Principles of a Second Quantum Mechanics - A concise and improved English version of the French text in arXiv:1310.1728v3 (original) (raw)

2015, arXiv (Cornell University)

This work is not an interpretation of the Hilbert-Dirac quantum mechanics QMHD. It exposes the principles of a new representation of microstates, a second quantum mechanics denoted QM2. This representation is rooted directly into the aconceptual physical reality wherefrom it is constructed bottom-up-by in physical-operational-conceptual terms, in uninterrupted relation with the physical factuality and with the constraints imposed by the involved cognitive situation. First-independently of any mathematical formalism-is constructed in qualitative but general and formalized terms, a framework for reference-and-imbedding of any acceptable theory of physical micro-entities that-radically-cannot be perceived directly by human observers-conceivers. The construction is achieved under exclusively the physical-operational, methodological and conceptual constraints entailed by the cognitive situation that is involved. The obtained representation is called infra-(quantum mechanics) and is denoted IQM. By reference to IQM is then worked out a preliminary critical examination of QMHD. Thereby it appears that: (a) QMHD is devoid of any general formal representation of the individual physical entities and operations that-quite essentially-it does involve: The whole level of individual conceptualization of the microstates is lacking inside QMHD, massively. Inside QMHD are endowed with clear but directly mathematical definitions-flawed by lacunae, approximations or a priori idealizations-exclusively abstract statistics that express results of ghostly and fallaciously specified acts of measurement performed on ghostly sketched out physical entities. (b) Contrary to the orthodox general interdiction of any model of a microstate and to the unanimous assertion of absence of such a model inside QMHD, it is found that the mathematical formalism of QMHD does involve a model of microstate, and in a quite fundamental role, namely de Broglie's model of a wave with a "corpuscular-like" singularity in its amplitude. But inside QMHD both this fact and its meaning remain implicit. So their consequences are not systematically recognized and made use of. This entails a catastrophic hole in the very definability of the acts of measurement: no general and explicit rules are formulated for coding the directly observable effect of an act of quantum-measurement-just marks on registering devices-in meaningful terms, of a definite value of the measured quantity. From (a) and (b) it follows that the nowadays Hilbert-Dirac Quantum-Mechanics QMHD is simply devoid of an acceptable representation of the quantum measurements. The lacunae mentioned above are then compensated via a radically constructive bottom-up approach that starts from local zeros of knowledge on, specifically, the physical microstate to be studied. It starts there by a conceptual-physical operation of extraction from the physical factuality, of specimens of the microstate to be studied. These specimens carry in them the factual germs of any possible individual knowledge on a given sort of microstate. This is what entails the emergence of a Second Quantum Mechanics QM2 that is rooted in factuality and is constructed bottom-up. The elaboration of QM2 begins by a new representation of the quantum measurements. The measurements on un-bound microstates devoid of a quantum-potential are treated in the first place. The elaborated treatment is then extended to also the un-bound interference-microstates, by recourse to the de Broglie-Bohm guiding law. The case of bound states does not raise specific questions of principle). The predictive probability measures on results of quantum measurements are constructed by a factual-conceptual procedure-directly via measurements, in a way identical to that which one is obliged to make use of for verifying the predictions-and they are expressed in Hilbert-space terms on the basis of Gleason's theorem. The factual output of this procedure parallels the mathematical output of the Schrödinger equation of the problem when this equation can be written and solved. When the equation involves gross idealizations or/and approximations, this entails control upon tits mathematical output. While when the equation of the problem cannot be solved or cannot be defined, it can be radically replaced by the conceptual-factual procedure defined in this work. This is a notable improvement consonant with the progresses realized in nanotechnology and informatics. Around the core constituted by the new representation of the quantum measurements is then structured a very synthetic global outline of a fully intelligible Second Quantum Mechanics QM2. This theory emerges as a synthesis between IQM, QMHD and the de Broglie-Bohm approach. Its basic descriptional structure is represented by a "factual-probability-tree" rooted in the physical factuality and endowed with a two-level statistical-probabilistic crown. Thereby QM2-via the particular case of microstates-illustrates a strongly deepened and extended, new and general "Theory of Factual Probabilities" belonging to the Mathematical Physics, where all the involved probability measures tied with one studied physical entity can be collectively expressed by a Hilbert-vector and are genetically interconnected by meta-probabilistic correlations. Dirac's bra-ket calculus permits to express formally certain semantic contents involved by a factual-probability-tree. This explains the universal characters perceived by many authors in the Hilbert-Dirac formulation of Quantum Mechanics, while distinguishing clearly between the features mentioned above-that are purely probabilistic-and on the other hand the concept of "microstate" to which these features do just apply in particular. The GENESES of IQM and QM2 indicate a path toward a METHODOLOGICAL sort of unification of Physics.