A SECOND QUANTUM MECHANICS 2ème MÉCANIQUE

PRINCIPLES OF
A SECOND QUANTUM MECHANICS
PRINCIPES D’UNE
2ème MÉCANIQUE QUANTIQUE
A strongly improved second version replacing
arXiv :1310 :1728v1 [quant-ph], October 2013
French text with an incorporated more detailed English
abstract.
Mioara Mugur-Schächter*
By use of a reference structure called infra-[quantum mechanics], a new representation
of microsystems is constructed that is endowed with a theory of quantum measurements
acceptable from all viewpoints. This new representation is called a second quantum me-
chanics.
283 pages, 8 figures (the figures from reproduced documents are not counted).
*Centre pour la Synthèse d’une Epistémologie Formalisée et adMCR
http://www.mugur-schachter.net ;http://www.mugur-schachter.jimdo.com
arXiv:1310.1728v3 [quant-ph] 23 Oct 2014

II
Abstract
This work is not a ‘reinterpretation’ of nowadays Quantum Mechanics. It consists of a new represen-
tation of microstates, fully reconstructed conceptually and formally, and freed of ‘interpretation problems’.
First a qualitative but formalized representation of microstates is developed – rigorously and quite
independently of the quantum mechanical formalism – under exclusively epistemological-operational-
methodological constraints. This is called ‘Infra-Quantum Mechanics’ and is denoted IMQ. The specific
and definite aim of Infra-Quantum Mechanics is to endow us with a reference-and-imbedding-structure ex-
pressly organized outside nowadays Quantum Mechanics, in a way such as to insure detailed and maximally
efficient comparability with the current Hilbert-Dirac formulation.
This – and only this – can permit a clearly significant, exhaustive and coherent re-examination of no-
wadays fundamental Quantum Mechanics, of its inner structure as well as its global structure grasped
from its outside.
By use of Infra-Quantum Mechanics, a critical-constructive examination of the Hilbert-Dirac forma-
lism is first worked out, step by step. It thus appears that :
(a) Nowadays Quantum Mechanics is devoid of any explicit mathematical representation of indivi-
dual, physical, actual microstates, even though the statistical-probabilistic predictions asserted by the theory
concern precisely these physical entities.
(b) Nowadays Quantum Mechanics is simply devoid of a theory of measurement. What is now called
‘the quantum theory of measurement’ concerns clearly only one particular category of microstates –those
that do not involve quantum fields – and for this particular category it is found to be unacceptable as much
from a mathematical point of view as from a conceptual one. So we are confronted with the question :
What significance can be assigned to a theory of microstates that cannot be directly perceived, if it
does not include a general and fully acceptable theory of measurements ?
This question leads to a thorough investigation on the conditions required by the possibility to specify
the content and the result of an act of measurement achieved upon a microstate, of a ‘mechanical’ quantity
assigned to this microstate by postulation, and to make verifiable predictions concerning the statistical results
of such acts of measurement. This investigation brings forth that inside the Hilbert-Dirac mathematical fra-
mework such conditions can be realized only for the particular category of microstates that do not involve
quantum fields.
Whereas for microstates that do involve quantum fields it is unavoidably necessary to make explicit
conceptual use of de Broglie’s ‘wave-corpuscle’ model of a microstate. This recourse, however, can become
conclusive only if the de Broglie-Bohm ‘guidance trajectories’ can be observed experimentally.
We have proved that – contrary to what is believed – the de Broglie-Bohm representation of microphe-
nomena is in fact formally compatible with observability of a guidance trajectory. Retroactively this proof can
be incorporated to the category of experiments called “weak measurements”. So we propose an experiment
from this category for establishing whether yes or not the observability of a guidance trajectory can also
be physically realized for heavy microsystems. A way of realizing this experiment is thoroughly described
inside the mentioned proof of formal compatibility.
In order to achieve and close our conceptual exploration, we have then admitted by hypothesis that
the mentioned physical observability of the guidance trajectory of a heavy microsystem has been established.
On this basis, a theory of quantum measurements is delineated that takes into account all the categories of
microstates, free or bound, and involving quantum fields, or not.
The general principles of the new representation of microstates that incorporates this theory of quan-
tum measurements are then explicitly stated. This new representation of microstates is called ‘a second quan-
tum mechanics’ and is denoted QM2.
Inside QM2 all the major problems raised by the current Hilbert-Dirac formalism, vanish. QM2 is
directly rooted into the individual, physical, actual factuality. This, while it permits insertion in the mathe-
matical representation, on the other hand entails operational-predictional independence with respect to the
mathematical representation specific of QM2. In the time of Big Data this seems useful.
QM2 is an intimate synthesis between Infra-Quantum Mechanics, the Hilbert-Dirac formulation of
Quantum Mechanics, and a variant of the de Broglie-Bohm representation of microphenomena that is drawn
into observability via explicit connection with Infra-Quantum Mechanics.

III
La construction exposée dans cet ouvrage
est dédiée à mon Maître
Louis de Broglie
dont le modèle séminal ‘onde-particule’
a fondé la Mécanique Quantique
et permet de la re-fonder
presque 90 ans plus tard

IV
Reconnaissances et Remerciements
Ni ce travail ni mon entière œuvre n’auraient pu se constituer sans le
très long soutien, constant et ferme, de Sully Schächter, mon mari.
Je remercie de tout cœur mes fils François et Vincent pour leur indé-
fectible présence.
Je remercie vivement tous ceux qui m’ont témoigné confiance, et tout
particulièrement Henri Boulouet, Geneviève Rivoire, Jean-Marie Fessler et
Jean-Paul Baquiast.
Les échanges professionnels sur fond d’amitié m’ont été singulière-
ment précieux : ma reconnaissance très vive va vers Geneviève Rivoire.
Neuilly-sur-Seine, 17 juin octobre 2014.
Mioara Mugur-Schächter

V
SOMMAIRE
Introduction Générale 1
I L’infra-Mécanique Quantique
Introduction à la Première Partie 5
1 Naissance d’un projet 6
1.1 Sur le processus d’émergence de la mécanique quantique ...................... 6
1.2 Une hypothèse ........................................... 6
1.3 Un projet .............................................. 7
1.3.1 Formulation du projet ..................................... 7
1.3.2 Nouveauté du projet ...................................... 8
1.3.3 Intermède : une conférence sur la localité en 1979 ....................... 9
1.3.4 But latéral : réaction à un danger épistémologique ....................... 23
2 L’infra-mécanique quantique 24
2.1 Préalables .............................................. 24
2.2 Comment introduire un microétat en tant qu’objet de description ? ................. 25
2.2.1 Une opération de génération d’un micro-état .......................... 26
2.2.2 Étiquetage et communicabilité ................................. 27
2.2.3 Une décision méthodologique inévitable ............................ 29
2.2.4 Une catégorie particulière d’opérations de génération d’un microétat : Opérations de ‘génération
composée’ ........................................... 30
2.2.5 Mutation du concept de “définition” d’une entité-objet-d’étude ................. 34
2.2.6 Une scission remarquable ................................... 36
2.3 Qualifier un microétat ....................................... 38
2.3.1 Comment qualifions-nous habituellement ? Grille normée de qualifications communicables et
consensuelles ......................................... 38
2.3.2 De la grille usuelle de qualifications communicables, à une ‘condition-cadre générale’ pour la
qualifiabilité d’un microétat .................................. 41
2.3.2.1 Préalables : Spécificités d’une opération de qualification d’un microétat ........... 41
2.3.2.2 La codage-cadre d’espace-temps et la grille ‘primordiale’ de qualification d’un microétat ... 46
2.3.2.3 Descriptions transférées de base fondées sur des représentations de “grandeurs” importées de
la conceptualisation classique ................................ 53
2.3.2.4 Conclusion sur 2.3.2 .................................... 56
2.3.3 Deux conséquences du concept de grille de qualification applicable à des microétats ...... 57
2.3.3.1 Qualifications de microétats et ‘propriétés’ ......................... 57
2.3.3.2 Retour sur la relation entre qualifications ‘mécaniques’ de microétats versus modèle ..... 58
2.3.4 Conclusion globale sur les qualifications transférées primordiales de microétats, et modélisation
de celles-ci .......................................... 60
2.4 Description qualitative de microétats progressifs (non-liés dans une microstructure) ........ 60
2.4.1 Annonce générale ....................................... 60
2.4.2 Quelques définitions fondamentales .............................. 61
2.5 Construction d’une ‘description’ de microétat ........................... 63
2.5.1 Le caractère primordialement statistique des qualifications ‘mécaniques’ d’un microétat .... 64
2.5.2 Exigence de quelque stabilité des manifestations observées (consensus) ............. 65
2.5.3 Exigences de spécificité face à meGd’une loi de ‘probabilité’ p(G,Xj), versus grandeurs mutuel-
lement incompatibles ..................................... 66