Measurement Theory in Einstein's General Relativity

From: Jack Sarfatti (sarfatti_at_pacbell.net)
Date: 03/29/05 

Date: Tue, 29 Mar 2005 23:49:49 GMT

If you read first sections of Landau & Lifshitz Ch 10 Classical Theory
of Fields one sees that in Newton's 17th Century gravity theory, that
gravity is a force seen in a Galilean inertial frame F.

There is a Newton potential energy V per unit test mass, where the
universal acceleration on any test particle independent of its mass m
and composition is

g = - GradV

in the inertial frame.

What about the rest frame F' of this test particle. It is, in Newton's
theory non-inertial because V is also giving a force on it so that what
you have is a cancellation

g - g = 0

Z wants to use this same idea in Einstein's GR where the connection
field (LC) is analogous to -GradV in Newton's picture. You cannot do that.

The basic reason you cannot do that is that the very meaning of
"inertial frame" and "non-inertial frame" is exchanged when you pass
from Newton's force picture to Einstein's geometrodynamical picture.

The freely falling test particle is, at any instant, in a LOCAL INERTIAL
FRAME or LIF. The locus of these tiny LIF origins is a timelike
geodesic. The geodesic mean the straightest world line path in 4D curved
space-time. Such a straight line in 4D can be a closed elliptical orbit
in 3D. So this idea of the geodesic in curved space-time is
counter-intuitive to common sense.

What was Newton's "inertial frame" e.g. his lab at Cambridge is
"non-inertial" in Einstein's GR because of the electrical forces of the
Earth's rock as well as the Paul exclusion principle of quantum theory.
See Viki Weisskopf's "Knowledge & Wonder" for details on quantum hardness.

The upshot is that there is no gravity force at all in Einstein's GR
picture. It's a "force without force". Test particles in curved
space-time merely freely fall weightless along the timelike geodesics.
"Timelike" means inside the local invariant light cone from 1905 special
relativity. In common-sense terms all test particles locally move slower
than the speed of light in vacuum.

Thus, you only feel weight, i.e. g-force in a local "accelerated
non-inertial frame" called the LNIF. The locus of origins of LNIF's are
timelike, but they are not geodesic. There is always some other
non-gravity force, electrical most usually, pushing the detectors off a
geodesic.

*When you make the transition from (LNIF) to (LIF) what you do is SWITCH
off ALL non-gravity forces ON THE DETECTORS (not necessarily on the test
particles). The local frames are physically defined by the detectors. So
there is no non-gravity force to compensate the gravity force which is
not even there in Einstein's picture or "paradigm".

(LC) = 0 does NOT mean what Zielinski writes as

Inertial Non-Gravity Force - Gravity Force = 0

with

Inertial Non-Gravity Force =/= 0

Gravity Force =/= 0

That does make sense in Newton's picture.

Because in Einstein's picture

Gravity Force = 0 ALWAYS

Indeed in Einstein's picture

(LC) ~ Inertial Non-Gravity Force on the Local Frame (not on the test
particle)

Therefore (LC) = 0 in any LIF always.

Under a GCT X

(LC) -> (LC)' = XXX(LC) + XY

where Y involves inhomogeneities in X

Now in the Yang-Mills gauge force substratum picture of the above

When the warp B field = 0 (LC) = 0 and the only way to get a (LC)' =/= 0
is to apply a GCT X to it. And even then, you will not get anything
unless Y =/= 0! You cannot get Y =/= 0 unless some non-gravity force
acts on the detectors! We only switch off the non-gravity forces on the
detectors (not on the test particle under observation).

But suppose B =/= 0, i.e. space-time is objectively curved independent
of the 4D coordinates induced by X in GCT.

In that case,

(LNIF) = (I + B)(LIF)(I + B)

(LC) depends on inhomogeneities in (LNIF). Let the subscript "comma" ,
be such an inhomogeneity (ordinary partial derivative)

The (LIF) metric is homogeneous, so that (LC) = 0 in any LIF.

EEP means it is always possible to LOCALLY JUMP to a LIF in which all
non-gravity forces on the detectors are switched off.

Therefore,

(LC) ~ I(LIF)B, + B,(LIF)I + 2BB, =/= 0

The only way now to get (LC)' = 0 is to look for some X' in GCT such that

X'X'X'[I(LIF)B, + B,(LIF)I + 2BB,] + X'Y' = 0

Formally this PARTICULAR choice of X' in GCT is equivalent to finding
the inverse TETRAD operator (I + B)^-1 such that

(LIF) = (I + B)^-1(LNIF)(I + B)^-1

* REMEMBER all of these X transformations are LOCAL, i.e. at FIXED
SPACE-TIME EVENT P that can involve several EQUIVALENT manifold points
p, q ... since an active diff moves p to q =/= p, but such a "move" is
an unphysical gauge transformation like when A -> A' = A + GradChi in
U(1) Maxwell EM.

In Alcubierre warp drive using exotic vacuum repulsive zero point dark
energy the test particle (ship/flying saucer) globally moves
faster-than-light although locally it stands still with no g-force
weight in its local rest frame and also no time dilation with respect to
a twin in the outside universe on a round trip. However, it can, we
think, time travel to the past and future as well as elsewhere - another
story for later.

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