About time for elementary particles
I assume some knowledge of the axiom of choice.
Let us start the set theory ZFU (with urelements, non sets)
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.
(Reminder : about space for elementary particles
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.)
Adib Ben Jebara.
http://www.freewebs.com/adibbenjebara
