC)
Tweaking a bit:
"In a gravitational field, all objects, whatever their size or composition, fall at the same rate. A person in a freely falling elevator will experience weightlessness: objects will either float alongside, or drift at constant speed; since everything in the elevator is falling together, no gravitational effect can be observed. As far as the motions of objects are concerned, the experiences of such an observer in free fall will be similar to those of an observer freely adrift in deep space, far from any source of gravity.
"But for observers adrift in deep space, the laws of physics should be the same as for a certain class of privileged ("inertial") observers Einstein described in his theory of special relativity. In particular, they should find that light travels along straight lines at constant speed. Such observers feel no acceleration, and they need not introduce what physicists call fictitious forces (such as the force pressing the driver of an accelerating car into his or her seat) to explain what happens around them. (Similar fictitious forces occur when an observer is rotating; we have tacitly assumed that none of our observers are.)[10] Einstein hypothesized that the similar experiences of weightless and of inertial observers in special relativity represented a fundamental property of gravity: for an observer in free fall, all the physical laws of special relativity should hold. Not only is it impossible for any free-falling observer to tell by the motion of nearby objects whether or not they are in free fall, but also there will be no other experiment involving electromagnetism, thermodynamics or any other physics within the realm of special relativity which allows such a distinction; every such experiment would give the same result in free fall and for an observer at rest (or moving uniformly) in deep space, far from all sources of gravity. This is what is known as Einstein's equivalence principle, the starting point of his development of his new theory of gravity.[11]"
I guess Willow really is harvesting now. --Markus Poessel 07:42, 26 September 2007 (UTC)
Eeep! I have been busy — this past weekend was exhausting and the next one promises to be worse — but I've also been neglectful; forgive me? I got distracted by sundry things and blind-sided recently by criticism of X-ray crystallography, which I took under my wing back in May. Give me a day to think it over and through again, and I'll get right back to you — thanks for being so forbearing! :) Willow 17:15, 26 September 2007 (UTC)
Please, don't worry – as long as we keep making progress, I don't mind if the pace is leisurely (in fact, I'm quite glad it is). --Markus Poessel 09:50, 27 September 2007 (UTC)

[edit] Navbox

Unresolved. This seems just about resolved.

As ever with vertical-format Navboxes - {{General relativity}} is making it hard to format images for all displays - I've got a wide format and it looks pretty bad. I've suggested reformating the template so it spans. Any opinions? Please comment here. regards --Joopercoopers 13:27, 18 July 2007 (UTC)

The box looks very crowded. Can you do a horizontal one at the bottom of the page? Is that what you meant by "spans"? Awadewit | talk 14:22, 18 July 2007 (UTC)
yeah - something like this maybe - without the hide function --Joopercoopers 14:48, 18 July 2007 (UTC)
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That is what I was thinking of (I like the hide function, but, whatever. I'm certainly not going to start saying ridiculous things like "This article cannot be an FA without a "hide" function in the navbox.). Awadewit | talk 14:54, 18 July 2007 (UTC)
Go no - nothing to do with the FAC, just a nicety. Actually perhaps more something along these lines.... --Joopercoopers 14:57, 18 July 2007 (UTC)
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[edit] Help at Introduction to special relativity

Hi,

The sister of this article, Introduction to special relativity, is in need of work. I've worked on it to clearly motivate special relativity and have tried to build geometric intuition to explain the counterintuitive concepts. Now I need some of the people who have done so much wonderful work in this article to bring Intro to SR upto GA status. It is currently rather focussed and needs to be rounded out to provide a self-contained introduction. The language can also probably do with some brush-ups. Thanks. Loom91 06:48, 30 July 2007 (UTC)

  • Thanks for the invitation. At the moment, I'm focusing on the other sister article (general relativity), but once I've done more of what I mean to do there, I'll have a look at "Intro to SR". --Markus Poessel 06:24, 1 August 2007 (UTC)

