Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxt!houxm!whuxl!whuxlm!akgua!gatech!seismo!brl-adm!brl-smoke!gwyn From: gwyn@brl-smoke.UUCP Newsgroups: net.physics Subject: Re: Coordinate frames in GR Message-ID: <2193@brl-smoke.ARPA> Date: Sat, 29-Mar-86 02:23:47 EST Article-I.D.: brl-smok.2193 Posted: Sat Mar 29 02:23:47 1986 Date-Received: Tue, 1-Apr-86 07:23:03 EST References: <438@batcomputer.TN.CORNELL.EDU> <1005@lanl.ARPA> <1035@lanl.ARPA> Reply-To: gwyn@brl.ARPA Organization: Ballistic Research Lab (BRL) Lines: 31 I finally dug out my copy of MTW to see what was in Box 1.3. If a region of space-time is indeed inertial, then the coordinate-free representation of special relativistic physics is correct. The introduction of coordinates can be done in many ways; if done carefully so that a local Lorentz frame results, then the simplified form of special relativistic coordinate-based equations can be used, since the metric tensor is diagonal is such a frame; if a more general frame, such as a rotating one, is introduced instead, then one has to treat the metric tensor correctly, in addition to being more careful in formulating the coordinate-based equations of special relativity. Despite this, one does not have to resort to general relativity to treat physics in an inertial space, even if one chooses to use rotating coordinate systems; however, some of the tools commonly employed in general relativity are needed. On the other hand, to relate events at non-neighboring points of the space-time continuum to each other when space-time is noninertial (e.g. in the presence of gravitating bodies), it is essential to use general relativity rather than special relativity. This can be traced to the existence of a non-trivial gauge field in such a region. The question of rotation of the whole universe about a stationary Earth definitely is the non- local type of question that requires general relativity. One final point: Empty space-time is NOT necessarily flat, even in conventional general relativity. In the generalized theory of Eddington/Schr"odinger, in fact, space-time cannot be flat anywhere.