Quick comment on Gubarev's paper that I have only read the first few pages of so far. On the translational equivalence principle - there are several ways to state it.
1. Global Galilean-Newtonian picture: Inside of the Newtonian paradigm where gravity is an external force field that in the Galilean inertial frame can be approximated by the Lagrangian for a NON-ORIENTED point test particle, i.e. the internal relative coordinates are neglected here. They are not neglected in Shipov's torsion theory extension of Einstein's 1916 "translational" GR that only strictly applies to idealized "point" test particles. Einstein's theory only locally gauges the 4 parameter translation group. Einstein, of course, did not think in those modern terms back then. Shipov's theory locally gauges the additional 3 space-space rotations generated by angular momentum and the 3-space-time Lorentz constant velocity boosts. A still further generalization beyond Shipov's extension of 1916 GR would be to locally gauge the 4 conformal boosts of constant proper acceleration to what is called hyperbolic motion in special relativity, and the dilation. This would give dynamical compensating fields to the complete Lie algebra "charges" of the conformal "twistor" group of 4D space-time. Einstein's 1916 plain vanilla GR only locally gauges the four "momenergy" generators of flat spacetime translations whose compensating field is that of the GCT tensor curvature with the non-tensor connection field {LC} as the "potential". The curvature is the 4-D covariant curl of the {LC} connection exactly like the EM tensor Fuv field is the 4D curl of the EM potential Au. The EM potential Au is also a connection field for parallel transport in the internal space beyond 4D spacetime. The {LC} connection is for parallel transport of geometrodynamic fields inside curved spacetime. Getting back now to Newton's simple picture:
L = (1/2)mv^2 - mgz
z is height above surface of the Earth APPROXIMATED as a Galilean inertial frame (neglecting Earth's rotation about its polar axis etc)
One can also consider a uniformly accelerated frame out in deep space far from any sources so that the conformal curvature tensor Cuvwl = 0.
There is an APPROXIMATE equivalence between these to cases so long as one confines one's measurements to the CENTER OF MASS of the test particle of mass m. Obviously Cuvwl =/= 0 near surface of the Earth, which is actually a non-inertial frame in Einstein's paradigm.
Note also that this is a GLOBAL comparison of two physical situations very far apart from each other! Hal Puthoff's PV theory's Table's I & II only have the equivalence principle in this global Galilean - Newtonian sense.
Therefore, in this common way of stating the equivalence principle one is only asserting an approximate correspondence between two situations both really described in terms of Galilean relativity without the complications of special relativity's time dilation, which, in fact, introduces enormous counter-intuitive complications.
2. Within Einstein's paradigm of LOCAL GEOMETRODYNAMICS: "translational" gravity force is abolished. That is the POINT CENTER OF MASS of an extended elastic test particle follows a timelike geodesic in the curved spacetime. Translational inertial forces are zero in this free float weightless "inertial motion".
The motion of a bullet is non-inertial in Newton's paradigm, but is inertial in Einstein's. The surface of the Earth is not even approximately an inertial frame in Einstein's paradigm.
The local laws of nature must be GCT TENSOR transformations, i.e. no preferred coordinates in the LOCAL field equations from the action principle. The CLASSICAL action is an extremal critical point in the bundle of alternative histories of the motion of the system. This corresponds to constructive interference of the micro-quantum Feynman quantum amplitudes. How to extend this to the macro-quantum case, with the breakdown of linearity, nonlocality and unitarity, relevant to Einstein's local nonlinear gravity needs further study.
The tensor laws also contain within them the tetrads which provide a purely LOCAL formulation of the equivalence principle at the SAME point event neighborhood P of a physical event. The "event" has has more structure than merely a point in a manifold.
Consider two observers Alice and Bob in empty space-time (generally curved) this time near a large gravitating source Tuv(matter) =/= 0 in a region near the experiment in a small neighborhood of localized event P. Alice is on a timelike INERTIAL geodesic, Bob is on a timelike NON-INERTIAL geodesic. Bob must be using a non-gravity force to do this. At least a non-gravity "translational" force e.g. ejecting propellent in a rocket, using the Lorentz force on charges, using quantum presssure. Usually, it is all of the above. Alice and Bob are on near collision course, narrowly missing each other, to the degree of coarse-graining of the scale-dependent metric. The LOCAL TETRAD GR formulation of the equivalence principle is
guv(Bob) = eu^aev^bnab(Alice)
nab is the constant INERTIAL LIF geodesic metric of special relativity.
guv is the curved NON-INERTIAL LNIF non-geodesic metric of general relativity.
Geodesics and non-geodesics are DEFINED only relative to the metric {LC} connection from locally gauging ONLY the 4 translations. When adding torsion et-al fields one is also adding to the connection so one must be very clear which group of transformations for "tensors" one is talking about!
On Dec 8, 2004, at 9:21 AM, Jack Sarfatti wrote:
Thanks Gennady - looks good. I will study it. :-)
On Dec 7, 2004, at 8:50 PM, Gennady Shipov wrote:
"Jack and Paul!
I send you work of my pupil - Gubarev Evgeni.
Pay attention to that part of work in which localization of Galilean group
is considered. Localization of Galilean group - is a correct way to pass
from inertial 3-dimensional reference frame in accelerated. Other methods
are limited or incorrect.
From looking briefly at the paper your student seems to come to same conclusion I did with Paul that the idea of uniform gravity g-field for LNIFs is a Galilean approximation needing gz/c^2 << 1.
From Gubarev's work follows, that the correct description accelerated
systems of reference in physics impossible without use of Ricci torsion
fields."
Shipov Gennady.
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