P.S. A suggestion: is it really necessary to introduce the Einstein tensor? After the explanation of the metric tensor and the Ricci tensor, introducing yet another (scantly explained) tensor may well confuse the reader. Wouldn't it be clearer to write out the expression for G? Also, bold fonts are usually reserved for vectors in elementary texts. Using bold to represent tensors may be confusing. Perhaps it will be clearer to put in abstract indices. Loom91 06:48, 30 July 2007 (UTC)

  • While progress on the re-working seems to have slowed down, I still want to go through the whole article bit by bit. If things stay as quiet as they are now, I will probably just go ahead with gradual changes, and once I've reached the section you mention, I do think it can be simplified (the Einstein tensor is needed for the equation, though; I also do not think that the typical reader of the article will be confused by the boldface - abstract indices would look much more scary and distracting, would be my guess). --Markus Poessel 06:24, 1 August 2007 (UTC)
  • Why do you think G is needed for the equation? The equation can be written out in terms of the Ricci tensor, ricci scalar, metric tensor and the cosmological constant. Since the Ricci tensor and the metric tensor have already been explained, that would be clearer. Also, using indices will help the reader avoid the misconception that the Einstein field equation is one equation in the ordinary sense. To readers not familiar with matrix equations, writing a collection of equations as one equation may not be very clear. Loom91 07:16, 1 August 2007 (UTC)
  • As far as I can see, the Ricci tensor hasn't been explained. Neither has the Ricci scalar. Indices will help some readers realize that this is more than one equation (the others will just have to read the text), but the indices will certainly confuse other readers. I'd like to keep the equation as simple as possible - I think that if we write down the more complicated form, readers will not even see the part they can understand, e.g. how all the constants appear so neatly in the equation. --Markus Poessel 18:42, 1 August 2007 (UTC)

The Ricci tensor is briefly explained as "The amount of stretching there is at each point of a space (or spacetime) determines how curved it is. More precisely, the metric function and the rate at which it changes from point to point can be used to define a geometrical quantity called the Riemann curvature tensor, which describes exactly how the space (or spacetime) is curved at each point. In general relativity, the metric and the Riemann curvature tensor are quantities defined at each point in spacetime." But the Einstein tensor is not explained. In fact, it is not very clear from the text that G is an explicit function of R_ab and g_ab. To me, introduction of an additional tensor seems to complicate rather than simplify. The metric tensor and Ricci tensor have already been discussed, so why not use them, instead of the undiscussed Einstein tensor? And why do you think indices will confuse most readers? Indices are merely notation, rather than a concept. Also, it seems physicists (as opposed to mathematicians) usually prefer to put the indices in.Loom91 07:16, 2 August 2007 (UTC)

The Riemann tensor is briefly mentioned, yes. The Ricci tensor isn't explained at all. Neither Riemann nor the metric have been given in terms of components. If we write the Einstein equations in terms of Riemann the metric, it will be rather longish, and it will look like nothing that the reader can possibly understand with the information we have given him or her. Indices, especially Einstein summation, will add to the confusion - if you have no idea what vector components are, what can you be expected to make of these indices? And why are some indices up, others down? The fact that they are "merely notation" seems to me to be a good reason to avoid them, if we can. If there are indices, readers will feel that there is something they should understand at this point, but cannot. If there are merely symbols T and G in boldface, readers are more likely to feel that all they are meant to understand is what is written in the text about these symbols - and they would be right. Mentioning that G can be written in terms of Riemann and the metric sounds sensible, though. --Markus Poessel 18:42, 2 August 2007 (UTC)
How about giving the expression for G in a separate line and explaining that it is ultimately a functional of the metric and therefore the EFE are a set of equations relating various derivatives of the metric to the energy content of space? Loom91 14:39, 3 August 2007 (UTC)
If by "giving the expression for G", you mean writing down the formula, again, I think this would be more confusing than helpful. I agree, though, that mentioning that Riemann and G depend on the derivatives of the metric might be good (if only in parentheses). --Markus Poessel 16:19, 7 August 2007 (UTC)

[edit] Confusing sentence

The part about Equivalence Principle reads:

"roughly speaking, this principle states that a person in a free-falling elevator cannot tell that they are in free fall; every experiment in such a free-falling environment has the same results as it would if the observer were at rest or moving uniformly."

This is confounding me. I think what it's saying is that a person in a gravity-free environment can't tell if they are in a freefall or in space; the effects are the same. However, to me, it seems to say that a person in freefall can't tell if they're in freefall or resting on the ground. I think it would be more clear if it read:

"roughly speaking, this principle states that a person in a free-falling elevator cannot tell that they are in free fall; every experiment in such a free-falling environment has the same results as it would if the observer were in space or moving uniformly."

However, I don't feel comfortable making this change. TribeCalledQuest 12:26, 7 August 2007 (UTC)

Thanks for the feedback. You're right in that the reference to space went missing. It should be "at rest (or moving uniformly) in deep space, far from all sources of gravity", which I've now put in. Thanks again! --Markus Poessel 16:14, 7 August 2007 (UTC)
Much clearer, and thanks to all for a well-written article. TribeCalledQuest 19:56, 7 August 2007 (UTC)

[edit] "Introduction to" articles

Regarding the discussion about "Introduction to..." articles at this article's Featured article candidacy discussion, I've followed the kind advice given by some of you and made my argument into an essay, which is now online as Wikipedia:Many things to many people.

(Strangely, I could have sworn I wrote something like this yesterday evening. No record of it, though... may be forgot to press "save page".) --Markus Poessel

[edit] Part need clarification

In the part of "physical consequences" it says

"the second observer will measure a lower frequency for the light than the first"

but there is no mentioning before of which observer is the first and which is the second Dy yol 19:08, 8 September 2007 (UTC)

Also, in the part of "physical consequences" it says "Assume that there are two observers, both of them at rest in an accelerating rocket-ship." then it goes on to say "If the lower observer sends a light signal to the higher observer, the acceleration causes the light to be red-shifted"

I wonder if this is correct! The two observers are in the same rocket ship thus by equivalence they should be at the same gravitational potential irrespective of their location within the ship, thus no wavelength shift. No? - Hemanth

Hello, unsigned editor. The answer is, in fact, no. The easiest way to see this is to follow the link (Harrison 2002) given in that particular section; that sketches how the shift follows from the equivalence principle. Markus Poessel (talk) 13:27, 23 March 2008 (UTC)
Another way to look at it: since an accelerated frame is equivalent to a uniform gravitational field, points higher in that "equivalent g-field" must have higher "equivalent gravitational potential energy" than lower points. So the assertion that points in an accelerated frame are at the same potential must be false. Wwheaton (talk) 19:15, 23 March 2008 (UTC)
Perfectly correct. What I like about the p.o.v. I cited is that it doesn't require you to know anything about potentials or somesuch, and uses what I think is the simpler version of the equivalence principle (the one that translates directly to geometry - local flatness). Markus Poessel (talk) 22:44, 23 March 2008 (UTC)

I am Hemanth the above unsigned - Sorry I confused gravitational acceleration with gravitation potential. I understand the gravitational potential will be different at the two points. Thank you. —Preceding unsigned comment added by Hchari (talk • contribs) 22:59, 25 March 2008 (UTC)

You're welcome. A more practical tip: if you add four tildes at the end of a comment, like this: ~~~~, this will be automatically transformed into your signature (with link to your user page) and date. It's a standard way of signing stuff on Wikipedia. Here's what it looks like when I do this, right now: Markus Poessel (talk) 00:57, 27 March 2008 (UTC)

[edit] Question About http://en.wikipedia.org/wiki/Image:Cassini-science-br.jpg

What is that red ball between earth and cassini is not explained in narration of image. So in beginning itself new reader get confused.

viran 13:26, 20 September 2007 (UTC)

It's the Sun. --EMS | Talk 16:01, 20 September 2007 (UTC)

That deflection and shapiro delay can also be due to Arago spot.

