Talk:General relativity/Archive 4

From Wikipedia, the free encyclopedia

Archive This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Contents

Relativité générale

Whoa--- I certainly don't agree that exact solutions = physical comoslogy! But over all, this is a nice article--- certainly more stylish than the English one. EMS, at first it seems too short/limited compared with yours, which is much more ambitious, but the comment about EP and that NASA plane that flies in a parabolic arc to "cancel" Earth gravity might be worth adding somewhere---CH (talk) 01:57, 14 August 2005 (UTC)

Alpher-Bethe-Gamow theory

I am trying to have the Alpher-Bethe-Gamow theory article deleted. People may want to look at this article and them post their opinion on its "votes for deletion" page. I see little redeeming value in this page, although if someone wants to expand and correct it, then I would support it's being moved to Alpher-Bethe-Gamow paper. (However, even then the remaining redirect would be a joke.)

Just for background: The creator of this article is an anonymous editor who is very ill-informed and yet very opinionated. Here are his/her contributions. I think they speak for themselves, and why this article is as it is. --EMS | Talk 15:25, 19 August 2005 (UTC)

Nothing positive to tell about the contributor, but the Alpher-Bethe-Gamow paper was a historically important step in the development of theories of nucleosynthesis. --Pjacobi 16:22, August 19, 2005 (UTC)
I am not opposed to an article on the paper, but unless someone wants to do it now I don't see much sense in letting what is there remain. Everything about it is "off", including the name. Even the business about Bethe's name being added is incomplete. (Bethe did give his blessing to it, but admitedly nothing else.) --EMS | Talk 18:32, 19 August 2005 (UTC)

Hawking radiation explanation

The following was added to end of the black hole section, describing Hawking radiation:

(A form of radiation believed to emanate from black holes, arising from the creation of pairs of subatomic particles in the space adjacent to the black hole, with one particle falling into the black hole and the other radiating away. The energy lost to such radiated particles is believed to cause the eventual disappearance of the black hole).

There is nothing wrong with the text itself. Instead my complaint is that it is covering ground that is already and more appropriately covered in the Hawking radiation article itself. This is an overview article. If it is expanded, it should be by mentioning additional phenomena and not by elaborating on what is already here. --EMS | Talk 14:37, 24 August 2005 (UTC)

Spacetime curved by stress-energy (not the tensor)

At the start, it's stated that 'Spacetime is curved by... (or stress-energy)...'. The stress-energy link goes to the tensor, but this renders the sentence misleading as it suggests that spacetime is curved by the tensor - but, in a way, maybe this is ok, as the spacetime is an abstraction, as is the tensor, so 'spacetime is curved by stress-energy' actually does make (abstract) sense. This is a very subtle point, but one I believe worth correcting. Perhaps I'm digging further than is necessary here, but I think the statement should be changed to, 'Spacetime is curved by...(described by the stress-energy tensor)...'. But maybe this is too detailed at the start. Hmmmm. Am I making any sense at all here ? I think I might be tired... ---Mpatel (talk) 17:21, August 25, 2005 (UTC)

The full statement is
Spacetime is curved by the presence of mass, energy, and momentum (or stress-energy) within it.
So stress-energy is a certain combination of the mass, energy, and momentum in the spacetime. That said, you have run up against one of the weak points in this article: The semantics of the relationship between "mass, energy, and momentum" and curvature. I have chosen to use the term "stress-energy" to package up "mass, energy, and momentum" since other sources refer to stress-energy too, and have carried that syntax forward into the rest of the article. So I am at that point introducing "stess-energy" as a compact term for "mass, energy, and momentum", with an oh-by-the-way-it-is-described-with-a-tesor added in.
The problem is that I include momentum in the list of things that affect spacetime. Most people think of mass-energy but momentum is also a part of the picture, and so I refuse to leave it out.
So you have a point there, but I don't think that your initial idea is going to work. At the least please be aware that changes to that sentence may affect how the rest of the article is read. OTOH, I would like to find a better way of achieving the same result. --EMS | Talk 19:34, 25 August 2005 (UTC)

External Links - GR tutorials

there used to be a section for external links that had at least two references that this neophyte found useful:

The Meaning of Einstein's Equation

No-Nonsense Introduction to General Relativity

can such a section be restored at the bottom of the article. also, i would include this quote, a plain language meaning of the EFE, explicitly in the section of EFE:

