**Stephen P. King** (*stephenk1@home.com*)

*Wed, 13 Oct 1999 01:07:41 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 937] Does time really exist?"**Previous message:**Matti Pitkanen: "[time 935] Re: [time 933] Re: [time 931] Re: [time 928] Re: [time 923] Unitarity"

Dear Friends,

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.

Kindest regards,

Stephen

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