Quantum-Information Conservation. The Problem About ‘Hidden Variables’, or the ‘Conservation of Energy Conservation’ in Quantum Mechanics: A Historical Lesson for Future Discoveries

Abstract

The explicit history of the "hidden variables" problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the "conservation of energy conservation" in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the "fourth Heisenberg uncertainty", that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli's truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters's argument would be valid. The link between the "conservation of energy conservation" and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg's matrix mechanics and Schrödinger's wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann's definition of "ordinal number"). The same condition interpreted in the proper terms of quantum mechanics means its "unitarity", therefore the "conservation of energy conservation". In other words, the "conservation of energy conservation" is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg's approach and Schrödinger's version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished "quantum gravity" as well as a "manual" of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered ...

Natural Cybernetics of Time, or about the Half of any Whole

“…Immediately granting conclusions of a previous work (Penchev 2020 August 17) as to the latter, one can admit that "evolutionary tree" and time as "well-ordering" may be as equated (if the system is accepted to be conservative as after energy conservation) as subordinated (if "well-ordering" comprises only a true subclass of evolutionary trees, which can be called "conservative evolutionary trees", each of which coinciding with its "temporal projection).…”

“…That extraordinary epistemological relation is the subject of discussion in: Penchev 2020 August 30. 11 The necessary existence of entanglement and all phenomena implied by it (among the most important ones is "dark field" unifying "dark energy" and "dark matter") can be deduced even still from the postulate of the totality by means of "physical and mathematical transcendentalism" (in detail in: Penchev 2020 August 31) via the "conservation of quantum information" (in detail in : Penchev 2020 August 17).…”

“…An intermediate link is the concept of quantum information once its equivalence to the classical information of infinite series or sets has been proved (Penchev 2020 June 18). Then, the result after eidetic reduction can be a single qubit in the final analysis, furthermore, doubled by a dual qubit for psychological reduction.…”

“…The thermodynamic theories involve a new fundamental physical, but physically dimensionless quantity of entropy and specific for them: featuring only them. Quantum mechanics is reformulable equivalently and exhaustively as theory of quantum information, in which "quantum information" can be defined as a physical quantity related or generalizing physical entropy, on the one hand, and can be considered as a generalization of the classical concept of information referring to infinite series or sets (Penchev 2020 June 18), on the other hand. Besides by introducing "entropy", the physical theories of irreversible time can be featured or defined in a few ways independent of each other only at first glance:…”

The Generalization of the Periodic Table: The 'Periodic Table' of 'Dark Matter'

“…The eventual generalizing law of quantum information as well as its inference and proof are suggested in another previous paper(Penchev 2020 August 17), and the link of that law to the problem about dark matter and dark energy, in: Penchev 2020 August 31.…”