Given a small ball of freely falling test particles initially at rest with respect to each other, the rate at which it begins to shrink is proportional to its volume times: the energy density at the center of the ball, plus the pressure in the x direction at that point, plus the pressure in the y direction, plus the pressure in the z direction.

if the wikipedia GR article is meant to be a tutorial for boneheads like me, would this not be useful?

r b-j 21:21, 25 August 2005 (UTC)

The material that you are asking about got exported to general relativity resources, and is featured under the category "web tutorials" there. --EMS | Talk 03:16, 26 August 2005 (UTC)

Featured article status

Regarding making this page a featured article, I still think an awful lot of work needs to be done. EMS' revision constituted an outstanding improvement over the previous versions. If we are looking for featured article status, whilst trying to stick to the conventions of the GTR project, then the bar is really being raised quite high. One point for improvement that should render the article more elegant is to reduce (eliminate?) the 'bullet-point' approach, especially at the start, as I think it looks ugly. ---Mpatel (talk) 17:32, September 1, 2005 (UTC)

I tried to do a paragraph style write-up, and ended up with an unreadable morass. I was not after beauty. I was after an effective mechanism for separating out the important points of the theory. --EMS | Talk 03:52, 7 September 2005 (UTC)

Reversed edits by JimJast

User:JimJast put in some "tidying" that I consider a bit off the point. Sorry, Jim, but your explanation with c varying kind of leads readers down the garden path to dealing with the coordinate velocity of light. Its velocity in any inertial frame is defined to be 299 792 458 m/s. Using coordinate-velocity in a rigid frame, one can play with simplified ways to understand GR (varying mass-energy) but really the mass energy of a piece of rock, e.g. should be considered as just m c^2 where m is the rest mass. Using changing rest mass-energy can be worked out and used in some cases, such as in the solar system, by using a rigid reference system, but look at the contrast to the description down the page of a person standing on Earth. Pdn 00:41, 2 September 2005 (UTC)

Expanding section of the article on "cosmological predictions"

I added to this section the predictions resulting from replacing the present assumption of non conservation of energy in GR with assumption of strict conservation of energy (and so necessarily also replacing the Riemannian geometry with a different geometry of spacetime with proposed by Einstein in 1950 non symmetric metric). Those predictions resulting from strict consrvation of energy seem interesting enough not to be hidden from the readers however I expect that lots of people will hate them. I'd appreciate those people discussing the matter with me before reversing my edits. Thank you. Jim 14:01, 3 September 2005 (UTC)

Wikipedia is an encyclopedia, not a bulliten board. (See Wikipedia:What Wikipedia is not for more clarification.) The predictions that you were trying to present are not predictions of general relativity. Because of that, they are wholely inappropriate, and were immediately reverted for just that reason. The involvement of Einstein is irrelevant to this. --EMS | Talk 03:48, 7 September 2005 (UTC)

Mpatel's sandbox version of GR

I've created my version of the general relativity page. Main reason for this: I'm planning to make the article of featured article status. Feel free to edit my version. Beware that the article will need a lot of work to reach featured status. ---Mpatel (talk) 16:18, September 6, 2005 (UTC)

I've made a start in rewriting the intro. Comments ? ---17:37, September 6, 2005 (UTC)

The mathematics of general relativity

I've just seen some anon adding a cleanuo tag to this section, and I must confess, I find the section somewhat strange. All those alternative explanations of redshift should go to non-mainstream cosmology. And perhaps I'm only having a abd day, but can't this section be deleted entirely? Or replaced by Mathematics of general relativity? --Pjacobi 13:04, September 8, 2005 (UTC)

I have reverted the section to it's form of two weeks ago. I don't know how that extra stuff (apparently of JimJast's) got overlooked, but that is taken care of now. --EMS | Talk 18:36, 8 September 2005 (UTC)

Dilligence needed

We need to exercise dilligence in watching this page. Recently, a user decided that a speculation which he claims was embraced by Einstein in 1950 should be enshrined in this page, instead of being placed in a separate article on the speculation itself. To do so, that user made changes to the sections on "Predictions of general relativity" and also on the "Mathematics of general relativity". The changes to the Predictions section were caught at the time, but not the ones to the Mathematics section.

It is important that whenever a change to this page is detected in the watchlist that not only the current change be reviewed but also that the "History" tab be used to determine what all has been happenning to the page since the page was last checked by yourself. The totality of those edits should have been reverted out at the time. It is much more of a nuisance to come back later and need to determine how to fix the article while preserving newer and usable edits.

--EMS | Talk 18:48, 8 September 2005 (UTC)

misleading first line?

The first line goes: General relativity is the geometrical theory of gravity published by Albert Einstein in 1915 Sorry to say, but that sounds like bullshit to me. Any reference to back up that claim? -> thus, where in that publication (or shortly afterwards) does he describe it as a geometrical theory? -> and where in it does he claim it to be just a "theory of gravity"? See also Erkdemon's comments on the Principle of relativity talkpage(range of applicability). Harald88 10:07, 31 October 2005 (UTC)

GR is a geometrical theory, whether Einstein claimed it (and he did) or not. "Just a theory" gives me a bad taste in my mouth. --MarSch 14:13, 31 October 2005 (UTC)
I demanded, if he did so in 1915 as the line suggests, then please show it! If it's not backed up in a reasonable time then we must delete or correct that sentence into something that corresponds to facts. What I saw from Einstein's writings and sayings (printed speech) is that GRT is an ether (field, space) theory - which indeed makes use of advanced geometry. He pointed out that with "space-time" he simply meant the sophisticated math that he needed. And 1916 (1915?) GRT certainly was not just a theory of gravity, but a (failed?) attempt to make all motion (incl accelerated motion) fully relative, as Erkdemon pointed out and on which you commented zip (nothing). Note also that you misquoted me, thus giving yourself a bad taste (and it makes me wonder...) Harald88 17:31, 31 October 2005 (UTC)

In contrast, see the featured French version: "La description géométrique de la théorie physique due à Einstein " - and that's much better as it presents GRT as a physical theory (or physics?) with a geometrical description and it doesn't claim that it was presented as "a theory of gravitation" in 1915. Let's adopt that. Harald88 17:31, 31 October 2005 (UTC)

Can you explain the difference between "a physical theory with a geometrical description" and "a geometrical theory"? Also, are you trying to deny that Einstein perceived GR as a theory of gravitation? One of the key 1915 articles is even called "Die Feldgleichungen der Gravitation".

--Itinerant1 19:57, 31 October 2005 (UTC)

A "geometrical theory" may be understood to have geometry as physical model. How that is supposed to work I don't know, but there are many modern physicists who treasure such a concept. I didn't have a look at the Talk page of the French version, but surely the original or later editor of that page understands the difference, otherwise he/she wouldn't have used the more complicated, correct formulation. Einstein's theory was first of all, as he explained, an extension of the Principle of Relativity to acceleration. Thus it's more correct to call GRT of 1916 the theory of the relativity of acceleration ("General Relativity"). Anyway, how Einstein perceived his theory he explained himself (1916):
in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to "produce" a gravitational field merely by changing the system of co-ordinates.
- http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf
IOW, 1916 GRT had as subset a theory of gravitation - it was not itself a theory of gravitation but a general theory of relative motion. And this fact is still quite well known, even I knew it before checking the 1916 paper!
OK, now I have cited Einstein showing the correctness of my claim, while in fact I asked for evidence for the claim that 1915 GRT is correctly depicted as "a geometrical theory of gravity [sic]". (indeed, gravitation is the better word, but that's a minor correction although illustrative for how knowledgable the original editor was). Harald88 21:08, 31 October 2005 (UTC)
General relativity equates gravitation to motion in non-inertial frame of reference. All phenomena described by GR are either gravitational or can be understood on pre-GR level simply by considering motion in curved space-time. So, it is not proper to consider GR to contain theory of gravitation as a "subset". If you remove all gravitational content from GR, there will be nothing left.
IOW, 1915 GRT was according to you not what Einstein said that it was. And you want this encyclopedia to pretend that it was what he said that it was not. Instead he claimed that acceleration is relative, and that acceleration may be regarded as the creation of a gravitational field, affecting the rest of the universe (more clairly exposed in his 1918 paper). That is not "nothing" at all, but it's outdated/incorrect for most (but not for all, I have a colleague who believes it).

