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Why does Gravity Attract?
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Why does Gravity Attract?
Paul Stowe (email@example.com) wrote: Newtonian gravity does not 'predict' instantaneous transmission, it's an assumption that is not part of the equation. Where in F = GMm/r^2 does propagation speed enter? Gerber had already gotten the precession of Mercury by removing this assumption from Newton's correlation in 1898, 17 years before GR. firstname.lastname@example.org (Steve Carlip) writes: This is off the main line of this thread, but I don't want to let this claim pass, especially since Gerber's work is obscure enough that most readers aren't going to know what to make of this. Paul Stowe's statement here is not correct. First, there are two natural ways to put in "noninstantaneous" or "retarded" transmission of gravity in Newton's equations. One is to start with the form F=GMm/r^2 and to specify that r is the time-delayed ("retarded") position of the source. This leads to a loss of conservation of energy and angular momentum and a drastic disagreement with observation---in such a model, the Earth's orbit spirals out from the Sun, and would have been located at the Sun's surface in historical times. (See exercise 12.4 in Lightman et al., _Problem Book in Relativity and Gravitation_.) The second is to start instead with Laplace's equation for the gravitational potential and to change the Laplacian to a d'Alembertian, that is, to require that the potential propagate at the speed of light. This also gives the wrong precession of Mercury's perihelian---it leads to a regression of about 13 seconds per century rather than an advance of 43 seconds. (See exercise 20.8 of Lightman et al.) What Gerber did was to simply assume a rather arbitrary extra velocity dependence of the Newtonian potential---that is, not just that the potential depended on the retarded position, but that it depended in a rather peculiar manner on the velocity of the source. There seems to have been no particular physical justification for this dependence---von Laue concluded that Gerber probably worked backward from the answer, and Pauli characterized it as "completely unsuccessful from the theoretical point of view." In any case, it was not surprising that *someone* came up with a formula that worked. With the discovery that the electromagnetic potential had a velocity dependence, it was natural to guess that the same might be true for gravity, and a dozen or so different functional forms were tried by various physicists (none with any particular physical justification). Gerber was lucky enough to come up with the combination that, in retrospect, we can recognize as the weak field approximation of general relativity. It is also worth mentioning that Gerber's expression for the gravitational potential predicts a substantially wrong (and observationally excluded) deflection of light in a gravitational field. If anyone wants to read more about this, I recommend chapter 6 of Roseveare's book, _Mercury's Perihelion from Le Verrier to Einstein_. In the meantime, rest assured that the advance of Mercury's perihelion is most certainly not an effect of the finite propagation speed of gravity. Paul Stowe (email@example.com) wrote: To get another considerd opinion on this and the related topics that this thread generated, I asked my colleague Barry Mingst to read through this, the 'pseudo' treads and to prove his input. Since he hasn't gotten 'write' ability to the NG straightened out yet he asked me to post his reply. He it is: Barry Mingst wrote: My apologies for not responding directly. My "reply" authority has not yet come in. I would like to address the subject of relativity, aether, and fictitious forces as tied into the thread of "why does gravity attract?" Messrs Fischer, Stowe, Carlip, Meron and others address various issues and make certain claims. 1) Relativity and Newton: The relativistic principle is part of Newton's mechanics. This principle states that it doesn't matter what reference frame you use to measure and interaction. The outcome of the interaction is depends only on the two bodies themselves. This was a revolutionary idea at the time (though Galileo's World Systems concept began the process). The only catch is -- you can't use an accelerating reference frame in Newton's mechanics without fudging the math. As soon as you use an accelerating reference frame for Newton's laws, you have to use "fictitious" forces to make the equations work. An alternate method would be to use a "space" curvature to build in a "tendency" for matter to deviate in predicted ways from Newtonian mechanics without a force. 2) Relativity and Maxwell: Maxwell's equations retain the relativistic principle from Newton. If one examines Maxwell's equations, one finds that the electromagnetic interactions between two matter/energy structures depend solely on the motion and composition of the two structures. Nothing in between has anything to do with it (including the EM "field"). 3) Relativity and Einstein: Einstein's variation on Newtonian relativity (special relativity) is the reaffirmation that measurable physical quantities between two matter/energy bodies were governed solely by their relative velocities. They were not dependent on the motion of anything in between. This was extrapolated from Maxwell's equations (which showed this for electromagnetic phenomena). Special relativity is also limited to non-accelerating reference frames. 