General Relativity Imaged Through The Coney Island of The Non-InertialMind

"Geodesic" means straightest possible path. It's a relative idea
depending on the space.

1. In Newton's 17th Century Theory of Gravity there is an objective
gravity force field.
For example, the conservative gravity potential energy per unit test
mass in Newton's geodesic global inertial frame of reference "the Lab
frame" of Physics 101 for a sphere of mass M is

V(Newton) = - GM/r

The objectively real gravity force per unit test mass is

f(Newton) = - GradV(Newton) = - GM/r^2 pointing radially inward

A freely falling cannon ball is not on a Newtonian geodesic. It is
generally on a parabolic path if it has initial speed perpendicular to
the radial vector with the above f(Newton).



This interpretation changes completely in the switch to Einstein's
General Relativity. Newton's above pure gravity force is completely
eliminated because the path of the freely falling cannon ball is now a
zero acceleration geodesic in the curved space-time. The Lab frame on
surface Earth is not a Global Inertial Frame (GIF) it is a non-geodesic
Local Non-Inertial Frame (LNIF) and the Lab Observer is objectively
accelerating off geodesic from the quantum electrical forces pushing on
him from the Earth's surface.

Locally frame-invariant objective accelerations vanish on geodesics.

Objective accelerations are contingent properties of contingent external
quantun electrodynamical forces acting on the accelerating bodies on
non-geodesic paths. Then and only then are 100% inertial g-forces
detected as when a pilot "pulls g's" in a dogfight or when you step on a
scale to weigh yourself. That is a non-intrinsic historical accident not
a feature of the objective geometry of the curved spacetime.

Objective local frame invariant curved spacetime geometry is 100%
geodesic deviation. It is only the zero objective acceleration geodesic
structure that determines the objective geometry or geometrodynamic
field. The accidental non-geodesics from external electrodynamic
internal symmetry gauge fields have nothing to do with the objective
geometry of the geometrodynamic field. The objectively real
geometrodynamic field is the geodesic deviation tensor curvature field.
That is the deep meaning of the equivalence principle misunderstood even
by some professional physicists.

Now in the counter-intuitive example below from Vilenkin the situation
is as follows.

The metric field guv looks different to different observers. For
geodesic observers the metric field is actually globally flat Minkowski
3 + 1 space-time with zero curvature tensor everywhere except on an
ideal zero thickness spherical 2D deSitter surface lightlike event
horizon of coherent macroquantum vacuum topological vacuum defect that
at time t = -infinity has infinite area. The sphere collapses and at
time t = 0 it stops at a finite area /\^-1 = c^4/g^2 and then reverses
expanding back to infinite area at t = + infinity. This is what the
inertial GEODESIC observers INSIDE the collapsing-expanding vacuum
defect sphere see. For them their spacetime patch is globally flat with
zero 3+1 curvature tensor. The situation is very different for observers
outside the sphere. Their spacetime patch is not globally flat.

Now there is a special class of uniformly non-accelerating LNIF "Rindler
observers" with local frame invariant radial uniform acceleration g for
which the really flat 3 + 1 Minkowski spacetime looks crazy with a
complicated metric field. These observers see a plane wall instead of
the sphere seen by the geodesic observers. If they compute the 3 + 1
curvature tensor they will get zero exactly like the geodesic observers.
If they compute the radial slice they see a 1 + 1 Rindler submetric
field. If they compute along planes parallel to the plane wall they get
a 2 + 1 constant curvature /\ = c^4/g where to these non-inertial
Rindler LNIF observers the geodesic test particles are in an effective
Newtonian potential

V(Newton) = -gx + g^2x^2/2c^2

with illusional "gravity force" per unit test mass

f(Newton) = -dV/dx = +g (repulsive) - (g/c)^2x (attractive)

However, this is artificial because these Rindler LNIF observers must
fire rockets (non gravity forces) to see this crazy artificial metric
field. What they see is not fundamental but a wacky contingency in a
Rube Goldberg contrived situation. The objective geometrodynamic field
inside the deSitter spherical vacuum defect surface of Dirac delta
function singularity is globally flat Minkowski spacetime. The so-called
g-field above is 100% inertial not of fundamental geometrodynamic meaning.

