Re: What is quantum measurement problem?
- From: markwh04@xxxxxxxxx
- Date: Thu, 29 Dec 2005 19:20:41 +0000 (UTC)
>>From Tony012; sci.physics.research; dated 2005 November 8
http://groups.google.com/group/sci.physics.research/msg/ea90208e4340eea7
>What is quantum measurement problem?
>Why do people say decoherence does not solve the quantum measurement
>problem?
It's the problem of determining why and how a pure state seems to turn
into a mixed state upon "measurement".
Decoherence brings you much of the way by not only showing how
"mixtures" can arise in a world of "pure" states (i.e., states which
describe part of an overall system can be in what are called "improper
mixtures" even if the total system is in a pure state), but also why
"measurements" seem to delineate a specific frame of eigenmodes for the
states to decohere into, even though any basis serves just as well as
another to describe the space of pure states.
There is an additional feature described in the FAQ of that of
determining why or how a mixed state turns into one of the pure states
comprising its mixture. But I don't see any reason for recognizing that
as anything but a null operation, since "mixed state" *already* means
probabilistic combination of pure states, and there's no reason for
interpreting it any other way. So that, when you say, "state W becomes
the mixture p W1 + q W2 with p and q > 0 and p + q = 1" this will be
nothing more than a fancy way of saying "state W becomes either W1
(with probability p) or W2 (with probability q)".
For instance, a thermal state is a mixed state, even though a system
lying in that state is really in one of its pure states, with
probabilities given by the coefficients of the mixture. The
probabilities reflect an absence of information in the mind of the
perceiver, not something out there.
So, in reality, the difference between "mixed" and "random pure" is all
in the mind of the person seeing it and depends entirely on who much
they know of the system. The mixture represents nothing more than an
absence of information.
Moreover, the latter feature of "mixed -> one of the pure state at
random", which I deem a null operation, would have nothing to do with
quantum physics, per se, even if it were something. Mixed states are
not quantum theoretic in the first place. They're a generic feature of
all classical and quantum physics.
Quentum theory left the discussion as soon as you quit talking about
the superpositions of the original pure state. You could just as well
discuss the question of why a thermal mixed state "became" one of its
pure states after being looked at through a microscope, yet you don't
hear anybody pretending here that this "becoming" was anything more
than a change of perception in the mind of the observer, rather than
something that actually happened out there.
The real issue is not the latter step (or, more appropriately,
non-step), but the former one. Decoherence gets you 99% of the way to
resolving a pure state into one looking very much like a mixed state.
But not all the way.
It still leaves the universe in a pure state. So, all you end up doing
is shifting the issue over to a "Wigner's friend" problem and resolving
nothing.
The more fundamental question is this: why does there appear to be a
non-trivial superselection structure in the universe? Superselection is
just a fancy way of describing this situation. It is what underlies
decoherent superpositions.
To be more precise, a superselection structure consists of what is
called a partition of unity:
1 = P1 + P2 + ... + Pn (+ ..., possibly infinite
sum or even integral)
with Pi Pj = 0 if i != j and Pi' (adjoint) = Pi Pi = Pi ... such that
every observable commutes with every Pi. Each of these operators
identifies what is known as a superselection sector. States from two
different sectors will only combine decoherently.
But in reality, the whole question (and whole problem) is based on a
false premise -- namely, that the universe is a purely quantum system.
Nobody ever said that all degrees of freedom or all modes in all
systems had to be quantum. It is entirely consistent to discuss hybrid
classico-quantum systems in which some modes are classical and some
quantum.
In fact, at one extreme, every single degree of freedom in a system
will be its own superselection sector. In that case, there are no
coherent superpositions at all -- you're in a pure classical world.
At the other extreme, there will be no superselection at all -- then
you're in a pure quantum world.
But there is a whole continuum of possibilities in between these two
extremes.
The appearance of the world is actually that of one which has a few
classical degrees of freedom; e.g. classical degees that come from the
"outside", with the entire universe, itself, being effectively an open
system, and weave into every system to create a striation of
superselection sectors which provide the framework for decoherent
superposition and fill out the remaining 10% of the gap that
decoherence, itself, cannot close; ... and quantum degrees of freedom.
So it is natural to assume that the world actually is what it appears
to be -- a hybrid classico-quantum universe, which possesses some
classical degrees of freedom and perhaps a large majority of degrees of
freedom that are quantum.
Again, nobody ever said the quantum hypothesis had to be universal or
that the universe had to be entirely quantum.
This occurs, in particular, if (a) the universe, itself, is NOT in a
pure quantum state, e.g. a thermal state at a temperature of 3 degrees
Kelvin, or (for that matter), (b) if there doesn't even exist a
universal state space (as Smolin has argued), but only state spaces
associated with finite regions. In the latter case, there is ALWAYS an
outside and you have no recourse but to prescribe "improper mixtures",
since there will be no universal pure state, to begin with.
Case (a) is imminent (give the foregoing) from the fact that all
observers are finite. So they will all cut off the world at a boundary
and see the universe as being an (improper) mixture. But case (b) goes
even further and brings up the possibility that even from God's
perspective, the universe is STILL a mixture, and that there are no
proper mixtures at all (so that mixture means improper mixture) because
there is no universal state space in the first place!
Case (b) must also occur if the Universe is not globally hyperbolic.
What global hyperbolicity means is that you can layer the universe into
a sequence of "snapshots" such that every maximal worldline passes
through each one exactly once. That is, global hyperbolic universes are
those in which you can regard time as "flowing" globally along the
sequencing of snapshots comprising any of its layerings.
To define a universal state space requires, almost as a prerequisite,
that the universe be globally hyperbolic.
If there are time-like loops, or in the presence of time travel routes,
you need not have global hyperbolicity and you're then forced to resort
to the notion of time given in relativity as being "all there", and not
"flowing" since there would be no consistent global flow in such a
universe.
In that case, you can't even do the basic things required to set up a
universal state space (e.g. formulate the Cauchy problem), so that the
conclusion Smolin hypothesized would blindside even him from an oblique
angle, coming home to bear -- no universal state space.
.
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