# Incompleteness of trajectory-based interpretations of quantum mechanics

@article{Hall2004IncompletenessOT,
title={Incompleteness of trajectory-based interpretations of quantum mechanics},
author={Michael J. W. Hall},
journal={Journal of Physics A},
year={2004},
volume={37},
pages={9549-9556}
}
• M. Hall
• Published 9 June 2004
• Physics
• Journal of Physics A
Trajectory-based approaches to quantum mechanics include the de Broglie?Bohm interpretation and Nelson's stochastic interpretation. It is shown that the usual route to establishing the validity of such interpretations, via a decomposition of the Schr?dinger equation into a continuity equation and a modified Hamilton?Jacobi equation, fails for some quantum states. A very simple example is provided by a quantum particle in a box, described by a wavefunction that is initially uniform over the…
A Bohmian approach to quantum fractals
A quantum fractal is a wavefunction with a real and an imaginary part continuous everywhere, but differentiable nowhere. This lack of differentiability has been used as an argument to deny the
Quantum phenomena modelled by interactions between many classical worlds
• Physics, Mathematics
• 2014
We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical "worlds," and quantum effects arise
Non-differentiable Bohmian trajectories
• Physics, Mathematics
• 2010
A solution ψ to Schrödinger’s equation needs some degree of regularity in order to allow the construction of a Bohmian mechanics from the integral curves of the velocity field ~= (5ψ/mψ) . In the
Derivation of the postulates of quantum mechanics from the first principles of scale relativity
• Mathematics, Physics
• 2007
Quantum mechanics is based on a series of postulates which lead to a very good description of the microphysical realm but which have, up to now, not been derived from first principles. In the present
Macroscopic Quantum-Type Potentials in Theoretical Systems Biology
This paper reviews the use of the theory of scale relativity and fractal space-time as a tool particularly well adapted to the possible development of a future genuine systems theoretical biology and emphasizes the concept of quantum-type potentials.
Scale relativity theory and integrative systems biology: 2. Macroscopic quantum-type mechanics.
• Computer Science, Medicine
Progress in biophysics and molecular biology
• 2008
The effects induced by the internal fractal structures of trajectories on motion in standard space are described and their main consequence is the transformation of classical dynamics into a generalized, quantum-like self-organized dynamics.
Quantum states for primitive ontologists
Under so-called primitive ontology approaches, in fully describing the history of a quantum system, one thereby attributes interesting properties to regions of spacetime. Primitive ontology
Two-time correlation functions: stochastic and conventional quantum mechanics
• Physics
• 2002
Abstract. An investigation of two-time correlation functions is reported within the framework of (i) stochastic quantum mechanics and (ii) conventional Heisenberg-Schrödinger quantum mechanics. The
Why isn't every physicist a Bohmian?
This note collects, classifies and evaluates common criticism against the de Broglie Bohm theory, including Ockham's razor, asymmetry in the de Broglie Bohm theory, the surreal trajectory''
A SUBTLETY OF THE SCHRÖDINGER PICTURE DYNAMICS
We address a mathematical and physical status of exotic (like e.g. fractal) wave packets and their quantum dynamics. To this end, we extend the formal meaning of the Schrodinger equation beyond the

## References

SHOWING 1-10 OF 25 REFERENCES
Derivation of the Schrodinger equation from Newtonian mechanics
We examine the hypothesis that every particle of mass $m$ is subject to a Brownian motion with diffusion coefficient $\frac{\ensuremath{\hbar}}{2m}$ and no friction. The influence of an external
Fractal noise in quantum ballistic and diffusive lattice systems
• Physics
• 2004
We demonstrate fractal noise in the quantum evolution of wave packets moving either ballistically or diffusively in periodic and quasiperiodic tight-binding lattices, respectively. For the ballistic
Unravelling quantum carpets: a travelling-wave approach
• Physics
• 1999
Generic channel and ridge structures are known to appear in the time-dependent position probability distribution of a one-dimensional quantum particle confined to a box. These structures are shown to
Time evolution of quantum fractals
• Physics, Medicine
Physical review letters
• 2000
A universal relation D(t) = 1+Dx/2 linking the dimensions of space cross sections Dx and time cross sections of the fractal quantum carpets is proved.
Quantum fractals in boxes
A quantum wave with probability density , confined by Dirichlet boundary conditions in a D-dimensional box of arbitrary shape and finite surface area, evolves from the uniform state . For almost all
Quantum Theory of Fields
To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject. But it is a very good and most useful book. The original was
Schrödinger equation from an exact uncertainty principle
• Physics, Mathematics
• 2001
An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with
Do Bohm trajectories always provide a trustworthy physical picture of particle motion
No. When particle detectors are included particles do not follow the Bohm trajectories as we would expect from a classical type model.
Physica Scripta
• 2004
Creation and existence of order are of philosophical significance and practical utility. This paper spells clear, succinct, yet comprehensive directives for order creation, existence and total
Quantentheorie in hydrodynamischer Form
ZusammenfassungEs wird gezeigt, daß man die Schrödingersche Gleichung des Einelektronen-problems in die Form der hydrodynamischen Gleichungen transformieren kann.