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

A case study of quantum mechanics is investigated in the framework of the philosophical opposition “mathematical model – reality”. All classical science obeys the postulate about the fundamental difference of model and reality, and thus distinguishing epistemology from ontology fundamentally. The theorems about the absence of hidden variables in quantum mechanics imply for it to be “complete” (versus Einstein’s opinion). That consistent completeness (unlike arithmetic to set theory in the foundations of mathematics in Gödel’s opinion) can be interpreted furthermore as the coincidence of model and reality. The paper discusses the option and fact of that coincidence it its base: the fundamental postulate formulated by Niels Bohr about what quantum mechanics studies (unlike all classical science). Quantum mechanics involves and develops further both identification and disjunctive distinction of the global space of the apparatus and the local space of the investigated quantum entity as complementary to each other. This results into the analogical complementarity of model and reality in quantum mechanics. The apparatus turns out to be both absolutely “transparent” and identically coinciding simultaneously with the reflected quantum reality. Thus, the coincidence of model and reality is postulated as necessary condition for cognition in quantum mechanics by Bohr’s postulate and further, embodied in its formalism of the separable complex Hilbert space, in turn, implying the theorems of the absence of hidden variables (or the equivalent to them “conservation of energy conservation” in quantum mechanics). What the apparatus and measured entity exchange cannot be energy (for the different exponents of energy), but quantum information (as a certain, unambiguously determined wave function) therefore a generalized law of conservation, from which the conservation of energy conservation is a corollary. Particularly, the local and global space (rigorously justified in the Standard model) share the complementarity isomorphic to that of model and reality in the foundation of quantum mechanics. On that background, one can think of the troubles of “quantum gravity” as fundamental, direct corollaries from the postulates of quantum mechanics. Gravity can be defined only as a relation or by a pair of non-orthogonal separable complex Hilbert space attachable whether to two “parts” or to a whole and its parts. On the contrary, all the three fundamental interactions in the Standard model are “flat” and only “properties”: they need only a single separable complex Hilbert space to be defined.

Download Full-text

Quantum-information conservation. The problem about “hidden variables”, or the “conservation of energy conservation” in quantum mechanics: A historical lesson for future discoveries

10.31235/osf.io/3uaym ◽

2020 ◽

Author(s):

Vasil Dinev Penchev

Keyword(s):

Hilbert Space ◽

General Relativity ◽

Quantum Mechanics ◽

Energy Conservation ◽

Ordinal Number ◽

Hidden Variables ◽

Mathematical Structure ◽

Complex Hilbert Space ◽

Conservation Of Energy ◽

The Universe

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 as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore representable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries.

Download Full-text

Quantum mechanics teaching resources from the Institute of Physics

New Directions in the Teaching of Physical Sciences ◽

10.29311/ndtps.v0i10.515 ◽

2014 ◽

pp. 40-43

Author(s):

Antje Kohnle ◽

Derek Raine

Keyword(s):

Quantum Mechanics ◽

Quantum Information ◽

Teaching And Learning ◽

Hidden Variables ◽

Mathematical Structure ◽

Teaching Resources ◽

Creative Commons ◽

Introductory Course ◽

Interpretations Of Quantum Mechanics ◽

Two Level Systems

In December 2013, the Institute of Physics (IOP) launched a set of freely available resources at quantumphysics.iop.org for the teaching and learning of quantum mechanics. The website includes about 80 short articles written by experts in the field and 17 interactive simulations with accompanying activities for an introductory course in quantum mechanics starting from two-level systems. The articles are arranged according to five themes, including a focus on quantum information, interpretations of quantum mechanics, the mathematical structure of the theory, physics applications and historical experiments. The resources make topics such as entanglement, hidden variables and quantum information theory accessible to introductory-level students. They can be used flexibly for a variety of instructional aims at both the introductory and more advanced level. The website includes links to pre-readings, suggestions for further reading, a glossary of technical terms and allows users to rate their understanding of articles.Sharing of these resources is encouraged, with all usage under the Creative Commons CC BY-NC-ND licence. Solutions to problems and activities are available for instructors by emailing [email protected]. Instructors interested in evaluating these resources with their students in order to help us further develop and optimize the site are requested to contact the corresponding author.

