Adib

Physics and the actual infinite (simplified) About Galileo and about the infinite After Archimedes, Galilei Galileo applied mathematics to physics. Alexandre Koyré wrote in "D'un monde clos à l'univers infini" that Galileo threw Earth in the Sky. For almost all ancient greeks, the Earth and the Sky were not connected and mathematics applied only to the Sky. Nowadays, scientists and philosophers think that the actual infinite cannot be applied in physics. So now is the time for furthering of Galileo of applying mathematics to physics. Establishing a link between the actual infinite and the Big Bang is furthering the insight of Galileo. The physical space is infinite because in assuming so, you can understand why the Big Bang occured. It is because space vanished as is applied the negation of the mathematical axiom of choice to describe space. It is difficult to imagine the contained without the containing, but it is what happened because space is infinte in the Big Crunch followed by the Big Bang. There was always an universe (in a sequence of universes). It is not clear whether this theory is confirmed or not as I publish in "The bulletin of symbolic logic" but without any feedback and I am not quoted. Adib Ben Jebara http://www.freewebs.com/adibbenjebara

I am asked by Klaynos "how about with maths ?" : An interpretation about space and time in quantum mechanics There was a repeated experiment where at first, two protons are joined and of opposite spins. Then, the second is taken far away, and it is acted upon the first to modify its spin. The second proton will change its spin to keep it the opposite of the spin of the first. Now, if you will assume with me that we can apply the set theory ZFU to physical space, U (urelements,non sets)) being physical space, you will see that we get an interpretation of the experiment. Indeed, as it is not possible to define a usual distance in U, the second proton will not be any more far away from the first. Also, if we consider time to be U, we cannot say that the protons were separated a long time ago and that there should be no more influence. [...] There was another repeated experiment with a photon, expected to go one way, going both two quite separated ways. Here, again, if we assume something else about space, the two ways would be not that much separated. Regards, Adib Ben-Jebara. One reason why the negation of the axiom of choice is true We apply set theory with urelements (non sets) ZFU to physical space of elementary particles; we consider locations as urelements, elements of U, in number infinite. 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(2 through m), countable choice for k elements sets k=2 through m, the set of paths will be the void set. So, after an infinite time, physical space would become void, the universe would collapse and a Big Crunch would happen. The matter would have to go somewhere and indeed the Big Bang happened. So, n is indeed greater than m. Let us notice that physical space is infinite. It's rather complicated but what do you think ? Isn't it most likely that the negation of the axiom of choice is true ? It is like the non-euclidian geometry which is known in physics as true. Regards, Adib Ben Jebara.

About every day life of the elementary particles (simplified) This is what I think about some of elementary particles behavior, avoiding much math. The elementary particle jumps from one location to another with the set of locations discontinuous and not linearly ordered. What is far with the standard distance can be near with the jumps. So, two particles can have an action one on the other after having taken a "distance" one from the other. The two particles could be within a limited number of jumps one from the other. Therefore, there could be an unexpected correlation. Time itself is discontinuous and not linearly ordered. So, there are no causality relationships unless time is ordered by the observation set up. Help is welcome for deducing other consequences of this behavior. Adib Ben Jebara. http://www.freewebs.com/adibbenjebara

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

About set theory with urelements and elementary particles Platonists seek a reality in mathematics, associated with the truth of axioms. Logicists and formalists are concerned about consistency and independence of axioms but not about their truth. I suggest, as a Platonist, that the axioms definitely true are those applied to previously unsolved mathematical problems or to physics or social sciences or ethics. For the case of the axiom of choice, I state that the negation of the axiom of choice is true because I apply it to quantum mechanics and cosmology which are part of physics. It is because of the lack of interdisciplinary research that the status of the axiom of choice remains ambiguous. People do not think unity of knowledge a good thing. In XiUi with Ui a set of locations, i does not have to be a count of time. We consider simple sequences of locations. Let S be a finite well ordered subset of U, we can define a distance by counting the number of urelements(non sets) between two urelements. Mr Andreas Blass corrected with number of urelements between two urelements +1. This applies for space and time as well. Mr Andreas Blass pointed out the lack of useful coordinates and that there is no vector space because it would be non denumerable. My idea might insert itself where a reality is out of reach of the usual model. Then, there is the embedding theorem of Sochor and Jech of U in V. Mr Andeas Blass pointed out that the embedding is complicated, involving sets of sets of ordinals. As time as U is not well ordered, except in S above, there are less causality relationships at the level of elementary particles than at our level because causality is based on time ordered. Adib Ben Jebara http://jebara.topcities.com

