User talk:Mpatel/sandbox/General relativity

Introduction

The intro. is still way too technical; need more 'wordy' or 'flowery' language. ---Mpatel (talk) 17:27, September 6, 2005 (UTC)

I think that the intro needs to be smoothed out a bit. I hope that you don't mind if I take a stab at it.

As for its being technical, that unfortunately is a result of the subject itself being highly arcane and technical. A seperate "GR for beginners" article may therefore be needed to help make this one accessible. In this article, the technical stuff is needed, as it defines the theory. I will try to add some text to the intro to help orient people, but if this article is to remain at a decent size there is not too much that we can do. --EMS | Talk 16:39, 7 September 2005 (UTC)[reply]

I don't mind if you take a stab at smoothing out the introduction. Feel free to change things as you see fit. We can experiment on this version and after agreement of the changes, we can incorporate the changes into the general relativity article. Yes, I just wanted to make the article accessible to all whilst keeping the article size reasonable, but maybe that is asking too much - a separate article GR article for beginners is maybe a good idea; I think something similar was done for the SR articles. ---Mpatel (talk) 17:43, September 7, 2005 (UTC)

There needs to be accessibility, but the issue is how to get it. This article cannot be a GR textbook in it's own right. (There is a Wikibooks project for that anyway). That is why I am advocating the creating of a beginner's page, while this one remains somewhat technical (although I would like to get the more technical stuff of the Comparisons section into another page). As you noted, a beginner's page was done for SR. That is where I got the idea from.

I am also wondering if now is a good time to "move out" the current contents of this page to the article space. I think that some good edits now exist that will enhance that page. Doing that will also give us a chance to "sync up" this page and the article space one before proceeding further. --EMS | Talk 16:07, 9 September 2005 (UTC)[reply]

I've been busy the past few days, which is why I could not be on 'GR-patrol' to edit and revert changes on the general relativity page. I've just made a few edits to the intro. (as well as other sections) of my sandbox version. Hence, "moving out" may have to wait a little while, at least until we can agree on the changes. I always seem to have some obsession about the intro. not being as good as it could be. Anyway, you may want to take a look at my changes (mostly minor) and we can start moving out some things if you want. ---Mpatel (talk) 09:44, September 10, 2005 (UTC)

Pdn's reverted edit

Pdn added to the Spacetime as a curved Lorentzian manifold section:

To understand the analogy even better requires one to recognise that most of the four-dimensional velocity of a nonrelativistic object is directed into the future; in other words, v << c means, in relativity, that the object (even a person!) is travelling into the future much more rapidly than making any progress in the spatial dimensions. The result is that even a tiny curvature within the spacetime diverts this large time-component a bit into the spatial domain, so we see notice this big acceleration (the so-called "acceleration of gravity.") We think we're standing still on the Earth's surface, but we are in fact moving rapidly (sad to say - who wants to get old) into the future. The curvature of spacetime, due to the Earth's mass, is trying to divert this timeline motion into a falling motion, and it will do so if we jump off a cliff. With the solid earth beneath us, we will feel its upward support instead.

I don't see this as helping that section. There are a number of things wrong with this added text, including limiting it's scope to v << c. (All objects are heading into the future, even photons.) However, the point that we are always moving into the future and the the acceleration that we perceive is due to the behavior of interial motion a curved spacetime as we move through time is a valid point. None-the-less, I find this to be a wordy attempt to restate what has just been stated. We need to make this article smaller, not bigger. --EMS | Talk 15:43, 9 September 2005 (UTC)[reply]

It would be possible to shorten the section, which I will agree rambled a bit. But you have misunderstood the whole point ov v<<c and have satisfied yourselves with a representation by a 2-sheet in 3-d, which fails to explain why a brick dropped from a tower falls. It is very important that this brick, when supported, goes only along the time axis and that, when it is released, the velocity is bent into the spatial domain, causing the falling motion. The explanation with the curved sheet misses the 4-dimensional aspect. Of course, light rays are also affected by spacetime curvature. But since you can't hold them in place (unless you use something like Kruskal-Szekeres coordinates, which are out of scope), you cannot simply explain how their 4-velocity is bent from a pure increase of x_4 into the spatial domain; in fact the deflection of light rays is a rather different problem. The brick sitting on the table goes only into the future in Schwarzschild or similar coordinates, when dropped it acquires a 3-velocity. Pdn 02:29, 10 September 2005 (UTC)[reply]

You are somewhat off track here. The operative phenomenon is called geodesic deviation, and it applies to light just as much as to a falling brick. I realize that light does not start out moving parallel to the time axis, but that does not keep its motion from being affected. Indeed, once your brick starts to fall, it is no longer traveling parallel to the time axis anyway, but it is still being accelerated and so the analogy you are trying to use still applies.

