The Instantaneous Creation of Infinite Space

From: Perfectly Innocent (perfectlyInnocent_at_as-if.com)
Date: 06/28/04 

Date: 28 Jun 2004 09:29:09 -0700

The 3-space in which we live is one of an infinite variety of possible
geometries. http://arxiv.org/PS_cache/gr-qc/pdf/9804/9804006.pdf. No
mortal can identify the right spatial form. The Big Bang creation
story comes in two incomprehensible versions. No human knows which
version is correct. This thread is a request that knowledgeable
mathematicians answer questions as simply as possible on the very
essence of mathematical cosmology and what is knowable and provable.

The most delightful creation story is that, in an instant, out of
nothing, infinite space suddenly came to be. The infinite and
everywhere appeared instantly, inexplicably; and time was also born.
The second creation story is a plain and simple alternative to the
first. Space (the everywhere) was born finite, with zero volume and
grew from that; and time also came to be.

The birthing of geometry in time has associated with that space and
time, a flow of idealized, mathematical trajectories. Each trajectory
is easily pictured as the spatial trace of an abstract idealized clock
moving effortlessly through that geometric space, parameterized by its
own clock time. Each clock, therefore, is defined by a timelike
geodesic.

The most glaring fact that I see in the simultaneous emergence of
space and time is the existence of the above mentioned global flow of
abstract coordinate clocks, all initially synchronized by God Himself.
Obviously, attempting mathematical physics by coordinatizing space
and time, if space is infinite and flat, can not produce the Lorentz
transformation. It isn't the Creator's choice. It doesn't harmonize
with creation. Going the route of conventional special relativity
would imply that imagining an event at some time in one frame of
reference would necessarily translate to the same event happening
in another frame before time even began. It's against nature.

Imagine the second creation story and the birthing of a hypersphere
(or projective 3-space if you prefer) from an initial inexplicable
point. The symmetry of this space demands a corresponding symmetry in
the global multidirectional flow of abstract coordinate clocks. My
intuition says that this flow is measurable in spacetimes like this,
whereas, the measure of flow would diverge in any spacetime that is
not spatially compact. Am I inquiring about a mathematical object
that's definable or indefinable?

Perhaps the energy-momentum tensor comes to mind. How would you define
with geodesics the scalar quantity analogous to the average number
density?

Is this a Feynman integration problem or is it something easier?
If it's difficult, does the Feynman integral exist in this instance?

Eugene Shubert
http://www.everythingimportant.org

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