Gravity Force in Newton & Einstein
In other words Paul

In Newton's gravity theory you can explain the weightlessness felt by that freely-falling object as an objective g-force

g = - GradV(Newton)

cancelled by the object's local rest frame fall.

to get

g' = 0 for the object in the object's local rest frame, which in Newton's theory

is NON-INERTIAL because Newton's geodesics for his first law are straight lines without acceleration.

That is you have

Objective g-force - Inertial force = 0 on the parabolic path of the cannon ball for the vertical component because

Einstein's geodesic = Newton's non-geodesic.

But in Einstein's theory the geodesic g-force is zero from the equivalence principle.

There is no objective g-force at all like there is in Newton's theory. Newton's objective g-force in flat Euclidean space with absolute time is replaced by a free-float geodesic in curved space-time! The only "g-force" is felt on a non-geodesic in curved space-time caused by a non-gravity force! You have never understood General Relativity Paul. Your whole short career in relativity has been predicated on attempting to force inappropriate concepts of the earlier smaller theory on the later covering theory - a basic error.
On the formal aspects of Einstein's equivalence principle

i.e. with Einstein-Cartan tetrad fields eu^a

guv = eu^a(Minkowski Flat)abev^b

Define the local frame invariant

e = eu^adx^u&a

e = 1 + L

L is the curved tetrad local invariant

L^a are L's 4 tetrads that Waldyr got all hot and bothered about because he did not like my index-free notation above. This is a symbolic compact notation and is a very useful piece of "mathematical nonsense."

Define the spin connection 1-forms

W^a^b = W^a^budx^u

Or W = W^a^b&a&b

Define symbolically

D = d + W/\ exterior covariant derivative for T4 local gauging

The torsion field 2-form is

T = De = 0 by definition of this limited 1915 GR theory.

i.e.

dL is a 2-form.

In my theory

(Quantum of Area)^1/2dL is the area flux density 2-form A

dL = 2(Quantum of Area)^1/2d@/\d&

where

d(@/\d&) = d@/\d&

d((d@)/\&) = -d@/\d&

Therefore

L ~ @/\d& - d@/\&

is a non-closed 1-form.

This is essentially the World Hologram Ansatz

@ and & are two effective Goldstone phases in 4D space-time projected out of a larger set in hyperspace.

T = de + W/\e = dL + W/\(1 + L) = 0

since d1 = 0

The curvature 2-form is

R = DW

Bianchi identities are

DR = 0

To make a partial analogy with Maxwell's electromagnetism

W is like A

R is like F

dF = 0 is Faraday's law and no magnetic monopoles

But now the analogy breaks down. In Maxwell's theory

d*F = *J are the source Ampere's law and Gauss's law.

d^2*F = d*J = 0 is local current density conservation

The false analogy would be

D*R = *J

but that is not Einstein's source equation.

Rather the Einstein-Hilbert geometrodynamical action density is ~ the 4-form

~ R/\e/\e

The Euler-Lagrange field equation is then for this vacuum case

R/\e = 0 ---> Ruv = 0

D(R/\e) = DR/\e + (-1)^2R/\De = 0

Since zero torsion De = 0

DR = 0

But in general

DR/\e + R/\T = 0



On Aug 2, 2006, at 6:37 PM, Jack Sarfatti wrote:


On Aug 2, 2006, at 5:24 PM, Paul Zielinski wrote:

All the math you need to understand this is F = ma. Jack, you are making things much too complicated.

Einstein said "Physics should be as simple as possible, but not simpler than is possible." Your last remark on "F = ma" is simpler than is possible.

The covariant "F = ma" is the local frame-independent NON-GEODESIC equation

x^u;s;s = F^u/m

in the coincident LNIF

In the coincident LIF x^u;s;s ---> x^u,s,s

However in the REST LNIF (c = 1) of the test particle

{i00} ~ F^i/m is the g-force/mass reaction to the non-gravity force F^i

i = 1,2,3


You are the one making extraordinary claims here Paul not me.

Whereas I think the thesis that an observer-dependent inertial field is the same as an objective physical g-field caused by the presence of matter is, if taken seriously, an extraordinary claim that needs to be justified.

Your statement above is not even wrong. There is no "objective physical g-field" caused by the presence of matter! Therefore, your whole thesis is bogus. You have misunderstood the equivalence principle and Einstein's vision. You have not been able to get outside of Newton's prison. For you it is a prison.

Look Paul you can REPRESENT Einstein's metric field for small M/r (G = c = 1 convention) above Earth's surface as

ds^2 = -(1 - 2M/r)dt^2 + (1 - 2M/r)^-1dr^2 + r^2d(angle)^2

This is only for local LNIF HOVERING NON-GEODESIC OBSERVERS.

When you stand on Earth you are such an observer!

When you get at Earth's surface

g = -M/r^2

that comes from the connection field {uvw} in this hovering LNIF REPRESENTATION

{i00} = -F^i(electric)/m = g

Your "weight" W = m{i00} is the reaction inertial force to the classical electric forces + quantum exchange Pauli Exclusion Principle potentials from the atomic electrons in the ground.

You have compensation only in the HOVERING rest LNIF

g-force + non-gravity force = 0

Actually Bernie Haisch got that part right in one of his wrong "ZPF Origin of Inertia" papers.

In contrast on a geodesic, logically independent of curvature, g-force = 0, i.e. people on geodesics are in free float i.e. weightless whether there is curvature or not! When the curvature gets strong every one feels it whether on geodesics or not! That's the physical meaning of curvature as a tensor field.

In short, there is no such thing as an objective gravity force created by matter in Einstein's geometrodynamics although there is in Newton's theory of gravity. Quantum field theorists speak loosely in a Newtonian way of gravity as a force. This is one reason that "quantum gravity" is muddled.

You can think that way in Newton's theory but not in Einstein's. That is because the two theories have different concepts of "geodesics". Newton's geodesic assumes implicitly flat space-time. Therefore a parabolic path must be caused by an objective g-force in Newton's picture. You are stuck in the 17th Century Paul.