Re: Is State Vector Reduction a 'Process'?

Aaron Bergman wrote:
> In article <1117448074.219697.96620@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

> > This is the born rules, a postulate of QM.
>
> Not so much. It works as a good effective description, but if it refers
> to an explicit nonunitary collapse process, it fails to give a
> description of it. If it does not refer to collapse, then it fails to
> explain our perception of (one part of) the reduced density matrix
> (say), rather than the full coherent wavefunction.
>
In my opinion, I think you are trying to say more than QM theory says.
You seem to be a adept of the wave function reality hence you try to
define something out of the scope of the current QM theory formulation
(an explication of the collapse) while I simply take the born rules as
statistics of outcomes and the collapse postulate the property where a
given outcome value of a system is true ("Outcome A=a" true).
If I compute the frequency of identical independent measurement
results, I get the probability law of the event. I do not explain how
to find these identical independent systems (out of scope) as I do not
explain how I get a particle at the place and time (qo,to) in classical
mechanics (the initial condition).

> [...]
>
> > > > I can only understand this sentence as the quest for a deterministic
> > > > (causal) description of outcomes compatible with the statistics of QM.
> > >
> > > QM is deterministic and causal. That's the problem.
> > >
> > I do not understand where the problem is. I have a deterministic time
> > evolution of the probability law. I may also have a deterministic
> > evolution of the set of eigenvalues (the Heisenberg representation).
> > Where is the problem?
>
> You'll get the wrong answer if you apply such a prescription. If you
> apply the Born rules without nondeterministic state reduction you get
> nonsense. If you lack an explicit state reduction, you are forced to
> explain why, as I said above, we only perceive on 'branch' of the
> wavefunction (given that decoherence effectively shields us from
> macroscopic interferences).
>
No I do not need to explain why I have a state reduction if I do not
attach any reality to the state and the collapse. It is simply a formal
view like Kolgomorov probability theory.
In this formal point of view, the collapse postulate is just the
logical assertion that a given property of a given system is true (e.g.
"Outcome A=a at time t"). We use it to select the systems (what you
may call a 'branch' of the global unitary evolution) where it is
true. Note that there is no time signification on this formal property:
it is either true or false once forever for a given system.
In practical experiments, we have a detector, when this detector
triggers we know that we have a system instance with a given property.

>
> I hadn't known of this attempt at a relativistic generalization.
> Nonetheless, I believe that Bohmian mechanics still has a problem with
> the reproduction of classical trajectories (although perhaps decoherence
> can go a long way towards solving that).
>
Please, do not try to mix the mathematic formulation of bohmian
mechanics with its interpretation (the reality of the bohmian paths).
There is no problem with the mathematical formulation while the
interpretation of bohmian paths is subject to problems.

> >
> > Ok, I will try to explain what I mean. I have no problem with the
> > preferred basis (the basis where I have the experiment outcomes). I
> > just have a problem with the prediction of such a basis by QM. I mean,
> > where in the QM theory do I have results inferring the preferred basis?
> > Up to now, I just know the preferred basis after I have done the
> > experiments. For example the interference pattern of double slit
> > experiments observed on the screen. I know, from this experiment, if I
> > place a screen, I will do a position measurement. But I have not seen
> > anywhere in QM, where the mathematics can predict such a basis as every
> > basis is possible from the theory point of view.
>
> No, you know ahead of time that, if you place the screen, you do a
> position measurement.

Because I have already learn it in an experiment before: I see an
interference pattern when I place a screen, hence the position
measurement.

> Inherent in any experimental design, you know which
> macroscopic observable you are entangling you system with and that
> determines, via decoherece, a preferred basis. (Up to technicalities, I
> suppose, like overcompleteness and the like).
>
Therefore, your view is equivalent to the one saying QM theory does not
predict the preferred basis. In this case, decoherence just explains
why we have stable outcome values for this basis.

> [...snip experiment...]

> > Now how can you deduce (from QM theory) the preferred basis and what we
> > "really" measure in this experiment?
>
> You need to describe to me the macroscopic degrees of freedom in your
> experiment, ie, the macrostates by which you are performing your
> observation. With that, simlply wait a period equal to a couple times
> the decoherence time and pick the basis in which the reduced density
> matrix is diagonal. You don't have to worry about uniqueness of schmidt
> bases or whatever.
>
> Aaron

I have forgotten in the hamiltonian of the system the free hamiltonian
of the slit plate in the previous post:

H= Ho+ Ho_plate+Ho_screen+H_int_plate+H_int_screen

Hint_plate: |plate><plate|(x) V(r)
Hint_screen=|Screen><Screen|(x)Vdiff(r)

My model supposes (see above) that the free Hamiltonian of the plate
and the screen commutes with the different interaction Hamiltonian:

a) [Ho_screen,Hint_plate]=0,
b) [Hint_screen,Hint_plate]=0
c) [Ho_plate,Hint_plate]=0,
b) [Hint_plate,Hint_plate]=0

Therefore if I have at time 0:

|state(o)>=|psi(o)>|plate>|screen>

I will have at *any* time t (whatever the form of the local interaction
V(r) and Vdiff(r) is):

|state(t)>=|psi(t)>|plate>|screen>

=> No entanglement occurs with the state of the photons |psi(t)> and
the states of the plate and screen.

(|plate> and |screen> are the eigenvectors of the free Hamiltonians of
the plate and the screen)

For a sufficient time, the initial wave packet has been partly
reflected by the slit plate and partly transmitted before it interacts
with the screen (due to the local interaction that does not entangled
the photon/electron state with the slit plate):

|psi(t)>= |psi_reflected(t)>+ |psi_slit1(t)>+ |psi_slit2(t)>

Where |<x|(|psi_slit1(t)>+ |psi_slit2(t)>)|^2= interference pattern for
a sufficient time.

Then the part |psi_slit1(t)>+ |psi_slit2(t)> is scattered later by the
screen interaction potential without entanglement with the screen
state.

Therefore, where is the preferred basis as in this model there is no
entanglement between the photons and the plate or the screen (the state
of the plate and the screen are not changed during the experiment)?

Seratend

.

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