Results for 'quality, quantity, quantum information, qubit Hilbert space, space-time'

998 found
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  1.  71
    Quantity in Quantum Mechanics and the Quantity of Quantum Information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (47):1-10.
    The paper interprets the concept “operator in the separable complex Hilbert space” (particalry, “Hermitian operator” as “quantity” is defined in the “classical” quantum mechanics) by that of “quantum information”. As far as wave function is the characteristic function of the probability (density) distribution for all possible values of a certain quantity to be measured, the definition of quantity in quantum mechanics means any unitary change of the probability (density) distribution. It can be represented as a (...)
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  2.  62
    Both Classical & Quantum Information; Both Bit & Qubit: Both Physical & Transcendental Time.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (22):1-24.
    Information can be considered as the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information, particularly by their units, bit and qubit, correspond and unify the finite and infinite. As classical information is relevant to finite series and sets, as quantum information, to infinite ones. A fundamental joint relativity of the finite and infinite, of the external and internal is (...)
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  3. Fermat’s last theorem proved in Hilbert arithmetic. III. The quantum-information unification of Fermat’s last theorem and Gleason’s theorem.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (12):1-30.
    The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a (...)
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  4.  81
    Is Mass at Rest One and the Same? A Philosophical Comment: on the Quantum Information Theory of Mass in General Relativity and the Standard Model.Vasil Penchev - 2014 - Journal of SibFU. Humanities and Social Sciences 7 (4):704-720.
    The way, in which quantum information can unify quantum mechanics (and therefore the standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit. The (...)
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  5. The 'Noncausal Causality' of Quantum Information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (45):1-7.
    The paper is concentrated on the special changes of the conception of causality from quantum mechanics to quantum information meaning as a background the revolution implemented by the former to classical physics and science after Max Born’s probabilistic reinterpretation of wave function. Those changes can be enumerated so: (1) quantum information describes the general case of the relation of two wave functions, and particularly, the causal amendment of a single one; (2) it keeps the physical description to (...)
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  6. Main Concepts in Philosophy of Quantum Information.Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (31):1-4.
    Quantum mechanics involves a generalized form of information, that of quantum information. It is the transfinite generalization of information and re-presentable by transfinite ordinals. The physical world being in the current of time shares the quality of “choice”. Thus quantum information can be seen as the universal substance of the world serving to describe uniformly future, past, and thus the present as the frontier of time. Future is represented as a coherent whole, present as a (...)
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  7.  62
    Quantum information as the information of infinite collections or series.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (14):1-8.
    The quantum information introduced by quantum mechanics is equivalent to a certain generalization of classical information: from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The “qubit”, can be interpreted as that generalization of “bit”, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of (...)
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  8. The Kochen - Specker theorem in quantum mechanics: a philosophical comment (part 1).Vasil Penchev - 2013 - Philosophical Alternatives 22 (1):67-77.
    Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum (...)
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  9.  58
    The Symmetries of Quantum and Classical Information. The Ressurrected “Ether" of Quantum Information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (41):1-36.
    The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (...)
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  10. Natural Cybernetics of Time, or about the Half of any Whole.Vasil Penchev - 2021 - Information Systems eJournal (Elsevier: SSRN) 4 (28):1-55.
    Norbert Wiener’s idea of “cybernetics” is linked to temporality as in a physical as in a philosophical sense. “Time orders” can be the slogan of that natural cybernetics of time: time orders by itself in its “screen” in virtue of being a well-ordering valid until the present moment and dividing any totality into two parts: the well-ordered of the past and the yet unordered of the future therefore sharing the common boundary of the present between them when (...)
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  11.  81
    Fermat’s last theorem proved in Hilbert arithmetic. I. From the proof by induction to the viewpoint of Hilbert arithmetic.Vasil Penchev - 2021 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 13 (7):1-57.
    In a previous paper, an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for (...)
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  12. Negative and complex probability in quantum information.Vasil Penchev - 2012 - Philosophical Alternatives 21 (1):63-77.
    “Negative probability” in practice. Quantum Communication: Very small phase space regions turn out to be thermodynamically analogical to those of superconductors. Macro-bodies or signals might exist in coherent or entangled state. Such physical objects having unusual properties could be the basis of quantum communication channels or even normal physical ones … Questions and a few answers about negative probability: Why does it appear in quantum mechanics? It appears in phase-space formulated quantum mechanics; next, in (...)
