Sarfatti Lecture in General Relativity of Oct 16, 2013 v1

Jack Sarfatti

Oct 16, 2013 from Jack Sarfatti’s Stargate book under construction
Returning to Wheeler:
1) Equivalence principle
2) Geometry
3) Geodesic equation of motion of point test particles (aka Newton’s 1st Law first-order partial derivatives of the metric tensor field describe fictitious inertial pseudo-forces on the test particle corresponding to real forces on the detector)
4) Intrinsic tensor curvature geodesic deviation (disclinations of vectors parallel transported around closed loops in spacetime) from second order partial derivatives of the metric tensor field describing relative covariant tensor accelerations between two neighboring geodesic test particle each with zero g-force proper acceleration

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Jack Sarfatti One must use the LIF to distill the intrinsic geometry of the real Einstein gravity field. The LNIF is fool’s gold, MAYA, illusion, the shadow on the wall of Plato’s Cave that has ship wrecked many a careless mariner including Isaac Newton listening to the wiles of Circe. The LNIF is contingent random noise, all sound and fury a tale told by an idiot, and believed by sorry bastards, a fairy tale, a mask. Only Einstein escaped the Cave that Newton was trapped in. Of course, Newton had a good excuse. Newton’s “gravity force” is simply the real quantum electrodynamic force sustaining the static LNIFs. It is a fictitious pseudo-force as far as the observed test particle is concerned without any intrinsic objective reality, same ontic status as Coriolis and centrifugal pseudo-forces all parts of the LNIF Levi-Civita Christoffel symbols that depend only on first order partial derivatives of the metric tensor field. Einstein’s equivalence principle (EEP) relegates them to Prospero’s phantoms, the illusions of the Wizard of Oz behind the theater curtain of the world stage.

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Jack Sarfatti There are three levels of the equivalence principle:
1) Weak – uniqueness/universality of free fall known to Galileo – the motion of any freely falling point test particle (or center of mass of an extended object) in vacuum is independent of its composition and structure. “A test particle is … electrically neutral … negligible gravitational binding energy compared to its rest mass … negligible angular momentum … [negligible] inhomogeneities of the gravitational field within its volume … the ratio of inertial mass to the gravitational passive mass is the same for all bodies.” In every LIF the path of a force-free geodesic test particle is a straight line with constant speed in accord with Einstein’s 1905 special theory of relativity that works increasingly well as the scale shrinks compared to the scale of curvature radii until quantum gravity is reached where the curvature field itself has large random zero point quantum fluctuations. Although this scale is thought to be 10-35 meters, the hologram conjecture combined with cosmology give a quantum gravity scale that is twenty powers of ten larger at 10-15 meters ~ (Planck length x area-entropy of our future dark energy de Sitter event horizon) 1/3.
2) Medium strong – metric theories of gravity. Einstein went beyond the weak form to the hypothesis that all the non-gravity laws of physics obey special relativity in a LIF in the same shrinking limit as above.
3) Very strong – replace non-gravity laws of physics with all the laws of physics.
In this book we assume 3) the very strong form as there is no experimental evidence yet that it is false.

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Jack Sarfatti Fermi Normal Coordinates for the LIF’s Image of Intrinsic Geometry
“The metric tensor can indeed be written using the Riemann (curvature) tensor, in a neighborhood of a spacetime event, in a freely falling non-rotating local inertial frame to second order in the separation δxi from the origin” where i,j,k,l are spacelike (outside local light cones with origins at the spacetime event of interest) 1,2,3 indices. The Taylor series expansion to lowest non-vanishing order for the LIF is
g00 ~ - 1 – R0i0jδxiδxj for the gravity redshift
g0k ~ - (2/3)R0ikj δxiδxj for the LIF drag gravimagnetic field
gkl ~ δkl – (1/3)Rkilj δxiδxj for the curved spacelike 3-geometry
Next, consider what the physically coincident LNIF metric looks like including the first order terms that are zero in the LIF. Here u,v,w,z = 1’,2’,3’ for LNIF like i,j,k,l = 1,2,3 for the coincident LIF.
g’0’0’ ~ - 1 – Γu0’0’δxu – R’0’u0’vδxuδxv
g’0’v ~ - Γu0’vδxu - (2/3)R’0’uvw δxuδxw
g’uv ~ δuv - Γwuvδxw – (1/3)R’uwvz δxwδxz
Newton’s gravity force is purely 100% fictitious and corresponds to the first order in separation δxu from the origin of the LNIF Levi-Civita connection Γ terms, which by the equivalence principle, vanish in the physically coincident LIF.
Kornel Lanzcos in “On the Problem of Rotation in the General Theory of Relativity” proved that in any LNIF for test particle rest mass m:
1) mg0’0’-1Γu0’0’ independent of the test particle’s velocity corresponds both to Newton’s gravity fictitious force – GMmr/r3 in the particular contingent choice of the static LNIF and to the centrifugal force mwxwxr in the particular contingent choice of a uniformly rotating LNIF with angular momentum pseudo-vector w along the rotation axis. That we are in the slow speed weak curvature limit is understood.
2) 2mg0’0’-1Γu0’v’dxv/dτ linear in the velocity of the test particle is the Coriolis fictitious force 2mwxv analogous to the magnetic Lorentz force in Maxwell’s electrodynamics and to the vortex force in irrotational hydrodynamics. The Greek symbol τ refers to proper clock time along the world line of the test particle.
3) Finally, mg0’0’-1Γuvw (dxv/dτ) (dxw/dτ) quadratic in the velocity of the test particle is also a fictitious force that has no name and is usually too small to measure.
All of these fictitious forces blow up at horizons where the LNIF g0’0’ vanishes.
The relative covariant tensor acceleration between two freely-falling geodesic test particles each with zero local proper tensor acceleration, is
d2δxα/dt2 ~ Rα0μ0δxμ equation of geodesic deviation

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