Dear Michael,
I in your Email, see below, you discuss the problem of #entanglement
between a system and measuring appratus.# The problem of measurement
is the hardest problem of QM. By the orthodox Copenhagen interpretation,
by von Neumann projection postulate, the system which was in the
superposition of a few states is projected to one of eigenstates of the
operator representing the measuring device. There are two different
types of evolution: continuous and unitary Schrodinger eveolution and
the jum-like evolution in the process of measurement. It is rather
strange situation that it is impossible to unify in any way these two
processes.
The projection postulate is used in the conventional derivation of
quantum nonlocality through measurements on entangled pairs.
Today at the conference #Beyond QM# we had the talk of Professor Laloe,
who discussed measurements on Bose-Enstein condensates, and in
particular, the EPR experiment for two condensates. These are huge
systems. He pointed out that a measurement by laser impuls could induce
the collaps of the state of teh Bose-Einstein condensate, it is even
more hard to imagine that this projection will immediately be transmited
to another #entangled# condensate. Everything is macroscopic.
I cannot explain this experiment in another way than to assume that QM
is really incomplete,as Eistein supposed, and these condesates really
have properties which are not given by their quantum states.
Andrei
> Dear Andrei,
>
> I sent an e-mail to Steven E. which I hope he might find helpful. If
>
> you\'d care to do so, I\'d be honored if you would choose to comment on
>
> it. The message I sent to Steven follows:
>
> Steven,
> Im reluctant to submit this message to FIS since we are only allowed
>
> some limited number per week. Ive only glanced at one of the two EPR
>
> articles you mention, but I might be able to help, anyway. Among the
>
> battalions of works written about EPR, one of the very best came from
>
> the philosopher of science, Arthur Fine. His book, The Shaky Game ,
>
> lucidly and comprehensively details the historical information and
> logical arguments associated with the EPR problem. Unfortunately,
> Fines
> proposed solution is not as valuable.
> Fine found that Einstein was not well pleased with the EPR article as
>
> published. Podolsky had written it. Einstein was concerned that the
> EPR
> article might confuse the essential issue with commutation of quantum
>
> observables. There is no necessary connection. In fact, Fine suggests
> a
> simple EPR experiment performed with just a single observable. As we
>
> know, the fundamental conundrum is not commuting observables, but how
>
> one particle can speak instantly, over some finite distance, to
> another.
> I suspect the article by Tommasini is not of serious concern. Most
> physicists, it seems, regard the Aspect experiment, and its
> descendants,
> as crucial. A wonderful, comprehensive, comprehensible review of EPR
>
> reasoning and experiments was given by Franco Selleri in his
> introduction to the conference proceedings, Quantum Mechanics vs.
> Local
> Realism
> And, we recognize that the question is not whether real information
> is
> transmitted instantly across some separation, in violation of
> Einsteins
> tenet that c is the maximum speed for information. No EPR experiment
>
> demonstrates instantaneous exchange of real, physical, information,
> as
> Andrei has reiterated. There is never a transmission of energy in
> these
> experiments. Instead, as in the Aspect experiment, measurement of the
>
> spin direction of one photon - choice of an axis in space - instantly
>
> determines the axis for spin direction of another, widely separated
> photon. Two separated human observers cannot communicate via such a
> channel.
> Perhaps you know that quantum entanglement was precisely defined by
> von
> Neumann, at the beginning of his mathematical development of Q.M. In
> the
> last chapter of Mathematical Foundations of Q.M., von Neumann
> carefully
> explained quantum measurement. (His work is difficult and sometimes
> obscure, but its the bible.) He explained that exactly two
> autonomous
> physical objects are required - the observed object, O, and the
> apparatus A. Each, of course, is depicted by its own vector in
> Hilbert
> space (or wavefunction).
> So long as each is an isolated physical object (no energy exchange,
> at
> all) we continue to describe each by its wavevector, which evolves in
>
> time according to Schrodingers equation. Significantly, and most
> interestingly, von N. said that if there is no energy exchange
> between
> O+A and the outside world, the compound system of object plus
> apparatus
> must also be a single physical object, also depicted by a single
> vector
> in Hilbert space. The compound OA object, too, will continue to
> experience unitary, Schrodinger development, even as A exchanges
> energy
> with O (the measurement of O by A), as long as no energy is
> transferred
> between OA and its environment.
> Von Neumann showed that the OA wavevector is the direct product of
> the
> individual wavevectors of O and A. And he proved that if A measures O
>
> (as O+A remains isolated from the rest of the world) there exists a
> one-to-one correlation between each possible eigenvector of O
> determined
> by the measurement, and just one eigenvector of A. This is the
> quantum
> measurement correlation. Its called entanglement.
> A very important theorem was demonstrated by Wigner in 1952, and
> later
> enlarged by Araki and Yanase. They proved that the exact measurement
>
> correlation can exist only for a subset of all physical observables.
>
> They showed that only if an observable commutes with all additive
> conserved quantities (energy, momentum, spin direction, etc.) can it
>
> form a measurement correlation. But, there is an approximate
> correlation
> for other observables, if the apparatus is macroscopic.
> Continuing v.N.s argument, we notice that if O+A is a single
> physical
> object described by one wavevector in Hilbert space, then O+A+S is
> also
> a single physical object described by Schrodingers equation (quantum
>
> object), where S is some other physical object, as long as OAS
> remains
> isolated from energy exchange with its environment. And so on, to
> Fullerene molecules, viruses, cells, people, galaxies, etc.
> Crucially,
> unitary Schrodinger development describes the compound object only so
>
> long as no energy is exchanged with its environment. Obviously, the
> larger the object, the shorter the duration, on average, before it
> experiences some energy transfer with its environment, due perhaps to
> a
> cosmic ray, or atmospheric molecule, etc. Zurek has called that
> process
> of annihilation of the Schrodinger evolution of an object by
> interaction
> with the environment decoherence . For macroscopic quantum objects,
> the
> duration of unitary evolution, before another environmental exchange,
>
> can be exceedingly short.
> Hope Ive been of some help, Steven.
> Cordially,
>
> Michael Devereux
>
>
With Best Regards,
Andrei Khrennikov
Director of International Center for Mathematical Modeling in Physics,
Engineering, Economy and Cognitive Sc.,
University of Vaxjo, Sweden
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Received on Mon May 29 19:24:23 2006
