User talk:Ems57fcva/sandbox/General relativity 2

Chris's comments

Huge improvement in organization and emphasis! Good job, EMS. I can see some room for minor improvements in wording here and there, but the main comment I have right now is that in the discussion of the four classic tests, it would be nice to try to clearly but concisely separate predictions which are specific to gtr and predictions which are much more general, like red shifting---CH (talk) 04:47, 12 July 2005 (UTC)

Thank you very much.

BTW - I have reworked the predictions section somewhat in response to these comments. --EMS | Talk 15:48, 12 July 2005 (UTC)

Mpatel's comments

Very well re-organised. Just a few picky comments:

• I know there is a link to spacetime, but maybe a few words could be said in this article to explain quickly to the general reader roughly what spacetime is - maybe.

I don't see an obvious way of doing that, and it is discussed elsewhere. It is worth thinking about however.

• I think the statement, 'Instead what we perceive as gravity is a result of our being continuously accelerated by the physical resistance of whatever surface that we are standing on.' needs a little adjustment - a person near a black hole still feels gravity, but the person doesn't necessarily have to be standing on anything - let's not forget a poor, drifting astronaut.

Are you thinking of tidal effects? In my opinion, an observer in freefall is not feeling gravity at all, but instead is experiencing it as (s)he watches the ground rise up.

• 'spacetime is curved by the presence of stress-energy within it' - the link actually takes us to the stress-energy tensor page; perhaps 'spacetime is curved by the presence of matter (energy) within it' would be better for the general reader, as later on it is mentioned that this matter (energy) is described by the stress-energy (energy-momentum) tensor. Btw, should stress-energy be merged into energy-momentum tensor ?

Maybe call for a vote on the proper wording of what I now call "stress-energy"? This is one of the weak points in this article, as I am left caught between a need to communicate a fairly abstract concept and the Wikipedia injuction against neologisms. Your "matter (energy)" will work, but it leaves out momentum. I myself had thought of using the term "substance" but as best I can tell that use of the word is itself a neologism.

As for merging the stress-energy tensor and energy-momentum tensor pages: I like that idea. Perhaps you should get a discussion going about it on the GR and affected pages. (BTW - A reference to the 4-momentum, which is another energy-momentum tensor is needed in the merged page.)

• The geodesic equation is described on a separate page called geodesic - maybe you already knew that, and you wanted to write something more detailed on the geodesic equation, in which case, ignore this comment. I still think the geodesic equation has a + sign :).

Equation fixed.

Some thought is needed on what to do about the geodesic equation link. I want that to be the link. However, that stub needs to either be redirected to geodesic or turned into a real article. Another idea is to do a geodesic equation (general relativity) article, as there are details to that which may not be appropriate to a more general article. However, these are just ideas at this time.

• The fact that (1) matter/energy curves spacetime and (2) inertial motion occurs along timelike geodesics have been mentioned separately - I really think that it's important to mention somewhere that there is, strictly speaking, an approximation being made when using the geodesic equation - e.g., in exterior Schwarzschild, planetary motion is assumed to be dictated by the geodesic equation, but only because the local curvature of spacetime created by the planet can be ignored (compared to that created by the star) - or, to put it another way, the energy-momentum tensor for the planet is miniscule and dwarfed by that of the star, so it can be ignored.

I think that this is a level of detail that is inappropriate to this article.

• In relation to the previous comment, I thought the medicine ball - ping-pong ball - trampoline analogy was a good one to keep in the article (probably because I included it :)) - it's very illustrative and helps the general reader to visualise the image better.

See the previous response. Perhaps you would like to create the inertial motion as geodesic motion article and mention it there?

• Perhaps I read the article too quickly, but I think there should be a link to the equivalence principle page - I know it's mentioned implicitly in the article.

Good point. See the modified section on fundamental principles.

• After that onslaught of criticisms, now for a positive comment - I really like the section on coordinate vs physical acceleration ! ---Mpatel 10:56, 12 July 2005 (UTC)

Thank you much. It is good to know that that innovation is approved of. I also thank you for all of your comments. --EMS | Talk 15:48, 12 July 2005 (UTC)

Pdn's comments

This part very early on is misleading: "Instead what we perceive as gravity is a result of our being continuously accelerated by the physical resistance of whatever surface that we are standing on."

I agree it is true for many cases. But in weak-field cases with Minkowskian or, e.g. Friedmann boundary conditions at infinity in space, we get the weak-field case which looks and acts (but does not quack) like Newtonian theory. One is not standing anyplace where the quoted remark applies. Pdn 17:34, 12 July 2005 (UTC)

Since you are not the first to comment on this I will clarify it: "... we here on the surface of the Earth perceive as the force of gravity ...". Hopefully that will alleviate the concerns being expressed.

