Talk:General relativity/Archive 1

Older discussions
For the purposes of readability perhaps the sentence "Early on, Gauss decided to test this assumption and found (with experiments using the crude equipment of that age)." should be modified to include what he found :)

I don't have the knowledge to update and thought I would mention it here so that someone more informed in the area could execute the update.

Steve.

I put in some links and rescued the field equation from the previous version. I think we also need to explain the differences between Newton's and Einstein's theory a bit, for instance as they relate to black holes. --AxelBoldt

The current text mentions 2 things as fundamental in general Relativity:
 * 1) You need a reference frame to describe motion
 * 2) Reference frames can only be defined with respect to material objects; the text seems to imply that these are gravitating and therefore G.R. is a theory of gravitation too.

I do not believe the 2nd assumption is true, and esp. not its implication. I have a different perspective: suppose that the principle of General Relativity can be formulated as follows:

"Laws of physics must be formulated in such a way that they are independent of the frame of reference of the observer."

So G.R. is a theory about theories of physics, as much as a theory of the physical universe itself. It is a recipe for making good theories, which may or may not be consistent with the universe as we actually observe it. The popularity of thought experiments in G.R. demonstrates that its focus is on how we should describe the world, rather than how we actually observe it. The theories work only as far as the universe itself is consistent, understandable, and can be described by logic and mathematics - and there is no a priori reason that it is this way. But to the extent that the universe can be described by theories, the principle formulated above gives an important property of a "good" theory.

Implications for the theory of G.R. based on this principle:
 * 1) Light has a constant velocity.  It is well known that Einstein was troubled by the description of induction in a coil in a variable magnetic field: depending if you are in the coil or in the magnetic field, the one generates the other depending from you perspective.  Indeed, the Maxwell-Heavyside equations do not require different formulae: exactly the same equations can be used and applied in your local frame of reference, and the results are identical if you go to the other frame.  So this is a "good" theory.  Now from these equations the velocity of light can be computed, and it is a constant, independent of your frame of reference.  Of course an absolute velocity that is not relative to observers is in conflict with Galilean dynamics.  Einstein drew the ultimate consequence, and chose to adjust the geometry of space rather than the theory.  The Lorentz transformations immediately follow from this choice, and are the only solution consistent with this choice.
 * 2) Gravity == acceleration.  In a thought experiment, you can play billiard in a train that moves with constant velocity, and not notice that it moves.  If it accelerates however, you will notice because the inertial mass of the  balls will drive them to one end of the table (your local frame of reference).  Now exactly the same will happen if the train moves up a slope with constant velocity: they will roll downhill because gravity pulls on their gravitational mass.  However, you are unable to distinguish this event from the previous one -- iff inertial mass is identical to gravitational mass.  So a "good" theory would describe both events with the same equations.
 * Now in another thought experiment you are in an elevator that is accelerated, and a beam of light is sent through one of the sides. Because light has a finite velocity, its path in the elevator case (your local frame of reference) is curved.  Now from the previous thought experiment, we require that our theory does not distinguish this situation from the situation that the elevator moves with constant velocity in a gravitational field.  Therefore a "good" theory of G.R. predicts (requires!) that light is deflected by a gravitational field - and this has been actually observed.

-- Tompeters

I am not a physicist, so I consider myself a good example of the intended audience for this article. Is it fair to say that the theory of General Relativity asserts that one can and should represent gravity and acceleration in the same terms? Parts of the artical seem to suggest this, but in very indirect and wordy ways. I realize that not being a phycisist I may be misunderstanding the article. Whether my supposition is right or wrong, either way it seems to me that this article could be clearer (and I do not mean to diminish the work of specialists who have already done much to put this in accessible prose) Slrubenstein
 * Yes. This is called the principle of equivalence (of Inertial mass and gravitational mass). The problem is "how to design an experiment to distinguish the effects of these posited features". Thus, the use of an eclipse to detect the bending of starlight. Or, the precession of the orbit of Mercury.

