Stephen P. King (stephenk1@home.com)
Wed, 17 Mar 1999 10:12:20 -0500
Hi all,
A quick note: Can we think of Turing Machines as existing under the
diffeomorphism invariance of GR, as Hitoshi explains it? It seems to me
that the same conditions that prohibit clocks from being definable also
imply that "a infinite length tape divided into square cells..." can
neither be read or written to by a "head which can be in in a finite
number of internal states" iff those cells are infinitesimal invariant
under diffeomorphism transformations!
cf. "Returning to the origin of the problem, i.e. to the idea of
relativity theories, a cause of
the problem of time seems to lie in associating time to each point
which has no positive
size. No clocks can reside in a sizeless point. At the stage of
special theory of relativity,
this difficulty does not appear: Time is associated to each
inertial frame which can
accommodate actual clocks. At the stage of general theory of
relativity, the field
equation with the invariance postulate with respect to
diffeomorphisms requires one to
eliminate the size of the frames in which clocks reside."
Later,
Stephen
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