Applying the negation of the axiom of choice

  Why a Big Bang ?

An equivalent  of the axiom of choice is 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 infinite set of urelements and Ui sets of
urelements associated with elementary pârtiicles. 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 space of quantum cosmology.
When we consider the empty infinite Cartesian product,
space disappears (not a point remains).

The particles collapse upon themselves. It is a Big Crunch.
The Big Crunch is almost immediatly followed by a Big Bang.
Space reappears.

There always exist a universe or another.
Physical space is infinite.
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, North Africa.

At the level of elementary particles, time could be stopped

The assumption is that at the level of elementary partcles,
time is the infinite set of urelements U of the set theory
with urelements (urelements not linearly ordered).

If a particle is at the time u1 and "then" at the lateral
time u2, it could be again at u1 sideways.
Time would have stopped.

Time at the level of elementary particles is not the arrow
of time that we know at our level.

As a result of what could be happening at the level of
elementary particles, there might be disturbances of
time in an area, at our level, like time slowing down.
We cannot go back in time as we cannot jeopardize causality.
 
Adib Ben Jebara.
http://www.freewebs.com/adibbenjebara

Please, a comment. Mainly because of 2 specialities very few
reply.
I thank Mr Andreas Blass, Mr Jeff Rimmel, Mr John Halleck
and Mr John Truss.

About space and time in quantum mechanics

We apply set theory with urelements ZFU to physical space, we consider
locations as urelements, elements of U.
Ui is a subset of U with number of elements n.
XiUi is the infinite cartesian product and a set of paths.
Let us consider the set of paths of all elementary particles-locations
which number is n.
If n is greater than m in CC(2through m), countable choice for k elements
sets k=2 through m, the set of paths will be the void set.
So, physical space would become void, the universe would collapse and a Big
Crunch would happen.
But the matter would have to go somewhere and indeed the Big Bang happened.
So, n is indeed greater than m.

Let us start the set theory ZFU with two infinite sets of
urelements U1 and U2.
Mr Andreas Blass pointed out that their union is U, the usual
set.
Let physical space at the level of elementary particles be U1
and time be U2.
As U2 is not linearly ordered, there is no backwards time
causality.
In quantum mechanics, there are waves which go backward time,
see :
http://www.npl.washington.edu/AV/altvw08.html

But if U2 is time and is not linearly ordered, there is no
traveling backward time.
So, our notion of causality is less jeopardized than with backward time
causality.

May be using U1xU2 for space-time would be still better.

My idea is that Dedekind cardinals are cardinalities for space and for time.
For instance, the time ellapsed since 36 Big Crunches/Big Bangs ago is a
Dedekind cardinal.
The cardinality of the physical space of the previous universe (before the
Big Bang) is a Dedekind cardinal.

The negation of the axiom of choice is really true because it can be
applied in physics.