Hal Finney said

> Mitchell Porter, <[EMAIL PROTECTED]>, writes:
> > The many-worlds interpretation of quantum mechanics seems to 
> > have been developed with extreme carelessness, as far as I can tell.
> >
> > Suppose the universe is a one-dimensional harmonic oscillator
> > in an energy eigenstate. That's an extremely simple quantum
> > state for the universe to be in, it should be easy to 'interpret'.
> > So: if that's the global quantum state of the universe, where
> > are the many worlds? What are their states, their histories?
> 
> The MWI is what you get when you eliminate the projection postulate.
> Since the system you describe has no measurements, hence no projection,
> the MWI does not differ from any other QM interpretation.  There are
> not multiple worlds in that system.

So whether or not there are multiple worlds depends on whether
there are measurements? This is just a step away from saying
that 'whether or not there are multiple worlds depends on
whether or not there is a conscious being'.

What exactly is a 'measurement' anyway? It doesn't sound like an
elementary physical concept.

The fact that I have to ask such questions is the reason why I
make my accusation of careless formulation. Without doubt Everett
made some intriguing mathematical discoveries (in particular,
about the relative states of measuring devices with memories;
see below). But the significance of these discoveries is far
from straightforward! So I see two aspects to the Many Worlds
interpretation (at least in its Everett incarnation; the
Gell-Mann/Hartle version looks a little different in its
emphases). Firstly, there is the *idea* that there are "many
worlds", a natural enough concept given the role that
superpositions play in quantum theory, but one which I do not
believe has been formulated satisfactorily. Secondly, there
are Everett's mathematical discoveries - which themselves
require "interpretation".

> At http://threads.hotwired.com/cgi-bin/interact/view_stitch?msg.54097
> you ask:
> >   Describe for me - in the exact language of 
> >   mathematical physics - the *history* of a "world" 
> >   or a "branch".
> >
> >   I don't mean the universal wavefunction - that's
> >   supposed to describe *all* the worlds, not one.
> >   And I won't be satisfied just being pointed toward
> >   an element of a superposition, or a "relative
> >   state", since that is just an *instantaneous*
> >   thing. How are the instantaneous states of a world
> >   connected to each other? Is there some dynamical
> >   law governing the evolution of a single world? If 
> >   so, how do the other worlds contribute? 
> 
> I believe the relative-state formulation allows for time dependence in
> the relative state.  You have something like:
> 
>    State(t) = RelativeState1(t) * | Measure_as_1 >  +
>               RelativeState2(t) * | Measure_as_2 >
> 
> In other words, the total state function can be decomposed into two
> parts or branches, one which is relative to a measurement which comes out
> as case 1 (e.g. spin up) and one which is relative to a measurement which
> comes out as case 2 (e.g. spin down).

I presume that State(t) is the state of a measuring device, not
of a measured system. In that case, the state of the whole system
is something along the lines of

  (sum, 1<=i<=m,1<=j<=n) c_ij |system state i> |device state j>

Assuming that the 'measurement outcome' states form a basis for
the device subspace, then yes, the relative state of the device
can always be decomposed in this time-dependent fashion. But
this temporal sequence of relative device states depends on the
selection of a time sequence of measured-system states - and
what lies behind that selection?

Everett tries to get around this by talking about measuring
devices with memories. He tries to show that as time passes,
the set of memory states in which measurement outcomes diverges
from the ordinary quantum predictions (i.e. those derived using
Copenhagen interpretation and projection postulate) shrinks to
measure zero. But 

(i) these memory states are still instantaneous states; 
there's still no dynamical rule connecting successive
relative states of the measurement device;

(ii) he just postulates that the measure used will be a
function of the amplitudes. This is, as far as I can tell,
a whole new postulate, in which case it should be listed
as such from the beginning.

> If we want to debate this more fully, I will get a copy of DeWitt's book
> from the library to have at hand.

That would be good, I have access to that book also.

> If you have not read it, you might enjoy Mike Price's aggressively
> proselytizing MW FAQ, a copy of which can be found at:
> http://soong.club.cc.cmu.edu/~pooh/lore/manyworlds.html

I have read it. (Does anyone know where Mike Price has gone?
He seems to have disappeared off the net.)

-mitch
http://www.thehub.com.au/~mitch

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