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

Journal of Physics A Mathematical and General

Radiation damping in the pilot wave interpretation of quantum mechanics

M C Robinson, C E Aveledo, L A Lameda, D Bonyuet-Lee

Published Sep 11, 1983• 1 citation
Publisher

Abstract

To avoid the internal contradiction in the pilot wave interpretation inherent in the assumption of a charged particle moving in a closed orbit without radiating, it is proposed that the wavefunctions, psi n (r), corresponding to stationary states be real, implying that the particle is stationary. If the effect of radiation damping is included, the Hamiltonian contains a nonlinear term resulting in the stability of the stationary states.

DOI
10.1088/0305-4470/16/13/020

Related papers

Damping Effect of Electromagnetic Radiation and Time-Dependent Schrodinger Equation

Ji Luo

The inexactness of the time-dependent Schrödinger equation of a charged particle in an external electromagnetic field is discussed in terms of the damping effect of the radiation. A possible improvement is to add a nonlinear term representing this effect to the linear Schrödinger equation. Conditions for the nonlinear term are investigated and it is demonstrated that the obtained nonlinear Schrödinger equation may present state evolutions similar to the wave-function reduction and transitions between stationary states.

arXiv:1002.1116•Feb 5, 2010•0 citations

Stationary wave demonstrations and the quantum theory of radiation

K F Smith

The formal procedure used to predict the results of experiments by wave mechanical methods is closely related to the corresponding classical calculation and in many cases the result for a particular quantum state is essentially an average of the appropriate classical variable over the particle density function. The author presents a discussion of the way this concept can be applied to an elementary treatment of the emission of radiation from a system of charges and it also includes an account of an apparatus capable of demonstrating the conditions necessary for the emission of radiation.

Physics Education•Nov 1, 1972•0 citations

Radiation Damping and Nonlinearity in the Pilot Wave Interpretation of Quantum Mechanics

M. C. Robinson

Springer eBooks•Jan 1, 1985•0 citations

On the falsification of the pilot-wave interpretation of quantum mechanics

Jakub M. Ratajczak

Quantum mechanics has lacked a widely recognized interpretation since its birth. Many interpretations are under consideration because they are difficult to disprove experimentally. In this paper, we show that the results of a recent experiment go against one of them: the pilot-wave interpretation. This is because the key assumption of this interpretation, particle locality, contradicts the assumption of wave function nonlocality on which the experiment is founded. This is a rare example of a quantum model and an experiment not indifferent to the interpretation of quantum mechanics.

•Aug 26, 2020•0 citations

A critique of the major approaches to damping in quantum theory

Daniel M. Greenberger

We examine the two major approaches that have been suggested for the quantum mechanical treatment of the damped motion of a particle as a one-body problem. These are the linear, but time dependent, Kanai Hamiltonian, and the more recent nonlinear potentials which have been introduced to simulate the damping force. The most important criticism that has been leveled at the Kanai Hamiltonian is that its solutions seem to violate the uncertainty relations. We show that this Hamiltonian actually represents a particle of variable mass, whose classical behavior is identical to that of a damped particle of constant mass. But quantum mechanically, its changing mass does lead to unphysical behavior when misinterpreted as a constant mass particle. So this Hamiltonian cannot directly describe a constant mass damped quantum particle. The nonlinear model has been interpreted in terms of the hydrodynamical analogy of quantum theory, and a well behaved decaying wavepacket solution has been produced. However we generalize this result to produce solutions that ’’decay’’ to arbitrarily high energy. Thus it is not clear that this model specifically treats dissipation. Rather it seems to seek out any stationary state. At any rate, its physical interpretation is obscure at present. However we show, by analyzing the physical problem of damping at low energies, that one can modify the Kanai Hamiltonian to eliminate its unphysical features, so that this modified Kanai Hamiltonian can in fact be interpreted as representing a constant mass damped particle with physically reasonable solutions.

Journal of Mathematical Physics•May 1, 1979•113 citations

In Search of Schroedinger's Electron and Einstein's Atom Too !