Harald88 14:35, 1 November 2005 (UTC)

As for geometrical theory vs. geometrical description: there may be some narrow distinction, I seem to recall that there's a page or two in Wald on this subject. Geometrical theory states that being curved is in the nature of space-time. Physical theory with geometrical description states that it is convenient to consider space-time curved even if intrinsically it is not. For example, some theories attempt to arrive at unification of gravity with QFT using flat background metric and gravity as just yet another spin-2 field. It is suggested that such a theory would reduce to GR in classical limit. If this approach proves fruitful, then we may talk about using "geometrical description". But presently, for all we know, space-time _is_ curved. It's not just geometrical model, it is geometry. --Itinerant1 21:40, 31 October 2005 (UTC)

We don't "know" at all what some people speculate. That "narrow distinction" is essential concerning the first line: apparently Einstein disagreed with that, and it's therefore falsehood to claim that it was so according to his 1915 paper. This is not POV; it's a non-corraborated, misleading claim. Harald88 14:35, 1 November 2005 (UTC)

See this and this. Those are the reasons for the 1915 date. If you like, the word "published" can be replaced by "completed", but in terms of changing that line that is all that I see as appropriate. --EMS | Talk 15:57, 2 November 2005 (UTC)
Thanks ems, finally a constructive remark! Indeed, I don't think it suffices but it's a lot better like that, please go ahead. And then I will not insist anymore, I think we all wasted too much time about just one sentence! Cheers, Harald88 19:03, 2 November 2005 (UTC)

Einstein submitted the correct field equations for publication on Nov. 25, 1915 [1], and that article was promptly published. So GR was indeed first published in 1915. The exact reference is: Die Feldgleichung der Gravitation, Preussische Akademie der Wissenschaften, Sizungsberichte (1915), 844-847 [2].

Beyond that, I must express some sincere concern about Harald88 seeing fit to describe GR as "a (failed?) attempt...". GR is a major advance in the understanding of gravitation, which has so far survived all test it has been subject to. So it hardly deserves to be called a failure. I also cannot figure out how ether enters into GR. If Harald88 considers ether and spacetime to be synonymous, then my only objection to what he wrote above is semantic. However, the ether was originally an attempt to maintain the Newtonian physics that Einstein's work so thoroughly destroyed. --EMS | Talk 20:44, 31 October 2005 (UTC)

Thanks for the reference EMS. Apart of that, you evidently didn't read what was written after "a (failed?) attempt". Look again, and you will see that I didn't mention gravitation there (nor "gravity"). If you want to comment on that, then look up the page that I referred to.
Fine. You wrote:
... a (failed?) attempt to make all motion (incl accelerated motion) fully relative, ...
IMO, GR is a complete success in that regard. It shows how objects in intertial motion can accelerate with respect to each other, placing gravitation on a whole new footing. Furthermore, when GR and Newton's laws result in testably different predictions, it s the GR prediction that holds up. I don't see why anyone who understands GR would even hint at its possibly being a failure. --EMS | Talk 22:47, 31 October 2005 (UTC)
Strange, after admitting that I referred to an article that claims that GRT failed on the point of completely relativising acceleration, you switched again to the subject of gravitation! For your information: there are few physicists who believe that acceleration, and notably rotation, is "relative", and even Einstein admitted in 1920 that rotation is "absolute". Harald88 14:22, 1 November 2005 (UTC)
LOL! You really don't understand GR or what it is about, do you? Perhaps you should start with the equivalence principle, and at least general_relativity#Justification. As you surmised, acceleration is indeed an absolute, and remains that way in GR. Einstein's goal was never to make physical acceleration relative, but instead to create a theory the would describe how spacetime is perceived even in accelerated frames of reference. It is a job that was complicated by the realization the freefall is inertial motion. This means that standing on the surface of the Earth places you in an accelerated frame of reference. (This is the reason for gravitational time dilation. In fact, you would see the same effect on clocks at different distances from the rocket nozzle in an accelerating spaceship!) Einstein came to the realization that freefall cannot be inertial unless spacetime is curved, and the acceleration Newton claimed was due to gravity is in fact a result of that curvature. Eventually, all that led to the Einstein field equations and the complete theory that we call general relativity.
Anonymous, if you wanted to make me laugh, you succeeded! Obviously you are not familiar with Einstein's writings of that time, notably in 1918 he claimed that the gravitational field that the "travelling" twin feels at turnaround (and for him his own acceleration is nil), is just as "real" as any real gravitational field.

