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

arXiv:0904.1862

Quantum amplitudes are a consequence of elementary probability theory

Alexey L. Krugly

Published Apr 12, 2009• 2 citations
arXivHTMLPDF

Abstract

I suppose that quantum objects obey elementary probability theory. I consider a connection of elementary probability theory and complex quantum amplitudes by a matrix calculus. A special case of a discrete pregeometry is an example of this approach.
DOI
10.48550/arxiv.0904.1862

Related papers

The physical interpretation of the quantum dynamics

P. A. M. Dirac

Abstract The new quantum mechanics consists of a scheme of equations which are very closely analogous to the equations of classical mechanics, with the funda­mental difference that the dynamical variables do not obey the commutative law of multiplication, but satisfy instead the well-known quantum conditions. It follows that one cannot suppose the dynamical variables to be ordinary numbers (c-numbers), but may call them numbers of a special type (q-numbers). The theory shows that these q-numbers can in general be represented by matrices whose elements are c-numbers (functions of a time parameter). When one has performed the calculations with the q-numbers and obtained all the matrices one wants, the question arises how one is to get physical results from the theory, i. e., how can one obtain c-numbers from the theory that one can compare with experimental values ? Hitherto this has been done with the help of a number of special assumptions. In Heisenberg’s original matrix mechanics it was assumed that the elements of the diagonal matrix that repre­sents the energy are the energy levels of the system, and the elements of the matrix that represents the total polarisation, which are periodic functions of the time, determine the frequencies and intensities of the spectral lines in analogy to the classical theory. Schrodinger’s wave representation of the quantum mechanics has provided new ways of obtaining physical results from the theory, based on the assumption that the square of the amplitude of the wave function can in certain cases be interpreted as a probability. From this assumption one can, for instance, work out the probability of a transition being produced in a system (or the number of transitions produced in an assembly of like systems) by an arbitrary external perturbing force, and can thus, by supposing the perturbation to consist of incident radiation, obtain directly Einstein’s B coefficients. Again in Born’s treatment of collision problems it is assumed that the square of the amplitude of the wave function scattered in any direction determines the probability of the colliding electron (or other body) being scattered in that direction.

Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character•Jan 1, 1927•404 citations

Are classical probabilities instances of quantum amplitudes?

Italo Vecchi

A conjecture about the quantum nature of classical probabilites is set forth and discussed.

arXiv:quant-ph/0206147•Jun 20, 2002•2 citations

Probability and quantum mechanics

Daniel J. Velleman

We discuss the use of probability theory in quantum mechanics, and suggest that there are some interpretations of quantum mechanics in which probabilities may be used inappropriately.

American Journal of Physics•Nov 1, 1998•4 citations

Macroquantum effects in condensed matter

Alexander M. Ilyanok

Quantum relativistic probability description of continuous world is re-examined. The new conception of physical world is offered. It is based on deterministic description of elementary particles, on conception The standard probability quantum relativistic picture of world is reviewed. The new picture of world is proposed. It is based on deterministic approach to elementary particles, discrete model of space determined by segmentation of particles and their fields and also by introduction of 9 Lorentz groups of transformations between systems of reference. It is supposed that elementary particles are segmented in space and change their form dependent on phase and structural state of substance. This approach allow to use linear differential second order equations to describe interactions. Maxwell equations are the partial case of them. This approach allow to eliminate basic paradoxes of quantum field theory and quantum mechanics and gives a new interpretation of well known experiments. To confirm the theory proposed basic parameters of macroquantum effects in condensed medium including cosmic objects are calculated. Particularly, parameters of high temperature superconductors being stable till temperature 93,5 Centdegree are calculated. It is supposed that electrons in atomic hydrogen at 6000 Centdegree at the Sun can occur in superconducting state.

arXiv:physics/0111182•Nov 26, 2001•0 citations

Non-dissipative diffusion in classical and quantum systems

Zahid Zakir

The theory of non-dissipative diffusion is constructed on an example of diffusion of a light particle in a dilute medium of heavy particles and it is shown that in low dissipative systems there are specific effects of non-dissipativity similar to quantum effects.In a non-dissipativity region mean energy of the light particle is conserved and processes are described by two non-linear diffusion equations with forward and backward time derivatives.Then these two diffusion equations are linearized and give one linear Schrödinger equation for complex amplitudes of probability.As a result, in the non-dissipative classical diffusion should be added probability amplitudes and there holds the superposition principle for these amplitudes.A mean square length of free passage and a mean square momentum define an elementary phase volume and a diffusion constant and they obey the uncertainty relations.It is shown that the formalism of quantum mechanics describes the classical non-dissipative diffusion with a homogeneous diffusion constant and that quantum mechanics is only a particular case when the elementary phase volume of free passage is universal and equal to the Planck constant.

Theoretical Physics Astrophysics & Cosmology•Aug 29, 2008•0 citations

Are There Quantum Operators and Wave Functions in Standard Probability Theory

Leon W. Cohen

Trends in mathematics•Jan 1, 2017•2 citations
Abstract The new quantum mechanics consists of a scheme of equations which are very closely analogous to the equations of classical mechanics, with the funda­mental difference that the dynamical variables do not obey the commutative law of multiplication, but satisfy instead the well-known quantum conditions. It follows that one cannot suppose the dynamical variables to be ordinary numbers (c-numbers), but may call them numbers of a special type (q-numbers). The theory shows that these q-numbers can in general be represented by matrices whose elements are c-numbers (functions of a time parameter). When one has performed the calculations with the q-numbers and obtained all the matrices one wants, the question arises how one is to get physical results from the theory, i. e., how can one obtain c-numbers from the theory that one can compare with experimental values ? Hitherto this has been done with the help of a number of special assumptions. In Heisenberg’s original matrix mechanics it was assumed that the elements of the diagonal matrix that repre­sents the energy are the energy levels of the system, and the elements of the matrix that represents the total polarisation, which are periodic functions of the time, determine the frequencies and intensities of the spectral lines in analogy to the classical theory. Schrodinger’s wave representation of the quantum mechanics has provided new ways of obtaining physical results from the theory, based on the assumption that the square of the amplitude of the wave function can in certain cases be interpreted as a probability. From this assumption one can, for instance, work out the probability of a transition being produced in a system (or the number of transitions produced in an assembly of like systems) by an arbitrary external perturbing force, and can thus, by supposing the perturbation to consist of incident radiation, obtain directly Einstein’s B coefficients. Again in Born’s treatment of collision problems it is assumed that the square of the amplitude of the wave function scattered in any direction determines the probability of the colliding electron (or other body) being scattered in that direction.
Quantum relativistic probability description of continuous world is re-examined. The new conception of physical world is offered. It is based on deterministic description of elementary particles, on conception The standard probability quantum relativistic picture of world is reviewed. The new picture of world is proposed. It is based on deterministic approach to elementary particles, discrete model of space determined by segmentation of particles and their fields and also by introduction of 9 Lorentz groups of transformations between systems of reference. It is supposed that elementary particles are segmented in space and change their form dependent on phase and structural state of substance. This approach allow to use linear differential second order equations to describe interactions. Maxwell equations are the partial case of them. This approach allow to eliminate basic paradoxes of quantum field theory and quantum mechanics and gives a new interpretation of well known experiments. To confirm the theory proposed basic parameters of macroquantum effects in condensed medium including cosmic objects are calculated. Particularly, parameters of high temperature superconductors being stable till temperature 93,5 Centdegree are calculated. It is supposed that electrons in atomic hydrogen at 6000 Centdegree at the Sun can occur in superconducting state.
The theory of non-dissipative diffusion is constructed on an example of diffusion of a light particle in a dilute medium of heavy particles and it is shown that in low dissipative systems there are specific effects of non-dissipativity similar to quantum effects.In a non-dissipativity region mean energy of the light particle is conserved and processes are described by two non-linear diffusion equations with forward and backward time derivatives.Then these two diffusion equations are linearized and give one linear Schrödinger equation for complex amplitudes of probability.As a result, in the non-dissipative classical diffusion should be added probability amplitudes and there holds the superposition principle for these amplitudes.A mean square length of free passage and a mean square momentum define an elementary phase volume and a diffusion constant and they obey the uncertainty relations.It is shown that the formalism of quantum mechanics describes the classical non-dissipative diffusion with a homogeneous diffusion constant and that quantum mechanics is only a particular case when the elementary phase volume of free passage is universal and equal to the Planck constant.