Dear Emmanuel Moulay
Your essay is an interesting summary of more interpretation of quantum theories. Your message is hidden in the following sentences:
"So, we know what is beyond the Heisenberg uncertainty principle: nothing of physical nature. But this is a knowledge and also a problem because the Heisenberg uncertainty principle (2.3)-(2.5) is supposed to be a limit to the knowledge. So, we can state the first main result of this article. Proposition 1. The uniqueness of interpretation of quantum mechanics leads to a paradox."
This is a thought, which I also had many time in my head. But I not do yet believe in your interpretation (of interpretations :) ), and I offer a different by-pass of this problem:
1. I believe that a measurement should exist which distinguishes among different interpretations. (Word "measurement" should mean a lot of things ...)
2. Interpretation of quantum mechanics (QM) is uncompleted because explanations of quantum gravity (QG) and quantum consciousness do not yet exist. I claim that QG is more fundamental than QM and quantum field theory. I claim that space time is emergent.
3. (If consciousness is not a quantum phenomenon, explanation for it should be found first, only after this quantum consciousness can be ignored in such explanations.)
4. Copenhagen interpretation is uncompleted also because many other interpretations exist.
5. I like Brukner-Zeilinger interpretation, which is based on information, it agrees that finite volume has finite information, and it gives hope for explanation of QG.
6. I like also Cramer's Interactional interpretation, because it define that "everything" is interaction.
7. Space-time is emergent and quantum gravity will define, how it is with this.
8. I was motivated also from the claim that uncertainty principle is not valid in quantum gravity, because space-time is emergent. This is written in my article.
My article describes also a problem of physical explanation of consciousness.