| Topic: |
Science > Physics |
| User: |
"Jack Sarfatti" |
| Date: |
03 Nov 2006 07:02:22 PM |
| Object: |
Einstein's gravity as a local gauge theory |
On Nov 3, 2006, at 2:54 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
On Nov 3, 2006, at 1:58 PM, Paul Zielinski wrote:
CORRECTION:
"...and the non-metric affine connection A that I am using to effect the
decomposition of LC is quantitatively indistinguishable from LC -- I
think you'll eventually get it."
Hogwash - they represent very different physics - from localizing
different physical symmetry groups.
I haven't said anything about local gauging of external symmetry groups
here. Neither is there is any mention of such a thing in 1916 GR.
I know, but you SHOULD! You have not well-posed the problem.
Paul
You do not understand that from the modern POV Einstein's theory is
simply the local gauge theory of the 4-parameter translation group T4.
Of course, Einstein did not know that in 1915. Kibble proved it in 1961!
Your understanding of physics is at least 50 years out of date.
The Levi-Civita connection D in Waldyr's notation is built bilinearly
from the tetrads which are the compensating gauge fields of T4 symmetry
group of the source action.
The rigid global infinitesimal displacement
x^u -> x'^u = x^u + &^u
&^u/x^u << 1
&^u is a CONSTANT PHASE
Think of a crystal. What we have here is a uniform infinitesimal
displacement of each lattice point by the same amount and direction.
This gives from the action principle the local conservation of source
energy-stress current densities.
Tuv^,v(source) = 0
Obviously when you locally gauge T4 you get Einstein's GCTs
i.e.
x^u -> x^u(x^u')
Use Taylor series for the infinitesimal transformation
x^u(x^u') ~ x^u + x^u,u'dx^u'
i.e. the local gauging of T4 is
&^u constant ----> &^u(x^u') = x^u,u'dx^u' = X^uu'dx^u'
This means inhomogeneous small displacements of each lattice point
straining the crystal setting up reactive stress elastic-plastic forces
that correspond to the compensating gauge potentials, i.e. the
CONNECTION FIELD in geometric terms.
A GCT tensor is multilinear in X^u,u' and it's inverse X^u'u
e.g. at fixed LOCAL COINCIDENCE
Tuv = Tu'v'X^u'uX^v'v
etc.
For coincident observers Alice(uv) and Bob(u'v').
What is missing or wrong with Waldyr's program is that if he writes down
a new connection D' associated with Minkowksi metric n instead of the
above T4 connection associated with Einstein's g, then he better specify
which symmetry group is being locally gauged to get D' as the
compensating potential!
Physics DEMANDS that each connection used must emerge from the local
gauging of a symmetry group of the action of a source field. Otherwise
it ain't KOSHER physics even if it's correct pure math!
You guys have forgotten Einstein's remark
"As far as the laws of mathematics refer to reality, they are not
certain; as far as they are certain, they do not refer to
reality."--Albert Einstein
.
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