Talk:General relativity/Archive 5

Justification
"The justification for creating general relativity comes from the equivalence principle, which dictates that freefalling observers are the ones in inertial motion. A consequence of this insight is that inertial observers can accelerate with respect to each other. (Think of two balls falling on opposite sides of the Earth, for example.) This phenomenon violates Newton's first law of motion, and cannot be accounted for in the Euclidean geometry of special relativity either."

How do two balls falling on opposite sides of the Earth violate Newton's first law of motion? GoldenBoar 13:04, 3 January 2006 (UTC)


 * Under the law of inertia (as Newton devised it), inertially moving observers will maintain their relative direction and speed of motion. However, if freefall is intertial motion, then those inertial observers are accelerating towards each other.  --EMS | Talk 18:17, 2 January 2006 (UTC)


 * Newton's law of inertia is not violated, since the 2 balls where never in a state of inertial motion to begin with. Inertially moving observers will maintain their velocity, while an accelerating observers velocity will change. Clearly then, freefall is not inertial motion as devised by Newton.
 * GoldenBoar 13:04, 3 January 2006 (UTC)


 * This is kind of the point. According to the paragraph you're asking about, GR provides an expanded definition of "inertial motion", which covers cases that Newton considered non-inertial. I'd understood the equivalence principle to mean something different (that gravitational acceleration due to curved spacetime and acceleration via application of an external force produce identical effects), but GR is not my area of expertise. --Christopher Thomas 05:18, 3 January 2006 (UTC)


 * The paragraph seems totally contradictory to me, but I don't know GR. To my knowledge, freefalling means accelerating and inertial motion means non-accelerating. Inserting these changes into the paragraph, we get:


 * "The justification for creating general relativity comes from the equivalence principle, which dictates that accelerating observers are the ones in non-accelerating motion."


 * which is crazy.
 * GoldenBoar 13:04, 3 January 2006 (UTC)


 * Your mistake is in "inertial" = "non-accelerating". After all, if you are in an accelerated frame of refrence, then inertially moving objects must accelerate with respect to yourself.  This is true even in Newtonian physics.  Therefore, the detection of an acceleration is not prima facie evidence that the object is moving non-inertially.


 * When you are accelerated, inertially moving objects will be perceived to be reacting to a "fictitious force". Such forces can be identified by the strength of the force being proportional to the mass of the object it is acting on.  Centrifigual force is one example, where $$F=m\,r^2\,\omega^2$$, where the m is the mass of the object.  The gist of the equivalence principle is that gravity is really a fictitious force, and note that the rule for the Newtonian force of gravity, $$F = G\,M\,m/r^2$$, includes the same m.  The upshot of this is that freefalling objects are moving inertially.


 * So the point of that paragraph is that general relativity is needed to explain how freefalling objects move inertially. If you do not want to accept the assertion that freefall is a form of inertial motion, then be my guest.  Just realize that such a rejection leaves general relativity looking quite unnecessary if not completely non-sensical. --EMS | Talk 14:56, 3 January 2006 (UTC)

Alternative theories
In this subsection, the first sentence talks about alternative classical theories of gravitation; however, there is mention of a Fierz-Pauli spin-two theory, which is decidedly described as a quantum theory. Should this theory be mentioned here ? Maybe it's better to mention it in the QM section. MP  (talk) 09:10, 29 December 2005 (UTC)

History Section Appears to be Erroneous.
The history I was taught says that Einstein added Lambda because gravity would have caused the universe to collapse in on itself. He was later embarrassed about this because it seemed an unnecessary addition to the theory, but Hubble's work showed that a "lambda-like" factor was at work. 216.207.89.51 14:52, 3 February 2006 (UTC)Don Granberry


 * No, it didn't. This arose much later (1998) with the discovery of dark energy. –Joke 14:56, 3 February 2006 (UTC)

