Re: Is State Vector Reduction a 'Process'?

Arnold Neumaier wrote:
> Seratend wrote:
>
> > Arnold Neumaier wrote:
> >
> >>Seratend wrote:
> >>
> > We are at the heart of the problem between the formalism of the theory
> > and the interpretation.
> > Please note that the measurement part of the theory does not require
> > any interaction.
>
> The formalism itself has nothing to do with the real world, unless
> it is given _some_ interpretation.
>
> Real measurement requires real interactions.
>
QM formalism does not say what is a real measurement. QM formalism
speaks about the collapse postulate and the born rules and the unitary
evolution. That's all.

I need quantum interactions to describe the whole unitary evolution of
the system and the measurement apparatus object. Unitary evolutions
introduce statistical correlations between the system and the
measurement apparatus object (including the environment if necessary to
describe the evolution).
We use these statistical correlations on the statistics of formal
measurement results of this whole system (including the "measurement
apparatus" that has not to be confused with the formal measurement
result). That's what the formalism allows one to say (hence the
requirement of interactions to correlate the measurement apparatus to
the system). All the rest is interpretation. Saying the measurement
apparatus does a formal measurement is interpretation (completely out
of the scope of the QM formalism). I do not refute the interpretation,
nor I can't as long as it is consistent with the formalism.

> The theory models these by assuming collapse under measurement,
> no matter whether in the eyes of the observer or whether objective.
> At least this is the traditional way of viewing the formalism.
>
This is the traditional *interpretation* of the formalism.
I am just using the logic in the context of the formalism: I do not
explain why I observe a result, just that when this result is true, I
have a collapse. No interaction is involved in this logical
affirmation.
The formal measurement does not have "hidden" interactions. It is
not the measurement apparatus (its interactions).

The usual interpretation is "interpreted measurement result" =
{system, apparatus, all the interations with a global unitary evolution
and the formal measurement result}.

I do not question this label. However, I cannot subscribe to deductions
made on the interpretation that are out of scope of the theory
formalism.

>
> > The observer outside or inside the system has no
> > meaning in the QM formalism (only in the interpretations).
>
> The QM formalism is about closed systems in which no measurements
> happen by definition of what it means to be closed. There are no
> measurements in the formalism.
>
So, Do you claim the measurement postulates of QM formalism are wrong
in some obscure cases?
Where have you seen such a definition in the 6 postulates of QM theory?

(Note: I interpret the word closed system, as a system where the state
evolution on time follows the usual unitary evolution).

Now, if what you call "measurement" is an interpretation
measurement, I have nothing to say.

> If measurements are discussed within the formalism (as
> measurement theory), they have to be _defined_, and they _are_
> defined via an interaction. But the measurements as happening within
> the formalism alone cannot be related to actual measurements
> without an interpretation of what the formalism means in the real
> world. Without an interpretation no relation between formalism and
> reality.
>
This is the mapping between the outcomes of formal observables and the
outcomes of the reality. It is the common denominator of all the
interpretations (I know). Hence no other interpretation is required.
We can say that the QM formalism with the mapping of outcomes is the
minimum set to describe the reality: what I call the QM formalism.
Hence, any interpretation validates this formalism.
>
> > Moreover, an opened system is a closed system when we consider the rest
> > of the world (formal).
>
> But then one needs an interpretation of what it means for one subsystem
> of the closed world to measure another subsystem, and for lack of a
> probabilistic interpretation in our unique world this hasn't been given
> in _any_ of the current interpretations.
>
I need no interpretation (see above) I just need projectors and formal
hypotheses (e.g. the independence of systems, the low impact of
environment etc ...) and the final verification on a "real" system.
I have not a system that measures (in the sense of the postulates)
another system (no meaning), just a global measurement and its results.
>
> >>Thus the observer cannot claim convincingly to have observed the system.
> >>
> > I hope you understand better why this sentence has no meaning in the QM
> > theory formalism (in my opinion : ).
>
> I understand better why it has no meaning for you.
> But I don't accept your arguments as being valid for the QM formalism
> (which includes the Born rule, which makes sense only together with
> the collapse).
>
See above. I am just using the logical meaning of the QM formalism +
the mapping of the observables outcome to the real outcomes taht make
sense for any experiment we may think. I assume that whatever
interpretation you assume, my logical set is always valid, hence you
should logically accept my results.

