INTRODUCTORY NOTE The present message has been triggered by a post which accused me of disregarding "decadelong research" on the mental experiment of "Rotating Disk" RD.
But there was never any need to research it and people who did so, were barking up the wrong tree. RD was Einstein's mental experiment which, after having supported the derivation the GR was deposited to archives and, besides historic interest, may be useful only as an intuitive entry point for newbies to GR. Yet, if one pulls it back from archives, one should at least quote it correctly and the paragraph of the involved post misquoted it entirely. It erred, however, in good company. I have googled "Rotating Disk in general relativity" and out of 32 400!! hits have picked up 20 showing some grasp of physics. Not one bears a slightest resemblance to Einstein's train of thoughts. Here we touch a little problem, to wit, Einstein's impatience to run towards new horizons and reluctance to dwell on and to refine the done with steps. Such was the case of quick and dirty derivation of E*MC2, of which Infeld asked me to make a refined version, see: http://findgeorges.com/CORE/F_SPECIAL_RELATIVITY/f5_emc2.html Such was the case of badly muddled "Locality", which I repaired and present in http://findgeorges.com/CORE/D_RATIONAL_VIEW/d1_causality_and_implication.html Such was, finally, the case of the "Rotating Disk", which has never been published else than quick and dirty. Rather than refine, I had to reconstruct it from discussions with Infeld and from a few Einstein's letters. I show this reconstruction in http://findgeorges.com/CORE/G_GENERAL_RELATIVITY/g2_derivation_steps_1_and_2.html http://findgeorges.com/CORE/G_GENERAL_RELATIVITY/g3_derivation_step_3.html http://findgeorges.com/CORE/G_GENERAL_RELATIVITY/g4_derivation_step_4.html NOMENCLATURE In contradiction with his rigorous maths, Einstein was rather careless in metalanguage and muddled some basic terms. He used indifferently "reference object", reference body", "reference system" and the particularly incongruous "reference frame", wrongly suggesting some framework different from contents it encloses. I fall back on the gallicism "referential" dating back to Descartes, understanding by it "physical body" in Einstein's sense, associated with a human observer, or a physical detector. I reserve "reference system" for a system of coordinates describing mathematically the physical referential. A referential may be described by several systems. I distinguish non-accelerating Galilean "Inertial Referential" (IR) and accelerating "Non-Inertial Referential" (NIR). (The RD modifies this, mechanic criterion, see G) below). I use the capitalized "SPACE" to denote an abstract mathematical construct and to distinguish it from its homonym, the "space" of direct perception. COMMENTS I shall comment below on some essential features of the RD, totally ignored by all "research" articles I ever came across. A)NO GRAVITY AT OUTSET. RD mental experiment encompasses several steps. All articles I read present the RD as a single step intended to describe gravity warping SPACE. Yet, Einstein meant at the outset to extend over NIRs the SR restricted to IRs and used for it the simplest NIR, the rotating disk. Talking about gravity at the outset is a nonsense: the rotating disk experiences inertial, centrifugal field. Introducing at this moment the Equivelence Principle and considering the centrifugal field as gravity would request some virtual matter ring enclosing the disk and we know that such a ring does not generate any field inside. We shall see below that gravity is introduced to the rotating disk by inserting in its center a mass point generating a centripetal field. B)TWO DISKS. Rotation does not make sense in Relativity, unless specified with relation to what. RD experiment encompasses TWO disks, one stationary IR and one NIR rotating with respect to the former. As we shall see below, essential physical conclusions are based on comparing the two. C)SPACE. Once finding S>2piR, the inequality increasing with R, we conclude that rotation warps the SPACE into hyperbolic. From that moment confining ourselves in the R/S relation does not make sense and we must consider the whole warped Minkowski SPACE with coordinates: X1: lighttime ct X2: a particular R X3: orthogonal to X2 in the plane of S X4: orthogonal to the plane of S. Consequently, the first rough assumption that X2, perpendicular to rotation, rests unaffected is false. All coordinates are bent, however to a lesser extent than the primary, triggering dilation of X3 (S), so that the hyperbolic SPACE rests valid. D)APPROXIMATION. Exact determination of the SPACE would and its curvature requires some tensor like construct expressing all mutual actions of all 4 dimensions on one another i.e. having 16 dimensions reduced by symmetry to 10, corresponding to the continuum in which GR's curved 4D SPACE is embedded. It's not yet been conceived and in its absence, not only the RD, but the whole GR is an approximation of a virtual 10d cosmology, a bit as a geology restricted to earth surface and ignoring its inside would be. E)DETECTORS. Considering by analogy a fair turntable on which people try to hold against the centrifugal force, RD does not care about the turntable itself, but about what the people experience. Shelving the analogy, RD deals with and compares the experiences of detectors on both disks. F)CORIOLIS ACCELERATION AND EXTERNAL EVENT HORIZON. A free falling detector on the rotating NIR moves towards increasing curvature and thus experiences increasing Coriolis acceleration in the rotation direction. It finds all coordinates tending to infinity and the curvature - assisted by the Coriolis acceleration - faster than any of them. Consequently, detector's speed and trajectory is the relativistic composition of X2 and Coriolis speeds, bend increasingly by the latter in the rotation direction. At the limit, the resulting speed tending to C, the X2 component gets negligible with respect to the Coriolis and the detector turns along the Smax, or the Event Horizon, incapable to traverse it. G)FIELD REPLACING THE GALILEAN ACCELERATION CRITREION. Unlike on the rotating disk, the detector does not experience any force on the stationary, does not fall, stays where it is put and observes Euclidean SPACE. However, rotation being relative, the stationary disk appears to rotate, when seen from the rotating, while the latter appears to itself as stationary. Thus, relative acceleration cannot discriminate between IR and NIR and has to be replaced with the new criterion - the Field. Referential experiencing a field is a NIR, else it's an IR. H)GRAVITY. The RD mental experiment introduces Gravity by inserting in the center of the rotating disk a mass point, which generates a centripetal field of density increasing inversly to R. As the disk keeps on rotating, the inertial centrifugal field increasing with R acts against the gravitational centripetal field decreasing with R, so that they cancel each other at some R0. Thus, we practically distinguish 3 areas: gravitational <<R0, fieldless ~=R0 and inertial >>R0. Now, in the gravitational area -by virtue of G) and the Equivalence Principle the gravity field warps SPACE, -by virtue of C) X2 (R) gets warped with the curvature tending to infinity when approaching the mass singularity, while the tangential speed becomes negligible, keeping S uneffected by Lorentz contraction so that S=2piRe, where Re stands for a virtual Euclidean radius. But the real R is bent, thus longer than Re, so that S<2piR, which defines Riemannian SPACE. I)INTERNAL EVENT HORIZON AND BLACK HOLE. Gravitational area is a sort of inversion of the inertial. A detector falls towards the central mass singularity and moving through increasingly curved SPACE gets deviated by the Coriolis field and at the limit turns around a minimum circumference - the Internal Event Horizon bounding the inaccessible Black Hole. J)EQUIVALENCE PRINCIPLE. >From inside of a referential gravity and inertia fields are indistinguishable. Seen from outside, they may be distinguished by orientation - gravity is centripetal and inertia - centrifugal. Georges. -- You received this message because you are subscribed to the Google Groups "Epistemology" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/epistemology?hl=en.
