Re: relative state and decoherence

From: Hal Finney <hal.domain.name.hidden>
Date: Wed, 11 Feb 1998 21:30:58 -0800

Wei Dai, <weidai.domain.name.hidden>, 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
Received on Wed Feb 11 1998 - 22:21:11 PST