The main difference is on the collapse of the word meanings: what you
call measurement is not the measurement described in QM formalism.
Hence, you should change this word in order to avoid confusions.

>
> >>Observability by an external observer therefore demands openness of the
> >>system. At least under conventional assumptions about what the terms
> >>closed, interaction, observation mean.
> >>
> > H= sum_i Hi => unitary evolution, including the interactions of the
> > observer object.
> > + collapse postulate: property of an instance of a system governed by H
> > (including the observer object).
> > If I say, I have a system [including the observer object] with a given
> > property => I have the associated collapse. There is no "observer"
> > in the sentence "I have a system [including the observer object] with
> > a given property", just the logic affirmation of this property.
>
> I don't understand you. If there are interactions we have
> H= sum_i Hi + sum_ij V_ij.

Re-label the set of labels i,j by a new label i and call V_ij=H_inew =>
we recover the previous general relation.

> And I don't understand what a 'property' is; the traditional QM
> formalism has no place for it. If you want to stay on the formal
> side you are only allowed to talk about operators, states, Hilbert
> spaces and other on the formal level well-defined concepts.
>
With the outcomes mapping with the "reality", the property
"outcome of A is a" has both a signification in a real object as
well as in a symbolic one.
(here property: the mathematical signification. You can use proposition
if you it is more adequate).
In the traditional formalism of QM, when the collapse postulate is
true, the property "outcome of A is a" is true. This is a property
of the considered system (logic).If this property is false the
corresponding collapse postulate is also false => the collapse of a
system is a property of the system (QM formalism).

I am not inventing new words, I am just using mathematical results of
the QM formalism.

> >>
> > Well, as I have said before, I will not question the interpretation as
> > long as it does not change the QM theory formalism.
>
> I do not change the formal side of quantum mechanics.
> But it is meaningless without an interpretation in terms of the
> real world.
>
I think this post underlines that you may have at least given a
signification to the word measurement of the QM formalism that may be
not compatible with the formalism (If I have understood what you have
said).
>
> It would be good if you could give a concise formal definition of
> what you consider to be _the_ QM formalism. One can state everything
> in a few axioms, but it seems that your set of axioms is different from
> what I hold to be the common view.
>
The 6 usual postulates + the mapping of the observables outcomes
(defined by the collapse postulate) to the outcomes of real systems.
That's all.
>
> >>>Note, in the QM formalism, there is no classical/quantum boundary (only
> >>>in the interpretations of QM). Just postulates that may be applied,
> >>>hopefully (for the consistence of the theory) on closed systems as well
> >>>as opened ones.
> >>
> >>But there are different postulates for
> >>
> >>- closed systems (unitarity),
> >>- systems open just at some instant (collapse), and
> >>- continuously open systems (Lindblad type dissipative dynamics,
> >>or corresponding stochastic quantum processes).
> >>
> > I hope that no!
>
> My statement is based on assessing the heap of papers on QM that
> I read among the flood of papers published in the last 10 years,
> say. In particular, most realistic experimental analysis requires
> the open systems view in which energy is _not_ conserved but
> dissipates into unmodelled degrees of freedom. These systems are
> not unitary, but are as quantum mechanical as one could wish.
>
I understand that your statements as most of the written papers are
based on a mix of interpretation and formalism. I do not question the
effective results. Each time I read a new paper, I try to remove all
the interpretation stuff from the real logic content.
What you say is true: the local state of an opened system does not
evolve unitary. This is a result of QM formalism. No need to interpret
this result. The coupling of theses open systems define a global
unitary evolution and hence a local non unitary evolution that may have
some interesting properties (localisation of the state on a subset of
possible outcomes in a give basis, etc ...). This again is given by the
QM formalism.

Therefore, strictly speaking, you can only say that the evolution of a
local state of a given system is non unitary. However, in a more
common language you can say the system does not evolve unitary,
assuming implicitly you are speaking of the local state.

However, strictly speaking, a local outcome of a system is a global
outcome of the whole system (including the universe) in the QM
formalism: we always apply a projector
P=|local><local|(x)Id_restoftheworld when we say we have a peculiar
outcome. The property applies to the whole universe, strictly speaking.

> Von Neumann's 1932 postulates are no longer believed to be valid
> for small systems since it is well recognized that these are
> necessarily open.
>
This is a matter of words. What you say is that you always have
interactions with other parts of the world, even for a small system.
This in no case refutes the fundamental postulates.

> These postulates are only believed to govern a very large system
> (small system plus detector plus environment), from which a
> statistical mechanics type analysis (heat bath etc.) produces
> the reduced open description.
>
Again, QM formalism does not refute such a result. The probability
P~100% of some outcomes are possible.
Note this is the same thing in CM: we do not know no real system
without dissipation (in the absolute) however, the laws assume the
energy momentum conservation.


>
> > You have the unitary evolution and the measurement postulates: An Open
> > system is always a part of a closed system (otherwise, the unitary
> > evolution postulate is not true => problem with the consistence of the
> > QM theory). The collapse postulate always applies to the whole system
> > description.
>
> The closed system is always the whole universe.
In the absolute, yes as in the CM formalism.
> Since this cannot be observed from the outside, von Neumann's measurement theory > does not apply there.
Once again you are mixing the measurement formalism with your
measurement interpretation.

> It is never in the factorized state assumed to
> prevail before the beginning of a measurement. Interactions cannot
> be switched on and off to restrict the measurement to a short duration.

Interactions has not to be switched on/off in a formal measurement:

A formal measurement is the acknowledgement of a property (the
"outcome a") of an instance of a given system. There is not any
interaction in this acknowledgement. There is not any interaction
involved in a formal measurement.
Think on the god theory of the previous post: we just have properties
that are established once. Formal measurement is just the aknowlegement
of some of these properties and not the modification of these
properties, it does not change the system.

We use to mix in the word measurement, the interactions added by the
measurement apparatus and the formal measurement (the acknowledgement).
If you follow rigorously the QM formalism, you have to separate these 2
meanings: the apparatus (and hence its interactions) and the formal
measurement (no interaction at all, does not modified the considered
instance of the system+apparatus+ ...).

Seratend.

.

Relevant Pages

  • Re: Is State Vector Reduction a Process?
    ... be observed and hence cannot produce outcomes" is already an interpretation of the measurement formalism. ... If the observer sits in a different system then, because the first system is closed, it cannot have any interactions. ... At least this is the traditional way of viewing the formalism. ...
    (sci.physics.research)
  • Re: Is State Vector Reduction a Process?
    ... >> QM formalism does not say what is a real measurement. ... formalism (the 6 postulates below). ... The "measurement result" of a physical variable A_phys represented ... of the "measurement result" (by the non commutativity of observables). ...
    (sci.physics.research)
  • Re: Is State Vector Reduction a Process?
    ... >>>We are at the heart of the problem between the formalism of the theory ... >>Real measurement requires real interactions. ... Thus the formalism says nothing without interpretation, ...
    (sci.physics.research)
  • Re: Expressions versus the value they represent
    ... In FOL the expression c,1) is called a /term/. ... My point was that under interpretation, ... problem of how to encode values on a computer, ... appropriate for a formalism underlying database theory to distinguish ...
    (comp.databases.theory)
  • Re: Observer pattern limitations
    ... The OOPL has have a formalism that let's you map each ... It does not describe the semantics of the program, ... You're varying the interpretation on the *output* of the programs. ... the program of Ariane V was ...
    (comp.object)