# Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory

## Abstract

The same set of physically motivated axioms can be used to construct both the classical ensemble Hamilton-Jacobi equation and Schroedingers equation. Crucial roles are played by the assumptions of universality and simplicity (Occam's Razor) which restrict the number and type of of arbitrary constants that appear in the equations of motion. In this approach, non-relativistic quantum theory is seen as the unique single parameter extension of the classical ensemble dynamics. The method is contrasted with other related constructions in the literature and some consequences of relaxing the axioms are also discussed: for example, the appearance of nonlinear higher-derivative corrections possibly related to gravity and spacetime fluctuations. Finally, some open research problems within this approach are highlighted.

- Authors:

- Department of Physics, National University of Singapore, Kent Ridge (Singapore)
- (Singapore)

- Publication Date:

- OSTI Identifier:
- 20787710

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 810; Journal Issue: 1; Conference: Vaxjo conference on quantum theory: Reconsideration of foundations - 3, Vaxjo (Sweden), 6-11 Jun 2005; Other Information: DOI: 10.1063/1.2158745; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CORRECTIONS; EQUATIONS OF MOTION; FLUCTUATIONS; GRAVITATION; HAMILTON-JACOBI EQUATIONS; NONLINEAR PROBLEMS; QUANTUM FIELD THEORY; RELATIVISTIC RANGE; SCHROEDINGER EQUATION; SPACE-TIME

### Citation Formats

```
Parwani, Rajesh R., and University Scholars Programme, National University of Singapore, Kent Ridge.
```*Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory*. United States: N. p., 2006.
Web. doi:10.1063/1.2158745.

```
Parwani, Rajesh R., & University Scholars Programme, National University of Singapore, Kent Ridge.
```*Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory*. United States. doi:10.1063/1.2158745.

```
Parwani, Rajesh R., and University Scholars Programme, National University of Singapore, Kent Ridge. Wed .
"Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory". United States.
doi:10.1063/1.2158745.
```

```
@article{osti_20787710,
```

title = {Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory},

author = {Parwani, Rajesh R. and University Scholars Programme, National University of Singapore, Kent Ridge},

abstractNote = {The same set of physically motivated axioms can be used to construct both the classical ensemble Hamilton-Jacobi equation and Schroedingers equation. Crucial roles are played by the assumptions of universality and simplicity (Occam's Razor) which restrict the number and type of of arbitrary constants that appear in the equations of motion. In this approach, non-relativistic quantum theory is seen as the unique single parameter extension of the classical ensemble dynamics. The method is contrasted with other related constructions in the literature and some consequences of relaxing the axioms are also discussed: for example, the appearance of nonlinear higher-derivative corrections possibly related to gravity and spacetime fluctuations. Finally, some open research problems within this approach are highlighted.},

doi = {10.1063/1.2158745},

journal = {AIP Conference Proceedings},

number = 1,

volume = 810,

place = {United States},

year = {Wed Jan 04 00:00:00 EST 2006},

month = {Wed Jan 04 00:00:00 EST 2006}

}