Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Classical and Quantum Gravity

Preferred basis in the many-worlds interpretation of quantum mechanics and quantum cosmology

Andrei Olegovich Barvinsky, Alexander Yu. Kamenshchik

Published Dec 1, 1990• 22 citations
Publisher

Abstract

The authors revive an old proposal of Zeh (1986) for the preferred basis in the many-worlds interpretation of quantum mechanics. The algorithm for this basis reduces to the eigenvalue problems for density matrices of subsystems splitting the quantum system into the observer and the observable counterpart. A semiclassical calculational method for these eigenvalue problems is developed and the dynamical properties of the preferred basis are investigated. Applications of this proposal to quantum cosmology are discussed.

DOI
10.1088/0264-9381/7/12/010

Related papers

Preferred basis in quantum theory and the problem of classicalization of the quantum Universe

Andrei Olegovich Barvinsky, Alexander Yu. Kamenshchik

We revive an old proposal of Zeh for the preferred basis in the many-worlds interpretation of quantum mechanics. The algorithm for the basis reduces to the eigenvalue problems for density matrices of subsystems forming the whole system under consideration. We generalize this procedure to the case of degenerate eigenvalues of reduced density matrices. A semiclassical calculational method for these eigenvalues is developed and applied to some model problems. The classical properties of elements of the preferred basis are investigated. It is shown that classicality exists only in some part of many-worlds branches. Moreover, it depends crucially on the initial conditions and Hamiltonians and under some circumstances turns out to be a temporary phenomenon. Applications of the preferred-basis proposal to quantum cosmology are discussed. The relation between the preferred-basis approach and quantum-histories approach is discussed.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jul 15, 1995•26 citations

The basis problem in many-worlds theories

H P Stapp

It is emphasized that a many-worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved. The core basis problem is that the robust enduring states specified by environmental decoherence effects are essentially Gaussian wave packets that form continua of non-orthogonal states. Hence they are not a discrete set of orthogonal basis states to which finite probabilities can be assigned by the usual rules. The natural way to get an orthogonal basis without going outside the Schrödinger dynamics is to use the eigenstates of the reduced density matrix, and this idea is the basis of some recent attempts by many-worlds proponents to solve the basis problem. But these eigenstates do not enjoy the locality and quasi-classicality properties of the states defined by environmental decoherence effects, and hence are not satisfactory preferred basis states. This core problem is obscured by approaches that treat the universe as a quantum computer, but it needs to be addressed and resolved before a many-worlds-type interpretation can be said to exist. PACS No.: 03.65Bz

arXiv:quant-ph/0110148•Canadian Journal of Physics•Sep 1, 2002•21 citations

The Density-Matrix Method for the Preferred Basis in the Many-Worlds Interpretation of Quantum Cosmology

Andrei Olegovich Barvinsky, A. Yu. Kamenschik, V. N. Ponomariov

General Relativity and Gravitation•Jul 1, 1989•0 citations

The Basis Problem in Many Worlds Theories

Henry P. Stapp

It is emphasized that a many-worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved. The core basis problem is that the robust enduring states specified by environmental decoherence effects are essentially Gaussian wave packets that form continua of non-orthogonal states. Hence they are not a discrete set of orthogonal basis states to which finite probabilities can be assigned by the usual rules. The natural way to get an orthogonal basis without going outside the Schroedinger dynamics is to use the eigenstates of the reduced density matrix, and this idea is the basis of some recent attempts by many-worlds proponents to solve the basis problem. But these eigenstates do not enjoy the locality and quasi-classicality properties of the states defined by environmental decoherence effects, and hence are not satisfactory preferred basis states. This core problem is obscured by approaches that treat the universe as a quantum computer, but it needs to be addressed and resolved before a many-worlds-type interpretation can be said to exist.