An update earlier today changed static universe to steady state universe. This seems to me potentially misleading. There is an article on the steady state theory. This proposed that the universe was expanding, but that matter was being spontaneously created to maintain the universe's average density at a constant value. I am not certain of the situation in general relativity, but, reasoning by analogy with electromagnetism, I would hazard a guess that general relativity implicitly asserts the law of conservation of mass-energy in the same way that Maxwell's equations implicitly assert the law of conservation of charge. -- Alan Peakall 17:49 Feb 20, 2003 (UTC)

A small correction: nothing in special relativity implies that spacetime be non-Euclidean: indeed, the paradigmatic geometrical interpretation of special relativity, Minkowski spacetime, is Euclidean; it is sometimes called complex-Euclidean just because differently-moving observers map space and time axes onto it differently. But for any given coordinate system parallel lines never converge. In general relativity they can converge--spacetime is curved--and that's where Non-Euclidean geometry enters the picture.

I also agree with above comments that this article seems unable to decide whether it's written for physics majors who don't know relativity yet, or for laymen who don't know physics.

Michio Kaku's book on M-Theory, 2nd ed. spells vielbein as 'vierbein' as in 'eins' 'zwei' 'drei' 'vier', or 1 2 3 4. Ref: Kaku p.560, eqns. A.2.23
 * I've seen both spellings, and not knowing German, I have no idea which is right. Phys 11:36, 23 Aug 2003 (UTC)

Vier means four and viel means many --Dmr2 11:02, 21 Sep 2004 (UTC)

Explanation to User:62.211.229.30 for removing GR is inconsistent...

General relativity is inconsistent in several respects:


 * Do you mean internally inconsistent or inconsistent with other aspects of physics?

It claims that a physical action can result from a 'subject' (i.e. space-time) which has no physical reality but exists only as an idealized, mathematical concept;


 * All of modern physics assumes that physical reality has a one-to-one correspondence with idealized, mathematical models, but that at any given time, the favoured models are a limiting case of some deeper, more complex mathematical model. You are providing an argument against conventional philosophy of science in general, not against GR.

Although physical forces are frequently described by gradients of some potential function, this is in principle not acceptable as the fundamental form for the interaction as it implies a non-local nature (a gradient can not be defined through a point);


 * A gradient is a limit (mathematics). It can perfectly well be defined at (or towards is probably better) a point.

There is no reason why a motion due to gravitational forces should be described by a different concept than those for electrostatic interaction for instance; however for the latter the force does not depend on the mass (whereas the resultant acceleration does), therewith invalidating the concept of space-time curvature as an objective and unique quantity for describing the motion of objects in force fields;


 * You are saying that both electrostatic interaction and gravitation should be described by the same concept. This is a desire, not an inconsistency. See e.g. GUT or i guess supersymmetry or brane theory for attempts to unify all the forces.

Einstein claims that the alleged space-time curvature around massive objects will affect the path of light rays as well. This is an unallowed generalization as the concept was derived to describe the gravitational interaction, but electromagnetic waves are immaterial and massless physical objects. Effects that apparently confirm this prediction of General Relativity could well be explained by other mechanisms.


 * EM waves may be 'massless', but they do possess energy, and by E=mc ^2 they will respond to a gravitational field (i.e., they will be affected by spacetime curvature).


 * This is not an inconsistency. On the contrary, if massless objects did not respond to alleged geometry in the same way that massive objects do, then there would be an inconsistency in GR. BTW, the observations of gravitational lensing in clusters of galaxies are very nicely explained by GR.


 * In fact, the analogy that photons have equivalent mass is not so great. It works OK for the redshift/blueshift in a gravitational field (Pound/Rebka experiment) but simplistic attempts to get the deflection of light correct give half the right answer. Eventually, one has to face the fact that spacetime has a structure, which allows for timelike geodesics ("freely moving" particles, i.e. subject only to gravity,) null geodesics (light rays), spacelike geodesics (representing, for example a tightly stretched weightless string), and other timelike curves such as the world-lines of particles under electromagnetic or nuclear forces.

