Wei Dai, <[EMAIL PROTECTED]>, writes: > I am confused about the relationship between relative state and > decoherence in the Many Worlds Interpretation of QM. My understanding of > MWI is that as the universal wavefunction evolves, components of it > decohere from each other, and when this happens we can think of it as the > world spliting into branches and treat the components seperately from that > point on because they would be unlikely to interfere with each other. > > Now how does relative state fit into this? Is relative state still an > important part of the MWI, or is decoherence sufficient for the > interpretation?
I haven't been able to locate the references I was looking for, so this is based on having read Everett's paper a few years ago. As I recall, the term "relative state" referred to that component of the state which was relative to some particular basis vector. A quantum state can be split into basis vectors in any number of ways, of course, and having done so, you automatically create a set of relative states corersponding to each basis vector. The phenomenon of decoherence was not as well understood in Everett's day as today, so in analyzing measurements he simply chose basis vectors which corresponded to well defined macroscopic measured states. Today we can say that quantum systems of the kind we are interested in naturally decohere, and this leads to a natural set of basis vectors for which the relative states are effectivelly independent. So the way I see it, "relative state" is simply a term for a component of the wave function which evolves effectivelly independently of the other components. It is the term Everett used for what later writers would refer to as "one of the many worlds". Decoherence is a natural phenomenon which shows that there exist relative states which are effectivelly independent, hence that the relative state concept is physically useful. Hal