Saturday, December 18, 2004

Nonlocality in General Relativity

Ah BUT the solution does not cover ALL of spacetime - it's a LOCAL spacetime region - maximal finite proper distance so that Ruvwl =/= 0 outside it. Also it's not an EXACT UNIFORM g-field.

So it shows a kind of Bohm-Aharonov nonlocality in which {LC} =/= 0 where Ruvwl = 0 like A =/= 0 where CurlA = B = 0.

This {LC} is only measured for HOVERING LNIF non-geodesic observers not for geodesic LIF observers.

It's curvature without curvature i.e. A truly NONLOCAL MACRO-QUANTUM EFFECT consistent with NONLOCALITY of pure gravity energy!

So, it is beginning to look to me that Taub's "surprising" result is the gravity analog of the Josephson-Bohm-Aharonov nonlocal effect.

Curvature without curvature? this is the GR nonlocality analog to magnetic field without magnetic field of the Bohm-Aharonov effect also seen in the Josephson effect. That is, both the {LC} connection of gravity and the vector potential fiber connection of electro-magnetism have a nonlocal macro-quantum observability in regions where their respective covariant curls locally vanish!

A distant curved region where conformal Cuvwl =/= 0 makes a non-vanishing {LC} =/= 0 for HOVERING LNIF observers at fixed distance x from unstable vacuum domain wall (repulsive gravity BTW). Normally this would require local conformal vacuum curvature so that non-geodesic LNIF observers can hover at fixed distance from source by applying non-gravity forces (e.g. ejecting propellent - see Kip Thorne's "Black Holes and Time Warps" on hovering near event horizon of a small black hole and see picture in Hawking's "Universe in a Nutshell" of two antipodal LNIF observers accelerating directly away from each other but staying at FIXED separation in curved Schwarzschild spacetime. So what we have here is a NONLOCALITY from the non-trivial topology of the single-valued macro-quantum vacuum local (zero entropy) OLDRO parameter out of which Einstein's Guv + /\zpfguv = 0 emerges.

Vilenken writes "Surprisingly as Taub has shown..." p. 178 Definitely a surprise. The local {LC} =/= 0 is like the Bohm-Aharonov fringe shift where the two paths come together to make an interference pattern.

In any case that's how it's beginning to look to me at this moment. This is one more argument for the macro-quantum physical reality of the nonlocality of pure gravity energy as explained by Roger Penrose in "The Road to Reality".

On Dec 17, 2004, at 8:02 PM, wrote:

Here is a facsimile PDF of Vilenkin's 1983 Article.

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