User:Joke137 is correct, but terse. In detail, Einstein put in Lambda for two reasons: (a) it enters naturally as a constant of integration in solving his GR equations (b) The Universe was assumed to be static, and a static universe will collapse unless a positive Lambda is put in.
 * Three things have happened to change these issues: (I) Hubble found that the Universe is expanding, after which Einstein said that sticking in a positive value for Lambda had been a mistake. He may have gone farther to say that even bringing the constant into the theory was a mistake, but we all know that constants of integration are best not ignored, but are best used to fit boundary conditions.  (II) With the Universe expanding, cosmologists at first tried solutions with various values of Lambda and found that they could get away with zero within the available accuracies of the data.   Next the new distance determinations using supernovae appear to demonstrate that Lambda must be positive and of significant value - i.e. it does affect the dynamics.  Why it has a value that would start being important at redshift 3 or wherever in that vicinity would be a mystery.  Finally (III) elementary particle physicists have come to regard Lambda not as a constant of integration, but as a manifestation of poorly understood cosmic field representing some undiscovered particle or other source.  Then, they are free to assume that Lambda varies, and have set up an exponent "w" do describe that, with w=-1 returning one to the case of a constant.   If w is not equal to -1 there is a research area into what kind of field and particle is involved, what equations it obeys, and possible a connection to dark matter research.Carrionluggage 18:19, 3 February 2006 (UTC)

I don't think this is correct. It is incorrect to refer to &Lambda; as a constant of integration. Rather, it is the only covariantly conserved rank-2 symmetric tensor that you can consistently add to the vacuum Einstein equations without introducing higher order terms. So it is perfectly consistent to set it to zero, sweep it under the rug, and be done with it. That was not consistent with quantum field theory but it was classically perfectly consistent, and so why worry about it? Until 1998 that seemed like the best approach. –Joke 18:44, 3 February 2006 (UTC)

Axioms of GR - is one of them redundant (!!!!) ?
May want to take a look at this. MP  (talk) 11:35, 12 February 2006 (UTC)


 * That is interesting, but I fail to see how it directly impacts this artcile. The article in its current form lists "fundamental principles", not outright axioms.  That spacetime as a Lorentzian manifold may not be a necesary axiom is intriguing, but even if that Arxiv article should pan out the concept of Lorentzian spacetime is still something that has to be explicitly mentioned.  In the meantime, I would point out that the Arxiv has not yet been published in a journal.  --EMS | Talk 06:26, 13 February 2006 (UTC)

self creation cosmology
User:Garthbarber has added a link to self creation cosmology to the alternate theories part of the article. I for one have not heard of this myself, but the self creation cosmology article seems to have passed some basic sanity tests based on its talk page. It is also to be noted that Garthbarber is apparently one of the authors associated with the creation of this theory (which is not a good sign but does not automatically impeach it either). I see a need to a read on this: Either it gets bounced (and maybe the article AfD-ed), or we bring that page into category:theories of gravitation. Thoughts? --EMS | Talk 06:15, 13 February 2006 (UTC)


 * This article made a very interesting read. It certainly _looks_ like real science, now that the initial objections have been addressed. If the citations at the bottom of the SCC article can be vetted as being reputable, it would seen to me that this is as valid to present as any other alternative model. I am not an astrophysicist, so I can't vet this myself. --Christopher Thomas 07:04, 13 February 2006 (UTC)


 * That pretty much is my read on it. As best I can tell, the real issue is one of whether it is sufficiently encyclopedic to warrant mention in Wikipedia.  I suspect that there are more theories of a similar ilk out there, and it is a legitimate issue as to whether they should be covered and if so how. --EMS | Talk 18:22, 13 February 2006 (UTC)


 * Yeah, I marked this with OR for a while and discussed it with WMC a little bit. Of course, it is not exactly encouraged to write about your own work on Wikipedia, but it is not forbidden if the work is verifiable and notable, which this page meets the criteria for. However, perhaps this indicates that the time is ripe to bring some organization to the alternative theories section of this page. –Joke 18:37, 13 February 2006 (UTC)


 * FWIW, I have to agree with Joke that self creation cosmology is notable, but I too am concerned by the potential for abuse, so this bears monitoring.---CH 03:55, 21 April 2006 (UTC)


