On May 9, 2005, at 9:55 PM, email@example.com wrote:
Jack Sarfatti wrote:
Of course Einstein, Pauli et-al were not aware of this math 75 years ago.
[Z] But I still say the problem is one of objectivity of the definition of gravitational energy, and the recovery of sensible energy-momentum transfer and conservation laws in the "Newtonian" (i.e., slow-motion weak-field) limit of GR.
[JS] You are wrong. This is a completely bogus problem. You are stuck in the primal ooze and it is solidifying - hardening of the conceptual arteries.
This was exactly the problem as it stood in 1918 -- to find a unique objective definition of gravitational energy that would account for energy exchanged between moving gravitational sources and the vacuum, with sensible local conservation laws.
No Paul you (and others) fundamentally misunderstand the problem. Let's just stick with 1916 GR no dark energy /\zpfguv term for simplicity. Everything here IS simple and sensible.
Einstein's local Diff(4)/O(1,3) covariant tensor field equation is simply, to steal from Michio Kaku,
The Universe is a Free Lunch!
Guv + (8piG/c^4)Tuv = 0
This equation means
Stress-Energy Density of Pure Gravity (~ Guv) + Stress-Energy Density of all Sources of Gravity = 0
In simple terms
The total LOCAL energy density of everything vanishes!
FREE LUNCH PRINCIPLE
This even works when there are dark energy sources, i.e. /\zpf =/= 0.
Local conservation of stress-energy density currents is simply the vanishing of the total COVARIANT 4-divergence
Guv^;v + (8piG/c^4)Tuv^;v = 0
The BOGUS PROBLEM here is the (LC)ul^vTlv term. That describes the direct coupling between the curvature and the source field terms!
When there is no Shipov torsion or any other weird stuff like conformal gravity the
Bianchi identities give the INDEPENDENT CONSTRAINT
Guv^;v = 0 ----> Tuv^;v = 0 (local conservation of matter-gravity exchange currents)
but even if we violate them, as we must in practical LOW POWER metric engineering absent in Hal Puthoff's theory, it will not change the FREE LUNCH PRINCIPLE AKA
"Boundary of a boundary vanishes" (Wheeler)
In this theory the total pure gravity stress-energy current density VANISHES exactly in ordinary vacuum where
Tuv = 0
Guv = 0
For some reason Einstein was not happy with this, but he should have been. Everything is trivially locally conserved.
However, what disturbed Einstein & Co 90 years ago was essentially the geon
"Mass without mass" (though Wheeler did not formulate it that way until post Einstein's death.
That is, in multiply-connected manifolds integrating a local zero (closed non-exact Cartan form) on a closed hyperspace (without a boundary) that is ITSELF NOT A BOUNDARY is NOT ZERO!
Einstein surveyed the problem and decided in 1918 that this simply is not the case in GR, and that the energy stored in the gravitational vacuum is non-localizable.
That is correct. It comes from the macro-quantum Bohm-Aharonov nonlocality inherent the influence of global non-trivial topology on the curvature! Cohomology/homology/homotopy structure.
His reason was that there is and can be no objective (i.e. intrinsically
frame-independent) definition in GR of the gravitational vacuum stress-energy at any spacetime point.
No, Paul you have this all confused - very confused.
tuv(gravity) = (c^4/8piG)Guv
end of story
If you try to break this up into a FLAT piece + something, that extra something is NOT a real tensor. But when you think about it this was Einstein's REAL greatest blunder - not the cosmological constant.
I think that was Einstein's definitive word on the matter.
Hogwash. First of all what you said is actually meaningless under critical examination. It is very easy to define the frame invariant tensor which is always ZERO locally in ordinary vacuum. The problem is bogus.
Yilmaz is completely irrelevant. He is asking a BOGUS QUESTION.
Since you don't yet even know what Yilmaz's theory actually is, I think you're jumping the gun here.
Not true. I know enough about it to know it is excess baggage and it is ugly and no one needs it for anything important, which is why no one important in the field does anything with it - for good reason. I did actually look at the Yilmaz papers years ago.
I think Yilmaz has made some interesting discoveries that may well be relevant to the solution of the problem.
I think you are completely off base here, but it's a Free Country.
But of course now you're already convinced that your proposed multiply-connected topology solution is The Solution and that everything else is therefore now a waste of time.
Yes. I have as much interest in Yilmaz's nonsense as in Eric Lerner's who publishes faulty arguments that "The Big Bang Never Happened" - that's all lame crank stuff! In this area the mainstream i.e. Penrose, Thorne, Misner, Schutz,Hawking, Rees, Rindler, Visser, Unruh, Will et-al are completely correct!
Hestenes also thinks he's solved the problem -- but his mathematically sophisticated solution, recently published, has nothing to do with non-trivial spacetime topology.
Good for him. If he is correct, it will be equivalent mathematically to what I have proposed.
The Question is: What is The Question?" Wheeler
Yilmaz & Co is The Blind Leading The Blind - stuck deep inside Plato's Cave.
No, I still think he may have stumbled into something.
Your track record is batting zero.
However, I personally don't agree with Yilmaz's own explanation of
what it is that he has done.
You are wasting your time IMHO.