Anyway, I see now the first constructive reply, so all this fuss can stop. BTW, your comment that his theory was first of all about accelerated frames and thus not only a theory of gravitation was my main point. Harald88 19:03, 2 November 2005 (UTC)

How are your perceptions of space and time changed by acceleration? What paths will objects take when either unaccelerated or when subject to a given proper acceleration? How is this affected by the presense of mass/energy and momentum? GR gives answers to those questions, and does so very well. In addition, it describes things like the expanding universe which have been confirmed but which Einstein himself did not believe in at first. So it is a very successful theory. It is also quite beautiful, once you come to understand it. --EMS | Talk 16:15, 1 November 2005 (UTC)
If you want to know how ether enters into GRT: it's a field theory, it doesn't claim that light speed is affected by "gravitons" but by the gravitational field potential, which as Einstein explained (1920 but also later) implies an abstract ether concept. He explained that it rather corresponds to Newton's Space, but without an absolute velocity (which I find peculiar to say the least) and, of course, his genius was to infer that if matter is affected by space, then also matter should affect space (my paraphrase). I'm not sure anymore where he wrote that, but no doubt you can find it yourself - until now I'm the only one who quoted and paraphrased him, while that's the kind of facts to put in an encyclopedia! But he may rapidly have changed his opinion; if you can cite a place where Einstein claims that not space but spacetime affects matter, I like to see it. Harald88 21:36, 31 October 2005 (UTC)
You may be referring to the famous quote "Matter tells space how to curve and space tells matter how to move." However, it was not made by Einstein, but by a famous physicist John Archibald Wheeler, not in 1920 but at least 20 years later.
No, I referred to Einstein's descriptions in either his 1916 paper or his 1920 talk. Now, do you know one like that from Einstein about spacetime?Harald88 14:22, 1 November 2005 (UTC)
It is completely unnecessary ( in fact, excessive and contrary to the geometrical approach ) to introduce ether in order to describe propagation of gravitational field. Just as when we describe propagation of waves on the surface of the sea or on the membrane, we don't need any new fields or artificial constructs.--Itinerant1 22:05, 31 October 2005 (UTC)
You are completely right, we don't need to discuss water when giving the equaion for water waves. That's not the issue. The issue is that either the article describes what Einstein and not some editors claimed about his theory of 1915, or that it describes how it is generally interpreted today, with referral to the inception of the theory by Einstein in 1915. To put your words into Einstein's mouth is falsehood. Harald88 14:22, 1 November 2005 (UTC)
No, he is not refering to the Wheeler quote. Look at it this way: Deep in a gravitational field, light appears to travel slower that at higher potentials. This is the same kind of slowdown as would occur as light enters a physical medium, and even refracts light in the same way! (If you doubt me, then think of how light is bent as it passes the Sun.) That is the genesis of Einstein's "abstract ether concept", based on how Harald88 is presenting it. In any case, I am sure that your statement of its being "completely unnecessary" is the consensus today, and I suspect that even Einstein himself found little use for that concept. --EMS | Talk 22:59, 31 October 2005 (UTC)
Thanks for the precision; and it is actually how Einstein presented it, I didn't get this from some text book. And although it's of no relevance to this point, I look forward to see a quote to corroborate that suspicion of yours. Harald88 14:22, 1 November 2005 (UTC)
I think that the onus is on you to first dig up a reference to that quote. I know it exists. Certain -uh- types of people have a habit of referencing it when they are trying to challenge GR. I just wanted to make the case that it is not to be confused with the Wheeler quote. However, if you want to see where I am getting the light slowing down business from, see Einstein's 1911 article on gravitation in The Principle of Relativity, still published by Dover Books, or this discussion of it. Note that this effect is for an observer at a different gravitational potential than the light. Locally, the speed of light is always the same. --EMS | Talk 16:25, 1 November 2005 (UTC)
In fact I paraphrased him from both his 1911 and his 1916 article. But if you know that, then why did you suggest that this was my presentation and not Einstein's? And I'd still like to see if anyone can confirm your suspicion that Einstein later found little use for the ether concept. Harald88 19:03, 2 November 2005 (UTC)

