Preferred Basis in the Many-Worlds Interpretation in Quantum Theory and symmetries of the System

Meir Hemmo, Orly Shenker

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

Sara Foster, Harvey R. Brown

Andrei Olegovich Barvinsky, Alexander Yu. Kamenshchik

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.

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.

Michel Le Bellac