- Contemporary messages sorted: [ by date ] [ by thread ] [ by subject ] [ by author ] [ by messages with attachments ]

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

Date: Wed, 11 Feb 1998 21:30:58 -0800

Wei Dai, <weidai.domain.name.hidden>, writes:

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

*
This archive was generated by hypermail 2.3.0
: Fri Feb 16 2018 - 13:20:06 PST
*