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  13. The Quantity of Quantum Information and Its Metaphysics.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (18):1-6.
    The quantum information introduced by quantum mechanics is equivalent to that generalization of the classical information from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The qubit can be interpreted as that generalization of bit, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of (...)
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  14. Choice, Infinity, and Negation: Both Set-Theory and Quantum-Information Viewpoints to Negation.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal 12 (14):1-3.
    The concepts of choice, negation, and infinity are considered jointly. The link is the quantity of information interpreted as the quantity of choices measured in units of elementary choice: a bit is an elementary choice between two equally probable alternatives. “Negation” supposes a choice between it and confirmation. Thus quantity of information can be also interpreted as quantity of negations. The disjunctive choice between confirmation and negation as to infinity can be chosen or not in turn: This corresponds to set-theory (...)
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  15. The Frontier of Time: The Concept of Quantum Information.Vasil Penchev - 2020 - Cosmology and Large-Scale Structure eJournal (Elsevier: SSRN) 2 (17):1-5.
    The concept of formal transcendentalism is utilized. The fundamental and definitive property of the totality suggests for “the totality to be all”, thus, its externality (unlike any other entity) is contained within it. This generates a fundamental (or philosophical) “doubling” of anything being referred to the totality, i.e. considered philosophically. Thus, that doubling as well as transcendentalism underlying it can be interpreted formally as an elementary choice such as a bit of information and a quantity corresponding to the number of (...)
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  16.  69
    Fermat’s last theorem proved in Hilbert arithmetic. II. Its proof in Hilbert arithmetic by the Kochen-Specker theorem with or without induction.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (10):1-52.
    The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to (...) contextuality. The relevant mathematical structure is Hilbert arithmetic in a wide sense, in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem. (shrink)
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  17. The isomorphism of Minkowski space and the separable complex Hilbert space and its physical interpretation.Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier:SSRN) 13 (31):1-3.
    An isomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That isomorphism can be interpreted physically as the invariance between a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting another way for proving it, more concise and meaningful physically. (...)
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  18.  84
    The Homeomorphism of Minkowski Space and the Separable Complex Hilbert Space: The physical, Mathematical and Philosophical Interpretations.Vasil Penchev - 2021 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (3):1-22.
    A homeomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That homeomorphism can be interpreted physically as the invariance to a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting at another way for proving it, more concise and meaningful (...)
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  19. What Is Quantum Information? Information Symmetry and Mechanical Motion.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (20):1-7.
    The concept of quantum information is introduced as both normed superposition of two orthogonal sub-spaces of the separable complex Hilbert space and in-variance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen. The separable complex Hilbert space is considered as the free variable of quantum information and any (...)
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  20.  89
    Matter as Information. Quantum Information as Matter.Vasil Penchev - 2016 - Nodi. Collana di Storia Della Filosofia 2016 (2):127-138.
    Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and a qubit. The course of (...)
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  21. Quantum-information conservation. The problem about “hidden variables”, or the “conservation of energy conservation” in quantum mechanics: A historical lesson for future discoveries.Vasil Penchev - 2020 - Energy Engineering (Energy) eJournal (Elsevier: SSRN) 3 (78):1-27.
    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 (...)
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  22. God, Logic, and Quantum Information.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (20):1-10.
    Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and a qubit. The course of (...)
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  23.  82
    Quantum phenomenology as a “rigorous science”: the triad of epoché and the symmetries of information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (48):1-18.
    Husserl (a mathematician by education) remained a few famous and notable philosophical “slogans” along with his innovative doctrine of phenomenology directed to transcend “reality” in a more general essence underlying both “body” and “mind” (after Descartes) and called sometimes “ontology” (terminologically following his notorious assistant Heidegger). Then, Husserl’s tradition can be tracked as an idea for philosophy to be reinterpreted in a way to be both generalized and mathenatizable in the final analysis. The paper offers a pattern borrowed from the (...)
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  24. Cognition according to Quantum Information: Three Epistemological Puzzles Solved.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (20):1-15.
