scholarly journals Time and information in the foundations of physics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Physical World ◽  
Axiom Of Choice ◽  
Quantum Bits ◽  
Foundations Of Physics ◽  
The World ◽  
Time Order ◽  
The Axiom Of Choice

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.

scholarly journals Time: From the Totality to Quantum Information

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Physical World ◽  
Axiom Of Choice ◽  
Quantum Bits ◽  
The World ◽  
Time Order ◽  
The Axiom Of Choice

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.

scholarly journals Quantum information as the information of infinite series

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Coherent State ◽  
Infinite Series ◽  
Axiom Of Choice ◽  
Classical Information ◽  
The Axiom Of Choice

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

scholarly journals The Frontier of Time: The Concept of Quantum Information

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Natural Number ◽  
Set Theory ◽  
Peano Arithmetic ◽  
Axiom Of Choice ◽  
The Axiom Of Choice ◽  
Infinite Set ◽  
In Virtue Of

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.

scholarly journals The Quantity of Quantum Information and Its Metaphysics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Coherent State ◽  
Infinite Series ◽  
Mathematical Structure ◽  
Axiom Of Choice ◽  
Classical Information ◽  
The Axiom Of Choice

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.

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

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Coherent State ◽  
Space Time ◽  
Axiom Of Choice ◽  
Statistical Ensemble ◽  
Quantum Processes ◽  
Quantum Leap ◽  
Before And After ◽  
The Axiom Of Choice

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.,

scholarly journals The isomorphism of Minkowski space and the separable complex Hilbert space and its physical interpretation

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Special Relativity ◽  
Minkowski Space ◽  
Reference Frame ◽  
Physical Interpretation ◽  
Complex Hilbert Space ◽  
Axiom Of Choice ◽  
The Axiom Of Choice

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”.

scholarly journals On Russell’s 1927 Book The Analysis of Matter

Philosophies ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 40
Author(s):  
Said Mikki
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Building Blocks ◽  
Bertrand Russell ◽  
Important Work ◽  
Philosophy Of Nature ◽  
Foundations Of Physics ◽  
The World ◽  
Ordinal Space ◽  
Historical Fact

The goal of this article is to bring into wider attention the often neglected important work by Bertrand Russell on the philosophy of nature and the foundations of physics, published in the year 1927. It is suggested that the idea of what could be named Russell space, introduced in Part III of that book, may be viewed as more fundamental than many other types of spaces since the highly abstract nature of the topological ordinal space proposed by Russell there would incorporate into its very fabric the emergent nature of spacetime by deploying event assemblages, but not spacetime or particles, as the fundamental building blocks of the world. We also point out the curious historical fact that the book The Analysis of Matter can be chronologically considered the earliest book-length generic attempt to reflect on the relation between quantum mechanics, just emerging by that time, and general relativity.

scholarly journals Free Will in Human Behavior and Physics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Free Will ◽  
Human Behavior ◽  
Physical World ◽  
Classical Physics ◽  
Quantum Bit ◽  
The Past ◽  
The Mean ◽  
The One

If the concept of “free will” is reduced to that of “choice” all physical world share the latter quality. Anyway the “free will” can be distinguished from the “choice”: The “free will” involves implicitly a certain goal, and the choice is only the mean, by which the aim can be achieved or not by the one who determines the target. Thus, for example, an electron has always a choice but not free will unlike a human possessing both. Consequently, and paradoxically, the determinism of classical physics is more subjective and more anthropomorphic than the indeterminism of quantum mechanics for the former presupposes certain deterministic goal implicitly following the model of human freewill behavior. Quantum mechanics introduces the choice in the fundament of physical world involving a generalized case of choice, which can be called “subjectless”: There is certain choice, which originates from the transition of the future into the past. Thus that kind of choice is shared of all existing and does not need any subject: It can be considered as a low of nature. There are a few theorems in quantum mechanics directly relevant to the topic: two of them are called “free will theorems” by their authors (Conway and Kochen 2006; 2009). Any quantum system either a human or an electron or whatever else has always a choice: Its behavior is not predetermined by its past. This is a physical law. It implies that a form of information, the quantum information underlies all existing for the unit of the quantity of information is an elementary choice: either a bit or a quantum bit (qubit).

scholarly journals Quantum Information: A Brief Overview and Some Mathematical Aspects

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 273
Author(s):  
Maurice Kibler
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Short Review ◽  
Mutually Unbiased Bases ◽  
Quantum Bits ◽  
Mathematical Problems ◽  
Classical Information Theory ◽  
Main Ideas

The aim of the present paper is twofold. First, to give the main ideas behind quantum computing and quantum information, a field based on quantum-mechanical phenomena. Therefore, a short review is devoted to (i) quantum bits or qubits (and more generally qudits), the analogues of the usual bits 0 and 1 of the classical information theory, and to (ii) two characteristics of quantum mechanics, namely, linearity, which manifests itself through the superposition of qubits and the action of unitary operators on qubits, and entanglement of certain multi-qubit states, a resource that is specific to quantum mechanics. A, second, focus is on some mathematical problems related to the so-called mutually unbiased bases used in quantum computing and quantum information processing. In this direction, the construction of mutually unbiased bases is presented via two distinct approaches: one based on the group SU(2) and the other on Galois fields and Galois rings.

scholarly journals Quantum Invariance

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Information ◽  
Coherent State ◽  
Set Theory ◽  
Ordered Set ◽  
Axiom Of Choice ◽  
Statistical Ensemble ◽  
Planck Constant ◽  
Physical Processes ◽  
Statistical Representation ◽  
The Axiom Of Choice

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.

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