Re: Is State Vector Reduction a 'Process'?

Aaron Bergman wrote:
> In article <1118070553.900097.186040@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> "Seratend" <ser_monmail@xxxxxxxx> wrote:
>
> You accept the results of decoherence and you accept that they can (in
> principle) be derived from the law of unitary evolution, right?

Yes. I take the QM formalism for granted (otherwise it is no more QM).

> If so,
> then implicit in this statement is that you believe in the existence of
> the basis selected by decoherence. (I'm going to avoid 'preferred'
> because you seem to want to impart some ontological baggage there that I
> don't want.)
>
What I call the preferred basis is the basis where we notice the
outcomes of a QM experiment. Hence, I need to see if QM formalism
(hence the decoherence application) is able to predict the basis of
outcomes in some cases. We can remove the preferred attribute if you
want.

> I didn't think I was making any controversial statements here. This same
> idea appears in III.E (.3 in particular) of the paper that was referred
> to earlier on this thread, quant-ph/0312059.
>
Good, this was a paper I have studied a long time ago.

Let me quote the section F:

Pointer basis vs. instantaneous Schmidt states. The so-called
"Schmidt basis", obtained by diagonalizing the (reduced) density
matrix of the system at each instant t, has been frequently studied
with respect to its ability to yield a preferred basis, having led some
to consider the Schmidt basis states as describing "instantaneous
pointer states". However, as it has been emphasized, any density
matrix is diagonal in some basis, and this basis will in general not
play any special interpretive role.
Pointer states that are supposed to correspond to quasiclassical stable
observables must be derived from an explicit criterion for classicality
(typically, the stability criterion); the simple mathematical
diagonalization procedure of the instantaneous density matrix will
generally not suffice to determine a quasiclassical pointer basis.

(this sectionf is against your schmidt basis claim)

Now , take the formula (3.8) page 14 of the same document, change the
basis of the system, apparatus and environment and, apply the weak
argument of the mean time orthogonality of the environment basis (what
is done between 3.13 and 3.14 of section III.E => you end with the same
approximated decomposition but with completely different basis, for the
system and apparatus (eq. 3.14).

=> We have different possible basis for the measurements QED.

Seratend.

.

Relevant Pages

  • Re: A critique of textbook quantum mechanics
    ... I suppose you mean basis in Hilbert space. ... so why should decoherence operate in one basis rather than ... mystical quality to "the observer" as if he or she were not a QM ... caused by their interaction with an environment. ...
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  • Re: Is State Vector Reduction a Process?
    ... > the world into classical and quantum components. ... > comes with a preferred basis given by the macrostates of the measurement ... I understand decoherence tells us that there is ... a local basis where there is no interference (the projected density ...
    (sci.physics.research)
  • Re: Is State Vector Reduction a Process?
    ... >> (this sectionf is against your schmidt basis claim) ... pointer states well, ... different decomposition and hence a different basis. ... Once we use these approximations, ...
    (sci.physics.research)
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