Ben Goertzel (ben@goertzel.org)
Mon, 05 Apr 1999 12:35:39 -0400
Hitoshi,
A couple questions on reading of "Theory of Local Times".
I'm not trying to be confrontational, just trying to understand...
The proof of Theorem 2 (p. 11) seems very much a "physicist's proof" and
the mathematician
in me is a little dubious
The assumption of independence seems to me to be pulled out of a hat.
Please explain
where it comes from. I see that it is true that ~generally~, different
parts of the universe are going
to be ~mostly~ independent. But this is different than being able to
rigorously make the assumption,
as an axiom for the derivation of a theorem, that the observing local
system and the observed
local system are DEFINITELY independent.
In fact, quantum nonlocality means that independence is even ~less~ easily
assumed than
one would believe in classical physics.
What am I missing?
In the comments following Theorem 2, you refer to the alternate formulation
of your
theory as a vector bundle theory, involving X x R^6
But, I don't see how this solves the problem. Each point x in X is a point
in GR space, a
macroscopic point, and the copy of R^6 corresponding to x is the local
space of which
x is the centre of mass. Still, this doesn't show that in the REAL
universe, the different
copies of R^6 are going to be independent of each other, even though their
centres of
mass may be interacting.
You say that the L^2 representations of the local spaces are independent --
you mean
by this standard "linear independence", I assume.
But I just don't get how the local spaces can be truly independent while
the centres of
mass interact??
ben
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