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On Apr 3, 2014, at 2:09 PM, Paul Zelinsky  wrote:

"Also, what do you think the Minkowski fiber bundle represents in modern formulations of GR? It represents a local mapping of the curved base space inner products determine by g_uv onto the Minkowski fibers defined by the globally flat Minkowski metric n_uv."
To which I replied:
 
That’s precisely what I mean by LNIF <—> LIF (both local frames COINCIDENT)
 
frame field for LNIF is eu(LNIF) with curvilinear metric guv(LNIF).
 
One can always find LNIFs where in Taylor series about origin 
 
g^u^v(LNIF) ~ n^u^v(Minkowski) + {Levi-Civita Connection}^u^vw&x^w + {Riemann Curvature Tensor}^u^vwl&x^w&x^l + ….
 
ds^2 = guv(LNIF)e^u(LNIF)e^v(LNIF)
 
frame field for LIF (Cartesian coordinates a must as Einstein stipulates in his papers) eI(LIF)  tangent bundle fiber metric Taylor expansion is
 
n^I^J(LIF) = n^I^J(Minkowsk) + {Riemann Curvature Tensor}^I^JKL&x^K&x^L + ….
 
ds^2 = nIJ(LIF)e^I(LIF)e^J(LIF)
 
Small font indices u,v ... are in the LNIF base space
 
Caps I,J are in the LIF fiber
 
The tetrad transformation is
 
e^u(LNIF) = e^uIe^I(LIF) etc.
 
EEP means that
 
{Levi-Civita Connection}^I^JK = 0
 
though in general
 
{Riemann Curvature Tensor}^I^JK =/= 0
 
ARTIFICAL (FIRST ORDER NON-TIDAL) GRAVITY FIELDS IN SENSE OF EINSTEIN AND NEWTON CORRESPOND TO
 
{Levi-Civita Connection}^u^vw =/= 0
 
Riemann Curvature Tensor}^I^JKL = 0
 
REAL GRAVITY FIELDS IN THE SENSE OF MISNER, THORNE AND WHEELER (SECOND ORDER WEYL TIDAL VACUUM + RICCI MATTER COMPRESSION) CORRESPOND TO
 
Riemann Curvature Tensor}^I^JKL =/= 0
 
Note that e^I(LIF) is a set of 4-vectors with components e^Iu
 
e^u(LNIF) is a set of 4-vectors with components e^uI
 
e^uIe^Iv = kronecker delta uv etc. ORTHOGONAL GROUP O(1,3)
 
ds^2 = nIJ(LIF)e^Ie^J = guv(LNIF)e^ue^v
 
LIF Alice and LNIF Bob are COINCIDENT
 
LIF Alice has zero proper acceleration
 
LNIF Bob has non-zero proper acceleration
 
ds is invariant space interval between 2 neighboring events measured simultaneously by both Alice and Bob.
 
Since we impose COINCIDENCE no problem with simultaneity.
 
Also clock postulate that proper acceleration of clocks in LNIF can be synchronized to clocks in LIF if they are coincident.

 

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