1.1 Newton's force theory of gravity using Galilean relativity v/c << 1
and weak gravity fields where GM/c^2r << 1

The mass m of the point test particle in the external gravity force
field in flat 3D Euclidean space in a global inertial frame (AKA GIF
good over a large region of space) cancels out of the solution for its
motion. This is the Galilean principle of equivalence. If the test
particle is an extended rigid body then we are talking about the motion
of the center of mass. "Test particle" means we ignore the gravitational
field of the test particle itself in the given external gravitational
force field written in the global inertial frame.

More on the Galilean relativity equivalence principle, which is "an
analogy between the motion of a body in a gravitational field and the
motion of a body not located in any external field, but which is
considered from the point of view of a noninertial system of reference"
(#81 p. 226, Classical Theory of Fields. 1975 Pergamon ed M. Hammermesh).

The force-free geodesic equation for inertial motion of a point test
particle that is not "oriented" in G. Shipov's sense, is

d^2x^i/dt^2 = 0

i = 1,23

The gravity force in Newton's theory is on same footing as the
electrical force - not so in Einstein's theory where gravity force is
eliminated by curved 4D space-time i.e. "force without Force". This
causes confusion, e.g. Z's thesis & Hal Puthoff's "PV" theory. There are
also confusions from common sense Aristotelian relativity notions
discussed by Roger Penrose in "The Road to Reality" Ch 17 Aristotle ->
Galileo -> Newton-Cartan -> Einstein SR -> Einstein GR.

A "noninertial frame" is accelerated in some way including rotation.
Think of a spaceship firing it's rocket engine. That is a local
noninertial frame or LNIF. You only feel weight AKA g-force in
noninertial rest frames. In contrast, an advanced alien flying saucer
with "acceleration field" "G-Engine" "Geodesic Glider" "Vacuum
Propeller" "Warp Drive" is NOT an non-inertial frame but is a free-float
weightless local inertial frame LIF. This is just like the astronauts in
weightless orbit around the Earth with the big difference that the
alleged alien pilots are able to metric engineer their local geodesic
into any direction they desire. They will also be able to manufacture
Star Gates for quick passage to distant parts of our universe as well as
parallel universes next door across hyperspace. With old enough Star
Gates they can also, most likely, time travel to the past of their
starting point.

It is important to see how great minds in theoretical physics think, so
you can tell the difference between skim milk and real cream, between
pseudo-physics (all the "free energy schemes" and most, but not all, of
the "physics" in say Nick Cook's "The Hunt for Zero Point" on flying
saucer propulsion schemes) and physics:

"in an inertial reference system, the free motion of all bodies is
uniform and rectilinear, and if, say, at the initial time their
velocities are the same, they will be the same for all times. Clearly,
therefore, if we consider this motion in a given noninertial system,
then relative to this system all the bodies will move in the same way.
Thus the properties of the motion in a noninertial system are the same
as those in an inertial system in the presence of a gravitational field."

Note, that this last sentence breaks down in the passage from Newton's
force theory in flat space to Einstein's geometrodynamics in curved
spacetime. Hal Puthoff's PV theory is wrong http://www.earthtech.org/ ,
as is Yilmaz's and Z's, because they all fail to notice this subtle
conceptual shift in paradigm. In Einstein's theory the GIFs are replaced
by LIFs in which the gravitational field on the center of mass motion on
the test body is zero even though the tidal stretch-squeeze on extended
test bodies is generally not zero. We need to distinguish REST FRAMES of
the test body, that can be either LIF or LNIF, from EXTERNAL FRAMES,
again either LIF or LNIF that are tracking the motion of the test body.
It is important to realize that in Einstein's general relativity the
equations are LOCAL which means that the LIFs and the LNIFs are
"coincident" with the test body. Of course one can track distant objects
but then one is extrapolating back along the null geodesics of light
signals from the distant objects. "Coincident" in GR means in a
neighborhood of an event P that is small compared to the locally
variable radii of curvature of the fabric of spacetime, which is now a
dynamical variable rather than a fixed RIGID background of some sort as
it is even in Einstein's 1905 Global Special Relativity. Special
relativity is now demoted to only a local approximation, a fact not
recognized in its fullness by Z, Puthoff, Yilmaz & Co.

For example in Einstein's GR the geodesic equation in a locally
coincident LIF is simply

c^2d^2x^u/ds^2 = 0

Here we need to specify initial positions and velocities. If the LIF is,
in addition, the REST FRAME of the point test body then the initial
velocity is zero, also by convention take the initial position as zero.

This same equation in a locally coincident LNIF is

c^2d^2x^u/ds^2 + (LC)^uvw(dx^v/ds)(dx^w/ds) = 0

Where (LC)^uvw(dx^v/ds)(dx^w/ds) are the inertial forces in the LNIF.
They are caused by some non-gravity force F^u acting on the LNIF that is
not acting on the test body. For example, the LNIF may be a rocket ship
in space firing its engine ejecting propellant.

