My torsion field warp drive-stargate time travel equations.
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  • Jack Sarfatti On Oct 7, 2013, at 6:42 PM, jacksarfattiwrote:

    Sent from my iPhone

    On Oct 7, 2013, at 5:51 PM, Paul Zelinsky <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

    Thus by 1920 Einstein had understood that the g_uv were dynamical properties of a physical vacuum that are not fully determined by matter stress-energy. 

    It's the curvature R that is dynamical (also possibly torsion K in Einstein-Cartan)

    That is the transverse curl part of the spin connection that describes disclination defects aka curvature

    The exact part of the spin connection 1-form

    Sexact = df

    f = 0-form

    (actually a set of 0-forms fIJ where I,J are the LIF indices.

    It's really SIJ and RIJ , but KI and eI

    corresponds to artificial Newtonian gravity fields in Minkowski space

    Technically GR in a nutshell

    e is set of four tetrad Cartan 1-forms

    S is the spin connection 1-form

    The affine metric connection in general is

    A = S + K

    K = De = de + S/e 

    = torsion 2-form - corresponding to dislocation defects in Kleinert's world crystal lattice

    R = DS = dS + S/S 
    = curvature 2-form

    Einstein's 1916 GR is the limit

    K = 0

    Which gives LC = 0 in LIF EEP


    D*R = 0 Bianchi identity

    *R + A^-1e/e/e = k*T = Einstein field equation

    * = Hodge duality operator

    D*(T - A^-1e/e/e) = 0 is local conservation of stress-energy current densities

    Note if there is torsion De = K =/= 0 then we have a direct coupling between matter fields T and the geometrodynamic field K - for warp drive & stargate engineering?

    Einstein Hilbert action density including the cosmological constant A^-1 is the 0 form

    *R/e/e + *A^-1e/e/e/e

    A = area-entropy 

    of our dark energy future cosmological event horizon bounding our causal diamond.

    Gauge transformations (corresponding to general coordinate transformations) are

    d^2 = 0

    S -> S' = S + df'

    S/f = 0

    R = DS --> R' = DS' 

    R' = dS' + S'/S'

    = dS + d^2f' + (S + df')/(S + df')

    = dS + S/S + S/df' + df'/S + df'/df'

    / is antisymmetric

    df'/df' = 0

    (analogous to AxA = 0 in 3-vector analysis cross-product)


    Physically, the GR gauge transformations are

    LNIF(Alice) < ---> LNIF(Bob)

    where Alice and Bob are "coincident" i.e. separations small compared to radii of curvature.

    Zielinski wrote:

    He tried to call this new ether "Machian", but it is hard to see what is Machian about it, other than that the g_uv field is at least partially determined by T_uv. But that is an action-reaction principle, not a Machian relativity of inertia principle. So if this new ether is at all
    "Machian", it is only in the very weak sense that the spacetime geodesics depend on the distribution of matter according to the GR field equations (plus boundary conditions).


    On 10/7/2013 2:46 PM, jack quoted Harvey Brown et-al
    "The growing recognition, on Einstein’s part, of the tension between the field equations in GR and his 1918 version of Mach’s Principle led him, as we have seen, to effectively assign genuine degrees of freedom to the metric field in the general case (not for the Einstein universe). This development finds a clear expression in a 1920 paper,62 where Einstein speaks of the electromagnetic and the gravitational “ether” of GR as in principle different from the ether conceptions of Newton, Hertz, and Lorentz. The new, generally relativistic or “Machian ether”, Einstein says, differs from its predecessors in that it interacts (bedingt und wird bedingt) both with matter and with the state of the ether at neighbouring points.63 There can be little doubt that the discovery of the partial dynamical autonomy of the metric field was an unwelcome surprise for Einstein; that as a devotee of Mach he had been reluctant to accept that the metric field was not, in the end, “conditioned and determined” by the mass-energy-momentum Tμν of matter."
    In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a unified approach to defining integrands over curves, surfaces, volumes, and higher dimensional manifo...
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