Trick or Truth: the Mysterious Connection Between Physics and Mathematics by Jean-François Geneste

Jean-François Geneste

Essay Abstract

After asserting why mathematics and physics aim at describing the same world, ours, we concentrate on some appearent contradictions between both sciences. The biggest one in our opinion is that the probabilities of quantum physics do not fit the Kolmogorov axioms. From this point, we try to quickly study why this happens and why whereas some physicists have proposed the existence of hidden variables experiments have concluded that such variables cannot exist. This brings us to considerations which are quite original. We go through knots theory and propose a scheme for communications quicker than light without violating relativity theory, we propose our universe has a non-Archimedeam geometry with measurements in the field of the sureal numbers, we assert that this allows the very existence of an aether like the one in which believed the physicists of the 19th century. We alo give some clues, originating from experince and basic physics such as statistic thermodynamics to give clues why our universe must be non-Archimedean. We also propose an alternative point of view based on electromagnetic fields and the well known problem of embedding the Lobachevski plane in the euclidean 3-D space. This brings us to a very new conception of what our universe can be and allows us to propose an explanation of why mathematics are so "unreasonably efficient" in physics. Let us keep suspense there.

Author Bio

Jean-François Geneste is the Vice-President Chief Scientist of Airbus Group Innovations. He has written several books in several domains. He is all together an engineer, a mathematician and a physicist.

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Sujatha Jagannathan

Your assertions on various theories are quite mysterious!

With regards,

Miss. Sujatha Jagannathan

Jean-François Geneste

They are based on well known mathematics however...

Antonio Bodig

Jean-François Ciao,

I know that some QM variations admit hidden variable at expense of local phenomena. What do you think in terms of your theory. For example, pilot wave theory.

Good essay. I need to read it a few more times.

Antonio

Jean-François Geneste

My theory is consistent with all variations of QM in the sense that we can find ways of thinking respecting the Kolmogorov axioms to explain experimental phenomena. The main problem for a theory is to be predictive a priori and then to be confirmed a posteriori by experience. This raises the question of what kind of new phenomena could the proposed theory give birth to. I think that the example I give in my text of communications quicker than the speed of light is a good one to show the potential of what can be expected and the power of prediction of the theory I propose. Concerning the non-Archimedean part, it only can propose a physical nature to the entanglement link...

Jean-François Geneste

Dear Dr. Fisher,

Thank you for your support! I feel quite unable to comment on the main part of your text. However, please allow me some comment on the begining of your text. You say

Had you been taught the correct method for expressing truthfulness, you would have written: After abstractly asserting why abstract mathematics and abstract physics abstractly aim at abstractly describing the same abstract world, abstract ours, abstract we abstractly concentrate on some abstract apparent abstract contradictions between both abstract sciences."

I am affraid not completely sharing your point of view there. As I clearly say in the begining of my paper, I believe that all what is created, even by man, like mathematics, even "abstract" as you say, physically exist. You make a difference between abstract things and things which would not be abstract. But what does it mean? Probably you would agree that in common sense the contrary of "abstract" is "material". But why, on a physical point of view discriminate between "abstract" and "material" suggesting that abstract things would not really exist? Let's say that the physical nature of things is multiple and that we can appreciate them or qualify them differently, but in no case are we in the position to assert that because they would be abstract, they would not belong to the "true" physical world. At least, this is my opinion and this is probably not shared by many persons over the world. But, please, think about it deeply and just wonder if there is any serious alternative to that...

Joe Fisher

Dear Dr. Geneste,

Thank you for not requesting that my comment be removed as several other credentialed folk at this site have done, and for at least offering a refutation of my belief. The Universe can only be real. It cannot be partly real, or fundamentally real. Abstract interpretations of abstract creations are quite interesting, and they pay well, but they have nothing to do with reality.

I have no academic credentials. You can address me as Joe.

Impressed at your courage,

Joe Fisher

Dear Dr. Geneste,

If I am correct about only surface having the ability to travel at a constant speed, it means that scientists attempting to build a spaceship that would have a physical surface that could travel "faster" than that of a surface of a garbage can are engaged in an act of utter futility.

Warm Regards,

Joe Fisher

Vladimir Rogozhin

Dear Jean-François,

Your ideas are close to me in spirit deep Cartesian doubt.

Weierstrass expressed the soap so important for mathematicians and physicists: "The final object always to be kept in mind is to arrive at a correct understanding of the foundations of the science."