    The cognition of quantum processes raises a series of questions about ordering and information connecting the states of one and the same system before and after measurement: Quantum measurement, quantum in-variance and the non-locality of quantum information are considered in the paper from an epistemological viewpoint. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble (...)
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  25. Problem of the Direct Quantum-Information Transformation of Chemical Substance.Vasil Penchev - 2020 - Computational and Theoretical Chemistry eJournal (Elsevier: SSRN) 3 (26):1-15.
    Arthur Clark and Michael Kube–McDowell (“The Triger”, 2000) suggested the sci-fi idea about the direct transformation from a chemical substance to another by the action of a newly physical, “Trigger” field. Karl Brohier, a Nobel Prize winner, who is a dramatic persona in the novel, elaborates a new theory, re-reading and re-writing Pauling’s “The Nature of the Chemical Bond”; according to Brohier: “Information organizes and differentiates energy. It regularizes and stabilizes matter. Information propagates through matter-energy and mediates the interactions of (...)
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  26. Information, Physics, Quantum: The Search for Links.John Archibald Wheeler - 1989 - In Proceedings III International Symposium on Foundations of Quantum Mechanics. Tokyo: pp. 354-358.
    This report reviews what quantum physics and information theory have to tell us about the age-old question, How come existence? No escape is evident from four conclusions: (1) The world cannot be a giant machine, ruled by any preestablished continuum physical law. (2) There is no such thing at the microscopic level as space or time or spacetime continuum. (3) The familiar probability function or functional, and wave equation or functional wave equation, of standard quantum theory (...)
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  27.  68
    “Two bits less” after quantum-information conservation and their interpretation as “distinguishability / indistinguishability” and “classical / quantum”.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (46):1-7.
    The paper investigates the understanding of quantum indistinguishability after quantum information in comparison with the “classical” quantum mechanics based on the separable complex Hilbert space. The two oppositions, correspondingly “distinguishability / indistinguishability” and “classical / quantum”, available implicitly in the concept of quantum indistinguishability can be interpreted as two “missing” bits of classical information, which are to be added after teleportation of quantum information to be restored the initial state unambiguously. That new (...)
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  28. The Identity of Logic and the World in Terms of Quantum Information.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (21):1-4.
    One can construct a mapping between Hilbert space and the class of all logic if the latter is defined as the set of all well-orderings of some relevant set (or class). That mapping can be further interpreted as a mapping of all states of all quantum systems, on the one hand, and all logic, on the other hand. The collection of all states of all quantum systems is equivalent to the world (the universe) as a whole. (...)
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  29. Universal Logic in terms of Quantum Information.Vasil Penchev - 2020 - Metaphilosophy eJournal (Elsevier: SSRN) 12 (9):1-5.
    Any logic is represented as a certain collection of well-orderings admitting or not some algebraic structure such as a generalized lattice. Then universal logic should refer to the class of all subclasses of all well-orderings. One can construct a mapping between Hilbert space and the class of all logics. Thus there exists a correspondence between universal logic and the world if the latter is considered a collection of wave functions, as which the points in Hilbert space (...)
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  30. Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State.Eddy Keming Chen - 2021 - British Journal for the Philosophy of Science 72 (4):1155–1183.
    In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix that represents something objective. This stands in sharp (...)
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  31. If Quantum Mechanics Is the Solution, What Should the Problem Be?Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (32):1-10.
    The paper addresses the problem, which quantum mechanics resolves in fact. Its viewpoint suggests that the crucial link of time and its course is omitted in understanding the problem. The common interpretation underlain by the history of quantum mechanics sees discreteness only on the Plank scale, which is transformed into continuity and even smoothness on the macroscopic scale. That approach is fraught with a series of seeming paradoxes. It suggests that the present mathematical formalism of quantum (...)
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  32.  76
    Hilbert arithmetic as a Pythagorean arithmetic: arithmetic as transcendental.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (54):1-24.
    The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis of the world in a Pythagorean manner. Hilbert arithmetic unifies the foundations of mathematics (Peano arithmetic and set theory), foundations of physics (quantum mechanics and information), and philosophical transcendentalism (Husserl’s phenomenology) into a formal theory and mathematical structure literally following Husserl’s tracе of “philosophy as a rigorous science”. In the pathway to that objective, Hilbert arithmetic identifies by itself information related to finite sets (...)