Pdn 17:00, 27 Mar 2005 (UTC)

Of course, if you wish to start a page on alternatives to general relativity, please do so - there's been a lot of experimental work to try to find alternatives to GR - e.g. http://relativity.livingreviews.org/Articles/lrr-2001-4/node9.html - but please first read and understand the pages on calculus - with wikipedia it's much more efficient than in the pre-web era, but you do have to spend some time clarifying your intuition, searching out and replacing the fuzzy bits, and even, just maybe, doing some hand calculations with pen and paper, as well as computer-aided stuff.

Boud 13:37, 7 Nov 2003 (UTC)


 * ... its origins go back to the axioms of Euclidean geometry. ??

Does that make sense? It appears to be based only on the fact that general relativity relies on a non-Euclidean geometry in which one of Euclid's axioms does not hold. Is that fact enough to justify this assertion? Michael Hardy 23:13, 22 Nov 2003 (UTC)


 * More than one, actually. Remember we're really dealing with a pseudoRiemannian manifold here... Phys 18:30, 28 Nov 2003 (UTC)


 * There were attempts to prove it from the other axioms back in Euclid's time, implying that they did not believe that it was valid as an axiom(not sufficiently obvious), but thats about as far as the link goes

67.123.41.95

So a chunk of mass-energy distorts space-time around it, and any other chunk passing by would have its path changed in a manner we call gravity. So, what if we have two chunks that are stationary, where they would each set up space-time distortion. I think that two chunks would have so-called "gravitional attraction" towards each other, but why? Neither chunk had an initial motion. Or does the passage of time count as a motion in this case (which kick-starts the space-motion "attraction")? Or does every particle since the universe began have an inheirent motion (so the initial stationary assumption can never happen)?


 * I am not a physicist, but I'll give this a try. By stationary, I'll assume that you mean that the two objects are in an inertial state and have the initial condition that the distance between them is not changing (some exterior force has been keeping them stationary and has just released them). The curvature of space and time is such that for them to stay in their inertial states they will start moving towards each other. --Edwinstearns 15:47, 24 Sep 2004 (UTC)


 * Q: Why there is so called "gravitational attraction"?
 * A: Because speed of light (c) decreases in vicinity of a mass (M) (Shapiro effect) and so the internal energy of any object of mass (m) equal $$E=mc^2$$ drops along the distance towards mass (M) as $$dE/dr=G M m/r^2$$where (G) is Newtonian gravitational constant and (r) is the distance between centers of masses (m) and (M). So in Einsteinian gravitation it is not an "attraction" but a force resulting from the change of internal energy of mass (m) because of gravitational time dilation. The same force but different physics than Newton's. Jim 21:30, 2 September 2005 (UTC)

The article states: "A continuing unsolved challenge of modern physics is the question of how to correctly combine general relativity with quantum mechanics, thus applying it also to the smallest scales of time and space." Would such a combination necessarily constitute a theory of everything? If so, perhaps that should be noted. --LostLeviathan 15:34, 18 Nov 2004 (UTC)

1919 confirmation: bending of starlight during a solar eclipse
The fact that light is bent by gravity is not particular confirmation of general relativity: assuming Newtonian gravitational mechanics applies to light particles like everthing else also predicts bending. The issue is the amount of bending and the difference between the two predictions is a testable factor of two. But I thought something strange happened in 1919. I remember reading that there were three attempts to measure the degree of bending: one was clouded out, one was close to Newtonian predictions and one was close to General Relativity;      Eddington decide that the third was better technically than the second - and later measurements have confirmed this. --Henrygb 23:27, 19 Nov 2004 (UTC)
 * To the best of my knowledge Newtonian gravitaion would only predict the bending of light if light had mass. In Einstein's model its not so much that light is bent more that the geometry of spacetime itself is curved by mass so anything travelling in a 'straight' line will follow the curve. --LiamE 15:35, 15 September 2005 (UTC)

I think you can get half the Einstein ans by assuming mass = energy/c^2 and momentum equal to energy/c. But there it little point because so much else comes out wrong in Newtonian approaches. For example, although Pound and Rebka and Pound&Snyder were careful to talk of an equivalent weight of photons in their Mössbauer experiments, you also get a clock-rate difference which cannot be explained on Newtonian terms. In Einsteinean terms that's the whole reason for the frequency shift, but with the "equivalent mass" idea clocks run at a synchronous rate between tower top and bottom, while the falling photon gains mass-energy, and that's wrong.Pdn 16:42, 15 September 2005 (UTC)

