Re: entangled states

Hendrik van Hees wrote:
> Andreas Most wrote:
>
>> Things are perfectly consistent if you consider the wave function as a
>> mathematical object in which all information we have about a quantum
>> state is encoded. A measurement changes the knowledge about the
>> quantum state and thus the wave function.
>
> So far I can agree.
>
>> Then it is also obvious that different obervers may have different
>> description (wave function) of a quantum state based on their specific
>> knowledge about a state (consider e.g. the thought experiment about
>> "Wigner's friend").
>
> I think that's not what is meant when we say: "We assign the state [psi]
> (let [psi] denote a ray in Hilbert space represented by a vector |psi>)
> to a system." It's too subjectivistic a view.
>
> I think, what is meant by this statement is that a system was prepared
> by the experimenter in this state [psi]. Within the minimal
> interpretation that's a little bit unprecise, because the information,
> encoded in [psi] is only probabilistic. So what it really means is,
> that the system under consideration belongs to a (really prepared or at
> least in principle preparable) ensemble of independent systems which
> shows the statistic features encoded in [psi]. Different observers all
> assign this state [psi] and not any other to it, although one observer
> may use another observer's states mapped by a unitary (or antiunitary)
> operator. This covers also the case of observers in different frames of
> reference or using different pictures of time evolution (Schroedinger,
> Heisenberg, or Dirac).
>
> Of course, one also has the more common case of an incomplete knowledge
> about the system, and then different observers might assign different
> impure states (statistical operators) to the system, based on their
> knowledge of the system.

I agree with you so far. But I was heading into a different direction.
Consider an EPR-like setup with an entangled photon pair ("diphoton"
as it was mentioned in d.s.physik ;-) ) with the previously mentioned
wave function |psi> = 1/sqrt(2) (|HV> - |VH>)

Let Alice and Bob each receive one of these photons (Maybe they are
doing some quantum cryptography). If Alice has performed a measurement
and has reduced the state to, say, |psi(Alice)> = |HV>, what wave
function would Bob use to describe the system?

If Bob is spacelike separated, he cannot
possibly know whether Alice has performed the measurement at all.
And as long as he leaves the system unchanged and does not get
information from Alice, he must describe the system as
|psi(bob)> = 1/sqrt(2) (|HV> - |VH>). Anything else without better
knowledge would lead to contradictions (I think GHZ like setups
would show contradictions.)

As soon as he gets to know about Alice measurement, he can use
(so to say with 20/20 hindsight) |psi> = |HV> to interpret his
previous observations (measurements).

I am simply trying to say that spacelike separated observers might have
different descriptions for a quantum mechanical system. It might be even
possible for timelike connected events, if you do not receive any
information about a measurement like in the "Wigner's friend" thought
experiment, though I think that decoherence effects play a bigger role here.

>> And actually, the correlation of observables of an entangled system is
>> to me as mysterious as is in Newtonian mechanics an object moving on
>> a straight line forever if no forces are present. ;-)
>
> In fact, physics does not give an "explanation" for this. It's just an
> experimental fact about moving bodies which Galileo and Newton used to
> base their further analysis on. The principle of inertia is a basic
> observation, we cannot deduce from more basic observations (despite the
> fact that general relativity refines the principle of inertia in a
> subtle way).

Yes, and I think that quantum mechanical behaviour is fundamental in a
similar manner. There is maybe no explanation for it.

However, just to add "my two cents": I have the impression that the
so-called collapse of the wave function being related to information
gain has to do with the arrow of time (because of entropy...).
Maybe, If we sometime solve the "arrow of time" puzzle,
we might be able to solve also the so-called "measurement problem".
(please don't flame me on this. It's just my personal opinion...)

>
>> In order to not be in the urge of assuming such a preferred frame
>> I avoid using hidden variables. Apart from this I do not see that
>> Bohmian mechanics makes any testable (by experiment) prediction that
>> goes beyond the predictions of QM. (Also your paper makes no testable
>> predictions as far as I have read it).
>
> I agree completely.
>
>> I agree that the Bohmian interpretation does not contradict
>> experiment. But I think you give up to many well-established
>> principles without gaining anything new in terms of testable
>> predictions.
>
> You make an already complecated subject even more complicated by
> introducing unobservable "elements of reality" and name them
> trajectories to make QT sound a little bit more like classical
> mechanics.

Yes!

Regards,
Andreas.

.

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