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  33.  23
    On the Role of Inconsistency in Quantum Foundational Debate and Hilbert Space Formulation.Debajyoti Gangopadhyay - 2022 - Quanta 11 (Number 1):28-41.
    This article is intended mainly to develop an expository outline of an inherently inconsistent reasoning in the development of quantum mechanics during 1920s, which set up the background of proposing different variants of quantum logic a bit later. We will discuss here two of the quantum logical variants with reference to Hilbert space formulation, based on the proposals of Bohr and Schrödinger as a result of addressing the same kernel of difficulties and will give a (...)
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  34.  44
    Qubit Cosmology.Haikel Mubarek - manuscript
    Understanding the fabric and mechanism of the universe as an information processing procedure is one way of approaching the mystery of reality. And there should be ingredients of information for such a description. But if we are going to start from the origin of the universe, those ingredients should be found at the beginning. What is assumed, in this paper, to be found at the beginning of the universe is an outward-inward vanishing of a point. And those are taken to (...)
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  35. Quantum information theoretic approach to the mind–brain problem.Danko D. Georgiev - 2020 - Progress in Biophysics and Molecular Biology 158:16-32.
    The brain is composed of electrically excitable neuronal networks regulated by the activity of voltage-gated ion channels. Further portraying the molecular composition of the brain, however, will not reveal anything remotely reminiscent of a feeling, a sensation or a conscious experience. In classical physics, addressing the mind–brain problem is a formidable task because no physical mechanism is able to explain how the brain generates the unobservable, inner psychological world of conscious experiences and how in turn those conscious experiences steer the (...)
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  36. The Quantum Strategy of Completeness: On the Self-Foundation of Mathematics.Vasil Penchev - 2020 - Cultural Anthropology eJournal (Elsevier: SSRN) 5 (136):1-12.
    Gentzen’s approach by transfinite induction and that of intuitionist Heyting arithmetic to completeness and the self-foundation of mathematics are compared and opposed to the Gödel incompleteness results as to Peano arithmetic. Quantum mechanics involves infinity by Hilbert space, but it is finitist as any experimental science. The absence of hidden variables in it interpretable as its completeness should resurrect Hilbert’s finitism at the cost of relevant modification of the latter already hinted by intuitionism and Gentzen’s approaches (...)
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  37. Representation and Reality by Language: How to make a home quantum computer?Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (34):1-14.
    A set theory model of reality, representation and language based on the relation of completeness and incompleteness is explored. The problem of completeness of mathematics is linked to its counterpart in quantum mechanics. That model includes two Peano arithmetics or Turing machines independent of each other. The complex Hilbert space underlying quantum mechanics as the base of its mathematical formalism is interpreted as a generalization of Peano arithmetic: It is a doubled infinite set of doubled Peano (...)
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  38. Imprecise Probabilities in Quantum Mechanics.Stephan Hartmann - 2015 - In Colleen E. Crangle, Adolfo García de la Sienra & Helen E. Longino (eds.), Foundations and Methods from Mathematics to Neuroscience. Stanford: CSLI Publications. pp. 77-82.
    In his entry on "Quantum Logic and Probability Theory" in the Stanford Encyclopedia of Philosophy, Alexander Wilce (2012) writes that "it is uncontroversial (though remarkable) the formal apparatus quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over the 'quantum logic' of projection operators on a Hilbert space." For a long time, Patrick Suppes has opposed this view (...)
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  39. The computable universe: from prespace metaphysics to discrete quantum mechanics.Martin Leckey - 1997 - Dissertation, Monash University
    The central motivating idea behind the development of this work is the concept of prespace, a hypothetical structure that is postulated by some physicists to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the rest of reality as we know it, and the implications of the existence of this structure for quantum theory. Understanding how this structure could relate to space (...)
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  40. What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmetic.Vasil Penchev - 2021 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 13 (22):1-32.
    Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with (...)
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  41. Two Strategies to Infinity: Completeness and Incompleteness. The Completeness of Quantum Mechanics.Vasil Penchev - 2020 - High Performance Computing eJournal 12 (11):1-8.
    Two strategies to infinity are equally relevant for it is as universal and thus complete as open and thus incomplete. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, thеse phenomena can be elucidated as both complete and incomplete, after which choice (...)