The Sagnac Effect
Cleon Teunissen 12:01, 15 Jan 2005 (UTC)

Sagnac Effect

It seems to me an article on General Relativity should take account of the Sagnac effect. The Sagnac effect is demonstrated by the experimental setup called ring interferometry. You can split a beam of light, have the light go around a circuit in both opposite directions, and then you allow this light to create an interference pattern. For example, you can make the light take a square path by setting up mirrors on the corners of a square. This setup measures absolute rotation. One of the first experimentors to conduct this type of experiment was called Sagnac, he conducted his experiment in 1913, and the effect is now called the Sagnac effect.

According to the sources I studied the Sagnac effect is a genuine physics phenomenon. According to the sources I studied both special and General relativity imply that absolute rotation can be measured.

In the article it is stated: The fundamental idea in relativity is that we cannot talk of the physical quantities of velocity or acceleration without first defining a reference frame, and that a reference frame is defined by choosing particular matter as the basis for its definition.

It seems that ring interferometry doesn't measure rotation with respect to chosen particular matter. It measures absolute rotation.

A ring interferometry experiment in New Zealand

Problem: Yes, in simple cases one can discuss absolute rotation; in fact, with respect to what would a Kerr black hole rotate otherwise (ans: asymptotic spatial infinity). That argument points up that to define absolute rotation you have to go to infinite distance, asymptotically. Look at the confirmation of the Lense-Thirring effect using satellites recently, and in progress with Gravity Probe B. Locally, you can define a "nonrotating" frame with your ring laser (why bother?  Use a couple of gyroscopes! Gyroscope technology came long before ring lasers.)  Anyway, this local frame you just found does not tie in to a nonrotating frame defined by distant stars, quasars, etc. So if you believe that one, you are stuck. If you do not believe that frame based on distant obects is the nonrotating one, you have to explain how stars and galaxies many thousands of light years away are all orchestrated to move as they seem to. Pdn 19:12, 23 Mar 2005 (UTC)

Laws of physics are always formulated in one frame of reference
Cleon Teunissen 15:08, 21 Jan 2005 (UTC)

It is often stated:


 * "Laws of physics must be formulated in such a way that they are independent of the frame of reference of the observer."

It seems to me that for clarity it is better to phrase the condition above as follows:.


 * "To do physics it is necessary to have transformations available for transforming between frames of reference.

In newtonian dynamics, a velocity is transformed from one inertial reference frame to another by adding the velocity vectors. The newtonian laws of motion are formulated in just one frame of reference; independency of reference frame is provided by the assurance that in all calculations velocities can always be transformed. In the 19th century, it became apparent that if one assumes that the Maxwell equations are correct, and that the newtonian transformations apply, then it should be possible to measure velocity absolutely. Einstein recognized that if one assumes that the Lorentz transformations are the appropriate transformations, then all inertial reference frames are indistinguishable.

The Maxwell equations are formulated in just one reference frame, it's the physicists choice of appropriate transformation that determines whether any law of physics has effective independency of reference frame. A calculation is performed in the one reference frame that a law of physics is formulated in. If and only if the approppriate transformations are available, observers can scientifically agree. Their observations can come out differently, they can subsequently transform their results to the frame of reference of the other observer, and find agreement.

Einstein didn't reformulate any laws of physics individually: by providing the right transformations, all formulations of laws of physics were provided with extension into relativistic inertial frame indepence. (As it turned out, for example a new relativistic momentum had to be found, in order to have a momentum that displays conservation of momentum.)

In newtonian dynamics, it is relatively straightforward to transform between an inertial reference frame and an accelerating reference frame: linear addition of vectors. The acceleration vector (usually a function of time and/or spatial coordinates) is added to the velocity vector (also a function). For the reverse transformation, the same acceleration vector is used, with the sign reversed. So newtonian dynamics has transformations for non-inertial frames of reference.

