The problem of infinities in
cosmological theories is well known. Philosophically speaking the issue of
infinities is interesting especially as cosmologists develop mathematical
models of reality at the largest and smallest scales so far as possible.
The wikipedia article on real numbers
exemplifies the problem of infinities for theories. http://en.wikipedia.org/wiki/Real_number
If one has an x-y two-value coordinate
system with x meaning to go up horizontally and why being a lateral designation
a real number on the arrow of progress that needs to reach its last value
before moving higher never could go anywhere since there is an infinite
potential for extension laterally. There is in other words an infinite number
of real numbers between 1 and 2. It is the Eleatic paradox fully developed.
So what happens when infinities reach
the singularity within the event horizon of a black hole and the black hole
mass under compression of gravity shrinks infinitely forever moving further
toward a perfectly singular point? Regardless of what size it is it can shrink
infinitely farther perhaps. It is no wonder that nature has opted for quantum
mechanical structures instead so that the problem of real number structures for
infinities is limited to manageability.
If the Universe has quantum structures
rather than discrete real characteristics one would think that a consequence of
the individual elements cohering within a unified field. Why such a field as
gravitational-temporal characteristics is a mystery, yet a necessary fact for
the existence of time. What does seem plain is that contemporary theory seems
to assume that space necessarily provides virtual energy for itself in
contradistinction to gravity.
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