If there is an external electrical force f^u per unit charge on the test
body with charge q forcing it off a geodesic, then in an EXTERNAL LIF

mc^2d^2x^u/ds^2 = qf^u

This same equation in a coincident LNIF is

mc^2d^2x^u/ds^2 + mc^2(LC)^uvw(dx^v/ds)(dx^w/ds) = qf^u

Further if we go to the REST LNIF of this test body

dx^i/ds = 0 for i = 1,2,3

dx^0/ds = 1

d^2x^u/ds^2 = 0

Therefore

mc^2(LC)^i00 = f^i

Weight = mc^2(LC)^i00

Note that (LC) has dimensions 1/Length, where metric tensor guv is
dimensionless.

For neutral bodies there will be mutually induced electric dipole-dipole
Van Der Waal's-Polder forces that are related to the Casimir forces,
which, according to Ian Peterson at University of Coventry UK, cannot
extract energy from the virtual transverse polarized random zero point
photons at all. The only energy they can extract is from the weak
electrostatic forces of the dipoles that come from longitudinal virtual
photons in macro-quantum coherent states that are not random zero point
vacuum fluctuations. Puthoff, according to Peterson, has given a
misleading impression on this point in popular media like Nick Cook's
"Zero Point" book and Aviation Week's "To The Stars" as well as Eric
Davis's USAF funded teleportation study
http://www.fas.org/sgp/eprint/teleport.pdf .





On Dec 26, 2004, at 7:59 PM, Jack Sarfatti wrote:


On Dec 26, 2004, at 7:19 PM, Jack Sarfatti wrote:

Paul
Look at sections 84 & 97 in Landau & Lifshitz Classical Theory of Fields.
More anon.

BTW Landau & Lifshitz from the Soviet Era, in spite of Lysenko, is still
probably the best course, even today in 2004, in "classical" theoretical
physics including the earlier versions of quantum field theory. Better
than Weinberg because it is closer to observation and even in the
English translations the explanations are generally very clear. Better
than MTW in some respects.

Also in 82:

"in the general theory of relativity it is impossible in general to have
a system of bodies which are fixed relative to one another. This result
essentially changes the very concept of a system of reference in the
general theory of relativity, as compared to its meaning in the special
theory. In the latter we meant by a reference system a set of bodies at
rest relative to one another in unchanging relative positions. Such
systems of bodies do not exist in the presence of a variable
gravitational field, and for the exact determination of the position of
a particle in space we must, strictly speaking, have an infinite number
of bodies which fill all space like some sort of 'medium'. Such a system
of bodies with arbitrarily running clocks fixed on them constitutes a
reference system in the general theory of relativity."

Paul you cannot improve on Landau & Lifshitz, they have covered all the
real ground on the classical foundations.

"In connection with the arbitrariness of the choice of reference system,
the laws of nature must be written in the general theory of relativity
in a form which is appropriate to any four dimensional system of
coordinates (or, as one says, in 'covariant' form). This, of course,
does not imply the physical equivalence of all these reference systems
(like the physical equivalence of all inertial reference systems in the
special theory)."

Now Hal Puthoff's PV is not generally covariant in this sense as Hal's
coworker at IAS Austin, Michael Ibison, has written explicitly. This is
basically why Hal's theory is almost universally rejected by all the Top
Guns in spacetime physics down to almost the last man standing. Hal is
basically using the fixed background of special relativity in his action
principle with the variable "dielectric" whose controlled variation is
much too small for the practical metric engineering of Warp, Wormhole
and Weapon (from C^3 to W^3) anyway. That is not how to Make Star Trek
real. PV is not the "Right Stuff" to reach for the stars and beyond.

Note BTW that Landau & Lifshitz explicitly say that non-Cartesian CS are
only for "noninertial reference frames" on p. 228 "Thus, in a
noninertial system of reference, the square of the interval appears as a
quadratic form of a general type in the coordinate differentials, that
is, it has the form

ds^2 = gikdx^idx^k

... Thus, when we use a noninertial system, the four-dimensional
coordinate system ... is curvilinear."

Now there is no way to make such a non-inertial system of reference as
an approximation to "an infinite number of bodies which fill all space
like some sort of 'medium'. Such a system of bodies with arbitrarily
running clocks fixed on them constitutes a reference system in the
general theory of relativity" without non-gravity forces. That is, in a
purely gravitational universe noninertial systems of reference do not
exist! Actually gravity is not a fundamental field at all. It cannot
exist without the electromagnetic field to give it its light cones.
Indeed it also needs quantum theory to emerge as a macro-quantum
coherence effect.