ABOUT SPACE AND TIME OF ELEMENTARY PARTICLES
ADIB BEN JEBARA
ACKNOWLEDMENT
I thank Mrs Zinaida Belibov, Mr David Barnett and Mr Andreas Blass
for reading the book.
TABLE OF CONTENTS
About space and time of elementary particles : Introduction
ANNEX TO THE INTRODUCTION
CHAPTER ZERO SUMMARY AND COMMENTS
CHAPTER ZERO BIS SHORT SUMMARY
FIRST CHAPTER
BRIEF HISTORY OF THE NEGATION OF THE AXIOM OF CHOICE
SECOND CHAPTER
APPLYING THE NEGATION OF THE AXIOM OF CHOICE
CHAPTER 3
WHEN SPACE DISAPPEARS AFTER AN INFINITE TIME
CHAPTER 4
SPACE AND TIME ARE INFINITE
CHAPTER 5
ABOUT QUANTUM COSMOLOGY
CHAPTER 6
UNCERTAINTY PRINCIPLE BYPASSED
CHAPTER 7
ABOUT INDETERMINISM
CHAPTER 8
MORE ABOUT TIME
CHAPTER 9
MORE ABOUT SPACE
CHAPTER 10
ABOUT THE VALUES OF ELAPSED TIMES
CHAPTER 11
ABOUT SOME PROPERTIES OF SPACE
Chapter 12
About Dedekind cardinals
Chapter 13
More about the Big Crunch
Chapter 14
About teleportation
CHAPTER 15
MORE ABOUT THE AXIOM OF CHOICE
CHAPTER 16 ABOUT A DISTANCE
CHAPTER 17
MORE ABOUT TELEPORTATION
CHAPTER 18
MORE ABOUT ENTANGLEMENT
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.
CHAPTER ZERO SUMMARY AND COMMENTS
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.
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.
-----Message d'origine-----
From: TaCitS 2017
Sent: Saturday, April 15, 2017 1:51 AM
To: Adib Ben Jebara
Subject: TaCitS 2017 notification for paper 3
Dear Adib Ben Jebara,
We regret to inform you that your abstract, About time and indeterminism in
physics of particles was not selected for presentation at TaCitS. There was
significant competition for presentation slots, and many strong abstracts
had to be declined to maintain a balance of topics.
However, we hope you will still consider joining us for the conference in
Hoboken!
Best,
Samantha Kleinberg
-----Message d'origine-----
From: George Redlinger
Sent: Sunday, June 04, 2017 10:27 AM
To: adibbenjebara@gmail.com
Cc: Gershtein, Yuri ; Patrick Fox
Subject: [2017 Meeting of the APS Division of Particles and Fields (DPF 2017)] Abstract 22: About time and indeterminism in physics of particles
Dear Adib Ben Jebara,
We regret to inform you that we were not able to include your proposed
abstract in the DPF program. The number of contributions was very high
this year.
Regards,
Paddy Fox
Yuri Gershtein
George Redlinger
Dear Adib,
Although a final decision has not been made yet, I have seen the preliminary rankings from our advisory committee. We received many excellent submissions, and unfortunately, your abstract was not listed near the top. Although it is not 100% certain yet, it is most likely that we will not be able to offer you an oral presentation for the symposium.
Best Regards,
Greg Christian
Dear Adib,
We regret to inform you that your abstract for Models and Simulations 8 has not been accepted. Each abstract was evaluated by multiple members of our International Program Committee. Given the high number of interesting submissions and the limited space available, the decisions were not easy. Further information on the conference and the program will be available at our webpage http://www.meetabout.org/ms8/.
Yours sincerely,
Tarja Knuuttila (knuuttil@mailbox.sc.edu)
Michael Stöltzner (stoeltzn@sc.edu)
CHAPTER ZERO BIS SHORT SUMMARY
A research in philosophy of physics and physics
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.