About experimenting about elementary particles about space and time That ZFU (set theory with urelements, non sets) is applied to space and time explains the correlations between particles (in "An interpretation about space and time in quantum mechanics") in Logic Colloquium 2007. ZFU applied to elementary particles is most likely to explain the Big Bang, see http://www.scienceforums.net/forum/showthread.php?t=30616 As the usual distance is not defined, we consider the distance between particles number of urelements in between + 1 Mr Andreas Blass remarked that if the urelements are ordered by the experiment set up, measurement may vary with the order when the conversion to meters and seconds is made. But it seems to me that , whatever the order of urelements, the number of urelements in between + 1 stay the same. After a comment from Mr Andreas Blass, I feel the need to precise that the first and the last extremities of the sequence are not to be changed as they are associated to particles. I see the order between urelements as a distortion made by the experiment set up. The experiment set ups are so sophisticated that they can detect what exists but that might be with a distortion especially for space and time which are invisible. The experiment set up probably makes a particle move in a straight line. Without the experiment set up, may be the particle moves in approximately a straight line. We can say that we do not know what the particles do by themselves even if we know what they do when we make them appear to us. Mathematics help us see things as they are, without an experiment set up interfering but then experiment set ups are necessary because If mathematics and experiment set ups agree on some thing, then that is where the truth is. Adib Ben Jebara http://jebara.topcities.com

About a distance for elementary particles In "An interpretation about space and time in quantum mechanics" in Logic Colloquium 2007, we have seen that the usual distance is not defined for space and time because we apply the theory ZFU (set theory with urelements, non sets). We explained some correlations between particles. I would have doubts about the assumptions if I did not apply them for space successfully to explain the Big Crunch and the Big Bang in http://adibjebara.blogspot.com/ As time is but another dimension, I apply ZFU to time as well. Now, let U1xU2 be space time with U1 space and U2 time. Many things are discontinuous in quantum mechanics. So, why not space and time ? At the level of elementary particles, space and time are also not linearly ordered. As the experiment set up gives us meters and seconds, that means that the space and time considered by the experiment set up are the space and time at our level. I conjecture that when we measure, we introduce, finitely, order of urelements in U1 and U2, in a laboratory. A distance is number of urelements in between + 1 which is converted to the measurement at our level in meters and seconds. The experiment set up changes much what exists as space and time. The skeptics should be aware that some experiments needed interpretations and I provided them. As a Platonist, I see some reality in Dedekind cardinals and, thus, in ZFU. There is already an experiment where a particle goes both two separate ways. So, its space is different from ours. There remain to find other experiments to detect that locations and times are not linearly ordered. There remains also to comment on the lack of localism. I thank Mr Andereas Blass and Mr Abderazak Abadlia for their comments. Adib Ben Jebara http://jebara.topcities.com

An axiom to settle the continuum hypothesis ? (Logic Colloquium 2004 contributed abstract) Paul Cohen used a set of generic reals to prove the consistency of the negation of the continuum hypothesis with other axioms. It is my opinion that such sets do not really exist for a Platonist. My opinion is that the continuum hypothesis is true. Here is a tentative axiom from me to try to prove it. Axiom : An infinite subset of the power set of N has a bijection either with a countable union of (pair wise disjoint) sets of n elements or with a countable Cartesian products of (pair wise disjoint) sets of n elements. Mr Andreas Blass proved that this axiom is equivalent to the continuum hypothesis. So, the axiom is consistent with the other usual axioms and independent from them, from the works of Kurt Godel and Paul Cohen, respectively. Mr Andreas Blass used the assumption that the Cartesian product is not the empty set but he did not use the axiom of choice. The question which remains is : is it a good axiom ? My opinion is that it is realistic for a Platonist. But may be the axiom is not simple enough and may be a simpler one could be found. Adib Ben Jebara. http://jebara.topcities.com

I don't know how to Latexize it but if you write me at adib.jebara@topnet.tn I will send it as an email. Adib Ben Jenara.

