Re: a question on incompatibility of properties in a one particle system

From: bernard.chaverondier (bernard.chaverondier_at_wanadoo.fr)
Date: 10/20/04 

Date: Wed, 20 Oct 2004 21:54:40 +0200

"Bill Hobba" <bhobba@rubbish.net.au> a écrit dans le message de
news:8Chdd.32698$5O5.31178@news-server.bigpond.net.au...

> "bernard.chaverondier" <bernard.chaverondier@wanadoo.fr> wrote in message
> news:4174db5f$0$4015$8fcfb975@news.wanadoo.fr...

Bill
> Mixed state means a state that is a superposition
> of states of definite position say.

Chaverondier
No. Mixed states should not be mistaken for superposition states.
A superposition state is still a pure state because the interference
between the components of the state of the system is possible.

Bill
> In principle any state is 'pure'

Chaverondier
No. If a system S1 is entangled with a system S2, then
even if S=S1US2 is in a pure state |psi>, you cannot
separate system S1 from system S2 without loss
of information. This is explained on the slide
"What happens if you don't look at part of your system"
of the link you provided in this thread
http://www.physics.utoronto.ca/~steinber/Vienna_Lect2.ppt. )

When you look only the part S1 of a system S = S1US2 in a pure
but entangled state |psi>, the part S1 of S is not any more in a pure
state. It is in a mixed state that is obtained by the so called partial
trace operation rhô1 = somme_k <psi2_k| rhô |psi2_k>
  * where rhô denotes the density operator
      of system S = S1US2, rhô = |psi><psi|
  * where rhô1 denotes the reduced density operator of system S1
  * where the |psi2_k> denote an Hilbert basis of the
      Hilbert space state of system S2

You loose information when you try to define an entangled
part S1 of an inseparable quantum whole S=S1US2 separately
from the rest of this quantum whole.

See for instance, the slides "decoherence arises from throwing
away information" and "decoherence party line" of the link
http://www.physics.utoronto.ca/~steinber/Vienna_Lect2.ppt
you provided to me.

I quote the slide "decoherence party line" because it's very important
"coherence is never lost, as _unitary_ evolution preserves the purity
of states. In principle, the measurement interaction is _reversible_.
In practice, once the system interacts with the environment, ie
anything with too many degrees of freedom for us to handle,
we cannot reverse it. Just as in classical mechanics, it is the
_approximation_ of an open system which leads to effective
_irreversibility_ and _loss of information_ (increase in entropy)

         loss of information = loss of coherence"

Bill
> I am having trouble understanding the context
> of some of the terminology you use. Can you
> confirm you accept the terminology of the following presentation
> http://www.physics.utoronto.ca/~steinber/Vienna_Lect2.ppt

Chaverondier
First "shear state" is a translation error of mine. I wanted to say pure
state. Second, what I call the statistics Born rule is what you call the
Von Neumann statistical assertion.

Now, I read your link and I didn't notice any point of disagreement
except on the slide "what are the effect of measurement ?" where
there is a big mistake about the explanation of the collapse of a
system S1US2 in the state (|+->+|-+>)/2^(1/2) when measuring
one of the two entangled parts.

The explanation which is provided on this slide amounts
to a _local_ hidden variable interpretation which has been
discarded by the experimental verification of Bells inequalities
violations. Otherwise, your link is OK.

Bill
> What I find difficult in your writing is you seem to be taking
> a certain predetermined view of things that is known to
> yourself but is not spelt out clearly from the start and mixing
> it up with concepts that we simply do not know for sure.

Chaverondier
Presently; the only thing where my point of view seems to differ
from the most widely accepted one is that I don't believe in the
hypothesis that the so called collapse would be something different
from the unitary, deterministic and reversible evolution of the quantum
whole comprising all parts involved in the measurement process, ie
  * the observed system
  * the measuring apparatus
  * the environment interacting with them.

As in classical statistical mechanics, when an apparent
irreversibility and an apparent indeterminacy show up, that's
(in my opinion) a consequence of a loss of information of the
observer.

Surprisingly, your link seems to agree with this point of view
(which suggests that the views on that topic may be changing).

Bill
> The same for non locality - we simply do not know if QM has
> non locality or not - it is entirely interpretation dependant.

Chaverondier
You know that the result of a measurement on one part S2
depends on the measurement that has been performed on
The part S1 of an entangled system S=S1US2 (ie the state
of the measuring apparatus of S1 when the measurement
on S1 has been performed)

The best illustration is the Greenberg Horn Zeilinger
thought experiment that is even more striking that the
EPR experiment because only equalities are involved.
(see "do we really understand quantum mechanics ?" by Frank Laloe
http://www.phys.ens.fr/cours/notes-de-cours/fl-mq/mq-anglais.pdf
8 Mo unhappily, chapter 4.3 GHZ equality )

Now, the interpretation of EPR effect as an action at a distance
depends on the interpretation of quantum measurement indeterminacy.
The principle of relativity of motion is preserved if quantum
measurement indeterminacy is assumed to be fundamental.
In the case when quantum indeterminacy is interpreted as a
loss of knowledge of the local observer, then the principle
of relativity of motion is lost.

Bill
> Nothing a-priori demands that QM is determined
> by hidden variables as assumed in a Bell type analysis.

Chaverondier
The Bell experiment and the Bell's inequalities violation
that have been proven don't demand hidden variables.
They are incompatible with _local_ hidden variables
and are compatible with _contextual_ hidden variables.