From “About a time not totally ordered” in WSEAS MCSS’15 Dubai 22 February (brochure),
I consider lateral time.
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 .
“For elementary particles, time is a set of urelements of the negation of the
axiom of choice.
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.”
Mechanics theory has a tendency to progress by introducing more mathematics which may
receive industrial applications after some dozens of years.
The 2 coordinates of time are known, the probability of finding the particle in one place
is either zero or 1.
FIRST CHAPTER
BRIEF HISTORY OF THE NEGATION OF THE AXIOM OF CHOICE
The story begins with Cantor who was working on the functions theory and
noticing there could not exist any bijection between N and R. A tremendous
work made him able to give shape to the set theory, being encouraged by
Dedekind and criticized by Kroneker .
On about 1900, it happened to him tohit on two problems.
The first is a paradox which make it impossible for the set of all sets to exist.
The second , called continuum problem, is about the proof that there does not
exist a cardinal number between that of N and of R.
Indeed, Cantor was reasoning by taking for obvious what will later be called
the Axiom of choice as he is taking for granted a total order relationship
between cardinal numbers . This last issue made him exhausted.
Zermelo was trying to make the theory of Cantor formalized.
So on 1904, he defines the Axiom of choice as being the assumption
that the cartesian product of an infinite family of sets is always different
from the empty set. Zermelo and Russell gave at about the same time
another statement for the Axiom which is that there exists a function
which associates to each set of the infinite family one element .
The Axiom was called at the beginning the multiplicative Axiom.
Controversies started between mathematicians, particularly, the french
mathematicians Hadamard, Borel and Lebesque while Zermelo was going on with
his formalization work. The polish mathematician Sierpinski undertook the
identification of the theorems which need the axiom. The german mathematician
Fraenkel used the axioms of Zermelo to define as soon as 1922 a model where
the negation of the axiom of choice is an axiom.
Polish mathematicians like Tarski, Mostowski, Lindenbaum studied around the
thirties the negation of the axiom of choice.
However tragic deaths happened after Banach pointed out unrealistic consequences
of the axiom. The french mathematician Herbrand died, a disciple of Russell, also
Lindenbaum died during the second world war and some papers of Mostowski were
lost at that time.
Meanwhile , the reference to Zorn's lemma was taking the place of the reference
to the axiom.
Mostowski was the one who studied most the particular cases of the axiom :
denumerable or non denumerable family and above all, the case where all the
sets have the same number of elements n, whose notation is Cn. He made about
it a work remarkably difficult to access. In the fifties, the swiss Specker
and the french Fraissé studied also the negation of the axiom of choice.
But the coming of forcing on 1963 produced a fashion phenomena which relegated
Fraenkel Mostowski, as they were called henceforth, as of secondary
importance. However, the use of the axiom for the definition of infinite sums
and products was not drawing attention, although it was mentioned in the
“Principia Mathematica” of Russell and Whitehead before the first world war.
However, this use of the axiom was written about in a remarkable paper, from
Sierpinski, on 1918, which did not get the echo it deserved. Gauntt, in the
seventies, was the only one trying to complete the work of Mostowski on the
Cn. May be a contribution from Truss should be also mentioned.
THE IDEA OF BEN JEBARA
Ben Jebara wrote about the possibility that Fermat was a harbinger for the
Theories using the negation of the axiom of choice through the existence of
Infinite products. Fermat was reading Aristotle who wrote about the existence
of the actual infinite and Fermat's intuition could have enabled him to distinguish
between the infinite products existing and the others.
An extrapolation principle which enable to go from the equation zn=xn+yn to z.z....z...=x.x....x...+y.y...y....
Ben Jebara wrote about that in newsgroups in 1994 and in 1999 and was corrected
By Mr Andreas Blass who was helped by Mr Paul Howard.
