Friday, May 06, 2005

What are local frames in General Relativity

On May 6, 2005, at 12:33 PM, Jack Sarfatti wrote:

On May 6, 2005, at 12:08 PM, wrote:

This formula was taken from H. Yilmaz, "Toward a Field Theory of Gravitation",
Nuovo Cimento 107B, 941 (1992), p 948.

It has nothing to do with Kaluza-Klein. It is an expression for a derived physical
metric in terms of a flat-background field potential.


Kay zum Felde wrote:One mail about the Yilmaz paper, I got from you had an

That was the formula there:


I thought that phi was something like the dilaton.

It's not because of the uv indices. If it were independent of the uv it would be an over-all conformal dilation, but it's not. I first thought that also. Unless Mike Ibison can explain the physical foundations, the Yilmaz theory is a monstrosity from Dr. Frankenstein.

guv(P) -> guv(P)' = z(P)guv(P)

is a dilation.

No uv on z(P)

Also, Zielinski's confusion on local coordinate charts vs local frames:

The LOCAL REFERENCE FRAME RF at INVARIANT PHYSICAL EVENT P whether timelike geodesic LIF or timelike non-geodesic LNIF is a QUOTIENT STRUCTURE F/~ relative to an EQUIVALENCE RELATION ~ i.e. a set of non-overlapping cosets defined by ~ determined by the physics.

{RF} = {Local Charts at P}/~

~ are the GCTs Xu'^u(P), i.e. overlap transition functions between the local charts in the BASE SPACE of the tangent bundle that is the setting of GR. ~ defines equivalence classes of trivial GCTs that do not have space-time rotations, jerks, snaps, pops, crackles (nonlinear terms) etc, e.g. 3D change from Cartesian to polar i.e. that leave the ARBITRARY INSTANTANEOUS RELATIVE MOTION AT P INVARIANT!


{P} = {p}/~'

Where this other equivalence relation is all the ACTIVE GCTs of Diff(4) p -> p' where p & p' are distinct raw manifold points. That is, the set of distinct PHYSICAL EVENTS {P} is the Quotient Structure

{All Manifold Points}/{Active Diff(4)}

It's the idea of GAUGE FREEDOM applied to space-time rather than internal space! e.g. Faddeev on Yang-Mills theories in internal space - same archetypal idea!

If Alex is proposing GLOBAL FRAMES in GR as Zielinski claims, then that is an error.

No comments: