Trash "covariance" - all that matters are symmetry groups of the initial
non-gravity source dynamical actions in the pre-inflation "false vacuum"
of eternal chaotic inflation with its continual BIG BANGS making the
parallel pocket universes of the MEGAVERSE.
"Covariance" is what screws up all current attempts at quantum gravity
leading to ridiculous conclusions - like nonlocal gauge invariant
observables. What Einstein originally called "covariance" is simply
locally gauging T4 and keeping the large action with the compensating
warped tetrad field + "matter" invariant by "minimal coupling".
Equivalence principle = minimal coupling of compensating field
UNIVERSALLY generated by T4's total energy-linear momentum
"charges"/"generators" of Lie algebra t4.
Jack Sarfatti
sarfatti@pacbell.net
"If we knew what it was we were doing, it would not be called research,
would it?"
- Albert Einstein
On Nov 14, 2006, at 2:47 AM, Paul Zielinski wrote:
Looks like at least Yuval Ne'eman knows what I'm talking about:
"First — covariance. Is this really a gauge group? For one thing, it
does not have an active mode.
He is not talking about T4 which is really a gauge group.
"Diffeomorphisms" is excess baggage. The actual physics only needs T4
and O(1,3) - T4 alone is enough for 1915 GR. You are missing my point Paul.
Example: a change of scale is a diffeomor-
phism, and GR is indeed passively invariant under such a transformation
(i.e. changing the unit from centimeters to inches), but it is not invariant
under an active physical invariance, such as a doubling of all
distances. The
forces would really weaken, whereas in Weyl’s scale-invariant 1919
theory (or
in Englert’s modern version), they would not. One reason is that Newton’s
constant has dimensions. In Englert’s theory... there is no such constant,
it is replaced by a scalar field (whose vacuun expectation value happens to
have that value, but could take any other)."
"Secondly, mathematically, diffeomorphisms appear equivalent to “gauging
the translations”. Again, although this route has been explored by Cho and
others, I do not consider this as a valid mode because the translations ∂μ
are not covariant and we would not be able to perform active displacements
with them..."
Neeman made a COMMON mistake. Kibble showed how to do it. There is
WIDESPREAD methodological confusion on this, which is why no real
progress in quantum gravity. With the warped tetrads Au^a from locally
gauging T4 to T4* everything works fine!
Given a non-gravity source field Psi
Replace (d/dx^u)Psi by
eu^a(d/dx^a)Psi = (d/dx^u + Au^ad/dx^a)Psi
This is example of minimal coupling!
Note that Pa = -ihd/dx^a are the generators of GLOBAL T4 without
gravity before the local gauging.
is total 4-momentum in globally flat Minkowski space-time where
conservation of energy-momentum makes sense.
"As a matter of fact, gauging the 'modified Poincaré algebra', with
translations
replaced by the AGCT would be a conceptually clean answer, but this also
means that the group we are 'gauging' is not a Lie group with a Lie
algebra.
Its translations subalgebra has four generators — but structure
functions instead
of structure constants. As a result, even the variations of the gauge
potentials
are not [of the usual form] ...; instead, one has an additional piece..."
I don't need no AGCT. Kibble uses UN-modified Poincare algebra. Kibble
(& me) use physical translations.
"The Principle of Covariance is thus not really a physical gauge principle,
You are missing my point Paul. Of course Ne-eman is correct in above phrase.
THAT's WHAT I AM SAYING.
I AM SAYING WE DO NOT NEED COVARIANCE in the full sense. We only need
the simpler more restrictive T4!
but it is certainly mathematically useful. Equivalence, on the other hand,
has many of the attributes of a gauge theory (e.g. universality, a potential
that can be gauged away) but no mathematical derivation. Our third point,
indeed, is that the Lorentz subgroup SL(2,C) ⊂ Diff(R4) (the overline de-
notes the double covering group) is indeed actively implementable. And yet
the dynamical theory, as expressed — our points (a, b) — by the Noether
content of the coupled conserved current is not that of the Lorentz
group. On
the contrary, the relevant current is the energy-momentum tensor, i.e. the
density of the generators of translations, the quotient of the Poincaré
group
by that same Lorentz group! And yet in the implementation of our point
(d), i.e. gauging away the potential, we do have to use the local Lorentz
group!" - p 832
Y. Ne'eman, "Gauge Theories of Gravity", Acta Phys. Polonica B 29
(1998), 827
http://th-www.if.uj.edu.pl/acta/vol29/pdf/v29p0827.pdf
Ne'eman was the man who knew too much and, consequently, did not solve
the problem.
Too much excess math baggage obscures what experiments and observations
suggest and at times demand.
PS I met Ne'eman in 1980 with Max Jammer - interesting story.
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