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

From: bernard.chaverondier (bernard.chaverondier_at_wanadoo.fr)
Date: 11/02/04 

Date: Tue, 2 Nov 2004 16:00:54 +0100

"Bilge" <dubious@radioactivex.lebesque-al.net> a écrit dans le message de
news:slrncoefsr.ibg.dubious@radioactivex.lebesque-al.net...
Bilge
> >> An interference pattern occurs because the phases are
> >> completely indeterminate, i.e., there is a non-zero commutator
> >> between the phase and the photon number operator:
> >> [N, \phi] = -i

Chaverondier
> >This indeterminacy shows up only if you perform a measurement
> >of photon number (by a photographic plate for instance).

Bilge
> Try writing a wavefunction down that provides
> well-defined values for both caonical conjugates.

Chaverondier
You cannot find any quantum state that is a pure state in one
variable and a pure state in the conjugate variable. Such a
quantum state doesn't exist. That's not a surprise that it cannot
be found and doesn't entail the deterministic quantum evolution
of any really existing quantum state of an isolated quantum system.

Bilge
> I didn't assume anything was unknown. I assumed that you could
> write a wavefunction down that include any and all of the apparatus.
> You can certainly do that in principle, just by calling it \Psi. What's
> the commutator of p and x applied to this wavefunction that now
> includes the environment?

Chaverondier
The same : [x,p] = i hbar. You can assert that you have an
impossibility that a quantum state be in a pure state in x and
in a pure state in p. However a (coherent) superposition state of
position (for instance) is not a ill-known state. A known quantum
state has not to be an eigen state in variable x or in variable p
(and anyhow cannot be in an eigen state of both variables because
these are conjugate variables). No quantum uncertainty about the
quantum state evolution lies here.

Chaverondier
> >That's not that different from the case when I play head and tail by
> >flipping a coin. I can provide a mathematical statistical model which
> >will provide me with an excellent agreement with observed statistics.

Bilge
> But not a quantum mechanical model. If you think otherwise, write
> the appropriate quantum mechanical wavefunction for two identical
> coins in a singlet state, |heads> - |tails> and see if what you're
> flipping looks like that wavefunction.

Chaverondier
You have no observable (coherent) superposition state at a macroscopic
level. I am not arguing that quantum physics would be the same as
classical physics. I am only pointing out that the source of quantum
measurement uncertainty lies in the lack of knowledge of the quantum
state of the measuring apparatus and that of the environment.

Chaverondier
> >Nevertheless, this mathematical model doesn't oppose the interpretation
> >that this indeterminacy stems from my lack of knowledge of the little
> >details that cause the coin to fall on one face or the other one.

Bilge
> >> That occurs for a state of _maximum_ knowledge,

Chaverondier
> >Of maximum knowledge of _a part_ of the quantum whole
> >comprising the observed system, the measuring apparatus
> >+the environment that interact with them. The part comprising
> >only the observed system.

Bilge
> In the epr experiment, both photons are measured.
> There is no unobserved part of the system.

Chaverondier
Yes there is the unobserved quantum state of the polarizers.

During the polarization measurement, the involved system
is not only the EPR correlated pair of photons. If this was
so you wouldn't have any polarization measurement.

The involved system comprises the EPR correlated pair
of photons + the polarizers + the environment which
interact with the polarizers (and is responsible for the
decoherence of the superposition state of the polarizers)

Chaverondier
> >Now, when you measure the position of a photon you
> >cannot say that the photon was where you have measured
> >it to be before you performed the quantum measurement.
> >The measuring apparatus (hence its exact quantum sate)
> >participates strongly to the creation of this interaction event.

Bilge
> I'm sorry, but this is like reading ``In Search of Schroedinger's Cat''.
> You've made quantum mechanics out to be some mystical theory.
> It might be weird, but it's not nearly as weird as you are trying to
> make it out to be.

Chaverondier
I only argue that there is (in my opionion) no mysterious
source of quantum measurement indeterminacy (other than
the ignorance of the quantum state of the measuring apparatus
and that of the environment).

If the quantum state of the observed system + the measuring
apparatus + the environment were all known, the quantum
evolution of this quantum whole (hence the quantum measurement
outcome of the observed quantity) could be predicted deterministically
in agreement with the deterministic quantum dynamical principle
applying to isolated systems in a known initial quantum state.

This deterministic interpretation of quantum measurement doesn't
allow for a simultaneous knowlege of conjugate observables
because a pure state in a quantum observable destroys the pure
state obtained thanks to a previous measurement of the
conjugate observable.

http://perso.wanadoo.fr/lebigbang
Compatibility of Alain Aspect experiment interpretation
as an action at a distance with a formulation of relativist
invariance of phenomena that satisfy this invariance in
the framework of Aristotle space-time SE(1)xSE(3)/SO(3)
and the compatibility of possible instantaneous transfer of
information thanks to EPR effect with an explicitly non local
and deterministic interpretation of quantum measurement.

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