On Sunday, January 26, 2020 at 10:08:54 PM UTC-6, Alan Grayson wrote:
>
> When I offered my theory of a hyper-spherical universe, I was accused of
> being "Aristotelian". But why? My primary assumption was IF the universe
> had a start or beginning, that "time" must of been characterized by zero
> volume. My reasoning is that IF had non-zero volume, it must have begun
> *earlier*; hence, this situation wasn't its start or beginning. My
> prejudice, if that's what it is, is that the creation event, if there was
> one, couldn't have "started" without some time-requiring process. So, if
> there was something, rather than nothing at the beginning, the
> time-requiring process must have began *earlier*, thus contradicting the
> idea of a beginning with some thing already existing, say some volume of
> space. The logic here is sort-of a proof by contradiction. Whether you
> agree or not, what has this to do with Aristotle? TIA, AG
>
There is York time τ = 4/3 Tr(K) that measures time according to the
extrinisic curvature of a compact 3-manifold. This measures time according
to the extrinsic time, a curvature defined by the parallel translation of a
normal vector to a 3-manifold K = δN or
dN_i = (∂N_i/∂x^j)dx^j = K_{ij}dx^j,
for K_{ij} the extrinsic curvature tensor. This time parameter has some
conformal properties and is divergent for the volume of the manifold → 0.
This however only works on compact 3-spaces and are not applicable to open
or noncompact spaces.
LC
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