 * I see the "notability" line as currently being placed somewhere on the odder side of "odd". I am dealing for now with issues involving the speed of gravity and Le Sage's theory of gravitation as a result instead of taking the "easy road" and bouncing the non-standard stuff outright.  I will not say that this is the wrong place for the line to be, but do caution that some questionable material gets in under the current setting.  My advice is to monitor this line and how it shifts over time.  If left to its own devices, this line will move over so far that the original research policy will become ineffective.  However, I also expect the notability line to be reset long before that happens.  --EMS | Talk 03:02, 22 April 2006 (UTC)

New article
An article called Einstein's theory of gravitation has appeared, and I wish to endorse it. It seems to be an excellent bridge between the new gravitation page and this one, providing a breif and fairly non-technical explanation of what general relativity achieves. I advise watching it to ensure that it is not either vandalized, given inappropriate duplicate content, or redirected here. That page may also bear some editting and expansion. (For example, no mention is made of the cosmological implications of general relativity.) However, it is most important that the "Einstein's theory ..." article be maintained as a non-technical bridge article. That is it's value. That is why I want it kept. --EMS | Talk 17:10, 14 March 2006 (UTC)

I made the proposal to merge it into here just before I read your post. see below. Loom91 17:43, 15 March 2006 (UTC)

Proposed Merge
The article Einstein's theory of gravitation delas with the same thing as this article, therefore it should be merged into this article. As for it being a non-technical introduction, such an example of a trampoline aricle exists for Special relativity, but that's because the trampoline article is very well written and does provide some insights into the theory that can be grasped by the layman who is not very confident with hgigh-school math. This is not the case with the article Einstein's theory of gravitation, it does not say anything. Unless someone pledges to do some drastic improvements to that page in a few days, it should be merged (there is little to merge anyway). Comment. Loom91 17:43, 15 March 2006 (UTC)
 * BTW, Loom91, your markup in the gravitation article was failing in Firefox, so I have reverted it for now. You may wish to revise your edit so that it renders adequately. --Ancheta Wis 11:15, 16 March 2006 (UTC)


 * strongly oppose and keep - Einstein's theory of gravitation is a short, concise treatment of the issue of how general relativity deals with gravitation. OTOH, this article is an large, in-depth, and fairly technical treatment of GR as a whole (as it should be).  The "Einstein's theory ..." article can be improved, but because of it's narrow focus it is an excellent topic for this encyclopedia.  So I see the "Einstein's theory" article as complimenting this one instead of conflicting with it or unnecessarily duplicating content. --EMS | Talk 18:54, 15 March 2006 (UTC)


 * strongly oppose - I see nothing in Einstein's theory of gravitation which is not said better in this article, so I don't think there is anything to merge. Why not just delete Einstein's theory of gravitation? ---CH 19:32, 15 March 2006 (UTC)
 * I oppose deleting it. IMO, it fills a void, and can be referenced from both this article and the revised gravitation article.  If anything, it may be an idea to let some secondary GR content "live" there instead of this article.  To me, this article expands on both the subsection Treatment of gravitation in this article and the section Einstein's theory of gravitation in the gravitation article.  Let's not be insular.  Let's make this article a worthy and useful addition to both the GR and gravitation pages. --EMS | Talk 02:58, 16 March 2006 (UTC)


 * oppose and keep - Einstein's theory of gravitation is about gravitation, not about GR per se, and is intended as detail for those reading about gravitation. --Ancheta Wis 02:13, 16 March 2006 (UTC)
 * But Einstein's theory of gravitation IS GR. Einstein's theory of gravitation is simply a description of the theory named General Relativity. If ETOG article is intended as a non-technical intro (trampoline) like Special relativity for beginners, then we should rename it to something like Introduction to General relativity. I can not see how Einstein's theory of gravitation can be conceptually distinct from the General theory of relativity! Loom91 09:21, 17 March 2006 (UTC)


 * strongly oppose and rename - Einstein's Theory of Gravitation is GR, and the GR article is comprehensive enough to include all technical details and non-technical details. If ETOG is to be kept as a 'bridge article' as EMS suggested, then it should be renamed as 'Intro. to GR' or something similar. MP  (talk) 15:58, 17 March 2006 (UTC)


 * support - I agree that Einstein's theory of Gravitation is contained in GR, so it would suffice to have a summary section on gravitation in the GR article. CH advocates deleting the article, so I would think that counts as effectively "supporting" the merge rather than opposing it. Those arguing for a renaming of the article might consider just making this a section of the GR article. Djcastel 00:27, 6 April 2006 (UTC)


