| Topic: |
Science > Physics |
| User: |
"Jack Sarfatti" |
| Date: |
30 Dec 2004 07:25:38 PM |
| Object: |
The Birth of Einstein's General Relativity |
Metric Engineering Investigations 1.8
Landau & Lifshitz "Classical Theory of Fields" p. 228 explicitly say
that the guv curved metric form is only for a non-inertial frame not an
inertial frame. Since in 82 they are still operating in global special
relativity they do not distinguish global from local noninertial frames
at this stage in their pedagogical exposition:
"Thus, in a noninertial system of reference the square of the interval
appears as a quadratic form of general type in the coordinate
differentials, that is, it has the form
ds^2 = gikdx^idx^k (82.1)
i,k = 0,1,2,3
.... Thus, when we use a noninertial system, the four-dimensional
coordinate system x^0,x^1,x^2,x^3 is curvilinear. The quantities gik,
determining all the geometric properties in each curvilinear system of
coordinates, represent, we say, the space-time metric."
Many mathematicians have careers in relativity without paying attention
to the measurement theory behind the formalism. Each choice of
non-inertial coordinates is a possible physical configuration of
detectors requiring non-gravity forces to sustain. For example, in the
vacuum black hole Schwarzschild solution where, outside the event
horizon where gtt = 0:
gtt = - grr^-1 = (1 - 2GM/c^2r)
2GM/c^2r < 1
Where A = 4pir^2 is area of sphere concentric with origin behind the
event horizon
These are HOVERING REST LNIF observers that must fire their rockets
toward the event horizon to maintain constant r. That is, they must fire
rockets in order to stay still relative to the curvature field. This
would not happen in flat Minkowski spacetime where the rocket would move
away from say a flat Black Monolith from Kubrick's 2001 floating in
space. The one exception seems to be the "curvature without curvature"
effect from a highly unstable antigravitating thin wall of dark energy
given by Vilenken 1983 with Taub's comment that the local conformal
vacuum curvature is zero even though HOVERING observers need to fire
their propellant away from the thin wall in order to keep a fixed
distance from it. R. Kiehn points out that the LC connection field as a
Cartan 1-form like any p-form splits into 3 pieces
Connection 1-form = Exact 1-form + Closed Non-Exact 1-form + Non-Closed
1-Form.
Curvature 2-form = d(Connection 1-form) = d(Non-Closed 1-Form) =/= 0 LOCALLY
However, Kiehn also mentions that the GLOBAL Closed Non-Exact 1-form
describes topological defects like the Wilson loops for the dynamical
nonlocal Bohm-Aharonov phase and presumably the anholonomic Berry phase
that seem to give Taub's "curvature without curvature"? Since the smooth
fabric of curved spacetime emerges from the single-valued local
macro-quantum vacuum coherent world hologram Goldstone phase field with
topological defects from the vanishing of its Higgs amplitude, local
effects with nonlocal causes on the large-scale should be prevalent like
the vortices in superfluid helium. Or so it appears with the dark matter
Galactic Halo and the NASA Pioneer gravity anomaly of homogeneous a_g =
-cH = 10^-7 cm/sec^2 starting 20 AU out from Sun - exactly like an S^2
hedgehog point topological defect in the vacuum coherence at the center
of the Sun (David Thouless "Nonrelativistic Topological Quantum
Mechanics Ch 1).
It is obvious, that in the full context of GR's LOCAL EEP L&L use
"Galilean" the way MTW use "LIF" i.e. "In an inertial reference system,
when we use Cartesian space coordinates, x^1,^2,^3 = x,y,z, and the time
x^0 = ct,
goo = 1, g11 = g22 = g33 = -1, gik = 0 when i =/= k
we call a four-dimensional system with these values of gik 'Galilean'"
p. 228
In Galilean relativity: "A noninertial system of reference is equivalent
to a certain field of force. We now see that in (special) relativistic
mechanics, these (inertial) fields are determined by the quantities gik."
Zielinski has been trying to keep a "Victorian Station Master's" ledger
on just what is the "phony" gravity from the arbitrary contingent
acceleration of the non-inertial frame and what is the "true" gravity
from the non-contingent intrinsic curvature of the fabric of spacetime.
Is that possible?
* Note that our alleged alien super-technologists in their magnificent
unconventional flying machines having their way with us genetically for
thousands of years, we call them Jehovah etc. The Many Masks of The
Wizard of Oz with the Big Black Eyes and the spindly legs and arms
http://stardrive.org/cartoon/bovines.html
http://stardrive.org/cartoon/spectra.html
http://stardrive.org/cartoon/dan.html
http://stardrive.org/cartoon/coffee.html
are able to metric engineer the intrinsic geometry in their geodesic
gliders (AKA "G-Engines" George Trimble, "acceleration fields" Paul
Hill) to their will so that what we think of as "intrinsic" they think
of as "contingent". A similar problem was posed by Eugene Wigner in the
distinction between contingent initial conditions for the early universe
and the intrinsic laws of nature. Wheeler even questions that split in
his "Law without law" that we now see in Lenny Susskind's "Anthropic
Landscape" making a virtue of the vice of M-Theory's lack of
falsifiabilty. To such depths have The Pundits descended. :-)
Now L&L start to shift to the full GR paradigm almost imperceptibly at
first.
"The same applies to 'actual' gravitational fields. Any gravitational
field is just a change in the metric of spacetime as determined by the
quantities gik." In ADM's canonical method gik splits into a spacelike
3-geometry with 3 shift and 1 lapse function (from local gauging of the
translations) to push the time evolution of the geometrodynamic field
3-geometry forward. GCT Diff(4) requires that the physics be independent
of the way of slicing. Also one needs to use an infinite dimensional
superspace where each 3-geometry 3g is a "point". The same is done with
the EM field Fuv in the Bohmian hidden variable version of quantum field
theory. The latter is no good for practical computations however. We
must still fall back on Feynman diagrams for number crunching the sorts
of things Victorian Station Masters want to know. However, as
Mussolini's legacy we must have the trains run on time. ;-)
Enter Einstein's Geometrodynamics (incompatible irreconcilable
differences with Hal Puthoff's PV metric engineering in Eric Davis's
USAF "Teleportation" paper and the NIDS "High Strangeness" UFO paper and
the recent Journal Interplanetary Physics paper etc): "This important
fact means that the geometrical properties of spacetime (its metric) are
determined by physical phenomena, and are not fixed properties of
spacetime."
Note that Alex Poltorak's method of restoring locality to gravity energy
seems to demand a fundamental violation of Einstein's general relativity
principle because Alex invokes a "rigid nondynamical affine connection"
in contrast to the non-rigid dynamical Levi-Civita connection of
Einstein's 1916 GR. I say "seems" because I do not, as yet, understand
what Alex is really proposing.
Zielinski's claim that the Golden Age of Soviet Physics under the aegis
of Landau eschewed Einstein at least in V.A. Fock's "meta-theoretics" is
certainly not justified in Landau & Lifshitz's "The theory of
gravitational fields, constructed on the basis of the theory of
relativity, is called the general theory of relativity. It was
established by Einstein (and finally formulated by him in 1916), and it
represents probably the most beautiful of all existing physical
theories. It is remarkable that it was developed by Einstein in a purely
deductive manner and only later was substantiated by astronomical
observations."
Note that Landau does not say that David Hilbert thought of it first nor
does he say that Einstein's first wife Mileva thought of it first.
.
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