Einstein's effort to develop General Relativity was not a program to redesign the formulation of all laws of dynamics, it was a program with two goals: to find the appropriate transformations involving non-inertial reference frames, and to find a new theory of gravity in which gravity travels through space at lightspeed. The two goals turned out to be even more profoundly connected than anticipated: to an accelerating observer, space-time appears to be distorted; with gravity, space-time is. Cleon Teunissen 15:08, 21 Jan 2005 (UTC)

"Dynamic Universe"

 * Tuomo Suntola, Theoretical Basis of the Dynamic Universe, 2004. ISBN 9525502104. A highly promising new model of the universe.

I removed this from the article. From what I can find on the web, it is a replacement for GR that is based around the concepts of absolute space and absolute time. As far as I can tell, very few people take it seriously, as it hasn't yet been verified that it explains everything GR does, much less make new, testable predictions (in particular, one back-of-the-envelope calculation shows it getting the orbit of Mercury wrong; another says that it doesn't handle the orbital decay of binary pulsars). --Carnildo 00:59, 4 Feb 2005 (UTC)

This article is not good.
I do not like this article at all, and will rewrite it when I get a chance.

1) The central principle of GR is the General Principle of Relativity, which states that the laws of physics are the same in all frames of reference. The local uniformity of phyical constants is a consequence of the General Principle, NOT the Equivalance Principle.

2) The central tenant of GR is that spacetime is curved due to the presense of mass/energy/momentum within it as described by the Einstein Field Equations. This should be mentioned up front, instead of being left until later.

3) GR uses several other principles which are not mentioned: The principle of general covariance (the laws of nature are independent of the coordinate system), the principle of geodesic motion (inertial motion occurs along timelike geodesics), and local Lorentz Invariance (the rules of Special Relativity apply locally in all frames of reference).

4) The Equivalence Principle (EP) is best presented as a rule for determining whether one is in an intertial frame of reference. (The definition presented in this article is correct, but not comprehensive.) Historically, the EP is the jumping-off point for Einstein's derivation of GR. However, it is only a part of GR and is not the best place to start a popular article on the subject in my opinion.


 * please do the rewrite. there are lotsa reviewers here that will scrutinize it, and if it's good (and accurate) your work will not go to waste.  i am solely a spectator about the subject and am looking forward to learning some of the fundamentals.  i dunno if it will help but  and  were somewhat useful to me. anything you can do to add to or elucidate that is welcome.  also, i recommend that you get yourself a wikipedia identity. r b-j 17:47, 22 Mar 2005 (UTC)

More on rewrite
The requested ID has been obtained, and I have started drafting the changes in my sandbox.

However, I request that you do not hold your breath waiting for the rewrite. I am going to take my time and be very deliberate about it before doing the replacement. I may not like the current article, but I do not want to replace it with something that is almost as bad if not worse. The time that I can devote to this is also limited, but I very much want to produce an article that gives people a sense of what GR is really about.


 * ain't holding my breath. i would suggest that you sign your comments to "Talk:" pages with four tildes " ~ ~ ~ ~ ".  then your wikipedia ID with the date and time are stamped on your comments.  are you cool with the Tex editing?  you might want to check out How_to_edit_a_page or Help:Formula if you haven't yet.  good luck, and you have any encouragement from me. r b-j 17:55, 23 Mar 2005 (UTC)


 * I finally did the rewrite. See "Rewrite ready".  (This is actually not the rewrite I started drafting back in March.  That one bogged down and was dropped, but may reappear someday as a beginner's guide to GR.  The current rewrite was started in late June as an attempt to just redo the introduction, and quickly evolved into a comprehensive rewrite.)  --EMS | Talk 21:42, 18 July 2005 (UTC)

[A speculative response]
In reference to the null result of the Michelson-Morley experiment in the section on 'Foundations' (and other results ?) it says, '...Einstein explained these results in his theory of special relativity.' I'm not convinced he 'explained' the null result, but rather he used it as an assumption in SR. Then he developed a theory of mechanics.