Jean Louis Van Belle

This article explores a possible physical interpretation of the wavefunction. It zooms in on the physical model it implies for an electron in free space (further building on Schroedinger's ideas in regard to the apparent Zitterbewegung of an electron), but then also discusses the wavefunction for particles (including non-charged particles) in general. While it basically concludes that the mainstream interpretation of quantum physics (the Copenhagen interpretation) is and remains the most parsimonious explanation, it also argues that one or two extra assumptions – the wavefunction as a two-dimensional self-sustaining electromagnetic or gravitational oscillation in space – would make more frivolous explanations (many worlds, pilot wave, etcetera) redundant.

•Sep 1, 2018•0 citations
To avoid the internal contradiction in the pilot wave interpretation inherent in the assumption of a charged particle moving in a closed orbit without radiating, it is proposed that the wavefunctions, psi n (r), corresponding to stationary states be real, implying that the particle is stationary. If the effect of radiation damping is included, the Hamiltonian contains a nonlinear term resulting in the stability of the stationary states.
The inexactness of the time-dependent Schrödinger equation of a charged particle in an external electromagnetic field is discussed in terms of the damping effect of the radiation. A possible improvement is to add a nonlinear term representing this effect to the linear Schrödinger equation. Conditions for the nonlinear term are investigated and it is demonstrated that the obtained nonlinear Schrödinger equation may present state evolutions similar to the wave-function reduction and transitions between stationary states.
The formal procedure used to predict the results of experiments by wave mechanical methods is closely related to the corresponding classical calculation and in many cases the result for a particular quantum state is essentially an average of the appropriate classical variable over the particle density function. The author presents a discussion of the way this concept can be applied to an elementary treatment of the emission of radiation from a system of charges and it also includes an account of an apparatus capable of demonstrating the conditions necessary for the emission of radiation.
Quantum mechanics has lacked a widely recognized interpretation since its birth. Many interpretations are under consideration because they are difficult to disprove experimentally. In this paper, we show that the results of a recent experiment go against one of them: the pilot-wave interpretation. This is because the key assumption of this interpretation, particle locality, contradicts the assumption of wave function nonlocality on which the experiment is founded. This is a rare example of a quantum model and an experiment not indifferent to the interpretation of quantum mechanics.
We examine the two major approaches that have been suggested for the quantum mechanical treatment of the damped motion of a particle as a one-body problem. These are the linear, but time dependent, Kanai Hamiltonian, and the more recent nonlinear potentials which have been introduced to simulate the damping force. The most important criticism that has been leveled at the Kanai Hamiltonian is that its solutions seem to violate the uncertainty relations. We show that this Hamiltonian actually represents a particle of variable mass, whose classical behavior is identical to that of a damped particle of constant mass. But quantum mechanically, its changing mass does lead to unphysical behavior when misinterpreted as a constant mass particle. So this Hamiltonian cannot directly describe a constant mass damped quantum particle. The nonlinear model has been interpreted in terms of the hydrodynamical analogy of quantum theory, and a well behaved decaying wavepacket solution has been produced. However we generalize this result to produce solutions that ’’decay’’ to arbitrarily high energy. Thus it is not clear that this model specifically treats dissipation. Rather it seems to seek out any stationary state. At any rate, its physical interpretation is obscure at present. However we show, by analyzing the physical problem of damping at low energies, that one can modify the Kanai Hamiltonian to eliminate its unphysical features, so that this modified Kanai Hamiltonian can in fact be interpreted as representing a constant mass damped particle with physically reasonable solutions.
This article explores a possible physical interpretation of the wavefunction. It zooms in on the physical model it implies for an electron in free space (further building on Schroedinger's ideas in regard to the apparent Zitterbewegung of an electron), but then also discusses the wavefunction for particles (including non-charged particles) in general. While it basically concludes that the mainstream interpretation of quantum physics (the Copenhagen interpretation) is and remains the most parsimonious explanation, it also argues that one or two extra assumptions – the wavefunction as a two-dimensional self-sustaining electromagnetic or gravitational oscillation in space – would make more frivolous explanations (many worlds, pilot wave, etcetera) redundant.