# Derivation of quantum probabilities from deterministic evolution

@article{Philbin2015DerivationOQ, title={Derivation of quantum probabilities from deterministic evolution}, author={Thomas G. Philbin}, journal={arXiv: Quantum Physics}, year={2015} }

The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to justify the Born rule from other physical principles, and thus elucidate the measurement process, have involved lengthy statistical or information-theoretic arguments. Here we show that Bohm's deterministic formulation of quantum mechanics allows the Born rule… Expand

#### 4 Citations

Pilot-Wave Quantum Theory with a Single Bohm’s Trajectory

- Physics
- 2015

The representation of a quantum system as the spatial configuration of its constituents evolving in time as a trajectory under the action of the wave-function, is the main objective of the de… Expand

Understanding quantum mechanics: a review and synthesis in precise language

- Physics, Computer Science
- 2019

This review is broad in scope, and aims to reflect enough of the literature to be representative of the current state of the subject, and to contribute to achieving greater consensus on how to understand quantum mechanics. Expand

Justifying Born's rule $P_\alpha=|\Psi_\alpha|^2$ using deterministic chaos, decoherence, and the de Broglie-Bohm quantum theory

- Physics
- 2021

Aurélien Drezet Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Neel, F-38000 Grenoble, France∗ Abstract In this work we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based… Expand

The Hopf-Fibration and Hidden Variables in Quantum and Classical Mechanics

- Physics, Mathematics
- 2015

The quaternion is a natural representation of the magnetic moment of the fundamental particles. Under the hopf-fibration the parameter space of the quaternion separates into an intrinsic and… Expand

#### References

SHOWING 1-10 OF 21 REFERENCES

Quantum equilibrium and the origin of absolute uncertainty

- Mathematics, Physics
- 1992

The quantum formalism is a “measurement” formalism-a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from… Expand

Quantum Darwinism

- Physics
- 2009

Quantum Darwinism describes the proliferation, in the environment, of multiple records of selected states of a quantum system. It explains how the fragility of a state of a single quantum system can… Expand

A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II

- Physics
- 1952

In this paper, we shall show how the theory of measurements is to be understood from the point of view of a physical interpretation of the quantum theory in terms of hidden variables developed in a… Expand

A snapshot of foundational attitudes toward quantum mechanics

- Physics
- 2013

Abstract Foundational investigations in quantum mechanics, both experimental and theoretical, gave birth to the field of quantum information science. Nevertheless, the foundations of quantum… Expand

QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES

- Physics
- 1999

The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all… Expand

Bohmian Mechanics

- Computer Science, Physics
- Compendium of Quantum Physics
- 2009

Bohmian mechanics is a quantum theory with a clear ontology and the status and the role of of the quantum formalism is clarified. Expand

Quantum theory of probability and decisions

- Mathematics, Physics
- Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 1999

The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions… Expand

Origin of quantum randomness in the pilot wave quantum mechanics

- Physics
- 1997

We account for the origin of the laws of quantum probabilities in the de Broglie-Bohm (pilot wave) formulation of quantum theory by considering the property of ergodicity likely to characterise the… Expand

Signal-locality, uncertainty, and the subquantum H-theorem. II

- Physics
- 1991

Abstract We begin a statistical mechanics based on the pilot-wave formulation of quantum theory, without making the assumption that the probability density P is equal to ‖Ψ‖2. Instead, this relation… Expand