[quote]
Richard:
Well, true about Mach - he only speculated on inertia's source; and even Einstein used imaginary situations often; but shouldn't a valid theory go beyond these constructs?
So I encourage you, and yes, there will be plenty of opposition from entrenched 'relativists' - so what else is new?
Quote:
|
Now I must confess ignorance about gravitational force being parted and that one such part could vary otherwise than approximately 1/R^2, and would welcome enlightenment...... Regarding the bodies farther vs. nearer issue, my reasoning is based first on the general expectation that if an effect is produced on a body by a body distant from it, a similar body close to it will also produce the same effect. My second general expectation is that any effect that one body may produce on another will be greater when the bodies are close to each other than when they are far apart..... If either of those expectations cannot be taken as generally valid, I would be glad to learn why
|
I believe I already answered this.
The whole point I was making was that you were trying to show Mach to be invalid by using two fallacious arguments:
1. That tidal force was some how involved; (which I think you now recognize is not), and
2. That if Mach is correct, then nearby masses must of necessity result in anisotropic inertial effect.
Can't you see the assumption you are making in #2 ? You are saying first, that you know the equation that governs
how masses interact to originate inertia. (Mach never specified, but only said that there is some interaction that results in inertia).
**Secondly, you are assuming that the small, closely held mass acts to create greater inertial effect than the
mass of the entire universe simply because it is closer.
Let me ask you a question: How close would the rest of the universe have to get before the
inertial effect of the smaller, closer mass becomes negligible?
You can see why an equation is necessary.
Suppose the inertial effect was proportional not only to 1/R but also to the cube of the mass. Would the cube of the mass of the entire universe offset the greater distance?
Having said that, let be more factually specific:
Gravity is a general term referring to the acceleration of bodies due to the presence of matter. It is not required to have 1/R^2 dependence. Indeed, strictly speaking 1/R^2 relation only holds for spherically symetric masses; oblate spheroids, for ex., add another 1/R^4 term.
In fact, General relativity predicts that gravity also results from acceleration of matter linearly through space - the so called gravitomagnetic gravity field. Also called 'frame dragging' effect.
Also, a rotating acceleration of a massive 'shell' also produces acceleration of mass in the interior; the Lens-Thirring effect.
These gravito-magnetic or frame dragging fields, though typically calculated to be very small, (and I believe show 1/R dependence), can be correlated to inertia since they involve accelerations.
Quote:
|
Despite my ill-chosen effort to knock Mach, I’m still not happy with his hypothesis that the remotest of objects cause local inertial effects.
|
Neither am I, but for quite different reason than the illusory ones you suggest. The main problem in reality has to do with its irreconcilability with the finite speed of light, making it impossible for the mass of the entire universe to
instantaneously 'communicate' inertia upon a locally accelerating object.
Quote:
|
However, it is not crucial to my theory that the gravitational force responsible for inertia vary as 1/R^2. 1/sqr(R), 1/R, or 1/R^3 would do as well.
|
Yes, but it is crucial if you are going to try to invalidate Mach; which is what you were trying to do. But in order to do so you will need to ALSO account for mass density, not just radius.
What I suggest is that you forget Mach and go on with trying to establish the 'local' effect; I think you are on the right track there.
I like the concept that motion modifies the gravitational field. It reminds me of electromagnetic radiation reaction force upon the accelerating electron. Are you familiar? I suggest getting the equations and also go over the historical development which is loaded with difficulties, some which are still not satisfactorily answered to date. You'll get some ideas of how to put quantitative analysis into your situation.
BUT let me warn: Simple non-accelerating motion of a massive object is not likely going to be sufficient to account for inertia. The result would be the same effect of which you accused Mach - anisotropy of gravity on one side of a planet in the direction of motion, an effect never detected, though probably easily detectable from satelitte orbits, etc. Gravity doesn't compress on one side simply due to velocity. Even if we speculate the effect is very small, we still see no such effect even in relativistic orbits, say, of neutron stars etc.
Accelerated motion, analogous to the case of electrons, is necessary if you hope to show any correlation of inertia to the 'local' matter field.
G^2 [img]/phpBB/images/smiles/icon_biggrin.gif[/img]
<font size=-1>[ This Message was edited by: Gsquare on 2002-08-30 00:28 ]</font>