If we stick to the idea that the unitary, deterministic, reversible
quantum formalism that applies to isolated quantum systems
works fine and that no strange and unknown process breaking
this reversibility would show up, I don't see how it is possible
to escape the interpretation according to which the quantum
measurement indeterminacy stems from a loss of knowledge
of the contextual hidden variables (forgotten variables instead
of hidden would be better in my opinion) ie (in my opinion)
the quantum state of the measuring apparatus and its
environment

(see "Hidden Variables and Nonlocality
in Quantum Mechanics" Douglas Hemmick"
http://www.intercom.net/~tarababe/DissertPage.html )

and The sub-quantum (deterministic) theory of Micho
Durdevich, Universidad Nacional Autonoma de Mexico,
"Physics Beyond the Limits of Uncertainty Relations".
A picture of physical reality which is based on individual
physical systems, completely causal, and statistically
compatible with quantum mechanics.
http://www.matem.unam.mx/~micho/subq.html

Incidentally, the deterministic interpretation of the measurement
process seems to be shared by the author of the link you have provided.

Chaverondier
> > A mixed state indicates that the system is, or has been, EPR correlated
> > with its surrounding so that the knowledge of the local observer (which
> > is encapsulated in the reduced density operator of the observed
> > system) has been somewhat deteriorated and is now incomplete.
> > A part of the information that would be necessary to predict
> > deterministically future evolutions of the observed system is
> > lies in the EPR correlations of the system with its surrounding.

Bill
> I have no idea what your are trying to say.

Chaverondier
It is explained in the link you have provided.
I quote the last slide "summary"

"the reduced density matrix of an entangled sub-system appears
mixed because the discarded part of the system carry away
information. This is the origin of decoherence of the measured
subsystem."

Bill
> In QM the state tells us everything we can know about
> a system - EPR or no EPR

Chaverondier
When you consider the measurement process, the system
becomes EPR correlated with the measuring apparatus.
The whole comprising the system + the measuring apparatus
can still be represented by a pure state (as far as it is not
entangled with the environment) but the observed system
cannot be anymore modeled by a pure state. It is modeled
by a mixed state, ie by its reduced density operator
(which doesn't provide information about the EPR
correlation of the observed system with the environment).
This is explained on the link you have provided.

Chaverondier
> > The entropy increase that follows a quantum measurement of a
> > system which is not in a pure state of the measuring apparatus
> > (as a measurement of position of a system which is nearly
> > in a shear quantum state of momentum for instance)
> > indicates this deterioration of the knowledge of the local
> > observer when the quantum collapse process occurs.

Bill
> Again I have no idea what you are trying to say.

Chaverondier
See the slide "decoherence party line" of the
link you have provided for instance.

Chaverondier
> > Here I provide my one. The hypothesis that there would be
> > some unknown fundamental irreversibility and indeterminism
> > in quantum measurement is (in my opinion) both superfluous
> > and incompatible with the unitary, deterministic and reversible
> > propagation of the infinite Von Neumann chain.

Bill
> Then please provide the full mathematical details of the
> interpretation. An example of such would be primary state
> diffusion as proposed by Ian Percival
> http://arxiv.org/abs/quant-ph/9508021
> I would appreciate it if your ideas were expressed in a similar
> way because I have great difficulty understanding what you are
> on about.

Chaverondier
I am still working the bibliography and what you are asking
amounts to a work of several years (at least). Presently, I
am working about all that and use the net as a mean to
get a lot of valuable hints and links on the topic.

The point where I am presently is that one.

1/ I have stated the compatibility of faster than light propagating
interactions with an appropriate formulation of relativist
invariance of phenomena that actually satisfy this symmetry
in the framework of Aristotle space-time
see http://perso.wanadoo.fr/lebigbang/epr.htm
(unhappily written in French. Up to now, I have not
taken the time to translate it in English) and in English
http://perso.wanadoo.fr/lebigbang/transformation.htm
derivation of the Lorentz transforms and definition of
inertial frames in the framework of Aristotle space-time.

2/ I have pointed out that the proof on the no communication
theorem relies on the dubious hypothesis that quantum
measurement indeterminacy would be of fundamental nature.
see http://perso.wanadoo.fr/lebigbang/no_communication.htm

Now, I cannot see how this assumed fundamental indeterminacy
could be interpreted as compatible with the unitary, reversible and
determinist propagation of the Von Neumann chain. So, I rather interpret
the Copenhagen interpretation to be an efficient tool as for instance is
the Biot and Savart law of electromagnetism. I believe the quantum
measurement process to be a deterministic process as soon as the
quantum whole encompassing the observed system, the measuring
apparatus and the environment apparatus are accounted for.

Bill
> Then what is an observation?

Chaverondier
Of course, a model of quantum measurement is needed to support
a deterministic, explicitly non local interpretation of quantum
measurement and that's where I would like to go.

Presently, I just want to discuss these ideas to get all the objections
that can oppose this point of view and get valuable hints and links on
the topic. Indeed, I think it would not be a good idea to do a lot of
work without knowing in the first place all the objections that have
to be considered and the present "state of the art" on the topic.

Bernard Chaverondier
http://perso.wanadoo.fr/lebigbang/transformation.htm
Derivation of Lorentz transforms and definition of inertial
systems of coordinates in the framework of Aristotle space-time.
http://perso.wanadoo.fr/lebigbang/epr.htm
Quantum determinism or Relativist locality ?

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