 * No, I advocate deleting [Einstein's theory of gravitation], which means that I oppose merging it with anything (since merge implies that text is retained, rather than tossed). ---CH 02:33, 6 April 2006 (UTC)

James A. Green on the "Overthrow" of General Relativity
My work on the overthrow of classical General Relativity and the Unified Quantum Field Theory that will replace it is outlined at http://greenwdks.tripod.com/unifiedsummary.html. Also see my book on the topic, which is outlined at http://greenwdks.tripod.com/gravelec11.html, and the essay on the overthrow problem at http://greenwdks.tripod.com/overthrow.html. Fundamentally, the problem that convincingly overthrows classical GR is the manner in which the equations of the gravitational force themselves violate local Lorentz covariance. If the equations of motion between objects are linearized, we follow Einstein's analysis in The Meaning of Relativity page 102 and find after solving the field equations that

F_grav = m(E_grav_GR + v x B_grav_GR) + higher-order terms.

However, B_grav is 4 times stronger in General Relativity than it needs to be in order to be Lorentz covariant in the sense that this is so in classical relativistic electrodynamics. For an electromagnetic-like theory of gravity, B_grav = B_grav_GR/4.

To understand this better, it turns out that in classical electrodynamics and in electromagnetic-like gravitation theory the forces between two spheres on the y'-axis of the moving system K' parallel to the stationary system K and moving along the x-axis with velocity v obey

F_magnetic = -(v/c)2F_static.

In General Relativity, however, mu_GR = 4*mu_grav, so

F_magnetic = -4(v/c)2F_static.

Thus in the GR case, the grav_magnetic and the static gravitational forces balance when v = c/2, and for v > c/2 the grav-magnetic force is stronger, forcing the two spheres to move away from each other. That is, classical GR predicts there exists a frame of reference in which two gravitating bodies do not attract each other! Obviously this cannot be true in a locally Lorentz covariant field theory of forces. In this case the spheres must always seem to drift together according to an external observer, except in the limit as v approaches c, when the motion must seem to freeze. As long as forces are described by Lorentz-covariant force-field equations, The Principle of Relativity will be satisfied as Galileo understood it: cannonballs dropped from the top of a mast will strike the deck at the foot of the mast, and the action will always take the same time according to a local observer, although this is not the case in classical General Relativity! The unified quantum field theory developed in the book introduces classical vector-boson field theory in local coordinates, which yields suitably Lorentz-covariant representations for gravity, electromagnetism, the strong nuclear force, and the weak interaction. Introducing the principle of equivalence as Einstein did in 1911, one imbeds the generalized Maxwellian equations of classical vector boson field theory into a metric with gravitational time-dilation only to describe the forces. The falling-ruler thought experiments sometimes used to justify curvature in the spacial part of the metric do not hold for the stationary rulers described by the GR metric, so this book takes the spacial part of the metric to be flat. This turns out to yield the correct General Relativity 2nd order effects when superposition is used in connection with wave-particle duality effects, and guarantees that the Principle of Relativity holds. In addition to working out these revolutionary details, the book derives the details of the nuclear force from the generalized Maxwell equations, and also introduces the associated cosmology, which is better determined than in classical general relativity, so that it is possible to compute the maximum depth of vision into the expanding Big Bang fireball at about 8.1 billion light-years, the distance at which galactic red shifts hit the Red Limit, because then galaxies seem to be moving away with the speed of light. James A. Green, March 26, 2006, http://greenwdks.tripod.com/home.html. --JamesAGreen 21:59, 26 March 2006 (UTC)


 * Amazon book reviews (2 by author, 1 negative, 1 bizarre) at . Has anything more interesting been said about this book? --Alvestrand 23:20, 26 March 2006 (UTC)


 * Mr. Green, please read WP:NOR and WP:WIN. Keep it at your website, please; interested readers can follow the links you provided (and just one would have been enough).


