For a general introduction to the problem of measurement, see my:
For what is wrong (and what is right) with Bohr's theory of complementarity, see my
For the difficulties of formulating a covariant state-reduction theory, see my:
For a general argument that special relativity is incompatible with a stochastic dynnamics, see my:
In the case of the (deterministic) pilot-wave theory, it is well-known that Lorentz covariance is violated at the level of the "guidance" equation. But the difficulty with relativity runs deeper than that: no more can the pilot-wave theory account for particle creation and annihilation processes. It is true that one can make use of field-configurations as the underlying objects of the theory instead (as `beables'), but one must still make contact with the observed particle phenomenology; moreover, fields as beables, unlike particles, do not have to be localized. What guarantee is there that the pilot-wave theory, formulated in terms of field configurations as the underlying hidden-variables, still solves the problem of measurement? For details see my:
On the other hand, as goes the probabilistic interpretation of quantum mechanics, all of these approaches appear to be bound to the Born rule (and independent of the normalization of the state): the Born rule can be derived from operational assumptions common to them all. (Certain schools, however, may be better able to reject these assumptions than others. They may certainly be rejected by state-reduction theories; and even if accepted, the argument may be evaded in the pilot-wave theory, if it is supposed that the distribution of hidden variables is not controlled by the state. At the other extreme, there is no room for manouvre in Everett's approach, in the Copenhagen interpretation, or in any broadly operationalist approach to quantum mechanics.) For the details, see my:
Copyright Simon Saunders 2001. Last updated: 8 December 2007.