Please add this to improve quality of WiEncycLe (Wikipedia Encyclopedia Article).

viran 18:09, 20 September 2007 (UTC)

I see that someone added 'due to sun's mass' in narration of image. But it is not explained how this phenomenon differs from Diffraction in Arago spot. Instead of small circular body in ARAGO SPOT, there is sun.Diffraction in Arago Spot is also due to warping of space-time around electrons, atoms, molecules. And speed of light slows down in denser medium because warping of space-time in dense medium is more due to number of atoms. So it is shapiro delay. So this image is just repeat Arago Spot experiment on mega scale.

This explaination should be added to improve quality of this article.

viran 14:29, 21 September 2007 (UTC)

Some of the differences that come to mind: Gravitational light deflection depends on the lensing body's mass and the gravitational constant. Diffraction doesn't. Instead, diffraction depends on the wavelength. Gravitational light deflection doesn't, or we would see interesting spectral effects when looking at distant quasars. So, frankly, I do not quite see how diffraction could be behind the gravitational light deflection, let alone behind the Shapiro effect (which is not caused by the local matter density, but instead depends on the Sun's total mass).
Also note that this is the "Introduction to..." spin-off of the main article general relativity, so if you are convinced your assertion should be included in Wikipedia's general relativity coverage, then it would be much more constructive to start a discussion about it on the main article's discussion page, Talk:General_relativity. Be sure to provide a reliable source for your assertion (article in peer-reviewed journal would probably be appropriate as per WP:RELY). --Markus Poessel 16:21, 21 September 2007 (UTC)

If my above request is approved, I will explain how second postulate of relativity is right in simple words which will agree with common sense. People will understand it easily with logical and common sense approach. viran 15:00, 21 September 2007 (UTC)

You do realize this is an article about general relativity? Just asking because the expression "second postulate" is more usually associated with the special theory. --Markus Poessel 16:21, 21 September 2007 (UTC)
Viran - First of all, I must echo the sentiment that this article is about general relativity. The "second postulate" that you are so opposed to belongs to special relativity. In general relativity, the "second postulate" is implicit in the general theory being built on the special theory.
Secondly, it is sort of disingenuous of you to claim that the second postulate can be explained "in simple words which agree with common sense". Relativity itself does not agree with common sense! Things that are inutitively obvious (and which therefore form the basis of "comman sense") are shown in relativity theory to be just plain wrong. The second postulate itself is one example of that. --EMS | Talk 17:35, 21 September 2007 (UTC)

For stationary observer and moving observer speed of blades of fan is same i.e 'c'.

For stationary observer and moving observer, speed of particle travelling in coil of spring is same i.e. 'c'.

In two dimension, spring looks like transverse ~wave~.

Bonus contribution- When the spring between earth and flying away galaxy is stretched, the distance between two coils i.e wavelength increases resulting in redshift.

Good bye.

-neo. —Preceding unsigned comment added by Viran (talk • contribs) 10:28, 22 September 2007 (UTC)

[edit] Introduction to special relativity

That articles has again undergone some major work, and I feel is in a much better state. Before I apply for GA status, I'll be grateful if other editors review the article. In particular, it needs a few sections more fleshed out to give a well-rounded overview like this article, and it may also need some tinkering with the tone to make sure it reads more like an encyclopedia article than a textbook explanation. Thanks. Loom91 10:39, 4 October 2007 (UTC)

[edit] Introduction articles

Here's a thought - since this article is the introduction article, should the link to quantum mechanics also link to its introduction article? Not saying yes, just raising the question.71.37.28.223 (talk) 14:47, 28 February 2008 (UTC)

Sounds good. Done. Markus Poessel (talk) 01:01, 29 February 2008 (UTC)