Arithmetic for the unification of quantum mechanics and general relativity

Korotkikh, Victor

doi:10.1088/1742-6596/174/1/012055

Cited by 6 publications

(8 citation statements)

References 3 publications

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“…Therefore, as long as our description requires the existence of the minimum length of space l min > 0, according to (7), it determines that the velocity v j1 of the elementary part P j1 can not be equal to the maximum possible velocity c. Indeed, in this case we get…”

Section: Space and Time As Dynamic Variables In The Geometrization Ofmentioning

confidence: 98%

“…Let us present a picture that arises in the geometrization of a correlation structure with space and time acting as dynamic variables [5]- [7].…”

Section: Space and Time As Dynamic Variables In The Geometrization Ofmentioning

confidence: 99%

“…It is a challenging task to develop a theory that could operate with statements like 1 + 2 = 3 and produce results in agreement with observation. Remarkably, the description of complex systems in terms of self-organization processes of prime integer relations has been discovered [4]- [7]. It shows that certain self-evident integer relations can be organized into a hierarchical network, where an element of a level is formed from elements of the lower level so that all elements in the formation are necessary and sufficient.…”

Section: Introductionmentioning

confidence: 99%

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Integers as a Key to Understanding Quantum Mechanics

Korotkikh¹,

Khrennikov²

2010

AIP Conference Proceedings

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Section: Space and Time As Dynamic Variables In The Geometrization Ofmentioning

confidence: 98%

“…Let us present a picture that arises in the geometrization of a correlation structure with space and time acting as dynamic variables [5]- [7].…”

Section: Space and Time As Dynamic Variables In The Geometrization Ofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Integers as a Key to Understanding Quantum Mechanics

Korotkikh¹,

Khrennikov²

2010

AIP Conference Proceedings

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“…Significantly, by using the base D jl and the height H jl alone we can find the area of the geometrical pattern. In fact, although the geometrical pattern of the jth part j = 1, ..., 2 k−l at level l = 2, ..., k is not a triangle, yet, due to the condition (8), the boundary curve, as the graph of the function Ψ…”

Section: It Turns Out That [3]mentioning

confidence: 99%

On Possible Implications of Self-Organization Processes through Transformation of Laws of Arithmetic into Laws of Space and Time

Korotkikh¹

2010

Preprint

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In the paper we present results based on the description of complex systems in terms of selforganization processes of prime integer relations. Realized through the unity of two equivalent forms, i.e., arithmetical and geometrical, the description allows to transform the laws of a complex system in terms of arithmetic into the laws of the system in terms of space and time. Possible implications of the results are discussed.

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“…Remarkably, the description of complex systems in terms of self-organization processes of prime integer relations has been discovered [5]- [8] and showed promising results [9]- [14]. In particular, it turns out that self-evident integer relations can be organized into a hierarchical network, where an element of a level is formed from elements of the lower level so that all elements in the formation are necessary and sufficient.…”

Section: Introductionmentioning

confidence: 99%

On the Potential of the Irreducible Description of Complex Systems for the Modeling of the Global Financial System

Korotkikh,

Korotkikh

2009

Preprint

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The recent financial crisis has sharply revealed that current understanding of the global financial system is more than limited. In the recovery plan the confidence in the underlying theory is crucial.To address the problem we propose the description of complex systems in terms of self-organization processes of prime integer relations. The description suggests to consider the global financial system through the hierarchical network built by the totality of the self-organization processes. To make the description operational we propose an integration principle and support it by computational experiments using a multi-agent system. Remarkably, based on integers and controlled by arithmetic only the description raises the possibility to develop an irreducible theory of complex systems. These may open a fundamentally new perspective for the modeling of the global financial system.

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Arithmetic for the unification of quantum mechanics and general relativity

Cited by 6 publications

References 3 publications

Integers as a Key to Understanding Quantum Mechanics

Integers as a Key to Understanding Quantum Mechanics

On Possible Implications of Self-Organization Processes through Transformation of Laws of Arithmetic into Laws of Space and Time

On the Potential of the Irreducible Description of Complex Systems for the Modeling of the Global Financial System

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