Refuting Zielinski's Conjecture
On Dec 31, 2006, at 7:27 PM, Jack Sarfatti wrote:
Zielinski wrote incorrectly crossing out my correct equation:
> F^aFa torsion field Lagrangian density is local in this Minkowskiab
> Note that the geometrodynamics will still be nonlocal I think.
"Meaning what exactly?"
> ds^2 = guvdx^udx^v = e^aea = (Minkowski)abe^ae^b
"There is no such relationship between the Minkowski and Riemann
metrics. All you can say, even in a completely flat spacetime, is that
at any giv! en space time point both metrics have the same matrix value
*in Lorentz coordinates*."
On the contrary,
ds^2 = guv(curvilinear)dx^udx^v = e^aea = (Minkowski) abe^ae^b
is exact and it is local FRAME invariant.
On Dec 31, 2006, at 6:56 PM, Jack Sarfatti wrote:
It is not possible to define it inside of 1915 GR as anything other than zero.
I gave the proof that you cannot follow. It can be non-zero in Shipov's theory BUT there will still be a NONLOCAL component even then.
Weyl curvature part of gravity vacuum energy is nonlocal, i.e. zero local density yet non-zero global integral even when there is a non-zero local torsion field contribution from FaF^a in the Lagrangian density where
F^a = de^a + W^ac/\e^aTo make this clearer.
"curvilinear" means pure 100% local frame-dependent inertial force effect from non-geodesic motion of the local detectors that define the local frames. In this case there is always a non-gravity force pushing the massive on-mass-shell detector off its natural timelike geodesic inside the local light cone.
"warp" means either intrinsic objective local frame invariant curvature or torsion or both.
There are two kinds of curvature "Ricci" + "Weyl conformal"
Ricci contraction & expansion from a local non-gravity source including virtual zero point quanta of non-gravity fields i.e. both dark energy of negative pressure and dark matter of positive pressure. The latter has w = -1 in isotropic distribution but seen from a distance it gravity lenses light rays just like w = 0 CDM.
Weyl conformal stretch-squeeze. Gravity waves are ripples in the Weyl tensor.
ds^2 = guv(curvilinear + warp)dx^udx^v = (I^a(curvilinear) + A^a(warp))((Ia(curvilinear) + Aa(warp))
Note the cross term between inertial force and intrinsic warp effects. Since the geometrodynamic connection field is essentially for the spin 1 renormalizable e^a fields
it's obvious that one cannot eliminate the cross terms between inertial forces and intrinsic warps at the spin 0,1, 2 geometrodynamic level. Therefore, Zielinski's claim that the 1915 GR symmetric zero torsion LC connection splits into
(LC) = (LC|non-tensor inertial force) + (LC|tensor warp force)
(LC|tensor warp force) =/= 0
is obviously false. The real situation is
(LC) = (LC|non-tensor inertial force) + (LC|tensor warp force) + (LC|tensor warp-inertial force)
(LC|tensor warp force) = 0
because by going to local geodesic coordinates both
(LC|non-tensor inertial force) -> 0
(LC|tensor warp-inertial force) -> 0
separately and independently
and the total (LC) -> 0 from the equivalence principle.
However a tensor = 0 in all components is a local frame-invariant property.
This completes the proof refuting Zielinski's conjecture.
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein