scholarly journals Cognition according to Quantum information: Three Epistemological Puzzles Solved

2020 ◽  
Author(s):  
Vasil Dinev Penchev

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 invariance and the nonlocality 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 after measurement. Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results.A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. However the above equivalence requires it to be equated to a well-ordered set after measurement and thus requires the axiom of choice for it to be able to be obtained.Quantum invariance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information. Quantum invariance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity.The nonlocality of quantum information unifies the exact position of any space-time point of a smooth trajectory and the common possibility of all space-time points due to a quantum leap. This is deduced from quantum invariance.Epistemology involves the relation of ordering and thus a generalized kind of information, quantum one, to explain the special features of the cognition in quantum mechanics.,

2020 ◽  
Author(s):  
Vasil Dinev Penchev

Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. 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 after measurement.A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. It should be equated to a well-ordered set after measurement and thus requires the axiom of choice.Quantum invariance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information.Quantum invariance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity.


2020 ◽  
Author(s):  
Vasil Dinev Penchev

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 results in time after measurement. The quantity of quantum information is the ordinal corresponding to the infinity series in question.1


2020 ◽  
Author(s):  
Vasil Dinev Penchev

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 results in time after measurement. The quantity of quantum information is the ordinal corresponding to the infinity series in question. Number and being (by the meditation of time), the natural and artificial turn out to be not more than different hypostases of a single common essence. This implies some kind of neo-Pythagorean ontology making related mathematics, physics, and technics immediately, by an explicit mathematical structure.


2020 ◽  
Author(s):  
Vasil Dinev Penchev

The paper justifies the following theses: The totality can found time if the latter isaxiomatically represented by its “arrow” as a well-ordering. Time can found choice and thusinformation in turn. Quantum information and its units, the quantum bits, can be interpreted astheir generalization as to infinity and underlying the physical world as well as theultimate substance of the world both subjective and objective. Thus a pathway ofinterpretation between the totality via time, order, choice, and information to the substance ofthe world is constructed. The article is based only on the well-known facts and definitions andis with no premises in this sense. Nevertheless it is naturally situated among works and ideasof Husserl and Heidegger, linked to the foundation of mathematics by the axiom of choice, tothe philosophy of quantum mechanics and information.


2020 ◽  
Author(s):  
Vasil Dinev Penchev

The paper justifies the following theses: The totality can found time if the latteris axiomatically represented by its “arrow” as a well-ordering. Time can found choice andthus information in turn. Quantum information and its units, the quantum bits, can beinterpreted as their generalization as to infinity and underlying the physical world as wellas the ultimate substance of the world both subjective and objective. Thus a pathway ofinterpretation between the totality via time, order, choice, and information to the substance ofthe world is constructed. The article is based only on the well-known facts and definitions andis with no premises in this sense. Nevertheless it is naturally situated among works and ideasof Husserl and Heidegger, linked to the foundation of mathematics by the axiom of choice, tothe philosophy of quantum mechanics and information.


2020 ◽  
Author(s):  
Vasil Dinev Penchev

A 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 elementary choices to be defined. This is the quantity of information defined both transcendentally and formally and thus, philosophically and mathematically. If one defines information specifically, as an elementary choice between finiteness (or mathematically, as any natural number of Peano arithmetic) and infinity (i.e. an actually infinite set in the meaning of set theory), the quantity of quantum information is defined. One can demonstrate that the so-defined quantum information and quantum information standardly defined by quantum mechanics are equivalent to each other. The equivalence of the axiom of choice and the well-ordering “theorem” is involved. It can be justified transcendentally as well, in virtue of transcendental equivalence implied by the totality. Thus, all can be considered as temporal as far anything possesses such a temporal counterpart necessarily. Formally defined, the frontier of time is the current choice now, a bit of information, furthermore interpretable as a qubit of quantum information.


2021 ◽  
Author(s):  
Vasil Penchev

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 results in time after measurement. The quantity of quantum information is the transfinite ordinal number corresponding to the infinity series in question. The transfinite ordinal numbers can be defined as ambiguously corresponding “transfinite natural numbers” generalizing the natural numbers of Peano arithmetic to “Hilbert arithmetic” allowing for the unification of the foundations of mathematics and quantum mechanics.


2020 ◽  
Author(s):  
Vasil Dinev Penchev

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. Mathematically, the isomorphism means the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”.


Author(s):  
Antje Kohnle

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.


2021 ◽  
Author(s):  
Vasil Dinev Penchev

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 particular case of “unitary” qubits. The converse interpretation of any qubits as referring to a certain physical quantity implies its generalization to non-Hermitian operators, thus neither unitary, nor conserving energy. Their physical sense, speaking loosely, consists in exchanging temporal moments therefore being implemented out of the space-time “screen”. “Dark matter” and “dark energy” can be explained by the same generalization of “quantity” to non-Hermitian operators only secondarily projected on the pseudo-Riemannian space-time “screen” of general relativity according to Einstein's “Mach’s principle” and his field equation.


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