Mathematics and physics lost existential certainty in the 19th century. the problem of "bases" and "beginning" of fundamental knowledge is unsolved. Fundamental knowledge, mathematics and physics, requires a deep ontological justification (basification). It is necessary to introduce an ontological standard justification (basification) in fundamental physics along with the empirical standard . Mathematics should also make a sharp ontological turn.

Axiom? -Yes. The principle? - Yes. But it must be the deepest ontological axiom and principle: super axiom and super principle. It must come from the deepest understanding of "matter", "measure", "logos", "eidos" in the spirit of Plato's ontology and dialectics. I believe that only the deepest ontological turn of the fundamental science will provide an opportunity to get out of the "crisis of understanding", "crisis of interpretation and representation" to the new heuristics.

I invite you to see my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing of the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld» (E.Husserl), as a picture of the world lyricists , poets and philosophers.

Par ailleurs, Vladimir Voevodsky, auteur univalentes fondements des mathématiques, dans une interview exprimé un point intéressant et important: "Ce que nous appelons aujourd'hui la crise de la science russe ne est pas seulement une crise de la science russe. Ce est une crise de la science mondiale. Des progrès réels sera un combat très sérieux entre science et religion qui mettra fin à leur association. Et je ne ai pas besoin pour battre le le visage."

Sincèrement,

Vladimir

Jean-François Geneste

Cher Vladimir,

Je pense en effet que nous sommes d'accord sur bien des points. Je dois reconnaître qu'avant d'avoir lu votre essai je n'avais pas conscience réellement de la nécessité de ce que vous appelez un "super axiome". Je ne sais d'ailleurs pas si cela est possible. néanmoins, alors que cette question ne m'effleurait même pas, je reconnais que c'est effectivement une question fondamentale qui mérite d'être réfléchie.

Pour terminer, je partage totalement votre point de vue concernant la crise de la science russe et qui est avant tout une crise mondiale de la science. Si l'on se réfère à l'histoire, nous savons qu'un jour ou l'autre, il y aura basculement. Peut-être et hélas faudra-t-il que notre monde s'écroule auparavant pour qu'un nouveau monde naisse sur des bases plus saines.

Bien cordialement,

Jean-François.

Joe Fisher

Dear Dr. Geneste,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

Dear Jean-Francois,

Do you have a real complete skin surface? Does every real object in the real room you are presently in have a real complete surface? Does a real match have a real complete surface? Newton and Einstein were both completely wrong about the abstract motion of abstract objects. All surfaces must travel at the same constant speed otherwise, it would be physically impossible to see a plethora of surfaces instantaneously and simultaneously.

Counting the number of real matches you can see does not require an abstract zero. Seeing real surfaces does not require any mathematical ability at all.

Joe Fisher

Janko Kokosar

Dear Jean-François Geneste

About your model in section 3:

You wrote: ''we entangle on earth the the remaining particles.'' But I think that this means that entanglement between the earth star and 5 mars stars is lost, because this means meaurement and thus decoherence.

Am I wrong?

My essay

Best regards

Janko Kokosar

Jean-François Geneste

Dear Janko Kokosar,

Not exactly. You have 1+1 particles remaining on earth. And you have 5+1 on Mars. Let us number the particles from 1 to 8 and let us call H_i the Hilbert space associated to particle i. Let us call H_1 the space associated with the first particle remaining on earth and H_7 the one associated to the sceond. Now let us call /x_1,...,x_6> the vector associated with the 6 entangled particles and /y_1, y_2> the one associated to the 2 entangled ones. Now the global Hilbert space associated to the 8 particles is (H_1)X...X(H_8). The fact that we make interact the particles 1 and 7 (this is quite formal because indistinguishability of particles is at stake), makes vectors /x_1,...,x_6> and /y_1, y_2> interact. It does not really matter that the interaction takes place on earth or not. Now, we know on earth how to entangle 2 particles through interaction. The process, a priori, when it works, is instantaneous. This is this very fact which will imply the entanglement of the particles on Mars. But, and I do not know if it was your remark, the entanglement between the 5 particles of vector /x> is no more the same as before. But this is in no case any problem since what we are targeting is entanglement and not specific probabilities associated with it.

If your question is to know whether we can change the entenglement between entangled particles without disentangling (i.e. decoherence), the answer is yes. I refer to the well known protocol for teleportation which you can read in details in Le Bellac's book.