•Oct 25, 2001•36 citations

The preferred basis problem in the many-worlds interpretation of quantum mechanics: why decoherence does not solve it

Meir Hemmo, Orly Shenker

Synthese•Jun 1, 2022•6 citations

Many Worlds

Jeffrey Alan Barrett

Abstract This chapter explains the many-worlds interpretations, particularly the DeWitt–Graham interpretation — the splitting-worlds interpretation. The splitting-worlds theory proposes that one must choose what physical quantities one wants to be determinate in a world, which amounts to choosing a physically preferred basis. It discusses several traditional and real problems encountered with the splitting-worlds theory. It also describes another theory, where one might stipulate that the global state always evolves in the usual linear way, selects a preferred basis that makes observers' records always determinate in each local state, and then chooses a connection rule that will link local states at different times into trajectories — the many threads theory.

•Aug 16, 2001•0 citations
The authors revive an old proposal of Zeh (1986) for the preferred basis in the many-worlds interpretation of quantum mechanics. The algorithm for this basis reduces to the eigenvalue problems for density matrices of subsystems splitting the quantum system into the observer and the observable counterpart. A semiclassical calculational method for these eigenvalue problems is developed and the dynamical properties of the preferred basis are investigated. Applications of this proposal to quantum cosmology are discussed.
We revive an old proposal of Zeh for the preferred basis in the many-worlds interpretation of quantum mechanics. The algorithm for the basis reduces to the eigenvalue problems for density matrices of subsystems forming the whole system under consideration. We generalize this procedure to the case of degenerate eigenvalues of reduced density matrices. A semiclassical calculational method for these eigenvalues is developed and applied to some model problems. The classical properties of elements of the preferred basis are investigated. It is shown that classicality exists only in some part of many-worlds branches. Moreover, it depends crucially on the initial conditions and Hamiltonians and under some circumstances turns out to be a temporary phenomenon. Applications of the preferred-basis proposal to quantum cosmology are discussed. The relation between the preferred-basis approach and quantum-histories approach is discussed.
It is emphasized that a many-worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved. The core basis problem is that the robust enduring states specified by environmental decoherence effects are essentially Gaussian wave packets that form continua of non-orthogonal states. Hence they are not a discrete set of orthogonal basis states to which finite probabilities can be assigned by the usual rules. The natural way to get an orthogonal basis without going outside the Schrödinger dynamics is to use the eigenstates of the reduced density matrix, and this idea is the basis of some recent attempts by many-worlds proponents to solve the basis problem. But these eigenstates do not enjoy the locality and quasi-classicality properties of the states defined by environmental decoherence effects, and hence are not satisfactory preferred basis states. This core problem is obscured by approaches that treat the universe as a quantum computer, but it needs to be addressed and resolved before a many-worlds-type interpretation can be said to exist. PACS No.: 03.65Bz
It is emphasized that a many-worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved. The core basis problem is that the robust enduring states specified by environmental decoherence effects are essentially Gaussian wave packets that form continua of non-orthogonal states. Hence they are not a discrete set of orthogonal basis states to which finite probabilities can be assigned by the usual rules. The natural way to get an orthogonal basis without going outside the Schroedinger dynamics is to use the eigenstates of the reduced density matrix, and this idea is the basis of some recent attempts by many-worlds proponents to solve the basis problem. But these eigenstates do not enjoy the locality and quasi-classicality properties of the states defined by environmental decoherence effects, and hence are not satisfactory preferred basis states. This core problem is obscured by approaches that treat the universe as a quantum computer, but it needs to be addressed and resolved before a many-worlds-type interpretation can be said to exist.
Abstract This chapter explains the many-worlds interpretations, particularly the DeWitt–Graham interpretation — the splitting-worlds interpretation. The splitting-worlds theory proposes that one must choose what physical quantities one wants to be determinate in a world, which amounts to choosing a physically preferred basis. It discusses several traditional and real problems encountered with the splitting-worlds theory. It also describes another theory, where one might stipulate that the global state always evolves in the usual linear way, selects a preferred basis that makes observers' records always determinate in each local state, and then chooses a connection rule that will link local states at different times into trajectories — the many threads theory.