4) Accelerated Frames and Relativity: If we choose any non-accelerating frame in any of the above situations, the mechanics works out. F=ma and all that. But if we select an accelerating reference frame, the bodies appear to accelerate without our applying a force! Now in order to describe the actions of the bodies, we also have to take into account the accelerations of our reference frame. In order to "correct" the equations, we usually describe a "fictitious force" to make the dynamics come out right. The two fictitious forces we normally use are centrifugal (disk rotation) and coriolis (sphere rotation) forces. These two forces do not exist in nature. They have nothing to do with matter or energy. They are an artifact of our own human desire to use an accelerating frame of reference for our mathematical calculations -- but to use it as if it were not accelerating. Both of these "forces" are pure inertia in the real world. The "need" for coriolis forces in modelling a flat earth is one of the strongest proofs that the earth really isn't flat. If you model the earth as a rotating sphere, then there is no need for a coriolis force (but the math's harder). For coriolis force, we could just as easily say that the surface of the earth has an additional "sphere-time curvature". Moving objects will appear to accelerate along this curvature without experiencing a true force. Either explanation (fictitious force or curvature) makes the answer come out right -- but both are the wrong base cause of the observed phenomena. 5) Newtonian Gravity: Newton's gravitational force equation is an empirical relation as to what the force must be if the planets are to orbit in their observed fashion. There was and is no underlying theory of gravity or speed of propagation in F=GMM/d^2. This is the force equation that makes Kepler's third law out of Newton's three laws of motion. Functionally, this requires the speed of propagation of gravity to be much, much higher than the orbital speeds of the planets (or you don't get Kepler's third law). It does not require infinite propagation. There is no difference between "inertial" or "gravitational" mass in Newton's equation. G is an experimental constant that works only on "inertial" mass (or you don't get Kepler's law). If there is a difference and a ratio between the two, the difference would be buried in G anyway and we'd never know. 6) Adding Finite Propagation Speed to Newton's Gravity Equation: There are many ways to add finite propagation to Newton's empirical equation. Dr. Carlip mentioned two examples of at least seven major attempts (that I know of) prior to General Relativity. The Ansatze of Lorentz and others have no measurable differences in observed results from GR. Dr. Carlip's examples did, however, point the two major approaches: modify the Newtonian force equation or modify the gravitational "field" potential equation (Laplacian, etc). It's not a problem that Gerber's 1898 try worked backwards to get a "right" equation (and wrong cause?). Newton did the same. So did Plank to create quantum mechanics. So did Einstein to get GR. If you don't have an equation, finding the source is tremendously difficult. Maxwell's equations were one of the very rare derivations from first principles (even though those first principles were Hemholtz' "aether vortices"). It's also not surprising that there were unsuccessful attempts, since there was no underlying theory to start with. 7) General Relativity and Accelerating Reference Frames: General Relativity (GR) was Einstein's attempt to expand into accelerating reference frames. If everything gravitates, then everything is in an accelerating state. Contrary to Dr. Carlip's statement, GR does use a finite gravitational propagation speed to give the precession of Mercury's orbit. That this does not give rise to an increase in orbital speed is a result of the "feedback" built into the matrix of GR equations. GR states that one can represent a "curvature" to space-time that results in apparent (not true) acceleration. GR interprets gravity as a third "fictitious" force. The key is that so long as the answer comes out right, we can't tell whether it's s fictitious force with curvature or a real force without curvature. The math can't tell us. GR was backfit onto Newton's force equation (for sticklers, the expanded gravitational "field" potential) to get the right answers -- that's the "8 pi" part of GR. Just like Newton's equation, GR gives no theoretical "cause" for gravity. There is no explanation of why space is curved by mass. Or a derivation of the propagational speed of space-time curvature (postulated as c). Or a derivation of why objects follow the shortest "geodesics" without any external force. And so long as the answer comes out right why the acrimony? GR can't tell you why it works -- it's still empirical. Use the Ansatze of Lorentz, Minkowski, Sommerfeld, or Mie if you like (the answers are the same as GR). Or try your own hand at creating something new. No one has succeeded in unifying gravity with the other forces yet. The "graviton" theories of gravity are not ridiculed. But these appear to explicitly contradict General Relativity. This is because gravitons would create a "real" force, instead of a fictitious one. According to GR, no force is tolerable (if it REALLY is warping of space). Barry Mingst May 1998