The Big Crunch will happen after an infinite time
The collapse of the universe will happen after an infinite time.
For that, a singularity has to happen and I think no space (the
void set) must have a part in it.
We have seen that time can be infinite in "An idea about time in
cosmology" in ASL Annual Meeting 2OO4.
We have also seen that space at the level of elementary particles
can be described with only a particular case of the axiom of
choice holding, countable choice for a family of sets of n elements
n=2 through m ,in "About space and time of elementary particles"
in ASL Annual Meeting 2005 and in "About space being not a
continuum" in Logic Colloquium 2005.
No space (the void set) cannot be reached by a finite number of
times but by infinite Cartesian products of sets of locations.
The void set will be supplemented with particles and it will not
be the void set any more but without there being space.
Then, it will be again the singularity of the Big Bang which
creates space.
To explain more, in my view, space is the set U of urelements (non
sets) of a Fraenkel Mostowski model and the Big Crunch will occur
because of what happens with such a space.
The connection between that specific set theory and physical space
is my thesis, at the level of elementary particles.
The conclusion of the Big Crunch happening holds because bodies
are made of elementary particles.
The actual infinite means that the Big Crunch will really happen.
We have to notice that time can be countable or of the cardinality
of the set of urelements U or a continuum, like space can
be of the cardinality of U or a continuum, in different cases.
Adib Ben Jebara
