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On Aug 6, 2011, at 6:12 PM, Paul Zielinski wrote:
Sent: Sat, August 6, 2011 3:47:20 PM
Subject: Re: What Sciama means by the "origin of inertia" & Woodward's Interstellar Star Ship Time-Space Solution
It's all Zielinski's fault! :-)
Now that I read Sciama 1952 & 1969 I understand what Sciama means by "origin of inertia". He simply means deriving the geodesic structure of the entire spacetime history. Geodesics describe the universal (independent of rest mass) zero g-force "inertial motion" of neutral test particles - the very beginning of Sciama's 1952 paper. Sciama never claims to be able to derive the rest mass of the electron to be 10^-27 grams for example.
Let me explain how Mach's Principle is irrelevant in the modern local gauge theory.
Einstein's 1916 GR is simply 1905 SR when the rigid 4 parameter translation group T4 is locally gauged to T4(x).
Passive T4(x) gives you GCTs, active T4(x) gives you curved geometry. Right?
Wrong. There is no physical difference at all. You are confusing active with dynamical.
See Rovelli Ch 2 he explains that active & passive are simply two ways of looking at the same thing - the main thing are the gauge orbits (all solutions of field equations connected by elements of the gauge group are physically identical - gauge freedom is redundancy in the physical description explained e.g. by Dirac - it's also the solution of the Einstein hole problem).
active T4(x) does not change tensor fields.
You are looking for Kleinert's "multi-valued gauge transformations" - there it's the singularities that represent new physical differences. The T4(x) gauge transformations are not singular. All the solutions they connect are different representations of the same invariant dynamical configuration of fields as seen by different sets of detectors.
These are the general coordinate transformation which are gauge transformations just like in electromagnetism.rt But coordinate transformations can't change the intrinsic geometry!

If you're starting with a flat Minkowski spacetime, how can locally gaugiing passive T4 -> T4(x) give you the curved geometry of GR?
It doesn't. You misunderstand. The localization of the group is NOT the same as the gauge transformations. The tetrads e^I are induced by the local gauging T4 --> T4(x). They are gauge invariants under the GCT gauge transformations.
You got things garbled.
e^I (LIF) = e^Iue^u(LNIF)
the T4(x) gauge transformation is the GCT
e^Iu' = Xu'^ue^Iu
this is all in Rovelli Ch 2 very clearly explained.
All solutions of the field equations connected by local gauge transformation represent the same physical space-time! The same physics.
True if you're talking about passive T4. But then why not just go straight to Diff(R^4)? Why do we need to locally gauge passive T4 anyway? What does it add to the usual approach?

All the solutions are on the same gauge orbit correspond to what different sets of detectors measure when each is in an arbitrary world line that does not need to be a timelike geodesic. They can be in rocket ships in space firing their engines. See Rovelli Ch 2 Quantum Gravity free online.
The four LIF Cartan tetrad 1-forms and their six spin-connection 1-forms are induced by the local gauging and restore the symmetry to the enlarged system of matter + gravity. It's very beautiful and same idea as in the other electromagnetic - weak - strong forces. This is a real conceptual unification. The local gauge principle is simply Einstein's locality i.e. no signals outside the light cone. All of this ignores quantum theory entanglement of course - it's classical. With signal locality there is no conflict with quantum theory - what Abner Shimony calls "passion at a distance."
What this appears to boil down to is cancelling the physical manifestations of intrinsic curvature with GCTs -- which is just a "fancy shmancy" restatement of Einstein equivalence.

In the plain vanilla 1916 formalism the LC connection field locally cancels in free fall. Same thing. Same wine in different mathematical bottles.
The equivalence principle simply means universal minimal coupling of the gravity field tetrads to all the prior matter fields.
No it has to mean more than that if local gauging is to make theoretic sense Jack. How can one restore geometric symmetry by applying a GCT? Locally or otherwise?
Mathematically at least this is nonsense.

I have no idea what your sentences here mean. I never wrote that a GCT restores the symmetry. You got things garbled again. Its the induced tetrads e^I for the geodesic LIFs that restores the symmetry to the original matter field with the new gauge force connection in the larger configuration space. These induced tetrads are GAUGE INVARIANT "scalars" under the GCT gauge transformations.
That said, it's all "interior bulk physics" in the sense of the hologram virtual universe conjecture where we are retrocausal computations of the VALIS computer (see Seth Lloyd on event horizons as computers) at the future edge of time - the dark energy de Sitter future horizon. This brings back a super-strong Mach's principle using the ideas of Wheeler-Feynman -> Hoyle-Narlikar -> Cramer's transaction -> Aharonov's Destiny Vector. But this is really speculative. Will say no more about it here.
Far out.

For example, to couple the electromagnetic vector potential AI(LIF) from 1905 SR to 1916 GR with the 16 tetrad components (gravity field LNIF)
Au(LNIF) = eu^I(tetrad)AI(LIF)
For the Dirac spinor electron the universal EEP minimal coupling of say the electron to gravity is
Du(LNIF) = eu^IPI(LIF) + (Spin Connection)u^I^JPIJ(LIF)
=  generally covariant partial derivative matrix operator on the spinor Psi multi-component column vector
there are 24 spin connection components connecting the LIF to the coincident LNIF in accord with the EEP.

OK. Spin connection is a kind of covariant derivative.

Where PIJ is the appropriate matrix representation of the 6-parameter Lorentz group's Lie algebra acting on the spinor quantized field operator & PI are the Lie algebra of T4 (energy-momentum) together they are the Lie algebra of the Poincare group that form the global symmetries of 1905 SR.
OK this all seems to work formally, but why?
Local gauge principle.

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