Mathematics are applied to physics since a long time ago. I apply the negation of the axiom of choice. Adib Ben Jebara.

One reason why the negation of the axiom of choice is true We apply set theory with urelements (non sets) ZFU to physical space of elementary particles; we consider locations as urelements, elements of U, in number infinite. 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(2 through m), countable choice for k elements sets k=2 through m, the set of paths will be the void set. So, after an infinite time, physical space would become void, the universe would collapse and a Big Crunch would happen. The matter would have to go somewhere and indeed the Big Bang happened. So, n is indeed greater than m. Let us notice that physical space is infinite. It's rather complicated but what do you think ? Isn't it most likely that the negation of the axiom of choice is true ? It is like the non-euclidian geometry which is known in physics as true. Regards, Adib Ben Jebara. http://jebara.topcities.com

How do you know the value is complementary if you don't know it ? Urelements are non sets.

An interpretation about space and time in quantum mechanics There was a repeated experiment where at first, two protons are joined and of opposite spins. Then, the second is taken far away, and it is acted upon the first to modify its spin. The second proton will change its spin to keep it the opposite of the spin of the first. For further details : http://mist.npl.washington.edu/npl/int_rep/tiqm/TI_24.html#2.4.1 Now, if you will assume with me that we can apply the set theory ZFU to physical space, U (urelements)) being physical space, you will see that we get an interpretation of the experiment. Indeed, as it is not possible to define a usual distance in U, the second proton will not be any more far away from the first. Also, if we consider time to be U, we cannot say that the protons were separated a long time ago and that there should be no more influence. [...] There was another repeated experiment with a photon, expected to go one way, going both two quite separated ways. Here, again, if we assume something else about space, the two ways would be not that much separated. Regards, Adib Ben-Jebara. http://jebara.topcities.com adib.jebara@topnet.tn

Thank you for remembering the topic, a new idea about space in quantum mechanic. Some posts are very complcated, I wonder if it is necessary that they be so.

We have drifted far from the subject. Why don't you ask for instance if the time needed to reach a Big Crunch is infinite ? It is.

I explain why the Big Bang happened which is not yet done. What does IMO mean ?

About space in quantum mechanics We apply set theory with urelements ZFU to physical space, we consider locations as urelements, elements of U (non sets). 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. The negation of the axiom of choice is really true because it can be applied in physics. http://jebara.topcities.com

About space 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. The negation of the axiom of choice is really true because it can be applied in physics. http://jebara.topcities.com

More details are to be found in my web page http://jebara.topcities.com Adib Ben Jebara.

Negation of the axiom of choice and Evil Beside the particular case of the axiom of choice CC(2 through m), countable choice for sets of n elements n=2 through m, there is the particular case where the whole axiom is negated, no choice at all. In "All things are numbers" in Logic Colloquium 2001, and in "About the strength of Evil" in ASL Winter Meeting 2004 2005, I wrote that the numbers of attributes of Evil are infinite sums and products of integers. If there is no choice at all, which is a standing valid case, as I am changing my mind to include this case beside CC(2 through m),the only infinite sums or products well defined (existing) is the infinite sum 1+1+1+.... which is equal to aleph zero. So, Evil is really restricted. The case where the whole axiom of choice is negated is not a parametric case. We apply it to ethics. Another way for clarification is the following : Let us consider the infinite cardinal product XiAi Ai being sets of attributes of Evil of size the same or different integers, without the ai being urelements. In some model of the negation of the axiom of choice, the product is void. So, the number of combined attributes of Evil is not like with the axiom of choice an infinite product of integers (which is the cardinality of the continuum), but 1+1+1+....(which is aleph zero). As for the numbers of attributes of Good, I wrote in "All things are numbers" in Logic Colloquium 2001 that they are Dedekind cardinals. A criticism that I am making to myself is that, in such a case, attributes must be indistinguishable as urelements are. Attributes would go like : Good, Good, Good, ...

