Path: ...!news.mixmin.net!news2.arglkargh.de!news.karotte.org!fu-berlin.de!uni-berlin.de!individual.net!not-for-mail From: Luigi Fortunati Newsgroups: sci.physics.research Subject: Re: Experiments on the validity of Relativity Date: Sat, 18 May 2024 15:40:47 PDT Organization: A noiseless patient Spider Lines: 99 Approved: Jonathan Thornburg [remove -color to reply]" References: X-Trace: individual.net ppI8TZ+4e0/7jTenzhbzNApD/7DKhHNB2qlmPoOvVIea/khP+xLzRsLQ9n Cancel-Lock: sha1:R0NX3Tn8gy7xzqaSNt2eIQXCx6c= sha256:d3qKYyCirkISL26h4XEN1Ctdt4Xfc4ZoIjqEN/GnSIQ= X-Forwarded-Encrypted: i=2; AJvYcCVYvPpCgA1n5IvYOtBPrMaZyRyEyfHugnvXNVfFxNLi5zOTLELQvSk0fBFqrfW+7/OJMMnMTw924dwju2iQ0TBJcHidwMfKhAY= X-Auth-Sender: U2FsdGVkX1826ubB1idr9+QykGzCDRl/vFvyKm4a4Ne/6s1caHzdJRoWLv2kJBQ5 Bytes: 4796 Il 16/05/2024 09:24, Tom Roberts ha scritto: >> [...] two massive bodies (which fall gravitationally and freely >> towards each other) *accelerate* both in the reference of one and >> both in that of the other. > > Sure. This does not refute GR, because of your confusion between > coordinate acceleration and proper acceleration. In my animation https://www.geogebra.org/m/ttgky8xu there are two small planets (A and B) that accelerate gravitationally and simultaneously towards the common center of mass P. Is this acceleration what you call "coordinate acceleration"? And what is your "proper acceleration"? Is it, perhaps, the acceleration of planet A with respect to itself and of planet B with respect to itself? Or is it something else? Luigi Fortunati [[Mod. note -- For your specific questions, a careful reading of https://en.wikipedia.org/wiki/Proper_acceleration together with its references, would likely be useful. In your animation, while A and B are initially stationary (before the animation starts): * in the coordinate system of your animation, A's center of mass has zero coordinate acceleration * in the coordinate system of your animation, B's center of mass has zero coordinate acceleration * A's center of mass has nonzero proper acceleration * B's center of mass has nonzero proper acceleration In your animation, while A and B are free-falling towards each other: * in the coordinate system of your animation, A's center of mass has a (time-dependent) nonzero coordinate acceleration * in the coordinate system of your animation, B's center of mass has a (time-dependent) nonzero coordinate acceleration * A's center of mass has zero proper acceleration * B's center of mass has zero proper acceleration Notice that I've referred explicitly to A's and B's *center of mass*: both coordinate and proper acceleration are properties of a *point* or an *observer* (more precisely, in GR, a "worldline"). Applying these concepts to an extended body may be ok if the body has negligable self-gravity. But, it's tricky try to apply these concepts to extended bodies with non-negligible self-gravity, precisely because the answer to the question "what's the proper acceleration of this point on the body?" differs from one point to another. But more generally, as Tom Roberts has noted in this thread (and many people have said in past threads in this newsgroup), to learn GR you really need a more extensive treatment than newsgroup discussions. That is, you really need a good textbook or textbooks, and/or a university course or courses. For self-study, my suggestion would be to get copies of several textbooks and work through them in parallel -- often seeing multiple pedagogical treatments can help you better understand what's going on. A few book suggestions (in roughly increasing order of mathematical difficulty): Robert Geroch "General Relativity from A to B" University of Chicago Press, 1981 James B Hartle "Gravity: An Introduction to Einstein's General Relatiity" Cambridge University Press, 2021 Ian R Kenyon "General Relativity" Oxford University Press, 1990 (or you could go for the 2nd edition of this, which includes some cosmology as well as GR) Bernard F Schutz "A First Course in General Relativity", 3rd edition Cambridge University Press, 2022 Sean M Carroll, "Spacetime and Geometry: An Introduction to General Relativity" Addison-Wesley, 2004 Of these, the book by Geroch is notable for being almost completely non-mathematical and for being very cheap. The other books all introduce a certain amount of tensor calculus, because that's what's needed to cleanly present GR. -- jt]]