About space and
time of elementary particles : Introduction
The subject of
space and time of elementary particles is at the intersection of physics,
mathematics and
philosophy of science.
It was not
approached before because we are in an Age of partioning.
And also because
conjectures are not welcome, only evidence is.
What is difficult
to understand in the subject is the mathematical axiom of choice of
set theory as it
is applied or rather its negation.
The existence of a
second component of time at the level of elementary particles
is an idea which
did not occur to me directly.
I started by
trying to explain the Big Bang in quantum cosmology by introducing
more mathematics
for time and starting from scratch.
That was some 15
years ago while working in a company and corresponding with
Mr Andreas Blass.
The existence of
the Big Bang still meets undue skepticism with some people.
The existence of
the Big Bang is deduced by me from the existence of a Big Crunch
(collapsing) as
the Big Bang follows the Big Crunch.
And my idea of
space and time at the level of elementary is checked by the existence
of the Big Bang.
The Big Bang
following a Big Crunch is an idea quickly considered in 1930 by Einstein
who did not look
for arguments.
My argument is
from mathematical modeling or rather mathematical explanation as
space and time are
treated as mathematical variables.
The subject can be
applied to teleportation of elementary particles and then to groups
of elementay
particles.
Teleportation
where particles are not replaced by others with the same caracteristics
in the process.
That is the most
interesting part for physicists but most of it is still in preparation in
September 2017.
ANNEX TO THE
INTRODUCTION
Axiom of choice
for a countable family of sets
of number of
elements between 2 and m included,
that is CC(2
through m).
For an infinite
family of non empty sets,
an equivalent of
the axiom of choice :
A1xA2xA3x... is
not an empty,
We will see that
it could be a set of paths.
Cardinality means
number of elements.
A very
important idea is that from what is true in quantum cosmology, we can deduce
things in quantum
Mechanics.
SPACE AND TIME ARE
DISCONTINIOUS
WHEN SPACE
DISAPPEARS AFTER AN INFINITE TIME
After an infinite
time, we will see that the set of paths will be the void set.
Physical space
would become void, the universe would collapse and a Big
Crunch would
happen.
we consider
locations as urelements (non sets), 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.
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.
n>m
From what is true
in quantum cosmology, we can deduce in quantum
mechanics the
following :
We can us notice
that Newton first law is partly contradicted :
F=0 V constant but the particle does not move
indefinitely as there is no
infinite path.
Time is also a set
of urelements.
The particle could
be using the second component of time.
SPACE AND TIME ARE
INFINITE
Because of the Big
Bang explained by the
negation of the
axiom of choice, space is
a set of
urelements of the negation of the
axiom of choice.
Such a set is
Dedekind infinite.
Space is a
mathematical entity which is infinite.
As a set of
urelements, it is discontinuous.
The number of
urelements in between particles
can be used to
define a distance.
However, we do not
have a vector space.
Such a reasoning
can be made for time.
To write that time
has 2 components is to
make an
approximation.
A set which is
Dedekind infinite has a cardinality
which is not an
aleph of the cantorian infinite.
It is not only
that physical space and mathematical space are entwined, it is that
space is seen more
with the eye of the mind than with the eye.
People are so much
tied up to their
bodies that they
cannot see with
the eye of the
mind, as if Descartes
and Galileo did
not exist.
For time, it is
blatant that the eye of the mind should be used,
even more so since
the theory of Relativity.
Let us assume as
an approximation that CC(2 to m) holds for m<n,
n being the number
of locations of particles in the universe at a given
time.
The Big Crunch
occurs.
Such an idea could
be seen as looking for the particular
axiom of
choice which
applies in physics.
About
time and indeterminism in the physics of particles
Let Ui be a countable family of non empty sets of urelements (non sets), the
negation of
the axiom of choice implies that the Cartesian Product of the family is
empty.
We know from “A philosophical approach to Fermat Last Theorem” in "A
philosophy
for scientists" Adib Ben Jebara Shield Crest Publishing that only a
particular
case of the axiom of choice is true.
And from "About space and time in quantum mechanics" Adib Ben Jebara
Bulletin of Symbolic Logic September 2008, p. 410., we know that the
negation of the axiom of choice can be applied to particles.
That is a basis for the teleportation of the particle since the particle
will have much
“time” to move without the time at our level being much .
EXCERPT from “About a time not totally ordered
(published in the colloquium brochure WSEAS MCSS’15 Dubai 22 February) :
“For elementary particles, time is a set of urelements of the negation of
the
axiom of choice.
So, time is not totally ordered and there is a lateral time.
In an experiment, if a particle enters a hole twice that must be that it
enters and enters again from the same side in a lateral time.
The second time is perceived at our level as being after the first time
while it is not at the level of the particle.
In another experiment, the particle enters two holes at the same time, the
lateral time appears to be the same time.”
Mechanics theory has a tendency to progress by introducing more mathematics
which may
receive industrial applications after some dozens of years.
