"equivalence principle" has several meanings.
Formally it is the tetrad idea as in the Rovelli quotes you sent to Kiehn.
zero g-force LIF <-> non-zero g-forceLNIF at same P local coincidence
a lot of confusion sets in about "gravity force" = "weight" in non-inertial frames that should not be confused with curvature. Basically in those discussions the static hovering frames are tacitly meant as when one writes
g00 = 1 - rs/r = - 1/grr
rs/r < 1
so for example
g ~ c^2rs/r^2
is what you need in an off-geodesic LNIF that stands still, as it were, in the curved spacetime in that simplest of metrics.
On Oct 22, 2007, at 6:48 PM, Paul Zielinski wrote:
If Einstein's equivalence principle is the cornerstone, then I think it's important to be clear about what it actually is and what parts of it can still be considered valid in the 1916 theory.
It looks to me that the tetrad model is built around Einstein's version of the principle as presented very clearly by Einstein himself in 1916, and not Pauli's.
Einstein's version, unlike Pauli's, refers to uniform frame acceleration in a Minkowski spacetime.
No, it's more general, i.e. Pauli's. Look what Einstein says informally is not all that he had in mind.
Weight as gravity force (Newton's sense) is always an inertial force in a LNIF off-geodesic independent of the local curvature until and unless you contingently arbitrarily specify the static "shell" (Wheeler) frame which does not always exist. All inertial forces pushing test particles off timelike geodesics require non-gravity forces to create them.
However, in addition to this Mickey Mouse stuff I made a nice picture of quark forces today all from Sakharov's zero point energy induced gravity that is strong on short scale in 3D space - none of this extra-dimensional nonsense needed for this experimental problem - enough of excess mathematical baggage! Remember Feynman's "a beautiful theory is murdered by an ugly fact" - see Lee Smolin's "The Trouble With Physics" for examples.
Imagine two point monopole defects connected by a string "vortex" defect". By "defect" I mean Goldstone phase singularities (Michael Berry's term) in the several real Higgs fields of the vacuum. The "cores" of the point defects (the quarks) are spherically symmetric with uniform negative zero point energy density giving the induced Sakharov gravity potential energy per unit mass of
V(monopole quark) = -c^2(r/Lp*)^2
out to the coherence "annealing" length within which the quark force per unit mass is
f(UV) ~ c^2r/Lp*^2 -> 0 as r = distance between two point defects -> 0
this is UV "asymptotic freedom"
In the opposite IR limit of "confinement" assume that the zero point energy density in the line vortex core falls off as 1/Lp*r
f(IR) ~ c^2/Lp*
similar to the cosmic dark energy repulsion (but of different sign)
g(accelerating universe) ~ cH ~ 1 nanometer/sec^2 - same as Pioneer anomaly, but in opposite direction?
Note the UNIFORM large-scale dark energy density corresponds to /\zpf ~ 1/(Hubble radius)^2
i.e. V(cosmic) ~ c^2r^2/(Hubble)^2
~ c^2r/(Hubble)^2 ~ c^2/(Hubble) on large scale
compare to the IR quark force of similar origin c^2/Lp*
Newton saw the equivalence of the falling apple to the motion of the planets.
Sarfatti saw the equivalence of the quark force to the accelerating universe!
Supersymmetry? Extra dimensions? we don't need no damn supersymmetries and extra dimensions! ;-)
(well maybe we do :-))