 * Joke, Green appears to have randomly grabbed technical buzzwords from various places, but it is easy to spot clear indications in the above talkspam logorrhea that he doesn't have a clue what he's talking about.  He appears to have read somewhere of the Lorentz-like "force law" from the most common formulation of weak-field GEM (which involves nontrivial approximations; saying "force law" in the context of gtr of course telegraphs that further explanation is neccessary), but his assertion that grav_magnetic and the static gravitational forces balance when v = c/2, and for v > c/2 is flat out wrong under any interpretation I can think of. And it only gets worse from there.  Someone should submit his site to crankdot.  Sheesh, where oh where do they all come from? ---CH 00:10, 27 March 2006 (UTC)

Weightlessness and General Relativity
Consider the way in which the feeling of freefall (neglecting of course air resistance or any other upward force) is like the feeling of weightlessness (microgravity) in space. While most of us (myself included) have not experienced this, it is evidenced by NASA's Vomit Comet. Is this not strong evidence of GR? It makes perfect sense in the context of GR as observers in free fall are the ones in intertial motion, following the curvature of space-time (as mentioned in the Justification discussion above) and those at rest on the Earth's surface are undergoing acceleration and hence the "feeling" of gravity. Likewise in space the structure of space is relatively flat and so not plummeting towards the Earth is inertial motion and thus the same feeling results.

Newton's model of gravity on the other hand seems to contradict this similar feeling of weightlessness and freefall. In that theory gravity is a force thus those in freefall are experiencing accelerated motion (F=ma) whereas those on the surface are at rest (although according to the third law they experience the force of the Earth "pushing" back). In any case according to Newtonian mechanics one would expect the feeling of weightlessness (no forces/acceleration) to differ from that of freefall (the force/acceleration of gravity). Am I missing something big here or is this indeed an example of how GR succeeds where Newtonian gravitation fails?

I could be wrong about this and perhaps it is just too obvious to warrant mention, but I was surprised to find no mention of it in the article or discussion pages and it seems like a good observation to point out to those trying to grasp GR like myself. -Kyp4 08:08, 6 April 2006 (UTC)


 * From the Newtonian perspective, if the gravitational mass (gravitational charge) and inertial mass (inertial charge) are equal, different objects fall at the same rate in a gravity field. Thus, a freely falling reference frame (e.g., a vomit comet in a parabolic dive) appears to be free of any force field.  The natural question is "why are these two charges exactly equal?".  Whereas Newtons' theory doesn't address this, GR renders the question moot by discarding the notion of gravity as a force.  Alfred Centauri 13:45, 6 April 2006 (UTC)


 * Newton's theory correctly models weightlessness, as on the "vomit comet" and in orbit evenything is falling together and there are no relative accelerations (except for small tidal effects which are also called for by both theories) between objects in the "comet" or an orbiting capsule. --EMS | Talk 16:52, 6 April 2006 (UTC)


 * I see so in Newtonian mechanics it is never the force of gravity that's felt directly but rather the reaction force of the Earth and so in freefall this force is absent (the capsule does not exert force on the observer since both are in freefall) and so there are no forces acting on the observer and thus the feeling of weightlessness. Despite this resolution of my perceived conflict with NM I still think it exhibits the more elegant approach taken by GR. -Kyp4 17:55, 6 April 2006 (UTC)


 * I think this has less to do with physics and more with biology. Humans don't exactly feel forces, because our neurons aren't built that way. For example, if you are in water, the feeling of weightlessness still arises, even though there is a buyoancy force upwards. - George K

Need more intuitive explanations
I've wanted to understand relativity and gravity for a long time and recently have done a lot of reading. Now that I'm starting to understand it, I want to point out how it could be explained better.

The explanations of the type "bowling ball on a trampoline" or "gravity well" shaped plots don't help. For one thing, it is a circular explanation - it uses gravity in the example to explain gravity. It also suggests that the shape of the trampoline is the shape of spacetime. It suggests the curvature of spacetime from gravity is that of an N-dimensional surface curved into an N + 1 -dimensional space, as opposed to Gaussian or intrinsic curvature. These explanations imply that the curvature is drawn to scale with respect to the object, and that the peak of the curvature touches the object. I've noticed that all but one of the images I've seen are oriented the same way. A good explanation would use an image that works equally well when rotated 90 or 180 degrees.

