Space Force Academy
The whole idea of the practical metric engineering the fabric of spacetime to reverse engineer the alleged alien time travel ships from our future through the Star Gate(s) is to control the flying saucer's timelike geodesic from inside the saucer using tiny amounts of power.
"The Question is: What is The Question?" John Archibald Wheeler
Metric Engineering Investigations 1.5
Again L&L here only address Galilean relativity and Newton's gravity force theory in global inertial and noninertial frames. Much of this, but not all, will carry over to Einstein's geometrodynamics in which there are no global frames, except in very special solutions like the large-scale FRW cosmology solution. Local physics is in terms of COINCIDENT LIFs and LNIFs and there is NO GRAVITY FORCE in the sense of Newton. Newton's gravity force in flat 3D space is eliminated, replaced by WEIGHTLESS geodesic inertial motion in curved 4D space-time. John Wheeler's extended idea of geometrodynamics is that all elementary particles are sourceless curved vacuum solution with non-trivial topology and trapped quantized gauge force fluxes like vortices in superfluids and superconductors. These tiny wormholes would be Bohm's hidden variables guided by micro-quantum qubit pilot waves. They would exist both transiently off-mass-shell and more stably on-mass-shell in sense of micro-quantum field theory. Therefore, dynamical topology change is required. One also needs a strong short scale gravity field G* ~ 10^40G on scale of 1 fermi and smaller. This may be provided by the dark energy residue not absorbed into the Higgs-Goldstone macro-quantum vacuum coherence local field whose single-valuedness requires topological defects like are seen in the Pioneer Anomaly a_g = -cH back to Sun starting at 20 AU that fits the hedgehog configuration where the vacuum coherence is in a S^2 order parameter space. Various species of topological defects in the vacuum coherence would be essential to galaxy and star formation. It may be that ALL STARS have this hedgehog topological defect that the NASA Pioneers are showing for our Sun? Why should the Sun be special in that particular? See David Thouless's book on topological quantum theory for more on the hedgehog that fits the NASA Pioneer data perfectly with a plausible dark energy field between the two spherical boundaries concentric with the Sun. Where the outer boundary ends has not been measured yet. The inner boundary starts at 20 AU out from the Sun.
"Actual" vs "Fake" Gravity in Newton's Theory.
Therefore, in the flat 3D-space Galilean relativity with absolute simultaneity and the instant action at a distance of Newton's non-retarded gravity Force theory pre-1905 special relativity:
"However, the fields to which noninertial reference systems are equivalent are not completely identical with 'actual' gravitational fields which occur also in inertial frames. For there is a very essential difference with respect to their behavior at infinity. At infinite distances from the bodies producing the field, 'actual' gravitational fields always go to zero. Contrary to this, the fields to which noninertial frames are equivalent increase without limit at infinity, or, in any event, remain finite ... for example, the centrifugal force which appears in a rotating frame of reference increases without limit as we move away from the axis of rotation; the field to which a reference frame in accelerated linear motion is equivalent is the same over all space and also at infinity. The fields to which noninertial systems are equivalent vanish as soon as we transform to an inertial system. In contrast to this, 'actual' gravitational fields (existing also in an inertial reference frame) cannot be eliminated by any choice of reference system. This is already clear from what has been said above concerning the difference in conditions at infinity between 'actual' gravitational fields and fields to which noninertial systems are equivalent; since the latter do not approach zero at infinity, it is clear that it is impossible by any choice of reference frame to eliminate an 'actual' field since it vanishes at infinity."
Note how L&L hammer on this point of the importance of the global boundary condition in addition to the LOCAL Galilean equivalence principle. The elimination of Newton's actual gravity force in an inertial frame over a small region is done by switching to a local noninertial frame. This is completely opposite to Einstein's general relativity of course. So keep that cognitive dissonance, that "creative tension" (Ray Chiao) of the "identity of opposites" in mind.
"All that can be done by a suitable choice of reference system is to eliminate the gravitational field in a given region of space, sufficiently small so that the field can be considered uniform over it. This can be done by choosing a system in accelerated motion, the acceleration of which is equal to that which would be acquired by a particle placed in the region of the field which we are considering." p. 227
Now Zielinski is attempting to impose this Newtonian conception on Einstein's and, obviously as will become progressively apparent below, that is impossible and deeply offends Einstein's great Gestalt Shift on the creative tension between "inertial" and "noninertial". Noninertial non-geodesic gravity motion in Newtonian-Galilean flat 3D-space is inertial force-free weightless gravity geodesic motion in curved 4D spacetime. Indeed, Hal Puthoff's PV theory attempting to adapt 1905 Einstein special relativity to gravity, that Einstein soon gave up on 1910 - 1915, suffers from that same defect as Zielinski's doomed attempt.
L&L Then give an example writing the Lagrangian L of a test particle m in an inertial frame
L = mv^2/2 - mV (81.1)
dv/dt = - gradV (81.2)
where in a small region of space approximately
V ~ gz
z = height above Earth's surface. Earth's surface is here approximated as a inertial frame neglecting its rotation. Of course one cannot do that in Einstein's general relativity since a fixed point on Earth's surface is on a non-geodesic world line in curved 4D spacetime.
dv/dt ~ -g
"It does not contain the mass or any other constant characterizing the properties of the particle; this is the mathematical expression of the basic property of gravitational fields."
This universality, i.e. the irrelevance of any other constant characterizing the properties of the particle" allowed Einstein to eliminate gravity Force completely by shifting out attention away from flat 3D space to curved 4D spacetime. Now you cannot do that for the electromagnetic force in 4D. You can sort of do it however if you add one additional space dimension (Kaluza-Klein) which is the precursor of string theory now called M-Theory still highly speculative and possibly not falsifiable making it into a Cargo Cult pseudo-physics of seductive mathematical beauty no doubt, but not even wrong all the same. However The Fat Lady has not yet sung on M-Theory.