As a little aside, I'm not sure we really know why the speed of light is constant in all inertial reference frames, apart from the fact that otherwise there would arise theoretical contradictions - but to explain it physically is still a mystery (I think). I suppose it's a bit like asking why (physically) does the existence of matter cause spacetime to curve. What's the exact mechanism ? Food for thought ....


 * i think i have a feel for why the speed of E&M propagation should be the same for all inertial reference frames. it really just comes from Maxwell's Eqs. and the knowledge that there is no ether medium that E&M is propagated in.  i mean, how do we tell the difference between a moving vacuum and a stationary vacuum?  if we can't, if there really is no difference between a moving vacuum and a stationary vacuum, that such a concept is really meaningless, then whether the light that you are measuring originated from a flashlight mounted on a rocket moving past you at $$ c/2 \ $$ or from a stationary flashlight, how does that change the fact that a changing E field is causing a changing B field which is causing a changing E field, etc.?  that propagation of an E field and B field disturbance, which has velocity $$ 1/ \sqrt{ \epsilon_0 \mu_0 } \ $$?  how is it different?  whether you are holding the flashlight or moving past it at high velocity, Maxwell's Eqs. say the same thing regarding the nature of E&M in the vacuum.r b-j 05:28, 24 Mar 2005 (UTC)

Yes, the EM argument is a good (convincing) one. Now for the next question: why does matter cause spacetime curvature ? (lol, only joking).

Lightspeed, etc.
The constancy of the speed of light arises from the metric nature of spacetime. The Minknowski metric, whose line item is $$ ds^2 = dt^2 - dx^2 - dy^2 - dz^2 $$ (in units where $$ c=1 $$) demands it quite nicely.

However, this only leads to other "why"'s. I suggest that the purpose of Wikipedia be respected, which as I understand it is to report on the current state of knowledge, and hopefully to do so in a way that is accessible to the average person. So what is important here is the "what" and not the underlying "why".

EMS

I did say, 'as a little aside...' (lol)

A Convention
May I suggest that we try to use a consistent convention for the value of the speed of light ? After reading many textbooks/research papers etc... which put $$c=1$$ and don't tell us this, I think it might be better to just write c. Putting $$c=1$$ in equations confuses many people when they try to check units. It's especially annoying when they don't tell you this like in the 'vierbein formulation' part (which I have subsequently amended). Putting $$c=1$$ can be quite elegant in some formulae (esp. Maxwell's equations), but I think that for anyone (esp. beginners/newcomers) reading an encyclopedia it is better to have clarity rather than elegance. Also, if it's said that the speed of light is taken to be unity, you have to flap around with the formulae to see where it goes (and is it just $$c$$ or $$c^2$$ or $$c^{5} $$, like in some gravitational radiation formulae ? ).

Please let's try to keep $$c$$ in our formulae.

modifications to article
I've moved a few things around and included some new sections to make the article a little clearer; a lot of work still needs to be done. The 'well-known and popular metrics' have been moved to Einstein field equation. Should the maths of GR be moved to a separate article ?

The statements

"The fundamental idea in relativity is that we cannot talk of the physical quantities of velocity or acceleration without first defining a reference frame, and that a reference frame is defined by choosing particular matter as the basis for its definition. "

are incorrect. An ordinary accelerometer measures acceleration. Of course, you can say the accelerometer is stationary in some reference frame, and so, in a sense, it locally defines a reference frame, but the question of how to extend that reference meaningfully outside the world-line of the accelerometer will lead you into a morass if you are not expert, and into a lot of digressions if you are. One asks why someone is writing a new book on relativity here, when there are so many already. There are good old books by P G Bergmann and Steve Weinberg that can be mined for descriptions, and newer books too, e.g. by Robert M. Wald. As for the second statement it was already critiqued. A reference frame can be identified by imagining a swarm of massless observers, who define the coordinate gridpoints. They need not have mass, i.e. be material; they can be hypothetical. Only requirements are that their worldlines by timelike and form a smooth family - i.e. they do not intersect. There is a maths term for that - probably "manifold" but let someone with more maths settle that. Pdn 06:26, 16 Apr 2005 (UTC)