SECOND CHAPTER
APPLYING THE NEGATION OF THE AXIOM OF CHOICE
A philosophical approach to Fermat Last Theorem
Fermat did not make public his proof for two reasons :
it was only an outline of a proof and he was not satisfied with it (some case missing),
it would have been considered blasphemous by the Church because of some infinite not existing.
He would have had the same problem as Galileo Galilei.
Equation of Fermat :
Considering the equation
with infinite products
z.z.z.z………=x.x.x.x……………+y.y.y.y……….
and considering
countable axiom of choice for at most y elements sets
we assume 5<=x<=y
C(2 through y)
something which exists equal to something which does not exist (z.z.z…..z…..)
the equation has no solution.
Does it imply that the finite equations for n>= 5 have no solutions ?
Intuitively, for me, it is the case.
The relation between finite and infinite has to be investigated according to
Godel theorem that we are always in need of new axioms.
CUSTOM-MADE AXIOM FOR THE PROOF OF FERMAT LAST THEOREM :
The disjoint union of a Cartesian product of a set (of a number of
elements >=5) a number of times >=5 and of another (OF greater
CARDINALITY) set the same number of times being OF THE SAME CARDINALITY
THAN a Cartesian product of a third set the same number of times MAKES :
the equality of the sum of the two cardinalities of the two first infinite Cartesian products with the
cardinality of the third infinite product holds.
(for a set theoretical proof)
Mr Andreas Blass wrote in 2002 about a complication for x,y and z integers less than 5 in :
http://www.math.lsa.umich.edu/~ablass/dpcc.pdf
After centuries of research, we should have thought that a new axiom is needed for Fermat Last Theorem.
The creativity of Fermat should not be doubted.
The proof of Fermat used an equation with infinite products.
It is completed by a set theoretical explanation.
I am the author of « An axiom to settle the continuum hypothesis ? »Logic Colloquium 2004 (by title).
From my philosophy
About shortcuts
In front of (when
we face) complexity, there are short cuts.
The existence of short cuts is a consequence of the existence of God.
To know histories helps to find shortcuts.
To know where a doubt persists helps to find shortcuts.
We often have to be interested in 1963.
Until 1963 there was no option for extreme specialization.
This theory of short cuts fits in the theory of total quality management.
CHAPTER 3
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.
CHAPTER 4
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.
CHAPTER 5
ABOUT QUANTUM COSMOLOGY
Some time after the Big Bang, existed
only elementary particles, that is
what makes quantum cosmology
a field to study.
Quantum mrchanics apply in quantum cosmology
and what is true in quantum cosmology has
consequences for quantum mechanics.
From a mathematical model, we learned that space
is infinite and discontinuous and that the universe comes
from a previous universe.
We learned that time is also infinite and discontinuous
and not a Cantorian infinite.
CHAPTER 6
UNCERTAINTY PRINCIPLE BYPASSED
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.
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.
CHAPTER 7
ABOUT INDETERMINISM
it does not matter so much if fundamental indeterminism exist
because it will be reduced whenever physics progress.
The idea that only what is measured exists
is restricting research.
Chapter 5 is a bet on the experiments of the future,
that they will go beyond what was done until now.
I mean new measurements about times which will allow
new measurements about locations and speeds.
CHAPTER 8
MORE ABOUT TIME
I saw recently that Mr Itshak Bars had an idea not
very different of mine about time.
Mr Bars has no good argument according to me.
As time is not totally ordered, there are less causality
relations at the level of elementary particles than
at our level.
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.
Could a particle be blocked in our past for a while ?
That is a question that I am considering.
That could be the case when there is entanglement.
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.
CHAPTER 9
MORE ABOUT SPACE
Let U(m) the mathematical where CC(2 through m) is true.
CC(2 through m) is axiom of countable space for a family
of sets of same number of elements between 2 and m.
A particle has m potential moves.
If we move from U(m) to U(m+p), the particle will have
m+p potential moves.
That is when the particle is moving indefinitely.
When the particle has less potential moves, it moves faster.
CHAPTER 10
ABOUT THE VALUES OF ELAPSED TIMES
Values of elapsed time at our level and elapsed time of orthogonal
time can be linearly dependent.
The total elapsed time can be part of an axis especially when the elapsed
time is not big.
That makes time for instance in the first bisectrix.
What would be interesting for teleportation is to have
an elapsed orthogonal time much bigger than an
elapsed time at our level.
CHAPTER 11
ABOUT SOME PROPERTIES OF SPACE
There is an alternative to the boson of Higgs.
Einstein wrote about space being curved
at the level of stars and planets , I think that it is at the
level of elementary particles also curved or bent.
So, the properties of the Higgs boson are not needed
for explaining gravitation.
Is the size of an urelement of space constant ?
In this theory, the set of real numbers
cannot describe space.
Chapter 12
About Dedekind cardinals
Dedekind cardinals are infinite numbers.
For a Dedekind cardinal p, p+1 is different from p.
Because of that, they are ccalled Dedekind-finite.
D being the cardinality of the set of urlements,
D is not greater than aleph zero and not less,
there is no order between D and aleph zero.
Chapter 13
More about the Big Crunch
There is a problem with n>m with axiom of choice
CC(2 through m) if the quantity of particles is finite.
If the quantity of matter is not finite, there would be no
Big Crunch.
Mathematics related to time disappear with the
Big Crunch.
Chapter 14
About teleportation
Teleportation is quasi instantaneous move.
We consider the case where particles are not
replace by others in the process.
Mechanics tend to progress when we introduce
more mathematics.
To move backwards in orthogonal time is not
exluded.
Particles can move not straight in space.
In the most general case, the orthogonal time is different from one
particle to another.
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.
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.”
CHAPTER 15
MORE ABOUT THE AXIOM OF CHOICE
Let us assume as an approximation that the axiom of choice does not hold at all
or 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.
Such an idea could be seen as applied mathematics.
CHAPTER 16 ABOUT A DISTANCE
Number of urelements between 2 particles +1 except for d(part,part)
=0 is a distance, part being a particle.
d(part, part)=0
d(part1,part2)=d(part2, part1)
d(part1, part3) <= d(part1, part2) + d(part2, part3)
We have a metric space.
Properties of metric spaces apply.
CHAPTER 17
MORE ABOUT TELEPORTATION
We have seen m very large for CC(2 through m).
Now, we are looking for a number of urelements of time k
such as we cannot distinguish between them with an
infinite number of occurrences of that.
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 (pair made
with 2 urelements of time locally near one another) , 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
REFERENCES
[PDF]Abstracts presented by title
An idea about time in cosmology
www.aladdin.cs.cmu.edu/asl/abstracts/bytitle.pdf
Abstract presented by title ADIB BEN JEBARA,
adibbenjebara@gmail.com
ADIB BEN JEBARA
ACKNOWLEDMENT
I thank Mrs Zinaida Belibov, Mr David Barnett and Mr Andreas Blass
for reading the book.
TABLE OF CONTENTS
About space and time of elementary particles : Introduction
ANNEX TO THE INTRODUCTION
CHAPTER ZERO SUMMARY AND COMMENTS
CHAPTER ZERO BIS SHORT SUMMARY
FIRST CHAPTER
BRIEF HISTORY OF THE NEGATION OF THE AXIOM OF CHOICE
SECOND CHAPTER
APPLYING THE NEGATION OF THE AXIOM OF CHOICE
CHAPTER 3
WHEN SPACE DISAPPEARS AFTER AN INFINITE TIME
CHAPTER 4
SPACE AND TIME ARE INFINITE
CHAPTER 5
ABOUT QUANTUM COSMOLOGY
CHAPTER 6
UNCERTAINTY PRINCIPLE BYPASSED
CHAPTER 7
ABOUT INDETERMINISM
CHAPTER 8
MORE ABOUT TIME
CHAPTER 9
MORE ABOUT SPACE
CHAPTER 10
ABOUT THE VALUES OF ELAPSED TIMES
CHAPTER 11
ABOUT SOME PROPERTIES OF SPACE
Chapter 12
About Dedekind cardinals
Chapter 13
More about the Big Crunch
Chapter 14
About teleportation
CHAPTER 15
MORE ABOUT THE AXIOM OF CHOICE
CHAPTER 16 ABOUT A DISTANCE
CHAPTER 17
MORE ABOUT TELEPORTATION
CHAPTER 18
MORE ABOUT ENTANGLEMENT
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.
CHAPTER ZERO SUMMARY AND COMMENTS
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.
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.
-----Message d'origine-----
From: TaCitS 2017
Sent: Saturday, April 15, 2017 1:51 AM
To: Adib Ben Jebara
Subject: TaCitS 2017 notification for paper 3
Dear Adib Ben Jebara,
We regret to inform you that your abstract, About time and indeterminism in
physics of particles was not selected for presentation at TaCitS. There was
significant competition for presentation slots, and many strong abstracts
had to be declined to maintain a balance of topics.
However, we hope you will still consider joining us for the conference in
Hoboken!
Best,
Samantha Kleinberg
-----Message d'origine-----
From: George Redlinger
Sent: Sunday, June 04, 2017 10:27 AM
To: adibbenjebara@gmail.com
Cc: Gershtein, Yuri ; Patrick Fox
Subject: [2017 Meeting of the APS Division of Particles and Fields (DPF 2017)] Abstract 22: About time and indeterminism in physics of particles
Dear Adib Ben Jebara,
We regret to inform you that we were not able to include your proposed
abstract in the DPF program. The number of contributions was very high
this year.
Regards,
Paddy Fox
Yuri Gershtein
George Redlinger
Dear Adib,
Although a final decision has not been made yet, I have seen the preliminary rankings from our advisory committee. We received many excellent submissions, and unfortunately, your abstract was not listed near the top. Although it is not 100% certain yet, it is most likely that we will not be able to offer you an oral presentation for the symposium.
Best Regards,
Greg Christian
Dear Adib,
We regret to inform you that your abstract for Models and Simulations 8 has not been accepted. Each abstract was evaluated by multiple members of our International Program Committee. Given the high number of interesting submissions and the limited space available, the decisions were not easy. Further information on the conference and the program will be available at our webpage http://www.meetabout.org/ms8/.
Yours sincerely,
Tarja Knuuttila (knuuttil@mailbox.sc.edu)
Michael Stöltzner (stoeltzn@sc.edu)
CHAPTER ZERO BIS SHORT SUMMARY
A research in philosophy of physics and physics
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.
From “About a time not totally ordered” in WSEAS MCSS’15 Dubai 22 February (brochure),
I consider lateral time.
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 .
“For elementary particles, time is a set of urelements of the negation of the
axiom of choice.
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.”
Mechanics theory has a tendency to progress by introducing more mathematics which may
receive industrial applications after some dozens of years.
The 2 coordinates of time are known, the probability of finding the particle in one place
is either zero or 1.
FIRST CHAPTER
BRIEF HISTORY OF THE NEGATION OF THE AXIOM OF CHOICE
The story begins with Cantor who was working on the functions theory and
noticing there could not exist any bijection between N and R. A tremendous
work made him able to give shape to the set theory, being encouraged by
Dedekind and criticized by Kroneker .
On about 1900, it happened to him tohit on two problems.
The first is a paradox which make it impossible for the set of all sets to exist.
The second , called continuum problem, is about the proof that there does not
exist a cardinal number between that of N and of R.
Indeed, Cantor was reasoning by taking for obvious what will later be called
the Axiom of choice as he is taking for granted a total order relationship
between cardinal numbers . This last issue made him exhausted.
Zermelo was trying to make the theory of Cantor formalized.
So on 1904, he defines the Axiom of choice as being the assumption
that the cartesian product of an infinite family of sets is always different
from the empty set. Zermelo and Russell gave at about the same time
another statement for the Axiom which is that there exists a function
which associates to each set of the infinite family one element .
The Axiom was called at the beginning the multiplicative Axiom.
Controversies started between mathematicians, particularly, the french
mathematicians Hadamard, Borel and Lebesque while Zermelo was going on with
his formalization work. The polish mathematician Sierpinski undertook the
identification of the theorems which need the axiom. The german mathematician
Fraenkel used the axioms of Zermelo to define as soon as 1922 a model where
the negation of the axiom of choice is an axiom.
Polish mathematicians like Tarski, Mostowski, Lindenbaum studied around the
thirties the negation of the axiom of choice.
However tragic deaths happened after Banach pointed out unrealistic consequences
of the axiom. The french mathematician Herbrand died, a disciple of Russell, also
Lindenbaum died during the second world war and some papers of Mostowski were
lost at that time.
Meanwhile , the reference to Zorn's lemma was taking the place of the reference
to the axiom.
Mostowski was the one who studied most the particular cases of the axiom :
denumerable or non denumerable family and above all, the case where all the
sets have the same number of elements n, whose notation is Cn. He made about
it a work remarkably difficult to access. In the fifties, the swiss Specker
and the french Fraissé studied also the negation of the axiom of choice.
But the coming of forcing on 1963 produced a fashion phenomena which relegated
Fraenkel Mostowski, as they were called henceforth, as of secondary
importance. However, the use of the axiom for the definition of infinite sums
and products was not drawing attention, although it was mentioned in the
“Principia Mathematica” of Russell and Whitehead before the first world war.
However, this use of the axiom was written about in a remarkable paper, from
Sierpinski, on 1918, which did not get the echo it deserved. Gauntt, in the
seventies, was the only one trying to complete the work of Mostowski on the
Cn. May be a contribution from Truss should be also mentioned.
THE IDEA OF BEN JEBARA
Ben Jebara wrote about the possibility that Fermat was a harbinger for the
Theories using the negation of the axiom of choice through the existence of
Infinite products. Fermat was reading Aristotle who wrote about the existence
of the actual infinite and Fermat's intuition could have enabled him to distinguish
between the infinite products existing and the others.
An extrapolation principle which enable to go from the equation zn=xn+yn to z.z....z...=x.x....x...+y.y...y....
Ben Jebara wrote about that in newsgroups in 1994 and in 1999 and was corrected
By Mr Andreas Blass who was helped by Mr Paul Howard.
SECOND CHAPTER
APPLYING THE NEGATION OF THE AXIOM OF CHOICE
A philosophical approach to Fermat Last Theorem
Fermat did not make public his proof for two reasons :
it was only an outline of a proof and he was not satisfied with it (some case missing),
it would have been considered blasphemous by the Church because of some infinite not existing.
He would have had the same problem as Galileo Galilei.
Equation of Fermat :
Considering the equation
with infinite products
z.z.z.z………=x.x.x.x……………+y.y.y.y……….
and considering
countable axiom of choice for at most y elements sets
we assume 5<=x<=y
C(2 through y)
something which exists equal to something which does not exist (z.z.z…..z…..)
the equation has no solution.
Does it imply that the finite equations for n>= 5 have no solutions ?
Intuitively, for me, it is the case.
The relation between finite and infinite has to be investigated according to
Godel theorem that we are always in need of new axioms.
CUSTOM-MADE AXIOM FOR THE PROOF OF FERMAT LAST THEOREM :
The disjoint union of a Cartesian product of a set (of a number of
elements >=5) a number of times >=5 and of another (OF greater
CARDINALITY) set the same number of times being OF THE SAME CARDINALITY
THAN a Cartesian product of a third set the same number of times MAKES :
the equality of the sum of the two cardinalities of the two first infinite Cartesian products with the
cardinality of the third infinite product holds.
(for a set theoretical proof)
Mr Andreas Blass wrote in 2002 about a complication for x,y and z integers less than 5 in :
http://www.math.lsa.umich.edu/~ablass/dpcc.pdf
After centuries of research, we should have thought that a new axiom is needed for Fermat Last Theorem.
The creativity of Fermat should not be doubted.
The proof of Fermat used an equation with infinite products.
It is completed by a set theoretical explanation.
I am the author of « An axiom to settle the continuum hypothesis ? »Logic Colloquium 2004 (by title).
Fermat was reading Aristotle who wrote about the existence of the infinite.
An extrapolation principle enables to go from the equation zn=xn+yn to z.z....z...=x.x....x...+y.y...y....
Mathematicians are waiting for someone to come up with an axiom from an intuition, I did and they do not recognize it.
Excerpt from « All things are numbers (continuation)”, abstract from
the Logic Colloquium 2002 published in the Bulletin of Symbolic Logic :
The equation with infinite products zzz…z…=xx…x…+yy…y… with z>y
has no solution in the universe where only the restricted axiom CC(2
through x) is true.
It is because otherwise the infinite products xx…x…
and yy…y… exist but not zzz…z… and we cannot have a side of the equation
existing and the other not.
What could be a philosophical interpretation of the proof of Fermat Last Theorem
is that God is mysterious and not all powerfulness (the infinite is an attribute of God).
Fermat was reading Descartes about existence.
Fermat was also reading Desargues about the point at the infinite.
I published in “A philosophy for scientists” Adib Ben Jebara Shield Crest Publishing UK 2015
From my philosophy
About shortcuts
In front of (when
we face) complexity, there are short cuts.
The existence of short cuts is a consequence of the existence of God.
To know histories helps to find shortcuts.
To know where a doubt persists helps to find shortcuts.
We often have to be interested in 1963.
Until 1963 there was no option for extreme specialization.
This theory of short cuts fits in the theory of total quality management.
CHAPTER 3
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.
CHAPTER 4
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.
CHAPTER 5
ABOUT QUANTUM COSMOLOGY
Some time after the Big Bang, existed
only elementary particles, that is
what makes quantum cosmology
a field to study.
Quantum mrchanics apply in quantum cosmology
and what is true in quantum cosmology has
consequences for quantum mechanics.
From a mathematical model, we learned that space
is infinite and discontinuous and that the universe comes
from a previous universe.
We learned that time is also infinite and discontinuous
and not a Cantorian infinite.
CHAPTER 6
UNCERTAINTY PRINCIPLE BYPASSED
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.
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.
CHAPTER 7
ABOUT INDETERMINISM
it does not matter so much if fundamental indeterminism exist
because it will be reduced whenever physics progress.
The idea that only what is measured exists
is restricting research.
Chapter 5 is a bet on the experiments of the future,
that they will go beyond what was done until now.
I mean new measurements about times which will allow
new measurements about locations and speeds.
CHAPTER 8
MORE ABOUT TIME
I saw recently that Mr Itshak Bars had an idea not
very different of mine about time.
Mr Bars has no good argument according to me.
As time is not totally ordered, there are less causality
relations at the level of elementary particles than
at our level.
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.
Could a particle be blocked in our past for a while ?
That is a question that I am considering.
That could be the case when there is entanglement.
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.
CHAPTER 9
MORE ABOUT SPACE
Let U(m) the mathematical where CC(2 through m) is true.
CC(2 through m) is axiom of countable space for a family
of sets of same number of elements between 2 and m.
A particle has m potential moves.
If we move from U(m) to U(m+p), the particle will have
m+p potential moves.
That is when the particle is moving indefinitely.
When the particle has less potential moves, it moves faster.
CHAPTER 10
ABOUT THE VALUES OF ELAPSED TIMES
Values of elapsed time at our level and elapsed time of orthogonal
time can be linearly dependent.
The total elapsed time can be part of an axis especially when the elapsed
time is not big.
That makes time for instance in the first bisectrix.
What would be interesting for teleportation is to have
an elapsed orthogonal time much bigger than an
elapsed time at our level.
CHAPTER 11
ABOUT SOME PROPERTIES OF SPACE
There is an alternative to the boson of Higgs.
Einstein wrote about space being curved
at the level of stars and planets , I think that it is at the
level of elementary particles also curved or bent.
So, the properties of the Higgs boson are not needed
for explaining gravitation.
Is the size of an urelement of space constant ?
In this theory, the set of real numbers
cannot describe space.
Chapter 12
About Dedekind cardinals
Dedekind cardinals are infinite numbers.
For a Dedekind cardinal p, p+1 is different from p.
Because of that, they are ccalled Dedekind-finite.
D being the cardinality of the set of urlements,
D is not greater than aleph zero and not less,
there is no order between D and aleph zero.
Chapter 13
More about the Big Crunch
There is a problem with n>m with axiom of choice
CC(2 through m) if the quantity of particles is finite.
If the quantity of matter is not finite, there would be no
Big Crunch.
Mathematics related to time disappear with the
Big Crunch.
Chapter 14
About teleportation
Teleportation is quasi instantaneous move.
We consider the case where particles are not
replace by others in the process.
Mechanics tend to progress when we introduce
more mathematics.
To move backwards in orthogonal time is not
exluded.
Particles can move not straight in space.
In the most general case, the orthogonal time is different from one
particle to another.
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.
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.”
CHAPTER 15
MORE ABOUT THE AXIOM OF CHOICE
Let us assume as an approximation that the axiom of choice does not hold at all
or 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.
Such an idea could be seen as applied mathematics.
CHAPTER 16 ABOUT A DISTANCE
Number of urelements between 2 particles +1 except for d(part,part)
=0 is a distance, part being a particle.
d(part, part)=0
d(part1,part2)=d(part2, part1)
d(part1, part3) <= d(part1, part2) + d(part2, part3)
We have a metric space.
Properties of metric spaces apply.
CHAPTER 17
MORE ABOUT TELEPORTATION
We have seen m very large for CC(2 through m).
Now, we are looking for a number of urelements of time k
such as we cannot distinguish between them with an
infinite number of occurrences of that.
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 (pair made
with 2 urelements of time locally near one another) , 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
physics the axiom of choice is not true at all.
I took me about 10 years to move from a logical theory to the
right theory for our world.
Could the orthogonal time of a particle
be measured directly or not ?
I thought about orthogonal time of a particle that we may
know something about it by comparing 2 experiments not very different.
know something about it by comparing 2 experiments not very different.
Let us try to describe an experiment where a proton travels
a distance in a given time and another experiment where it
travels the same distance in less time.
How can entenglement of particles be used for teleportation
which is not teleportation of properties only ?
What are the links between teleportation and teleportation
of properties only ?
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.
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).
About entanglement of 2 particles,
is there instantaneous causation at a distance ?
From the words of Mr David Barnett.
CHAPTER 18 MORE ABOUT ENTANGLEMENT OF PARTICLES
The explation could be that the second particle
I conjecture that coupling 2 particles makes them use
Einstein forecasted the entanglement of paricles in 1935.
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.
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.
I am more interested in a case where a little time is past
at our level and the particle moved from a location to
a location far away.
their orthogonal times after the coupling is removed.
Einstein forecasted the entanglement of paricles in 1935.
The address for this webpage is
REFERENCES
[PDF]Abstracts presented by title
An idea about time in cosmology
www.aladdin.cs.cmu.edu/asl/abstracts/bytitle.pdf
Abstract presented by title ADIB BEN JEBARA,
adibbenjebara@gmail.com
