# Born rule in quantum and classical mechanics

@article{Brumer2006BornRI, title={Born rule in quantum and classical mechanics}, author={Paul Brumer and Jiangbin Gong}, journal={Physical Review A}, year={2006}, volume={73}, pages={052109} }

Considerable effort has been devoted to deriving the Born rule [i.e., that {psi}(x){sup 2}dx is the probability of finding a system, described by {psi}, between x and x+dx] in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert-space formulation of classical mechanics as well. These results provide insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.

## 20 Citations

### Chapter 26 Derivations of the Born Rule

- Philosophy
- 2020

The Born rule, a cornerstone of quantum theory usually taken as a postulate, continues to attract numerous attempts for its derivation. A critical review of these derivations, from early attempts to…

### Derivations of the Born Rule

- PhilosophyJerusalem Studies in Philosophy and History of Science
- 2020

The Born rule, a cornerstone of quantum theory usually taken as a postulate, continues to attract numerous attempts for its derivation. A critical review of these derivations, from early attempts to…

### From probabilistic mechanics to quantum theory

- PhysicsQuantum Studies: Mathematics and Foundations
- 2019

We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton’s function, which determines canonical equations, a…

### One world, one beable

- Philosophy, PhysicsSynthese
- 2014

It is argued that Humeans about laws can treat classical and quantum wave functions on a par and that doing so yields many benefits.

### Hilbert space theory of classical electrodynamics

- Physics
- 2014

Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman–von Neumann–Sudarshan prescription for classical mechanics…

### Operational dynamic modeling transcending quantum and classical mechanics.

- PhysicsPhysical review letters
- 2012

It is shown that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory, and should provide a basis for formulating novel theories.

### Quantum/Classical Interface: Fermion Spin

- Physics
- 2007

Although intrinsic spin is usually viewed as a purely quantum property with no classical analog, we present evidence here that fermion spin has a classical origin rooted in the geometry of…

### Quantum Mechanics as a Theory of Incompatible Symmetries

- Economics
- 2022

It is increasingly becoming recognized that incompatible variables, which play an essential role in quantum mechanics (QM), are not in fact unique to QM. Here we add a new example, the “Arrow”…

## References

SHOWING 1-10 OF 16 REFERENCES

### The statistical interpretation of quantum mechanics

- Physics
- 1970

The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions. Several arguments are advanced in favor of…

### Statistical Interpretation of Quantum Mechanics.

- PhysicsScience
- 1955

The published work for which the honor of the Nobel prize for the year 1954 has been accorded to me does not contain the discovery of a new phenomenon of nature but, rather, the foundations of a new…

### Quantum Mechanics: Foundations and Applications

- Physics, Chemistry
- 1993

I Mathematical Preliminaries.- I.1 The Mathematical Language of Quantum Mechanics.- I.2 Linear Spaces, Scalar Product.- I.3 Linear Operators.- I.4 Basis Systems and Eigenvector Decomposition.- I.5…

### Non equilibrium statistical mechanics

- Physics
- 2007

In part I of these lecture notes, I introduce the basic tools of non equilibrium statistical mechanics: linear response, Brownian motion, Langevin equation, (Pauli) master equation. Part II is…

### Non-equilibrium statistical mechanics

- Physics
- 1962

In the preceding chapter we discussed the microscopic foundations of extended irreversible thermodynamics through fluctuation theory. The present chapter deals with more general methods of…

### Lectures on Theoretical Physics

- EngineeringNature
- 1951

Vorlesungen über theoretische PhysikVon Prof. Arnold Sommerfeld. Band 1: Mechanik. Vierte, neubearbeitete Auflage. Pp. xii + 276. 18 D. marks. Band 2: Mechanik der deformierbaren Medien. Pp. xv + 376…

### Phys

- Rev. A 71, 052105
- 2005

### Phys

- Rev. A 55, 27 (1997); Phys. Rev. A 55, 43
- 1997

### Proc

- Roy. Soc. London A 460, 1771
- 2004