lkt@ukc.UUCP (L.K.Turner) (01/28/85)
< Line eater : I aint afraid of no mail -> munch... munch...>
Right all you out in net land get your teeth in this one !
I am confused about mach's principle which is used to describe the effect of
inertia, which is caused by distant galaxies affecting the motion of objects
on earth.
So if I try to move an object , the distant galaxies which attempt to keep a
hold on everything on earth , react to the objects movement and send a back
reaction, causing the object to resist the initial movement.
But if no signals can travel faster than the speed of light , then how does
said object instantaneously know how much it sholud resist my push - how much
inertia it should have ?
If I get enough reponses I will summarise.
Thanks,..
L.K.Turner.
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UUCP: ...!mcvax!ukc!lkt ( L.K.Turner)gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (01/30/85)
Mach's principle was that it should be possible to describe the "forces" on a rotating body in either of two ways, the more interesting of which is to conside the body at rest and the forces as due to the rotation of the rest of the universe w.r.t. the body. Einstein started out a firm believer in Mach's principle but rather lost interest in it (perhaps because it was difficult to show how the effect could be explained in general-relativistic terms). There is no "instantaneous action at a distance" involved, though. Remember that gravitational effects propagate via a field at the speed of light. In all such field theories one has to allow that the field itself can play an active role (e.g. the energy of a solenoid is in its field, which does not "instantaneously collapse" when the current is interrupted).
physics@utcs.UUCP (David Harrison) (02/10/85)
<>
Two points about Mach's principle:
1. The effect is local. The distant stars have created a local curvature
of spacetime (the gravitational field), and when you begin to
accelerate that curvature changes. In fact, given suitable
numbers about the mass distribution of the universe one can
derive F = ma from this effect.
2. There is a difficulty in stating Mach's principle, and many
people (including me) do not believe an accurate statement is
possible. The closest is Mach himself: "The universe is not
twice given." So be careful in believing too literally
statements like 'inertia here is due to mass there', etc.
Dave Harrison
Dept. of Physics
Univ. of Toronto
..utzoo!utcs!physics
..utzoo!utfyzx!harrison (preferred)gwyn@brl-smoke.ARPA (Doug Gwyn ) (03/20/86)
In article <12430@ucbvax.BERKELEY.EDU> desj@brahms.UUCP (David desJardins) writes: >In article <1825@brl-smoke.ARPA> gwyn@brl.ARPA writes: >>The idea that centrifugal force can be explained by the inductive >>effect of all matter in the universe is known as Mach's principle. >>This principle appears to be necessary for any theory that claims >>that there is no absolute motion. > > Am I stupid? I have reread the first sentence above many many times >and can't make any sense out of it. In an empty (flat) universe some >frames are accelerated and some are not. This is in the absence of any >matter. What does "the inductive effect of all matter in the universe" >have to do with centrifugal force?? No, David, there are some subtle issues involved here. The nonlinear system of PDEs that constitutes Einstein's general relativistic field law can be expected to have different solutions for different "boundary conditions". For instance, the original 1915 theory with asymptotically "flat" (Rijkl -> 0) spacetime might be a cosmological model; this particular model happens not to support Mach's principle. For another example, suppose the universe were to have some positive average density of matter; then spinning it around an axis would mean that a humongous amount of mass is being moved, most of it at great distances from the axis. If Mach was right, this would have an effect on local physics, indistinguishable from rotating the local frame in the opposite direction in a static universe. The "inductive effect" appears to actually exist for laboratory-scale mass motions, although it is hard to detect experimentally. Einstein was very much aware of the importance of boundary conditions. Since he (originally) strongly believed in Mach's principle, he looked for ways to make sure it was obeyed. One such attempt was the introduction of the "cosmological term" into the field law; another (not entirely unrelated) was to avoid boundary conditions altogether by imposing topological constraints on the space-time manifold (e.g. closed universe). In my favorite unified field theory, there is no such thing as an empty universe, which nullifies your objection. (This is a prediction of the theory, not an assumption.) Indeed, that theory produces the interesting effect that its universe is locally self-gauging, which has all sorts of ramifications, Mach's principle probably included. P.S. In conventional general relativity, flat => empty but not conversely. P.P.S. A fairly good discussion of Mach's principle from the conventional point of view can be found in Chapter 10 of "Principles of Relativity Physics" by James L. Anderson (Academic Press, 1967).