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Old 9th April 2008, 08:48 AM   #52
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frame dragging: acceleration, rotation ... and velocity

Originally Posted by Ziggurat View Post
Does the precession of Mercury's orbit fall into that category? I haven't heard that it does.
Yep, Mercury's "extra" precession is supposed to be a consequence of spacetime curvature. Some people had already been playing about with the idea of spatial curvature in the C19th, but the big change that happened in the C20th was the realisation that gravity also affected clockrates - so gravity curved "temporal" coordinates as well as "spatial" ones.

Originally Posted by Ziggurat View Post
And how about frame dragging? That wasn't measured in 1986, but it has been now.
Yep. In this model, the frame-dragging idea's taken further (and I'd argue, applied more thoroughly) than it is under SR/GR1915.
Simple accelerational frame-dragging can be argued for, generally, from the Principle of Equivalence and/or from Mach's Principle. If a forcibly-accelerated object feels gee-forces, and feels the apparent acceleration of the outside universe pulling on it, then for background observers watching the accelerated body, they should in turn experience an apparent gravitational effect, too, due to the body exerting a similar effect on them. It should be a mutual thing.

Rotational frame-dragging: ditto. If the relative rotation of a hollow shell of matter around a body causes outward “centrifugal” and sideways “Coriolis” fields in the rotation plane (Mach's principle), then these effects should again be mutual. In a spatially-closed universe, we can take this description and flip it inside out, and treat the outside universe as a solid ball whose surface faces outwards, and the outer surface of our body as an enclosing sphere whose surface faces inwards. The rotation of the universe-ball should therefore increase its overall equatorial attraction, and should also tend to pulls nearby objects around with it (Lense-Thirring effect).
So to someone alongside the equator of a rotating body, the receding section of equator should pull more strongly than the approaching part, but overall, the effect should be an increased equatorial attraction.
These arguments work for both GR1915 and the suggested alternative. Wheeler's already pointed out that to get the standard predictions for the Gravity-Probe B experiment, to the available experimental accuracy, we don't actually need general relativity, we only need to apply what he refers to as the “democratic principle”. If the rotational pull of the outside universe around a satellite and the rotational pull of the Earth below it both get to influence the choice of rotational frame that the satellite's gyros sense as “non-rotating”, and if both “bodies” get to “vote” on this choice of frame according to their contribution to the amount of gravitational flux at the satellite's position, then if we know that ratio, we can calculate the final GPB result as a back-of-an-envelope calculation ("A Journey into Gravity and Spacetime", J.A. Wheeler 1999, p.232-233).

Where the alternative model differs from GR is that it doesn't make a distinction between “gravitational” and “non-gravitational” bodies, it says that if you get close enough, the same effects ought to show up for anything (a tennis ball, a potato, a spaceship). For the “linear acceleration” and “centrifugal field” cases, this doesn't look like a big deal. We can probably get away with applying these to small objects under current theory, and say that since they involve geeforces, if the results ever seem to conflict with special relativity, it's not SR's fault (since SR wasn't derived to “do” gravitation or the Equivalence Principle, or to apply the principle of relativity to noninertial motion).

Where the two models diverge more unambiguously is with the extension of the third case, the “Coriolis” field, to small objects.
If we go back to the case of a rotating body, the receding redshifted parts of the body appear to pull more strongly than the approaching blueshifted parts, even when those parts are otherwise identical. So the Coriolis component suggests the existence of velocity-dependent dragging effects between masses with simple linear relative motion. If we look at strong gravitational bodies, the velocity-dragging argument seems legitimate: it's arguably the basis for the slingshot effect that NASA use to throw space probes around the solar system. It's also highly suggestive of a possible new equivalence principle that would relate all motion shifts to apparent gravitational effects, and associate velocity differentials with lightspeed differentials.

And that's pretty much what I've done: I've started with the general principle of relativity, derived a velocity-dragging effect from it, and used that effect to apply GR-style arguments to create and regulate local lightspeed constancy between bodies with simple relative motion.
Working backwards (and downwards) from GR in this way eliminates the need for a separate "special" theory and gives results like Fizeau's as the consequence of velocity-dragging or gravitomagnetic effects. It also makes for a simpler, cleaner model with fewer separate components and fewer arbitrary distinctions between different classes of effect.

It's the velocity-based frame-dragging effects in this model that allow the elimination of special relativity.

Originally Posted by Ziggurat View Post
As has already been asked, are there any alternative theories which not only explain everything GR does but also explain something GR doesn't?
Well, this one also predicts Hawking radiation from classical principles without needing to append it as a separate QM effect. That's quite handy, I think. Lots of smart people are still trying to work out how to integrate the conflicting GR and QM predictions about black holes, but with this sort of "GR mk2" that doesn't sit on a separate SR layer, there doesn't seem to be a conflict.
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