Logic of a Big Bang
The axiom of choice says that an infinite Cartesian product
of non empty sets is non empty.
Set theory with urelements was used to study the negation of
the axiom of choice.
The urelements are non sets and undistinguishable.
Let U be the set of urelements and Ui a set of urelements.
The infinite Cartesian product of U1, U2, U3,............
is empty if the negation of the axiom of choice is applied.
Let us assume that physical space is U with as elements
locations of elementary particles of quantuum cosmology.
When we consider the empty infinite Cartesian product,
space disappears.
The particles collapse upon themselves. It is a Big Crunch.
The Big Crunch is almost immediatly followed by a Big Bang.
There always exist a univers or another.
A Big Crunch will occcur after an infinite time.
Adib Ben Jebara.
http://www.freewebs.com/adibbenjebara(search by Google "negation of the axiom of choice")
Reference :
"About space and time in quantum mechanics" Adib Ben Jebara
Bulletin of Symbolic Logic September 2008 Volume 14,
number 3, pp. 410-411.
In an antanglement, the distance before measurement between
particles is in number of uurelements (number in between +1)
and could be small.
Difference in time itself is in number of urelements and
could be small.
Reference:
"An interpretation about space and time in quantum mechanics"
Adib Ben Jebata The Bulletin of
Symbolic Logic of March 2008 page 154
Regards,
Adib Ben jebara from Tunisia.