I changed that part of the intro a little more than expected. I occurred to me that the article could be written read by an astronaut, or even someone in an airplane. I figured that making the write-up a little more explicit would not hurt. --EMS | Talk 19:54, 12 July 2005 (UTC)

This part is wrong:"The general principle of relativity: The laws of physics must be the same for all observers (accelerated or not)." Here you are referring to the old idea of Newtonian acceleration and considering only cases where gravity is the only "accelerating" force. If you attach a mini-lab to a bunji cord and set the whole in motion, normal physics does not apply in that lab. The item should read: "The general principle of relativity: The laws of physics must be the same for all unaccelerated observers (where we do not consider motion under gravity an acceleration)" or ""The general principle of relativity: The laws of physics must be the same in all freely falling (inertial) reference systems." Pdn 17:41, 12 July 2005 (UTC)

Here I will stand my ground. The general principle of relativity is as stated. It was very much Einstein's goal to achieve that. You need to take a global view here: How distant objects behave with respect to my coordinate system is governed by the same covaraint laws whether I am being accelerated or not. For example, even at the other end of a space capsule, objects are being accelerated with respect to an astronaut because of tidal effects, and that is covered by GR.

What you are quoting is the strong equivalence principle. Under Schiff's conjecture that implies GR. However, in my mind what is important is that the underlying rules: geodesic motion, energy-momentum conservation, the laws of electromagnetism, etc., are all expressed the same way for the whole of spacetime independent of whether the observer is being accelerated or not, as demonstrated in those links. All that being accelerated changes is the operative metric of spacetime.

--EMS | Talk 19:45, 12 July 2005 (UTC)

P.S. See Mpatel's comment below. --EMS | Talk 15:36, 13 July 2005 (UTC)

Changes moved

A robot has changed the interwiki links for this article in the article space. I have moved those changes over. --EMS | Talk 02:59, 13 July 2005 (UTC)

Another robot!

First of all, I think that I should thank everyone else for laying off of the GR page while I have been making and with your help finalizing the rewrite. Now if only we could clue in these "robots"!

Actually the latest change has already been made in the rewrite. So we are ahead of the robots, even though the log will not reflect that. --EMS | Talk 03:35, 17 July 2005 (UTC)

Mpatel's comments 2

• There is actually a page geodesic (general relativity).

Tweaked a link to use that article. However, what was being discussed above was the geodesic equation. That is still an issue.

• I still believe that the balls and trampoline analogy should be kept here for the reason that it is illustrative and intuitively obvious. I agree about not going into details about ignoring curvature of relatively small bodies in this article. We can just mention that the idea that spacetime is curved can be visualised in this way - I feel strongly about this, as it's (one of) the most basic physical assumption(s) of GR and thus should be emphasised emphatically. I'm not convinced that just saying 'spacetime is curved by the presence of stress-energy' is sufficient for non-specialists to understand intutively what this means - which is why I think a little clarification of the meaning of spacetime here is necessary: maybe we can say that spacetime (consists of events and for the purposes of illustration) can be viewed as a flexible 'sheet' and then refer to the image, but the balls and trampoline analogy should help with intuition.

Then I tell you what: Draft a "Spacetime as a curved Lorentzian manifold" subsection and place it just after the Fundamental Principles subsection. Let's try it and see if it will work. All that I ask is that you make the changes here. I don't want multiple versions of this rewrite floating around needing to be merged.

• Just noticed something in 'Fundamental Principles': "the principle of general covariance: the laws of physics must be the same in all coordinate systems" can be clarified to ": ... laws of physics must take the same form in all coordinate systems" - I think this clarifies general covariance, as previously it was hardly any different from the GPR (if the laws are the same for all observers, then clearly observers who make measurements to test these laws must use a given coordinate system and the laws are still physically the same - e.g. Maxwell's equations - whichever CS is used; but "take the same form" clarifies the covariance principle slightly, as it refers to the mathematical form of the laws - e.g. replace partial derivatives by covariant ones in Maxwell's equations). I think what I am trying to say is that GPR leans more towards the physics and PGC leans more towards the maths.

Done. It looks good.

I totally agree - "the same form" - that means the equations are generally covariant, but it does not mean that measurements are independent of acceleration. Pdn 16:07, 13 July 2005 (UTC)

• Agree with EMS on general principle of relativity as Einstein stated it.

Thanks.

• What is Schiff's conjecture ?

This involves the strong equivalence principle. The strong equivalence principle states that all objects, even self-gravitating objects, will fall the same in the gravitational field of another object (if the effects of the first object on the second one are ignored). In essense, at any point in it's orbit the Earth's center of mass follows the same path as a ping-pong ball would given the position of the Sun for that event.

Schiff's conjecture is that only Einstein's general relativity has this behavior. Therefore a proof that the strong equivalence principle is true would mean that general relativity is true. --EMS | Talk 15:18, 13 July 2005 (UTC)

New section

Mpatel -

Thanks for creating the new section. I have expanded it somewhat and turned part of the introduction into a link to it. Both were done to integrate it fully into the artcile.

I will admit that I find it a bit wordy, but overall see your writeup as being a positive addition to this article. I may delete the last sentence since that point is being covered adequately elsewhere. --EMS | Talk 17:49, 14 July 2005 (UTC)

Periapsis precession text

Pdn's added text (added when the text refered to "perihelion precession" instead of "periapsis precession"), which came after the words "binary pulsar":

, (in which case it is called periastron precession, since "helios" refers to our Sun)

This is a good point. However, I think a found a more compact way of dealing with it. --EMS | Talk 14:38, 18 July 2005 (UTC)