ar X iv : q ua nt - p h / 99 01 07 7 v 1 2 9 Ja n 19 99 Collapse Models

This is a review of formalisms and models (nonrelativistic and relativistic) which modify Schrödinger’s equation so that it describes wavefunction collapse as a dynamical physical process. 1 Representing The World One of the major goals of theoretical physics is to find a useful mathematical object to represent the physical state of our world. In classical physics the object is a point in phase space. So far it has been possible to represent the world at an “instant,” i.e., on a spacelike hypersurface. One thing “useful” means is that a dynamical equation can be found for the object, enabling predictions about the state of the world on a future spacelike hypersurface. Is there such an object in quantum physics? In pursuing the research discussed here I have made some bets as to the nature of an eventually satisfactory physical theory. One of them is that there is such an object, a statevector in a suitable Hilbert space plus something more. I shall argue that more must be added because standard quantum theory (SQT) is a theory of choices without a chooser: more is a chooser. Along the way I shall make a few opinionated remarks about other points of view. However, mostly I shall try to give a coherent account of rationale (section 1), formalisms (section 2), nonrelativisitic (including gravitational, section 3) and relativisitic (section 4) models for a particular way of altering Schrödinger’s equation so the statevector behaves in a manner consistent with this bet. There is a point of view that the statevector does not represent the world but is only a mathematical tool enabling people to calculate the statistical outcomes of experiments[1]. There is a point of view that only an ensemble of experiments is represented by the statevector[2, 3, 4]. I disagree with both because I find it hard to believe such a successful theory as quantum theory either has no relevance to the unobserved world or to the individual world. There is a point 1 One can imagine other possibilities, e.g., a representation might only be possible on the spacetime volume between two hypersurfaces; there might be another time parameter whose specification is also required; etc.