Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

AIP conference proceedings

What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

Boris Khots, Dmitriy Khots

Published Jan 1, 2014• 0 citations
Publisher

Abstract

Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.

DOI
10.1063/1.4904615

Related papers

Observerʼs mathematics applications to quantum mechanics

Boris Khots, Dmitriy Khots

When we consider and analyze physical events with the purpose of creating corresponding models we often assume that the mathematical apparatus used in modeling is infallible. In particular, this relates to the use of infinity in various aspects and the use of Newtonʼs definition of a limit in analysis. We believe that is where the main problem lies in the contemporary study of nature. This work considers physical aspects in a setting of arithmetic, algebra, geometry, analysis, and topology provided by Observerʼs Mathematics (see www.mathrelativity.com). In this paper, we consider Dirac equations for free electrons. Certain results and communications pertaining to solutions of these problems are provided.

Physica Scripta•Dec 1, 2014•0 citations

Quantum Theory and Observer's Mathematics

Dmitriy Khots, Boris Khots, Guillaume Adenier +4 more

When we consider and analyze physical events with the purpose of creating corresponding mathematical models we often assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of infinitely small and infinitely large numbers in arithmetic and the use of Newton's definition of a limit in analysis. We believe that is where the main problem lies in contemporary study of nature (physics, genetics). We have introduced a new concept of “Observer's Mathematics—Mathematics of Relativity” (see references). Observer's mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. The concept of a quantum arises automatically from the human thought process, rather than from physics. From this point of view classical mechanics is brought closer to quantum mechanics.

AIP conference proceedings•Jan 1, 2007•2 citations

Quantum Theory from Observer’s Mathematics Point of View

Dmitriy Khots, Boris Khots, Andrei Yu. Khrennikov

This work considers the linear (time‐dependent) Schrodinger equation, quantum theory of two‐slit interference, wave‐particle duality for single photons, and the uncertainty principle in a setting of arithmetic, algebra, and topology provided by Observer’s Mathematics, see [1]. Certain theoretical results and communications pertaining to these theorems are also provided.

AIP conference proceedings•Jan 1, 2010•0 citations

Two-slit interference and wave-particle duality for single photons from Observer's Mathematics point of view

Boris Khots, Dmitriy Khots

When we consider and analyze physical events with the purpose of creating corresponding mathematical models we often assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We proved the following theorems: 1) Theorem A (Two-slit interference). Let Ψ1 be a wave from slit 1, Ψ2 - from slit 2, and Ψ = Ψ1 + Ψ2. Then the probability of that Ψ is a wave equals to 0.5; and 2) Theorem B (Wave-particle duality for single photons). If v is small enough, then λ is a random variable.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 8, 2011•0 citations

The foundations of quantum mechanics in Observer's Mathematics

Boris Khots, Dmitriy Khots

This work considers the Lagrange function in classical mechanics and Hamiltonian equations of general relativity and quantum theory, in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics. Certain results and communications pertaining to solutions of these problems are provided.

AIP conference proceedings•Jan 1, 2012•0 citations

Quantum mechanics and its interpretation

Peter Holland

The nature of the problem The quantum world is inexplicable in classical terms. The predictions pertaining to the interaction of matter and light embodied in Newton's laws for the motion of particles and Maxwell's equations governing the propagation of electromagnetic fields are in flat contradiction with the experimental facts at the microscopic scale. A key feature of quantum effects is their apparent indeterminism, that individual atomic events are unpredictable, uncontrollable and literally seem to have no cause. Regularities emerge only when one considers a large ensemble of such events. This indeed is generally considered to constitute the heart of the conceptual problem posed by quantum phenomena, necessitating a fundamental revision of the deterministic classical world view. Some of the principal phenomena, among those discussed in this book, are as follows: ( a ) Self-interference: a beam of electrons sent one at a time through a barrier containing two apertures builds up through a series of localized detection events on a screen an interference pattern characteristic of waves (cf. the frontispiece and §5.1). ( b ) Tunnelling: an α-particle trapped in a nucleus can pass through a potential barrier in a manner forbidden to a classical particle (§5.3). ( c ) The stability of matter: atoms and molecules are found to exist only in certain discrete, or ‘stationary’, energy states. For this reason they do not ‘collapse’, the result predicted by classical electrodynamics. During transitions between stationary states (quantum jumps) an atom exchanges a discrete quantity of energy with the electromagnetic field (§§4.5, 7.6). […]

Cambridge University Press eBooks•May 13, 1993•3 citations
Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.
When we consider and analyze physical events with the purpose of creating corresponding models we often assume that the mathematical apparatus used in modeling is infallible. In particular, this relates to the use of infinity in various aspects and the use of Newtonʼs definition of a limit in analysis. We believe that is where the main problem lies in the contemporary study of nature. This work considers physical aspects in a setting of arithmetic, algebra, geometry, analysis, and topology provided by Observerʼs Mathematics (see www.mathrelativity.com). In this paper, we consider Dirac equations for free electrons. Certain results and communications pertaining to solutions of these problems are provided.
When we consider and analyze physical events with the purpose of creating corresponding mathematical models we often assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of infinitely small and infinitely large numbers in arithmetic and the use of Newton's definition of a limit in analysis. We believe that is where the main problem lies in contemporary study of nature (physics, genetics). We have introduced a new concept of “Observer's Mathematics—Mathematics of Relativity” (see references). Observer's mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. The concept of a quantum arises automatically from the human thought process, rather than from physics. From this point of view classical mechanics is brought closer to quantum mechanics.
When we consider and analyze physical events with the purpose of creating corresponding mathematical models we often assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We proved the following theorems: 1) Theorem A (Two-slit interference). Let Ψ1 be a wave from slit 1, Ψ2 - from slit 2, and Ψ = Ψ1 + Ψ2. Then the probability of that Ψ is a wave equals to 0.5; and 2) Theorem B (Wave-particle duality for single photons). If v is small enough, then λ is a random variable.
The nature of the problem The quantum world is inexplicable in classical terms. The predictions pertaining to the interaction of matter and light embodied in Newton's laws for the motion of particles and Maxwell's equations governing the propagation of electromagnetic fields are in flat contradiction with the experimental facts at the microscopic scale. A key feature of quantum effects is their apparent indeterminism, that individual atomic events are unpredictable, uncontrollable and literally seem to have no cause. Regularities emerge only when one considers a large ensemble of such events. This indeed is generally considered to constitute the heart of the conceptual problem posed by quantum phenomena, necessitating a fundamental revision of the deterministic classical world view. Some of the principal phenomena, among those discussed in this book, are as follows: ( a ) Self-interference: a beam of electrons sent one at a time through a barrier containing two apertures builds up through a series of localized detection events on a screen an interference pattern characteristic of waves (cf. the frontispiece and §5.1). ( b ) Tunnelling: an α-particle trapped in a nucleus can pass through a potential barrier in a manner forbidden to a classical particle (§5.3). ( c ) The stability of matter: atoms and molecules are found to exist only in certain discrete, or ‘stationary’, energy states. For this reason they do not ‘collapse’, the result predicted by classical electrodynamics. During transitions between stationary states (quantum jumps) an atom exchanges a discrete quantity of energy with the electromagnetic field (§§4.5, 7.6). […]