Download Full-text

Two deductions: (1) from the totality to quantum information conservation; (2) from the latter to dark matter and dark energy

10.31226/osf.io/xustz ◽

2020 ◽

Author(s):

Vasil Dinev Penchev

Keyword(s):

General Relativity ◽

Dark Matter ◽

Quantum Mechanics ◽

Dark Energy ◽

Quantum Information ◽

Final Analysis ◽

Time Arrow ◽

The Standard Model ◽

Information Conservation ◽

Cognitive Screen

The paper discusses the origin of dark matter and dark energy from the concepts of time and the totality in the final analysis. Though both, and especially the latter, seem to be rather philosophical, nonetheless they are postulated axiomatically and interpreted physically, and the corresponding philosophical transcendentalism serves heuristically. The exposition of the article means to outline the “forest for the trees”, however, in an absolutely rigorous mathematical way, which to be explicated in detail in a future paper. The “two deductions” are two successive stage of a single conclusion mentioned above. The concept of “transcendental invariance” meaning ontologically and physically interpreting the mathematical equivalence of the axiom of choice and the well-ordering “theorem” is utilized again. Then, time arrow is a corollary from that transcendental invariance, and in turn, it implies quantum information conservation as the Noether correlate of the linear “increase of time” after time arrow. Quantum information conservation implies a few fundamental corollaries such as the “conservation of energy conservation” in quantum mechanics from reasons quite different from those in classical mechanics and physics as well as the “absence of hidden variables” (versus Einstein’s conjecture) in it. However, the paper is concentrated only into the inference of another corollary from quantum information conservation, namely, dark matter and dark energy being due to entanglement, and thus and in the final analysis, to the conservation of quantum information, however observed experimentally only on the “cognitive screen” of “Mach’s principle” in Einstein’s general relativity therefore excluding any other source of gravitational field than mass and gravity. Then, if quantum information by itself would generate a certain nonzero gravitational field, it will be depicted on the same screen as certain masses and energies distributed in space-time, and most presumably, observable as those dark energy and dark matter predominating in the universe as about 96% of its energy and matter quite unexpectedly for physics and the scientific worldview nowadays. Besides on the cognitive screen of general relativity, entanglement is available necessarily on still one “cognitive screen” (namely, that of quantum mechanics), being furthermore “flat”. Most probably, that projection is confinement, a mysterious and ad hoc added interaction along with the fundamental tree ones of the Standard model being even inconsistent to them conceptually, as far as it need differ the local space from the global space being definable only as a relation between them (similar to entanglement). So, entanglement is able to link the gravity of general relativity to the confinement of the Standard model as its projections of the “cognitive screens” of those two fundamental physical theories.

Download Full-text

Quantum Processes, Systems and Information by Benjamin Schumacher & Michael Westmoreland

New Directions in the Teaching of Physical Sciences ◽

10.29311/ndtps.v0i10.519 ◽

2014 ◽

pp. 64-65

Author(s):

Antje Kohnle

Keyword(s):

Quantum Mechanics ◽

Quantum Information ◽

Undergraduate Students ◽

Open Systems ◽

Hidden Variables ◽

Continuous Systems ◽

Wave Mechanics ◽

Quantum Processes ◽

Spin Particle ◽

Starting Point

Quantum Processes, Systems and Information is a textbook aimed at advanced undergraduate students that brings together more traditional quantum mechanics topics and quantum information theory. The book is novel both in this focus and its presentation of the material. The first five chapters discuss the basics of quantum theory using three isomorphic two-level systems: a photon in a Mach–Zehnder interferometer, a spin ½ particle and a two-level atom. These chapters also develop basic quantum information concepts such as the entropy of a message, interpreting unitary time evolution in terms of information capacity and the difference between distinct and distinguishable states in terms of the basic decoding and distinguishability theorems. The text then continues (chapters 6–9) with two-particle states, including entanglement, hidden variables, the no-cloning theorem, density operators and open systems. The transition to continuous systems, the starting point for many quantum mechanics textbooks, is made only in chapter 10, and the following chapters include standard wave mechanics found in many texts. The final three chapters revert the focus back to quantum information processing.

