The theory of the double preparation: discerned and indiscerned particles

In this paper we propose a deterministic and realistic quantum mechanics interpretation which may correspond to Louis de Broglie's "double solution theory". Louis de Broglie considers two solutions to the Schr\"odinger equation, a singular and physical wave u representing the particle (soliton wave) and a regular wave representing probability (statistical wave). We return to the idea of two solutions, but in the form of an interpretation of the wave function based on two different preparations of the quantum system. We demonstrate the necessity of this double interpretation when the particles are subjected to a semi-classical field by studying the convergence of the Schr\"odinger equation when the Planck constant tends to 0. For this convergence, we reexamine not only the foundations of quantum mechanics but also those of classical mechanics, and in particular two important paradox of classical mechanics: the interpretation of the principle of least action and the the Gibbs paradox. We find two very different convergences which depend on the preparation of the quantum particles: particles called indiscerned (prepared in the same way and whose initial density is regular, such as atomic beams) and particles called discerned (whose density is singular, such as coherent states). These results are based on the Minplus analysis, a new branch of mathematics that we have developed following Maslov, and on the Minplus path integral which is the analog in classical mechanics of the Feynman path integral in quantum mechanics. The indiscerned (or discerned) quantum particles converge to indiscerned (or discerned) classical particles and we deduce that the de Broglie-Bohm pilot wave is the correct interpretation for the indiscerned quantum particles (wave statistics) and the Schr\"odinger interpretation is the correct interpretation for discerned quantum particles (wave soliton). Finally, we show that this double interpretation can be extended to the non semi-classical case.Comment: 11 pages, 5 figure

A Potentiality and Conceptuality Interpretation of Quantum Physics

We elaborate on a new interpretation of quantum mechanics which we introduced recently. The main hypothesis of this new interpretation is that quantum particles are entities interacting with matter conceptually, which means that pieces of matter function as interfaces for the conceptual content carried by the quantum particles. We explain how our interpretation was inspired by our earlier analysis of non-locality as non-spatiality and a specific interpretation of quantum potentiality, which we illustrate by means of the example of two interconnected vessels of water. We show by means of this example that philosophical realism is not in contradiction with the recent findings with respect to Leggett's inequalities and their violations. We explain our recent work on using the quantum formalism to model human concepts and their combinations and how this has given rise to the foundational ideas of our new quantum interpretation. We analyze the equivalence of meaning in the realm of human concepts and coherence in the realm of quantum particles, and how the duality of abstract and concrete leads naturally to a Heisenberg uncertainty relation. We illustrate the role played by interference and entanglement and show how the new interpretation explains the problems related to identity and individuality in quantum mechanics. We put forward a possible scenario for the emergence of the reality of macroscopic objects.Comment: 20 pages, 1 figur

On a realistic interpretation of quantum mechanics

The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This opens the door for an interpretation that, while respecting the indeterministic nature of quantum mechanics, allows to speak of definite values for all observables at any time that are, however, only partially measurable. The analysis also suggests new ways to test the foundations of quantum theory.Comment: 21 page

Quantum Mechanics from Periodic Dynamics: the bosonic case

Enforcing the periodicity hypothesis of the "old" formulation of Quantum Mechanics we show the possibility for a new scenario where Special Relativity and Quantum Mechanics are unified in a Deterministic Field Theory [arXiv:0903.3680]. A novel interpretation of the AdS/CFT conjecture is discussed.Comment: 6 pages. Talk given at QTRF5, Vaxjo, Sweden. Updated reference