Continuing with Paul and the aether issues.......
The point that Paul is making, contra the physics establishment, is that most forms of the equivalence principle (EP) are incorrect..... you cannot nullify the gravitational field by means of a mathematical transformation, or by any other means. IOW, Einstein's elevator has windows. It is not a monad. Is this not a strike against Leibniz?
For the record, let me state the technical issues involved.....
Essentially, the Einstein covariant curvature tensor may be decomposed into its matter-field and free-field components, the Ricci and Weyl tensors, respectively. Unfortunately, the combination of these two components cannot be uniquely defined wrt their mutual boundaries, e.g. on the Earth's surface. This non-uniqueness is related to the hole problem of GTR.
So then we introduce the Levi-Civita Connection (LCC), q.v.......
TBMR, Paul is saying that the non-vanishing of the LCC, it being a first order derivative in the fields, disproves the EP, and thereby provides a 'window' for Einstein's elevator. But how this might relate to the hole/boundary problem presently escapes me.
The LCC is well understood within the physics community, so it's not clear why this violation of the EP is not more widely noted.
Be it further noted that the LCC, in being uniquely defined throughout a given Reimannian manifold, and in providing a basis on which parallel transport may be properly defined, does, itself, provide a mathematical handle on the 'physical' aspect of the gravitational field, which, by definition of 'physical', cannot be made to vanish, even locally, as in an 'elevator'.
Does the LCC, then, provide us with an argument against the positivism of the EP?
And how is positivism not actually an aid to, or a step toward, idealism? How does positivism differ from phenomenology, say? Is it not a form of solipsism?
Ah, yes, and here is, yet, another point that we discussed.......
At one time, Einstein stated, in effect, that the GTR proved Leibniz' relationalist view of space, over Newton's absolutist view. However, this was before the discovery of (matter-) free-field solutions of the Einstein equations.
Do these solutions bring us back to Newton's 'containerized' view of space?
11am-------
So, it is clear that the metaphysical conditions remain foggy, or are becoming increasingly so. This, in itself, could be a sign of the times, or, as the Germans like to say, ze zeitgeist. Postmodernists may revel.
There were, in the conversation with Paul, various metaphysical cross-currents being encountered. And what about the aether vis-a-vis gauge theory......?
Allow me to interject my own observation wrt 'physical' fields.....
Physical fields... electric, gravitational, etc. are best defined in terms of their corresponding 'potentials', which, in the electric case, is simply the voltage.
Now, the (static) electric field is defined in terms of its scalar voltage potential. But the Lorenz invariant (dynamic) E&M field is defined by its four-vector potential, A. Two biggies on the metaphysical side of physics are David Bohm and Yakir Aharanov. Together, they give us the Aharanov-Bohm effect..... to the effect that an electron may be effected by a magnetic field, despite the fact that said field and said electron have no direct, i.e. physical(?), interaction.
But is this not like Newton's problem with Gravitation? How could gravity be subsumed within a mechanistic worldview, when, clearly, it countenanced a 'spooky' action-at-a-distance? I.e. gravity, wrt the 18th century sensibility, was acting telepathically.
Us modern-minded folk, however, now, rather blithely, think in terms of force-fields, and pay no mind to such telepathic spooks, unless it is grandma going bump in the night!
My (chicken) little piece of advice...... beware the mind-field!
Let's start with this..... http://en.wikipedia.org/wiki/Aharonov–Bohm_effect#Significance .
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BTW, yesterday, Cy wrote and emailed an excellent piece on Thomas Jefferson. If it hasn't already been posted elsewhere, on OM, I would like to post it here.
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noon--------
The Aharonov–Bohm effect is important conceptually because it bears on three issues apparent in the recasting of (Maxwell's) classical electromagnetic theory as a gauge theory, which before the advent of quantum mechanics could be argued to be a mathematical reformulation with no physical consequences. The Aharonov–Bohm thought experiments and their experimental realization imply that the issues were not just philosophical.
Hmmm.........
(cont.)
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