desj@brahms.BERKELEY.EDU (David desJardins) (03/29/86)
Jim Giles writes to me: >> I don't know which "theorems are referred to," but you did in fact make >> the *demonstrably false* statement that "in GR all local frames are Lorentz >> frames." If you want I will find the article and quote it to you. > >I never said that ALL local frames in GR are Lorentz frames. Well, then, please explain the following: >Article 3198 of net.physics: >From: jlg@lanl.ARPA (Jim Giles) >Message-ID: <424@lanl.ARPA> >.... One of the paramount features of General Relativity is that the >laws of physics should appear the same in ALL reference frames. >.... The bottom line is that rotation is LOCALLY discernable and is >therefore NOT a property of Einstein's reference frames (whether they are >lorentz frames or not). One way of locally measuring rotation is with a >foucault pendulum (which you even mentioned). Meanwhile ALL Einstein >frames are LOCALLY indistinguishable from lorentz frames. Here you seem to be saying that all "Einstein frames" (a phrase which has not been defined, and which I take to mean all frames that can be used to solve Einstein's equations) are local Lorentz frames. False. Article 3233 of net.physics: >From: jlg@lanl.ARPA (Jim Giles) Message-ID: <556@lanl.ARPA> .... Note: I have always said 'local reference frame', which in GR is ALWAYS a Lorentz frame. See box 1.3 in "Gravitation". End of Note. Here you are very explicit. All local reference frames used in GR are Lorentz frames. False. Article 3246 of net.physics: >From: jlg@lanl.ARPA (Jim Giles) Message-ID: <853@lanl.ARPA> .... When I mean 'coordinate system' I say 'coordinate system'. I always use 'frame' as short for 'Lorentzian frame' .... In other words, your terminology is incorrect. You are confusing an arbitary local frame with a "Lorentzian [sic] frame" (presumably you mean Lorentz frame). Back to the letter: >I DID say .... Nobody is denying that you later said some true things. I just want to know if you admit that some of the things you said are in fact wrong. >Since you can't tell which theorems I am talking about, I can only assume >that you don't even HAVE a copy of MTW to check the context of my remarks - >much less have you read it! Since you didn't tell me in your letter what theorems you were talking about, it was hard for me to guess which ones you meant. I do in fact have MTW sitting right in front of me, and have had for this whole discussion. Was reading MTW supposed to make me a mind reader so I could guess what theorems you were talking about? >> But the *point* of the above is that you *can* do GR in *any* local >> frame, and the results are the same *because* of the analysis you describe >> above! What you are saying is, "Einstein realized that *if* you do your >> analysis in a rotating coordinate frame, the influence of all of that >> rotating mass gives you the same answer after all." Don't you realize >> that you need to be able to do GR in rotating frames in the first place >> for this to even make sense? > >I never claimed that you COULDN'T do GR in any coordinate system you wanted >to. YES YOU DID! See the above quotes. This is the whole problem. >You can invent a hyperbolic coordinate system with singularities in it >(even for an empty region of space) if you want to - and, with sufficient >mathematical sophistication, you can correctly work out what's going on. >This has NOTHING to do with the question: is rotation 'merely' a matter of >convenience? The answer is NO! The Earth rotates once per day, the Moon >once per month. Both the Earthling and the Selenite agree that their >pendulums and gyroscopes are linked to the distant stars, NOT the Earth or >the Moon. By claiming this to be 'merely convenience' is to disregard this >effect as purely coincidental. Using that particular coordinate system to do your computations is merely a matter of convenience. But neither Matt nor I nor anyone else has said that there is not a preferred frame, or that there is nothing special about nonrotating frames. All we have been saying is that GR says things about *geometry* of space-time that are true *independent* of which particular frame you choose to do your computations in. For example the coordinate- free statements in your favorite box, 1.3. >The effect makes perfect sense without rotating coordinate systems (it is, >after all, a Newtonian effect as well). Now, as you say, you should be >able to compute the effect in GR for rotating frames as well. This does >NOT imply that such rotating frames will satisfy the theorems of Special >Relativity (as you and Mr Weiner have actually said) - rotating 'frames' >DON'T obey the theorems of special relativity. NEVER has either of us said this. I can quote you the places in which you have said the things I attribute to you. You cannot, because we have not said those things! >No matter how long you and Mr. Weiner bang on your keyboards, you can't >make rotating coordinate systems obey the theorems of Special Relativity. Nor would we claim to. >Don't send me more mail about this issue until you have read and under- >stood at least chapter 1 of MTW or some other adequate text. It's a >useless discussion until you start making sense instead of meaningless >diatribes. I know so much more differential geometry than the small amount that is in MTW that this is just ludicrous. I have spent years as a graduate student studying geometry. I don't know how to convince you of this, except to repeat the same things I have been saying, and to point out the inconsistencies in the things you have said. -- David desJardins