Stephen P. King (email@example.com)
Wed, 13 Oct 1999 01:07:41 -0400
Perhaps I can get a conversation going on the nature of LS
interactions, specifically the nature of the base "space" X into (onto?)
which the LS's are fibered. As Hitoshi has pointed out, there is no
connection defined between the points of X, so I am wondering how we can
recover parallel transport, or at least the illusion thereof.
I have been considering using Weyl's generalization of a Riemannian
manifold (both angles and length are non-integrable) are figuring out if
the "clocking" action of the LSs can act to "partition" (if that is the
correct word ;^)) up the manifold into local space-time manifolds that
appear to be Minkowskian from the "point of view" of individual LSs.
The geometry that Weyl revealed to us is astonishing in its richness;
it is sad that we assume that our local definition of the line integral
is granted such divine status. We need to question the non-local nature
of assuming an absolute length scale for all possible observers. With
LS, we see that each particle has its own clock, what prevents us from
seeing that each has its own gauge?
I believe that the continuous spectrum "problem" is not a problem but a
freedom! If we could show that any given LS can only "see" a finite
subset of the continuum of possible spectra, then perhaps we can advance
another baby step toward the goal.
My thinking is that if LSs are clocks and if we allow for arbitrary
periodicities of these clocks, then we might consider how they might be
synchronized with each other, and it is in these "windows" of
synchronizations that we will recover the needed notions of causality
and interaction between LSs.
I am motivated by the idea of Spinoza of a "pre-ordained harmony" and
Ben's "a priori simplicity", but am considering that instead of using
the initiality concept that such seem to tacitly assume, we use the
concepts involved in co-induction as discussed in Peter's papers, e.g.
greatest fixed points, etc.
My worry is that we are only continuing an error when we continue using
the notion of initiality. In an Eternal and infinite Universe, such as
what Hitoshi envisions, there are no absolute beginnings or endings,
only relative ones. Perhaps the synchronization of clocks, like the
synchronization of musical instruments, gives us a way to metaphorically
think of this world we share in common.
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