Whenever the 3 + 1 curvature tensor vanishes in a region that region is
Minkowski relative to geodesic local observers. There is no such thing
as a Newtonian-like objective g-force in Einstein's theory ever. Any
curvilinear metric representations that show a uniform g-force in
particular must have zero objective curvature and such curvilinear
representations are 100% illusionary artifacts of firing rockets in
space in nutty ways like looking at an object through a Fun House Mirror
in the Coney Island of a Demented Mind! ;-)

On Aug 23, 2006, at 10:07 PM, Jack Sarfatti wrote:

OK Paul you are right that Vilenkin does say the 3 + 1 curvature tensor
R^uvwl = 0. But this 3 + 1 flat region is not the entire space-time of
the exotic vacuum wall source tensor Tuv.

In fact he says that for inertial geodesic observers in this coordinate
patch that does not cover the whole manifold

ds^2 = dt*^2 - dx*^2 - dy*^2 - dz*^2 Minkowski, but for them the wall
is not flat, it is a sphere!

x*^2 + y*^2 + x*^2 = /\^-1 + t*^2

This vacuum bubble sphere for the geodesic observers is 2 + 1 DeSitter,
it contracts from infinity to a minimum area /\^-1 then re-expands to
infinity with constant acceleration g.

Also the metric in question only covers a fraction of the space-time of
the source.

To review, the t-y,z slice is a 2 +1 DeSitter space. Therefore the 2 + 1
slice "parallel" to the plane is a subspace of constant positive curvature

/\ = g^2/c^4

embedded in the 3 + 1 flat space. So that's fine. No contradiction
there. You can embed a curved subspace in a larger flat space. Also the
1 + 1 x-t slice is flat for a constantly accelerating Rindler observers.
The metric field guv looks different for different sets of observers.

There are 3 separate metric fields here guv(3+1), gu'v'(2+1) & gu"v"(1 +
1) each with their own curvature tensors unto themselves.

We were talking apples and oranges.

The 3 + 1 curvature tensor of guv(3+1) can vanish and the curvature
tensors of subspaces gu'v'(2+1) & gu"v"(1 + 1) not vanish! In particular
the 2 + 1 slice parallel to the planar source is a DeSitter space of
constant positive curvature /\. Its curvature tensor components are
factors in the the larger 3 + 1 curvature tensor that vanishes. The
algebra is complicated but the general idea is simple.

the brachistocrhone problem actually helped Leibniz and Bernoulli
to establish "the" calculus. I'm sure, Newton had to weigh-in
with his cannonballs, but, Who cares?... I mean,
all he did was algebraize Kepler's orbital constraints, although
evidence points to his stealing the 2nd-power law
from what's-his-face (no-one knows, since Sir Duh destroyed all
of his portraits at the Society, which wrote a whole Philosphic Tract,
to obfuscate the basic idea.

Bernoulli's paper is fairly elementary,
even in French.

"Geodesic" means straightest possible path. It's a relative idea
depending on the space.

A freely falling cannon ball is not on a Newtonian geodesic. It is
generally on a parabolic path if it has initial speed perpendicular to
the radial vector with the above f(Newton).

This interpretation changes completely in the switch to Einstein's
General Relativity. Newton's above pure gravity force is completely
eliminated because the path of the freely falling cannon ball is now a
zero acceleration geodesic in the curved space-time. The Lab frame on
surface Earth is not a Global Inertial Frame (GIF) it is a non-geodesic
Local Non-Inertial Frame (LNIF) and the Lab Observer is objectively
accelerating off geodesic from the quantum electrical forces pushing on
him from the Earth's surface.

thus:
but, yeah; that seems like a nice way
to do the isoperimetric problem;
similar to the proof taht all trigona are isoceles?

your first trigon's apex is greater than or less
than 60 degrees?

would it alternate between those cases,
as it gets closer to equigonal?

thus:
to be featured in the next movie,
"Harry Potter's New Crusades and
the 'Public' Charter Schools: Faith-based Initiatives
in the New Millennium CCE: Come the Rapture,
No Child Left Behind!:"
http://larouchepub.com/other/2006/3333uk_scoop_soc.html

--it takes some to jitterbug!
http://members.tripod.com/~american_almanac
http://www.21stcenturysciencetech.co...litude.W05.pdf
http://www.rwgrayprojects.com/synerg...s/plate01.html
http://larouchepub.com/other/2006/33...o_science.html
http://www.wlym.com/pdf/iclc/howthenation.pdf