# Information measures for inferring quantum mechanics

@article{Parwani2004InformationMF, title={Information measures for inferring quantum mechanics}, author={Rajesh R. Parwani}, journal={Journal of Physics A}, year={2004}, volume={38}, pages={6231-6237} }

Starting from the Hamilton–Jacobi equation describing a classical ensemble, one may infer a quantum dynamics using the principle of maximum uncertainty. That procedure requires an appropriate measure of uncertainty. Such a measure is constructed here from physically motivated constraints. It leads to a unique single parameter extension of the classical dynamics that is equivalent to the usual linear quantum mechanics.

## 24 Citations

### A Physical Axiomatic Approach to Schrodinger's Equation

- Physics
- 2005

The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the…

### Information and Particle Physics

- Physics
- 2009

Information measures for relativistic quantum spinors are constructed to satisfy various postulated properties such as normalisation invariance and positivity. Those measures are then used to…

### Understanding quantization: a hidden variable model

- Physics
- 2012

We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement…

### Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory

- Physics
- 2005

The same set of physically motivated axioms can be used to construct both the classical ensemble Hamilton-Jacobi equation and Schrodingers equation. Crucial roles are played by the assumptions of…

### Variational principle for stochastic mechanics based on information measures

- PhysicsJournal of Mathematical Physics
- 2021

Stochastic mechanics is regarded as a physical theory to explain quantum mechanics with classical terms such that some of the quantum mechanics paradoxes can be avoided. Here we propose a new…

### Can (Quantum) Information be Sorted Out from Quantum Mechanics

- Physics
- 2009

We shall draw an affirmative answer to the question posed in the title. The key point will be a quantum description of physical reality. Once fixed at ontic level two basic elements, namely the laws…

### Properties of some nonlinear Schrödinger equations motivated through information theory

- Physics
- 2009

We update our understanding of nonlinear Schrodinger equations motivated through information theory. In particular we show that a q—deformation of the basic nonlinear equation leads to a perturbative…

## References

SHOWING 1-10 OF 30 REFERENCES

### Derivation of the equations of nonrelativistic quantum mechanics using the principle of minimum Fisher information

- Physics
- 1998

The many-particle time-dependent Schr\"odinger equation is derived using the principle of minimum Fisher information. This application of information theory leads to a physically well motivated…

### Schrödinger equation from an exact uncertainty principle

- 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…

### Why is Schrödinger's equation linear?

- Physics
- 2005

Information-theoretic arguments are used to obtain a link between the accurate linearity of Schr¨odinger's equation and Lorentz invariance: A possible violation of the latter at short distances would…

### Relativistic models of nonlinear quantum mechanics

- Physics
- 1978

I present and discuss a class of nonlinear quantum-theory models, based on simple relativistic field theories, in which the parameters depend on the state of the system via expectation values of…

### Gauge transformations in quantum mechanics and the unification of nonlinear Schrödinger equations

- Physics
- 1999

Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we…

### Information Theory and Statistical Mechanics

- Physics
- 1957

Treatment of the predictive aspect of statistical mechanics as a form of statistical inference is extended to the density-matrix formalism and applied to a discussion of the relation between…

### Quantum mechanics : a modern development

- Physics
- 1998

Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of…