Download Full-text

From the principle of least action to the conservation of quantum information in chemistry. Can one generalize the periodic table?

10.31235/osf.io/avyt2 ◽

2020 ◽

Author(s):

Vasil Dinev Penchev

Keyword(s):

Quantum Information ◽

Energy Conservation ◽

Periodic Table ◽

Chemical Elements ◽

Chemical Change ◽

Conservation Of Energy ◽

Least Action ◽

Principle Of Least Action ◽

Smooth Transformation ◽

As If

In fact, the first law of conservation (that of mass) was found in chemistry and generalized to the conservation of energy in physics by means of Einstein’s famous “E=mc2”. Energy conservation is implied by the principle of least action from a variational viewpoint as in Emmy Noether’s theorems (1918): any chemical change in a conservative (i.e. “closed”) system can be accomplished only in the way conserving its total energy. Bohr’s innovation to found Mendeleev’s periodic table by quantum mechanics implies a certain generalization referring to the quantum leaps as if accomplished in all possible trajectories (according to Feynman’s interpretation) and therefore generalizing the principle of least action and needing a certain generalization of energy conservation as to any quantum change. The transition from the first to the second theorem of Emmy Noether represents well the necessary generalization: its chemical meaning is the generalization of any chemical reaction to be accomplished as if any possible course of time rather than in the standard evenly running time (and equivalent to energy conservation according to the first theorem).The problem: If any quantum change is accomplished in all possible “variations (i.e. “violations) of energy conservation” (by different probabilities), what (if any) is conserved?An answer: quantum information is what is conserved. Indeed, it can be particularly defined as the counterpart (e.g. in the sense of Emmy Noether’s theorems) to the physical quantity of action (e.g. as energy is the counterpart of time in them). It is valid in any course of time rather than in the evenly running one. That generalization implies a generalization of the periodic table including any continuous and smooth transformation between two chemical elements.

Download Full-text

Quantum Mechanics is About Quantum Information

Foundations of Physics ◽

10.1007/s10701-004-2010-x ◽

2005 ◽

Vol 35 (4) ◽

pp. 541-560 ◽

Cited By ~ 31

Author(s):

Jeffrey Bub

Keyword(s):

Quantum Mechanics ◽

Quantum Information

Download Full-text

Beyond Causal Explanation: Einstein’s Principle Not Reichenbach’s

Entropy ◽

10.3390/e23010114 ◽

2021 ◽

Vol 23 (1) ◽

pp. 114

Author(s):

Michael Silberstein ◽

William Mark Stuckey ◽

Timothy McDevitt

Keyword(s):

Quantum Mechanics ◽

Quantum Information ◽

Causal Explanation ◽

Causal Structure ◽

Minkowski Spacetime ◽

Physical Principle ◽

Causal Principle ◽

Complete Rejection ◽

Epr Correlations ◽

Tsirelson Bound

Our account provides a local, realist and fully non-causal principle explanation for EPR correlations, contextuality, no-signalling, and the Tsirelson bound. Indeed, the account herein is fully consistent with the causal structure of Minkowski spacetime. We argue that retrocausal accounts of quantum mechanics are problematic precisely because they do not fully transcend the assumption that causal or constructive explanation must always be fundamental. Unlike retrocausal accounts, our principle explanation is a complete rejection of Reichenbach’s Principle. Furthermore, we will argue that the basis for our principle account of quantum mechanics is the physical principle sought by quantum information theorists for their reconstructions of quantum mechanics. Finally, we explain why our account is both fully realist and psi-epistemic.

Download Full-text