RP@MIT-MC@sri-unix (08/11/82)
From: Richard Pavelle <RP at MIT-MC> It seems the necessary arguments have been given for the finite propogation speed of gravity. Let me add some comments: (I am purposely oversimplifiying some things below so no nit-picking please) As in the electromagnetic case, gravitational radiation has two modes. There is a radiative field and an inductive field. The kind of radiation supposedly measured by Joe Weber and company is radiative caused by some non-spherically symmetric large scale event and predicted by Einstein's general relativity. Weber's detectors were sufficiently sensitive to detect the inductive field caused by the gravitational field of trucks passing by. Both fields propogate with velocity C. On a related matter, in the 1890's there was a high school teacher in Germany by the name of Paul Gerber. He theorized that the gravitational potential was velocity dependent. He was interested in explaining the anomalous advance of the perihelion of Mercury (the 43 seconds/century unaccounted for by Newtonian theory). He reasoned as follows: Suppose that in an elliptical orbit such as Mercury's the gravitational force increases more than the 1/r^2 factor when the planet is approaching the sun owing to a velocity dependent potential. Then the planet speeds up more than one expects at perihelion and slows down more at aphelion. He published several papers on this and came up with a remarkable differential equation from the equations of motion. Standard general relativity gives the orbital equation as u'' + u - m/h^2 = 3 m u^2 where u=1/r and r is radial component, ' is differentiation with respect to the angular variable in polar coordinates, m is the gravitational mass of the attracting body, and h is angular velocity of the planet. Gerber found the following: u'' + u - m/h^2 = - 6 m u u'' The left hand sides are the classical Newtonian equations for the inverse square law while the right hand sides represent the theories "perturbing term". An interesting point is that both differential equations give precisely the same value for the advance of the perihelion of Mercury (to order m^2 the solutions are identical). And note, Gerber gave this some 20 years before Einstein! Pauli (Theory of Relativity, Page 169) dismisses poor Gerber in 6 lines. One bad aspect of Gerber's theory is that it cannot predict an anomolous (non-classical) effect for a circular orbit whereas general relativity does. However, for anyone who is interested, Gerber's papers have alot of equations that look like those of special relativity and general relativity. Any interested persons can contact me directly for references, etc.