Re: Is State Vector Reduction a 'Process'?
Seratend wrote:
Arnold Neumaier wrote:
Seratend wrote:
However, the sentence "the closed system cannot
be observed and hence cannot produce outcomes" is already an
interpretation of the measurement formalism [of QM axiomatic theory].
No. How could a closed system be possibly observed from the outside???
If the observer sits in a different system then, because the first
system is closed, it cannot have any interactions. Thus the observer's
dynamics will be completely unaffected by the system. Thus the observer
will not be able to collect any information about the system.
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.
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.
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.
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.
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.
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).
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.
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.
For the universe as a whole, the situation is different since it is
observed by an observer _within_ the system. While this is not
analyzed in the trasditional setting, it can be analyzed within the
consistent experiment interpretation.
I am still working on your post reply dealing with the "consistent
experiment interpretation". I hope soon I will be able to give you
some feedbacks.
I am looking forward to this discussion.
This even holds in the traditional Copenhagen interpretation.
The view is that the system is closed most of the time and then
evolves unitarity. At certain very short moments, it is assumed
to be in contact with a detector for measurement - then the
system is open and evolves nonunitarily, by collapse.
This is interpretation,
Of course, I didn't claim otherwise.
It is the Copenhagen _interpretation_.
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.
In this
interpretation context, I do not know what you intend by collapse (you
seem to have studied deeper the CI than I : )). All what I know is the
logical meaning of the label "collapse" in the QM formalism and
definitively it does not say it is a non unitary evolution of the
system. Only the interpretation of the words "before" and
"after" may lead to such a conclusion (hence an interpretation).
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.
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 (collpse), 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.
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.
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.
At least that's the conclusion one gets when looking at how
people who analyze nontrivial experiments actually use quantum
mechanics. (There is of course lip service to tradition, though,
but one should measure people by what they do rather than what
they say.)
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. Since this cannot
be observed from the outside, von Neumann's measurement theory does
not apply there. 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.
Thus assuming the state of the universe to collapse has no basis in
either theory or empirical observation.
Arnold Neumaier
.
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... How could a closed system be possibly observed from the outside??? ... > If the observer sits in a different system then, ... We are at the heart of the problem between the formalism of the theory ... > consistent experiment interpretation. ...
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(sci.physics.research) |
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