Let's sort out this article.
I think it's about time this article had a serious facelift. The quantum mechanics article puts this one to shame. I've made a few changes: new introduction; removed a paragraph on curvature which used very loose language; replaced that with a more rigorous version. Don't want to remove large chunks, as some of the existing text has useful descriptions (and It'd be treading on other peoples' toes). Need to sift through it carefully. Moved image of spacetime curvature to start of article (grabs attention). Discussion of constancy of speed of light is already in special relativity. Mpatel


 * i want to encourage those of you who understand GR to do exactly this. usually wiki articles help me break through the ice and my understanding of a topic has been increased as a result.  sadly, i cannot say this about this article.  maybe the material is just too hard, or i am missing something.  i understand classical mechanics, a smattering of QM, SR, and a little bit of the Equivalence Principle (the man in an elevator descending at 9.8 m/s^2 is in the same instantaneous situation as other in weightless space or the man in a rocket accelerating at 9.8 m/s^2 has the same experience as one standing on the surface of the earth).  is there some way that you guys can start with the EP, and bring us to something like Einstein's Field Equation?   or to an equivalent statement like in the Baez and Bunn paper that is cited? r b-j 15:48, 20 Apr 2005 (UTC)

I know a fair bit about GR; believe me, the (non-mathematical) material is NOT hard - GR is probably the most intuitively pleasing theory in physics to date. The problem is, firstly, I don't want to suddenly remove a huge chunk of other people's work and, secondly, there is a lot to GR (EP, covariance principle, mathematical formulation, two-body problem etc.) - basically, the question is, what's appropriate for an encyclopedia article entitled 'general relativity' ? I think:

(1) the maths should be on a totally separate page.

(2) the unique role of GR as a theory which determines the geometrical background in which objects move should be emphasised.

(3) the nonlinearity of GR should be emphasised, and the consequences of this discussed (again, another major difference between other dynamical equations of physics - e.g. Maxwell's, Schrodinger's).

(4) Some of the intuitive descriptions present in the article are OK, but others are confusing.

I'm chipping away at this article to try and achieve these objectives. Mpatel 16:19, 20 Apr 2005 (UTC)

Sorting out article.
OK, I've made a start in seriously modifying this article. I've deleted, swapped and changed loads of stuff. I propose:

(1) In Description of Theory, we talk about how curvature arises through the use of non-inertial reference frames. Then talk about the principle of general relativity and the Equivalence Principle (and maybe covariance- but that might be better in the maths section).

(2) Then discuss some of the juicy effects of GR (light bending, grav. waves, evolution of universe etc...).

(3) Something on nonlinearity (probably in 'relationship with other physics theories' section).

(4) Something on the history of Einstein's discovery of GR.

(5) It might be OK to mention the field equation but not state it on this page (as elegant as it is) - I think it belongs in 'Mathematical formulation of GR', as should the geodesic equation; talking of which, deriving the equations of motion from the field equations might be worth a mention.

I await comments :) Mpatel 08:38, 21 Apr 2005 (UTC)
 * made some changes and then did not notice I was logged out by accident (dunno why or how). Further changes by 69.244.72.110

this morning were mine. Pdn 12:31, 21 Apr 2005 (UTC)

More modific's
Included a subsection on topology of spacetime; might link in nicely with a brief discussion of black holes, wormholes etc.

Is the section on foundations needed ? I think it's a little lengthy and possibly completely unnecessary - should it be moved somewhere else ? Mpatel 11:33, 22 Apr 2005 (UTC)

Perhaps it could be integrated to some other main subtopic. The overal distribution of the article is a bit weird to me. It seems like a bunch of separated articles one after another, the continuity is a bit strange IMHO. However as of yet, I haven't figured out how to improve this.

I'd like to ask also for a deeper explanation on how GR rises from SR. nihil 01:12, 23 Apr 2005 (UTC)


 * Agreed. I just made a start in improving the article. The more modifications that are made to this article by more people, the better. Mpatel 09:23, 23 Apr 2005 (UTC)