The basis problem in manyworlds theories
Abstract
It is emphasized that a manyworlds 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 nonorthogonal 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 manyworlds proponents to solve the basis problem. But these eigenstates do not enjoy the locality and quasiclassicality properties of the states defined by environmental decoherence effects, and hence are not satisfactory preferred basis states. The basis problem needs to be addressed and resolved before a manyworldstype interpretation can be said to exist.
 Publication:

Canadian Journal of Physics
 Pub Date:
 September 2002
 DOI:
 10.1139/p02068
 arXiv:
 arXiv:quantph/0110148
 Bibcode:
 2002CaJPh..80.1043S
 Keywords:

 Quantum Physics
 EPrint:
 This extended version is to be published in The Canadian Journal of Physics