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

From: chaverondier (bernard.chaverondier_at_wanadoo.fr)
Date: 10/21/04 

Date: 20 Oct 2004 23:12:53 -0700

dubious@radioactivex.lebesque-al.net (Bilge) wrote in message news:<slrncndns6.8l.dubious@radioactivex.lebesque-al.net>...

Bilge
> Actually the definition of a mixed state is a statistical mixture
> obtained from independently prepared states.

Chaverondier
It is also used to model the state of a part S1 of an EPR correlated
system S=S1US2. This so called mixed state is characterized by a
reduced density operator (a weighted sum of rank 1 projectors instead
of a rank 1 projector characterazing a pure state). This reduced
density operator provides the statistics of quantum measurements on
part S1 when the state of S2 is not accounted for.

The reduced density operator modeling S1 alone together with the
reduced density operator modeling S2 alone provide an incomplete
knowledge of S1US2 quantum state. The state of this quantum whole is
more completely modeled by a pure state of S1US2 (or a density
operator modeling the mixed state of S1US2 if S1US2 is not isolated
hence not in a pure state).

Bilge
> An epr pair is only an epr pair because the pair is described as a
> single state which is completely unpolarized, so that the total spin
> projection along any axis is S_z = 0. By contrast, if the photons were
> independent, i.e., a statistical mixture,

Chaverondier
Photons can be independant and in a pure state (ie in a known spin
state).

Bill
> >I am having trouble understanding the context of some of the terminology
> >you use.

Bilge
> Probably because he isn't using it in a very standard way and because he
> appears to be attributing the correlations to the measurement.

Chaverondier
The decoherence process induced by a quantum measurement creates EPR
correlations between the observed system and the measuring apparatus,
then
between the measuring apparatus and the environment. When the
decoherence
process is achieved, the observed system is not any more in a pure
state. As any entangled system, the state of the system alone is
modeled by a reduced density operator which doesn't comprise the
information about the quantum correlation of the observed system with
its surrounding.

This knowledge is embedded in the quantum state of the quantum whole
comprising the observed system and the measuring apparatus and the
environment it is interacting with _when the measurment process has
taken place_ (before the measuring process has taken place, the
quantum state of the observed system is completely modeled by a pure
state if this sytem is isolated).

Bilge
> [he thinks that] unknown information conspire at faster
> than light speed in order to only make the outcome appear to be given by
> the usual explanation.

Chaverondier
There is nothing unusual in the decoherence process. It gives rise to
the vanishing of the extradiagonal terms of the reduced density
operator of the observed system (caused by its entanglement with the
measuring apparatus when this reduced density operator is expressed in
the preferred Hilbert basis of the measuring apparatus). Neither is
there anything unusual or new in the entropy increase stemming out of
a quantum measurement. These are now well established facts.

Bilge
> Don't be concerned. To the best I can tell, it means that the quantum
> mechanical description of an epr pair as a single quantum state, in which
> the state vector contains all there is to know about the state is wrong.

Chaverondier
No. It is right.

Bilge
> and should be replaced by a mixed state in which there is more information

Chaverondier
This happens only AFTER one of the photons of the EPR correlated pair
has interacted with its polarizer, not before.

Bilge
>I think the overall bottom line is that you can call a theory
> deterministic by attributing the randomness to the unknowable and not
> differentiating between probabilistic and statistical.

Chaverondier
A theory is deterministic when the evolution it predicts is
deterministic. No known facts (only hypotheses which are still
awaiting for an experimental proof) are up to justify that the
unitary, reversible and deterministic propagation of the Von Neumann
chain may be broken at some moment.

Bernard Chaverondier
http://perso.wanadoo.fr/lebigbang/epr.htm
Quantum determinism or relativist locality
http://perso.wanadoo.fr/lebigbang/no_communication.htm
The no-communication theorem

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