Mitchell Porter, <mitch.domain.name.hidden>, 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.
> Frank Tipler (in _Physics of Immortality_) advances himself
> as a many-worlds advocate. When he tries to describe what the
> many worlds *are*, at one point he says they are *all* the
> trajectories through the classical state space. At another
> point he refers just to the Bohmian-mechanical trajectories
> through that state space, those corresponding to a particular
> choice of universal wavefunction.
>
> You can see more of my complaints about the MWI at
> http://threads.hotwired.com/cgi-bin/interact/replies_index?msg.53983,
> under "Challenge to many-worlds advocates".
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).
Now, I think your point is that this is normally expressed as the state
of the system after the measurement. However I believe it can be equally
well seen as the state of the system before the measurement as well.
We can decompose the state *prior to the measurement* into the sum of
two parts, one which is relative to a state where the measuring device
will measure case 1, and the other which is relative to the other state.
In that case, the history of the two branches over the time interval
during which the only wave function collapse is this measurement can
be describe as one branch being RelativeState1(t) and the other branch
being RelativeState2(t).
For longer time intervals, we would have a series of measurements which
represent all the state function collapses during that interval. The
Cartesian product of these would represent the set of branches or states
which would exist, and corresponding to each branch would be a relative
state which evolves over time within that branch.
If we want to debate this more fully, I will get a copy of DeWitt's book
from the library to have at hand.
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
Hal Finney
hal.domain.name.hidden
Received on Tue Jan 27 1998 - 10:18:14 PST