I will admit that I do not like the rubber sheet either, but that at least is a well-refined example. I also do like to point that you are trying to make, but I am also trying to make the same point in my discussions of inertial motion and accelerated frames of reference. If I am not succeeding in doing so, that is an issue. However, adding more text to a failed narrative is not going to solve the underlying problem. Instead, it adds more burden to the reader and leaves him/her with multiple and potentially inconsistent explanations to sort through. So some thought is needed as to how we can better express the relevant points. --EMS | Talk 03:52, 10 September 2005 (UTC)[reply]

Sorry but it is you who are "off track." Geodesic deviation has nothing to do with the issue. (I saw it misused somewhere else, too, in Wiki, but did not want to cavil.) Geodesic deviation would describe the tidal distortion of a stressless falling body such as a pressureless fluid or "rubble-pile" (model for some asteroids) - including an orbiting body, which is of course in free-fall. The deviation in the case of the release of a brick or stone from a tower (Galileo's experiment at Pisa) is deviation of its orbit from that of the original holding hand, clamp, or whatever - i.e. deviation of a geodesic from a most emphatically non-geodesic path. Tidal distortion is very small and irrelevant. The point (as explained in the existing article) is that from the standpoint of GR, the support is accelerated upwards (and by the way, that's not geodesic motion, which is part of the reason geodesic deviation is irrelevant), and the freely falling object is not. From a Newtonian standpoint, the support is stationary and the falling object is accelerated. All the time, gravity is trying to divert the purely timelike motion of the materials such as Earth, tower, and clamp into a spatial plus timelike one (a dropping one in the Newtonian sense). Only when the brick is released can it do that, and only to the brick; solid body forces maintain the tower and the person who dropped the brick on a non-geodesic path.

Geodesic deviation explains any change in separation of two bricks dropped at different times or at different launch points around the tower's rim (ignore the "leaning" and assume the tower has a flange from which you drop bricks or stones). Among the effects explained by geodesic deviation, then, is the (small) convergence of paths originating from (say) opposite sides of the tower - i.e. they are all leading towards Earth center.

N.B. the sandbank or pressureless fluid I mentioned would show distortion due to geodesic deviation only if its self-gravity could be ignored as being very small. The body is distorted such that the part nearest the central body gets ahead of the outer parts in orbit. Eventually you get a spiral, which will turn into a disk if there are random motions. Pdn 04:27, 10 September 2005 (UTC)[reply]

Tenuous link between adjacent sentences

In the article, we have,

In general relativity, phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as freefall, orbital motion, and spacecraft trajectories) are taken in general relativity to represent inertial motion in a curved spacetime. So what people standing on the surface of the Earth perceive as the 'force of gravity' is a result of their undergoing a continuous physical acceleration caused by the mechanical resistance of the surface that they are standing on.

The first sentence outlines the 'curvature' aspect as opposed to the 'force' aspect of the gravitational field; however, the second sentence seems to link this ('So,...') to something different, namely, by discussing what it means to feel a force - shouldn't the second sentence mention curvature somewhere ? What I'm saying is that the second sentence links to the first with the 'So', but then talks about something else (namely, why we feel a force). Perhaps why we feel a 'force' due to curvature needs to be discussed if it links to the first sentence. ---Mpatel (talk) 10:17, September 10, 2005 (UTC)

Status?

What is the status of this page? I like the edits that have been done to it, and would like to "export" it out to the article space. Note that I just added a new subsection here instead of in the article space due to my preference for this form of the article. Also, do note that exporting this does not preclude further edit here.

Thanks, --EMS | Talk 16:58, 16 October 2005 (UTC)[reply]

Oops! I missed the fact that you have moved them out! Sorry. --EMS | Talk 00:29, 17 October 2005 (UTC)[reply]

My fault - sorry. I should have wrote here that I moved them out. Minor (but good) edits are sometimes still made to the main GR article, so I try to keep up with those and implement them in here. ---Mpatel (talk) 07:13, 17 October 2005 (UTC)[reply]

Featured article - hints from other languages

Glancing at the length of the 3 GR featured articles (French, Portuguese and umm, don't know the other one... Swedish?), I'd suggest that if we want to cut down our article, we should concentrate on a few areas. In particular, we should probably address these issues:

There is too much mathematical detail in the Relationship to other physical theories section and I think these details be cut out, or transferred to relevant articles - mathematics of general relativity might be a good place.

The Predictions of GR section could possibly be reduced in size. I can't immediately see how to do this,... but perhaps the wording could be reduced in each description.

The EFE section could be made a little better (and hopefully shorter)- I might have a go at this soon.

Comments ? ---Mpatel (talk) 09:17, 22 October 2005 (UTC)[reply]