Harald88, you were very unclear in your original post, so you've only yourself to blame if I misunderstood you. I would like to reitereate that GR is a geometrical theory whether Einstein claimed it or not. The fact that GR can be cast in geometrical terms is enough. I think that gravitational theory would be the non-sense term. I don't think it is necessary to say that it is a geometrical physical theory, but I can live with it. And yse GR is a theory of JUST gravitation and it is not just a theory of gravitation it is the theory of gravitation.--MarSch 12:35, 1 November 2005 (UTC)

MarSch, you only have to blame yourself for misquoting. Please explain, what does make GRT a geometrical theory, and not for example Newton's theory of motion? Or do you want to put the label geometrical also on that? And I already cited Einstein pointing out that 1915 GRT was not a theory of gravitation (instead it led to a theory of gravitation), so who proposed that? Anyway, you don't seem to care about his description of his own theory, but apparently you want to impose your own POV and then sell that as his... Harald88 14:22, 1 November 2005 (UTC)
Geometrical has to do with being able to choose your own arbitrary coordinates for describing a physical theory. Newtonian mechanics has a distinguished time-coordinate, which might lead people to call it non-geometrical. I think I now finally understand your question though and will try to answer. Einstein wanted to also allow accelerating frames (non-inertial frames) as equivalent. He found that such an accelerating system is actually indistinguishable from an inertial one with a gravitational field. I don't know whether he perceived first of equilizing accelerating frames or of the equivalence of an accelerating frame with an inertial one plus gravity. Back to your other comment. I care about what Einstein said about his theory, but what he said is not per definition the truth. Einstein does not get to decide whether his theory is geometrical or not, it is or it isn't, once someone can think of a definition for geometrical. I don't want to sell my POV, especially not as Einstein's. This article is about GR and not about what Einstein said about it, so any claims in it for which it is not claimed that it is Einstein's POV, are hopefully general knowledge or some such.--MarSch 18:23, 2 November 2005 (UTC)

Possible change to the first line

From the above discussion:

...If you like, the word "published" can be replaced by "completed", but in terms of changing that line that is all that I see as appropriate. --EMS | Talk 15:57, 2 November 2005 (UTC)
Thanks ems, finally a constructive remark! Indeed, I don't think it suffices but it's a lot better like that, please go ahead. And then I will not insist anymore, I think we all wasted too much time about just one sentence! Cheers, Harald88 19:03, 2 November 2005 (UTC)

Any objections? --EMS | Talk 19:43, 2 November 2005 (UTC)

well he did publish it then, but who knows what completed means. --MarSch 12:42, 3 November 2005 (UTC)
I do see that as an issue too. I also remain bothered by Harald88 showing signs that he does not really get when GR is about, including the intimate relationship between acceleration and gravitation in GR. Harald88 may also be looking at the 1916 Annalen der Physik article as the actual publication of GR, whereas I see it as a post-mortem on the results of the research that led to GR. As I see it (and I think that you will agree with this), the 11/25/1915 article was the completion of GR including its publication, with GR at that point being completely known and published due to Einstein's previous articles on subject. --EMS | Talk 14:48, 3 November 2005 (UTC)

category:effects of gravity

I am trying to have this category deleted and most of its entries placed into category:general relativity. I figure that others who are involved with GR will want to have a say in this. --EMS | Talk 15:11, 14 November 2005 (UTC)

Duplicated fundamental principle

Isn't requiring that the laws of physics be same for all observers identical to requiring that they be valid in all co-ordinate systems? Masud 15:25, 23 December 2005 (UTC)

The principle ought to say "the same for all freely falling observers" and actually, "all coordinate systems" is a bit more comprehensive and sort of unnecessary. Coordinate transformations include things like rectangular to spherical (in flat space - it's more complicated in curved spaces but still the idea is that observers fixed in one coordinate system are fixed in the other) as well as frames related by a Lorentz transformation (locally; globally it can be more complicated due to curvature, but the concept is the same: observers in one reference frame are moving in regards to the other.) The key idea in relativity related to the latter situation - observers in relative motion. The other transformations that change coordinates without relative motion were allowed earlier and are less relevant. Tensor analysis is, however, required to properly deal even with these. Carrionluggage 16:21, 23 December 2005 (UTC)
I find disagrements with both of these postings. First of all to answer the initial question: "All observers" vs. "all coordinate systems" are two separate issues. In the first case, it is possible that the fundamental laws of physics could vary by time or position in the universe. For example, some researchers have proposed that c varies over time. In such a case, c as a constant would not be admissible as a fundamental priciple of physics under the "... all observers" rule, but is not relevant to the "... all coordinate systems" rule. For the case of "all coordinate systems", the meaning of "... with a constant velocity" in Newton's law of inertia very much assumes the use of a rectilinear coordinate system. If a spherical coordinate system was used instead, the velocity would in fact be constantly changing for an object following a chord with respect to the system's origin. In dealing with curvature, Einstein sought to get away from such restrictions, and succeeded.
For the intial response: Einstein very much sought rules that would apply to all observers, inertial and otherwise. For free-falling observer, it is the laws of special relativity that are expected to apply locally (a principle otherwise known as local Loerntz invariance). Otherwise, it is general relativity in all of its glory that must be used. --EMS | Talk 22:20, 23 December 2005 (UTC)
In that case, GR doesn't require to be valid for "all observers" since the stress-energy tensor might be given by third-order derivatives of the metric and not second. Is that right? Masud 02:17, 24 December 2005 (UTC)
What I mean is GR assumes that the derivatives of second order of the metric are proportional to the stress-energy tensor. In fact, since the Einstein tensor is the only covariantly conserved rank 2 tensor that can be built out of the metric, the field equations are determined up to a constant. My point is that assumptions of physics being the same over different times etc. are implicitly assumed. Do we need the "all observers" principle then? Masud 02:43, 24 December 2005 (UTC)

The way that arbitrary (even accelerated) observers are handled is by finding a local Lorentz ("freely falling") reference frame matching the velocity. In a first-order neighborhood, the laws of physics must be the same as everywhere. Oddly, then, a pendulum clock won't work in such a setting - you have to use a crystal oscillator, maser, rotating member under spring torque (like an old fashioned wristwatch escapement), etc.! Pendulum clocks work on the Earth's surface because they are accelerated upwards in regards to a freely-falling frame in which the usual laws of physics hold. So we have to regard such clocks as accelerometers if we wish to apply the rule that the laws of physics are the same in all frames. The claim that you can't do Newtonian physics in spherical coordinates is absurd - Newton knew how to do it, and any good mechanics text shows how to do that. The conservation of angular momentum in planetary motion is expressed most simply in such a frame. "Constant velocity" in the sense of Newtonian physics does NOT mean constant derivatives of the coordinate values.

Furthermore, the velocity of light is standardized (see NIST, IAU, etc) at a fixed velocity. If one measured a varying velocity of light, it has to be ascribed to inconsistent clock behavior (i.e. it violates the Equivalence Principle). Scientists do look for such effects in the laboratory and the cosmos. A recent example is the paper, Atomic Interferometer with Amplitude Gratings of Light and Its Applications to Atom Based Tests of the Equivalence Principle by Sebastian Fray, Cristina Alvarez Diez, Theodor W. Hänsch, and Martin Weitz, of the Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany, Sektion Physik der Universität München, 80799 München, Germany, and Physikalisches Institut der Universität Tübingen, 72076 Tübingen, Germany in Physical Review Letters, Vol 93, paper # 240404 (Dec 10, 2004) Carrionluggage 18:17, 24 December 2005 (UTC)

The non-relativistic example

This new section does not belong here (it is too specific for this overview article), but it does not deserve to be deleted outright. Instead it should be in its own article and can be referenced by this one. (We need an article with graphics like that showing how we conceptually go from classical mechanics to general relativity, and that is a start at such a thing.) Are there any suggestions on what to call the article that would hold this material? Or other suggestions of what to do with it. --EMS | Talk 21:39, 28 December 2005 (UTC)

Done Complexica 23:23, 28 December 2005 (UTC)

Not happy about the location of the revised new section. At the moment, it breaks right into the discussion of GR. If anything, it belongs in the 'Relationship to other physical theories' section further down in the article. MP (talk) 08:34, 29 December 2005 (UTC)
Ok, I've moved the section further down. The 2 equations may be redundant, as they are properly discussed in the relevant article. How about removing them and replacing them with some words instead ? MP (talk) 08:46, 29 December 2005 (UTC)
Done Complexica 16:26, 29 December 2005 (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)