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  42.  71
    The Completeness: From Henkin's Proposition to Quantum Computer.Vasil Penchev - 2018 - Логико-Философские Штудии 16 (1-2):134-135.
    The paper addresses Leon Hen.kin's proposition as a " lighthouse", which can elucidate a vast territory of knowledge uniformly: logic, set theory, information theory, and quantum mechanics: Two strategies to infinity are equally relevant for it is as universal and t hus complete as open and thus incomplete. Henkin's, Godel's, Robert Jeroslow's, and Hartley Rogers' proposition are reformulated so that both completeness and incompleteness to be unified and thus reduced as a joint property of infinity and of all infinite (...)
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  43. From The Principle Of Least Action To The Conservation Of Quantum Information In Chemistry: Can One Generalize The Periodic Table?Vasil Penchev - 2019 - Chemistry: Bulgarian Journal of Science Education 28 (4):525-539.
    The success of a few theories in statistical thermodynamics can be correlated with their selectivity to reality. These are the theories of Boltzmann, Gibbs, end Einstein. The starting point is Carnot’s theory, which defines implicitly the general selection of reality relevant to thermodynamics. The three other theories share this selection, but specify it further in detail. Each of them separates a few main aspects within the scope of the implicit thermodynamic reality. Their success grounds on that selection. Those aspects can (...)
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  44. Return of Logos: Ontological Memory → Information → Time.Vladimir Rogozhin - 2013 - FQXi Contest 2013:00-08.
    Total ontological unification of matter at all levels of reality as a whole, its “grasp” of its dialectical structure, space dimensionality and structure of the language of nature – “house of Being” [1], gives the opportunity to see the “place” and to understand the nature of information as a phenomenon of Ontological (structural) Memory (OntoMemory), the measure of being of the whole, “the soul of matter”, qualitative quantity of the absolute forms of existence of matter (absolute states). “Information” and (...)
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  45.  66
    Quantum Mereology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics.Sean M. Carroll & Ashmeet Singh - 2021 - Physical Review A 103 (2):022213.
    We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system" and "environment." Such a decomposition can be defined by looking for subsystems that exhibit quasi-classical behavior. The correct decomposition is one in which pointer states of the system are relatively robust against environmental monitoring (their entanglement with the environment does not continually and dramatically increase) (...)
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  46. Two deductions: (1) from the totality to quantum information conservation; (2) from the latter to dark matter and dark energy.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (28):1-47.
    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 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 (...)
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  47. On the (Im)possibility of Scalable Quantum Computing.Andrew Knight - manuscript
    The potential for scalable quantum computing depends on the viability of fault tolerance and quantum error correction, by which the entropy of environmental noise is removed during a quantum computation to maintain the physical reversibility of the computer’s logical qubits. However, the theory underlying quantum error correction applies a linguistic double standard to the words “noise” and “measurement” by treating environmental interactions during a quantum computation as inherently reversible, and environmental interactions at the end of (...)
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  48.  50
    Gentzen’s “cut rule” and quantum measurement in terms of Hilbert arithmetic. Metaphor and understanding modeled formally.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal 14 (14):1-37.
    Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical (...)
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  49. Atomism in Quantum Mechanics and Information.Vasil Penchev - 2020 - Metaphysics eJournal (Elsevier: SSRN) 13 (12):1-11.
    The original conception of atomism suggests “atoms”, which cannot be divided more into composing parts. However, the name “atom” in physics is reserved for entities, which can be divided into electrons, protons, neutrons and other “elementary particles”, some of which are in turn compounded by other, “more elementary” ones. Instead of this, quantum mechanics is grounded on the actually indivisible quanta of action limited by the fundamental Planck constant. It resolves the problem of how both discrete and continuous (even (...)
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  50.  98
    Quantum States of a Time-Asymmetric Universe: Wave Function, Density Matrix, and Empirical Equivalence.Eddy Keming Chen - 2019 - Dissertation, Rutgers University - New Brunswick
    What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition that accounts for the time-asymmetry of the universe. The natural choice is given not by a wave function but by a density matrix. I begin by classifying quantum theories into two types: theories with a fundamental wave (...)
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