We are no more in statistical mechanics, because the 2 coordinates of time
are known, the probability of finding the particle in one place is either
zero or 1.
Addendum : one has to pay attention to the weak structure of time at the
level of elementary particles.
it does not matter so much if fundamental indeterminism exist
because it will be reduced whenever physics progress.
Heisenberg uncertainty principle can be bypassed.
The principle states that the more precisely the position of some particle
is determined, the less precisely its speed can be known, and vice versa
That is if we do not know the orthogonal time for the particle but only the
time at our level.
If we know the orthogonal time, the speed is changed by it and the
uncertainty principle
with the time at our level does not apply.
Let us notice that Newton first law is partly contradicted :
F=0 V constant but the particle does not move indefinitely as there is no
infinite path.
Let Ui be a countable family of non empty sets of urelements (non sets), the
negation of
the axiom of choice implies that the Cartesian Product of the family is
empty.
We know from “A philosophical approach to Fermat Last Theorem” in "A
philosophy
for scientists" Adib Ben Jebara Shield Crest Publishing that only a
particular
case of the axiom of choice is true.
And from "About space and time in quantum mechanics" Adib Ben Jebara
Bulletin of Symbolic Logic September 2008, p. 410., we know that the
negation of the axiom of choice can be applied to particles.
That is a basis for the teleportation of the particle since the particle
will have much
“time” to move without the time at our level being much .
EXCERPT from “About a time not totally ordered
(published in the colloquium brochure WSEAS MCSS’15 Dubai 22 February) :
“For elementary particles, time is a set of urelements of the negation of
the
axiom of choice.
So, time is not totally ordered and there is a lateral time.
In an experiment, if a particle enters a hole twice that must be that it
enters and enters again from the same side in a lateral time.
The second time is perceived at our level as being after the first time
while it is not at the level of the particle.
In another experiment, the particle enters two holes at the same time, the
lateral time appears to be the same time.”
Mechanics theory has a tendency to progress by introducing more mathematics
which may
receive industrial applications after some dozens of years.
We are no more in statistical mechanics, because the 2 coordinates of time
are known, the probability of finding the particle in one place is either
zero or 1.
Addendum : one has to pay attention to the weak structure of time at the
level of elementary particles.
it does not matter so much if fundamental indeterminism exist
because it will be reduced whenever physics progress.
Heisenberg uncertainty principle can be bypassed.
The principle states that the more precisely the position of some particle
is determined, the less precisely its speed can be known, and vice versa
That is if we do not know the orthogonal time for the particle but only the
time at our level.
If we know the orthogonal time, the speed is changed by it and the
uncertainty principle
with the time at our level does not apply.
Let us notice that Newton first law is partly contradicted :
F=0 V constant but the particle does not move indefinitely as there is no
infinite path.
I think that
there are too many experiments using
particles accelerators
or cyclotrons
or colliders and not enough experiments about beams of
particles which are not of high energy such as
teleportation of a beam of
particles.
In the most
general case, the orthogonal time is
different from one
particle to another.
Teleportation is not the same
than teleportation of properties
because some other properties
may not be taken into account.
About Newton first law with
F=0, after an indefinte time (approximately a very long time),
the position and speed of a
particle will be not defined.
With the evolution of n
locations of space of the particles
in the
whole universe, we cannot distinguish an infinite number of
occurences between 2 urelements of time,
in the
whole universe, we cannot distinguish an infinite number of
occurences between 2 urelements of time,
We have a case where the axiom
of choice does not hold at all and that is
enough to have the axiom of choice not hold.
Such a reasoning can be made because the duration towards
the Big Crunch is infinite.
In mathematics (for integers), CC(2 through m) is true but in
enough to have the axiom of choice not hold.
Such a reasoning can be made because the duration towards
the Big Crunch is infinite.
In mathematics (for integers), CC(2 through m) is true but in
physics the axiom of choice is not true at all.
About entanglement of
particles
Entanglement of particles is
when one is still influencing
the other after the coupling
ended.
Coupled means touching one the
other.
The other is taken far away
and the spin
of the first is changed, the
spin of the
other will change.
The repeating of the effects
makes
some causality exist.
There is entanglement when the
state of a particule is
Influenced by the state of
another particle after the
coupling is over.
The particles are said to be
correlated.
The explation could be that
the second particle
is still at the moment when it
is touching the first
because it has been using its
orthogonal time ever since.
It seems that there is no
change or
change to expect for the
particle in orthogonal time.
How orthogonal time is unlike
time at our level ?
We cannot act on the particle
during orthogonal time
and may be that is something
which can be (may prove) useful.
Beside knowing that a Big
Crunch will occur after an infinite
time (not Cantorian infinite),
we know that
the axiom of choice is not
true at all in physics (the opposite
of what people think).
In mathematics, the countable
axiom of choice for sets of
number of elements between 2
and m (m included) is
true.
Besides, the first law of
Newton is not true for particles.
The litterature about
teleportation and entanglement of
particles is confusing (not
clear).
The entanglement
of particles was forecasted by Einstein in 1935.
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