Explain which kind of curvature is meant. Use plots or pictures to show the actual shape of spacetime. Maybe make some new kinds of images using color or gray scale to indicate the curvature. Use cross sections or show how gravity would work in a spacetime in fewer dimensions, or show the shape of spacetime around an infinitely long cylinder.

Give some actual values for the amount of curvature caused by an object.

A fundamental aspect, for everyday situations, is that the vast majority of motion is through time, not through space. The usual explanations beg the question "If an object is stationary, how can there be any geodesic motion?" Also, we don't see the curvature because the curvature is tiny.

There is no intuitive explanation of geodesic being a straight path, and explaining how there can be a straight path through curved spacetime. Mention parallel transport and Schild's ladder. I find the analogy of an insect crawling over a curved surface or a stretchable net, moving each leg forward the same "distance" or number of fibers, to be useful.

The text under the image "In fact this image represents Newton's view on gravitation." is wrong. I suggest adding a separate image for the Newtonian view. To the existing image add an explanation that it shows, greatly exaggerated, how the distances between points have changed when a mass is introduced. The planet should not touch the curved surface, but the inflection of the curvature should parallel the circumference of the planet.

I wish I was an artist and could draw the images I'm imagining.

—The preceding unsigned comment was added by 71.35.21.82 (talk • contribs). (Qwest Communications; geoloc Phoenix, AZ)


 * You are right to suspect that the trampoline imagery is seriously misleading, and this is in fact strongly deprecated by most physicists--- except when speaking to nonphysicists. Why lie to nonphysicists?  Well, in a subject as subtle as gtr, it is inevitable that a survey article like this can at best begin with tired shibboleths, proceed to half truths, dazzle (or annoy) readers with some verifiable facts expressed in mathematical notation, and fizzle out with citations of some good books.  The last bit at least is genuinely useful since with hands on experience in actually working with the theory, a diligent and well prepared student can eventually begin to understand what gtr really says (which is as you suspect far more interesting and useful than vapid nonsense about dents in trampolines).


 * The type of curvature meant when one speaks of spacetime curvature is intrinsic curvature, which doesn't depend upon any embedding in any higher dimensional space (by the way, one extra dimension rarely suffices, and there is a distinction between local and global embeddings which can be important). Specifically, the Riemann tensor is a fourth rank tensor which completely characterizes intrinsic curvature.  Various other tensors such as the Ricci tensor, Einstein tensor, and Weyl tensor can be constructed from it.  The Ricci and Einstein tensors measure two closely related notions of average curvature, while the Weyl tensor measures conformal curvature.  It is quite possible for a curved manifold to be Ricci-flat or conformally flat. The latter case is analogous to a nonzero matrix which has vanishing trace.


 * The type of curvature which measures the bending of some hypersurface (codimension one) which is embedded in some (possibly intrinsically curved) Riemannian manifold is extrinsic curvature. As an example of how quickly things become complicated: one can reformulate the EFE in many ways, including formulations which involve extrinsic and intrinsic curvature of spatial hyperslices which in some sense evolve over time.  However, this description is seriously misleading and for the real story you must consult a good graduate level textbook (see general relativity resources).


 * Your suggestion of using color to indicate intrinsic curvature (or some similar level line plot) is a good one, but unfortunately this works best for scalar functions, whereas the Riemann tensor is a multicomponent object (in 4 dimensional [pseudo]-Riemannian manifolds, it nominally has 256 components, but due to algebraic symmetries there are only 20 algebraically independent components).


 * Wait... Schild's ladder? So you already know what I was just saying?  I guess you may have seen the introduction to Misner, Thorne, and Wheeler, which provides just what you were asking for? ---CH 03:44, 21 April 2006 (UTC)


 * I see no reason to use misleading or wrong explanations when correct ones could be used. GTR is a simple concept. The mathematics is difficult, and there are many implications, but mathematics isn't required to explain the basic concept. A lot of people understand non-Euclidean geometry, such as people mapping and navigating the surface of the earth. Proceding to GTR and gravity is easy.


 * I have MTW, and reading it is how I finally could picture what's happening, but that's not what I'm asking for. The one thing in MTW that really helped me understand the actual shape of the curvature is Figure 23.1. It's a trampoline shaped plot, but the text with it is the only place I've seen a decent explanation of what the plot really represents. It also doesn't show the mass, it just shows where the circumference of the mass lies on that cross-section of spacetime. After I understood the actual shape of spacetime, gravity suddenly made sense at an intuitive level. Section 1.6 and Box 1.6 starts to explain it graphically, but doesn't finish.


 * I think most people reading articles like this want an accurate intuitive understanding of GTR and gravity.


 * I didn't mean to show all components on one plot. I was thinking that plots could be simplified first by reducing spacetime to 2 dimensions, x and time, or by using 2D cross-sections of 4 space. Then select one or two of the remaining components for each plot. --  Kolosiek 05:38, 24 April 2006 (UTC)


 * For those who don't keep in RAM an eidetic image of MTW, Fig. 23.1 depicts an idealized embedding diagram of a static hyperslice in the Schwarzschild perfect fluid model, with one dimension suppressed. Geometrically this is a radially symmetric surface consisting of a spherical cap (interior region) joined to a Flamm paraboloid (exterior region). The circle (really a sphere) where the two regions meet represents the surface of the star.


 * Yes, a fine figure indeed, which even bends the truth :-/ by bending down the Flamm paraboloid to suggest asymptotical flatness better than an accurate figure would do.


 * But now I am confused. I thought you (71.35.21.82, right?) were arguing against telling even a half-truth in the interests of saying something in non-mathematical language for the benefit of a general audience?  ---CH 12:09, 25 April 2006 (UTC)


 * BTW, wrt "show how gravity would work in a spacetime in fewer dimensions": it wouldn't! That is, in three-dimensional Lorentzian manifolds, the Weyl tensor vanishes identically, so gravitation would only be manifest in the immediate presence of matter.  That means it couldn't reach out across a vacuum region (or nearly) to hold two-dimensional planets in orbit around a two-dimensional star, and so on.---CH 12:21, 25 April 2006 (UTC)

accelerative effects or gravitational?
Under the "Acceleration effects" header, it lists only gravitational effects. I realize that those effects are equivalent, but I've been told that gravitational effects happen quite separately from acceleration. For example, if one was in the middle of two large masses with no net force on them, that person would experience time dilation when compared to someone infinitely far away from those masses (ie also with no net force on them). Also, if someone were in a void with no masses around, accelleration would cause time dilation when compared to an observer in a different accelerative frame. It seems to me that these effects happen very separately, and I wonder why they're treated like the same thing. Fresheneesz 21:51, 23 April 2006 (UTC)


 * Good question. See the equivalence principle.  (Simple answer:  The acceleration of a freefalling object is due to our being the ones in an accelerated frame of reference.  So gravitational fields are due to our being accelerated.  In the case of the person between point masses: He may not be accelerated with respect to a distant observer, but between himself and the distant position there is a gravitational field where such accelerations do occur.)  BTW - You need to remember that gravitational time dilation is due to gravitational potential, not due to acceleration alone. --EMS | Talk 00:04, 24 April 2006 (UTC)

Suggestion for where to move Ian B's additions
I haven't had a chance to examine these, but they seem to constitute a description of the hole argument and its resolution. If so, if they are basically correct, they can probably be incorporated into an article which is currently a stub. I was (am?) planning my own article on this, which is currently a stub.

If Ian moves the sections he added to here, I can refer to what he wrote while writing my own version and possibly incorporate some or all it. (I planned to give a much more explicit discussion than anything I've seen in the literature, while referring to papers by Norton). ---CH 23:51, 24 April 2006 (UTC)


 * I agree and have asked much the same of Ian on his talk page. I just want to give him a day to clean up his own mess.  After that I am all for doing it for him. --EMS | Talk 02:33, 25 April 2006 (UTC)

section removed
The only thing that I have heard from Ian was an anon (which apparently was Ian) removing the "please don't revert" notice and adding more text to that section. So since the day I gave him was up, I moved the section to Chris' suggested location.

This may be a case where we will do an edit war until Ian hits the "discussion" tab and finds this discussion of his work. However, I am hopeful that we can work with him. He seems knowledgable, but needs to learn how to edit here. --EMS | Talk 04:12, 26 April 2006 (UTC)