About the philosophy of the negation of the axiom of choice I refer to set theory with urelements ZFU as in "The axiom of choice", Thomas Jech, North Holland 1973. Let us assume the negation of the axiom of choice and that space of particles is U of ZFU. Let U1xU2X....XUiX...... be the void set with Ui a set of locations. We can see the Existence and the Non Existence linked, contradicting the Existence of Parmenides and the Becoming of Heraclites. We can see the Infinite and the Void tied up in an unexpected way. We can see that Non Existence is closer to the Infinite than to the finite. We can see that we can apprehend space with mathematics in a way that we cannot apprehend with direct experimentation. We can see that space is not so much fundamental data, contradicting Kant. It is to the philosophy of Plato and of Albert Lautman that we refer. As the Big Crunch and the Big Bang are explained by the use of the negation of the axiom of choice upon space, we can see the existence of a cyclical phenomenon. In the future, ZFU should be considered the foundations of mathematics. Historically it was an attempt to show that the negation of the axiom of choice is consistent with the other axioms. So, we see how the progress of science induces a change in the status of a theory. That physical space is infinite (with a quantity of matter finite) puts us in the border Between mathematics and physics. We can see the usefulness of interdisciplinary research. Giordano Bruno was sentenced to death by fire on 1600 in Italy for saying that the Universe is infinite. Nowadays, people still find it hard to think of an infinite physical space. Adib Ben Jebara Apt F3 Residence Badr Manar 1 Tunis 2092 Tunisia adib.jebara@topnet.tn or ajebara2001@yahoo.com http://jebara.topcities.com if a click does not work copy and paste please and insist

About the philosophy of the negation of the axiom of choice I refer to set theory with urelements ZFU as in "The axiom of choice", Thomas Jech, North Holland 1973. Let us assume the negation of the axiom of choice and that space of particles is U of ZFU. Let U1xU2X....XUiX...... be the void set with Ui a set of locations. We can see the Existence and the Non Existence linked, contradicting the Existence of Parmenides and the Becoming of Heraclites. We can see the Infinite and the Void tied up in an unexpected way. We can see that Non Existence is closer to the Infinite than to the finite. We can see that we can apprehend space with mathematics in a way that we cannot apprehend with direct experimentation. We can see that space is not so much fundamental data, contradicting Kant. It is to the philosophy of Plato and of Albert Lautman that we refer. As the Big Crunch and the Big Bang are explained by the use of the negation of the axiom of choice upon space, we can see the existence of a cyclical phenomenon. In the future, ZFU should be considered the foundations of mathematics. Historically it was an attempt to show that the negation of the axiom of choice is consistent with the other axioms. So, we see how the progress of science induces a change in the status of a theory. That physical space is infinite (with a quantity of matter finite) puts us in the border Between mathematics and physics. We can see the usefulness of interdisciplinary research. Giordano Bruno was sentenced to death by fire on 1600 in Italy for saying that the Universe is infinite. Nowadays, people still find it hard to think of an infinite physical space. Adib Ben Jebara Apt F3 Residence Badr Manar 1 Tunis 2092 Tunisia adib.jebara@topnet.tn or ajebara2001@yahoo.com

An interpretation about space and time in quantum mechanics There was a repeated experiment where at first, two protons are joined and of opposite spins. Then, the second is taken far away, and it is acted upon the first to modify its spin. The second proton will change its spin to keep it the opposite of the spin of the first. For further details : http://mist.npl.washington.edu/npl/int_rep/tiqm/TI_24.html#2.4.1 Now, if you will assume with me that we can apply the set theory ZFU to physical space, U (urelements)) being physical space, you will see that we get an interpretation of the experiment. Indeed, as it is not possible to define a distance in U, the second proton will not be any more far away from the first. Also, if we consider time to be U, we cannot say that the protons were separated a long time ago and that there should be no more influence. Such two hypothesis about space and time were already made in "About time and time of elementary particles" in ASL Annual Meeting 2005. It is not yet clear : are space and time alternatively U ? Is U space-time ? Continuums are still approximations. Mr Andreas Blass pointed out that, in the experiment, the first proton is acted upon for measurement, and he also pointed out that only the most used distances are not defined in U. He is skeptical about the assumptions. As the hypothesis apply to cosmology, the unity of physics would be increased in such a direction. There was another repeated experiment with a photon, expected to go one way, going both two quite separated ways. Here, again, if we assume something else about space, the two ways would be not that much separated. Adib Ben Jebara Apt F3 Residence Badr Manar 1 Tunis 2092 Tunisia adib.jebara@topnet.tn