Re: Layman Q: wave funtion and measurement

From: Fernando Cacciola (fernando_cacciola_at_hotmail.com)
Date: 09/21/04 

Date: Tue, 21 Sep 2004 19:24:29 -0300

"Edward Green" <spamspamspam3@netzero.com> escribió en el mensaje
news:eca320d0.0409141736.5623581b@posting.google.com...
> "Fernando Cacciola" <fernando_cacciola@hotmail.com> wrote in message
news:<2q60j4Fqog0qU1@uni-berlin.de>...
>
> Hi, Fernando. Just in case you are still poking about here, waiting
> anxiously for my latest philosophical pronouncment. ;-)
>
Oh, yes, I've been.. thanks!

>
> > "Edward Green" <spamspamspam3@netzero.com> escribió en el mensaje
> > news:eca320d0.0409061734.49be01b9@posting.google.com...
> > > "Fernando Cacciola" <fernando_cacciola@hotmail.com> wrote in message
> > news:<2q1b4fFqjseqU1@uni-berlin.de>...
>
> <...>
>
> > > > If I got your right, the wave function says that a system is in a
state
> > > > being a linear combination of eigenstates.
>
> Note that the state is expressible as a linear combination in _any_
> basis, and that in quantum mechanics, we are simply in the habit of
> taking the eigenstates of certain operators to form our bases.
>
I see

> > > > But how can an objective entity be in a combined state?
> > >
> > > It happens all the time, even to the nicest classical entities. ;-)
> > >
> > > Say a classical particle at time t1 has velocity v1, east at 1 m/s.
> > > And say at time t2 this particle has velocity v2, north at 1 m/s.
> > > Finally at time t3 the particle has velocity v3, northeast at sqrt(2)
> > > m/s.
> > >
> > > Since v3 = v1 + v2, I guess we have at t3 a "combined state"?
> > >
> > > To complete the quantum mechanical analogy, imagine that just after t3
> > > we pass the particle through a forked passage which ejects it moving
> > > either due east or due north, with probabilities 1/2,1/2.
> > >
> > Very interesting analogy.
> > What puzzles me is the fact that upon observation we see either v1 or
v2.
>
> Every theory has a "just the way it is" level. The fact that we only
> measure one of the eigenvalues of the observed variable is on this
> level. But QM tells us is how to calculate the probabilities.
>
OK

> I think I know what you are thinking, though, and it is certainly a
> point of view abetted by popular accounts. If you stop thinking of
> superimposed states in a particular basis as some ghostly
> superposition of classically incompatiable conditions and simply a
> definite physical state which happens to generate definite
> experimental outcomes according to some probabilistic rule, things
> will seem less weird.
>
OK, I've been definitely thinking that way.. mostly biased by the analogy
of a particle being "here and there" that I found on the book.

> > Perhaps it is as if we could view this system only thorugh an orthogonal
> > window frame aligned with v1 and v2
> > so that we only see it moving in those directions while it is really
moving
> > in both.
> > But my analogy breaks because in this setup we'll see some non-zero
value
> > for v1 _and_ some non-zero value for v2; no collapse here.
>
> The forked path idea comes closer to a quantum measurement: the system
> is forced into a particular eigenstate of the observable; it's not a
> passive observation, it's a physical process in which the measured
> system interacts with the experimental set-up.
>
Ha OK, I knew this, but somehow I assumed that this side effect was so
accidental that you could formulate (and understand) QM from the ideal of a
truly passive observation.

> <...>
>
> > oh, well, let me try again:
> >
> > The "state" of a system is a magnitude
>
> It's an element of an abstract space. "Magnitude" is not quite the
> term of art.
>
OK

> > that expresses what is knowldegble about it.
> > It is not a direct account of the objective reality of the system butan
> > account for what is observable about it.
>
> Ah... QM does force one to review one's philosophy, does it not?
>
More than anything else.. even GR!

> We don't have to be quite so global and absolutist. I don't know what
> is "knowable" about a physical system. But I do know within a
> particular formulation of quantum mechanics: the state vector. Even
> here, there is no "the" state vector: we may choose to ignore or
> include certain effects or interactions in our formulation, same as in
> other areas of physics. But, having chosen a particular model the
> state vector is indeed as complete a physical description as we can
> make of the system; under that model!
>
> Tautological but self-consistent.
>
Well, OK, being self-consistent is probably more important than "attempting"
to be ultimately complete.

> In this sense, the situation is no different from other physical
> theories: everything we can know about a region of vacuum as described
> by the classical theory of electromagnetism is embodied in a pointwise
> specification of the electric and magnetic fields. Everything we can
> know about a region of spacetime under the general theory of
> relativitity is embodied in a specification of the metric.
>
Good point

> I know something is made of an alleged qualitative difference between
> the quantum state description and other descriptions of physical
> states, but I would not make too much of it.
>
> To get farther into your desire to distinguish the model from the
> really real system we'd have to digress farther into the philosophy of
> science than I have a taste for right now.

Don't worry.. I better study the subject much much deeper anyway.
I dislike making phylosophy out of water, so to speak.
And btw, I just got a real book this time... one with sufficiently deep
math.. I knew there was no real point in trying to grasp QM without fully
understanding it's instrumentation.

> But I suggest there is
> really no brave new world of QM which is unlike any other physical
> theory; it's more that QM forces us to examine unexamined assumptions,
> and put equally muddled but new unexamined assumptions in their place.
> ;-)
>
Good point.
Is also that QM appears _so_ close to "the bottom" that one get's eager to
jump right to the final understanding of nature by the hand of QM.
But is just a theory with a very _usefull_ model, but just a model after
all.

> > Given the characterization of "state" I made above, saying that the
system
> > is "in a combined state" is merely telling something about what it will
look
> > like if looked upon; but nothing about what really _is_ in itself.
>
> Something not entirely unlike that. But forgetting about any
> distinction between our model and the world, I was more strongly
> trying to suggest that the "superimposed" quality of quantum
> mechanical states is not weird at all.
>
> Try to parse "superposition of states" like this:
>
> |A state which returns result 1 with certainty> +
>
> |A state which returns result 2 with certainty> =
>
> |A state which returns result 1 or result 2 with probabilities
> 1/2,1/2>
>
> The final state is _not_ a superimposition of results, but merely a
> new and definite state which is liable to return certain results under
> certain measurements with certain probabilities.

OK... there's still something here that don't quite close in my head.
I suppose is related to whatever is it that I assume about the measurement
process.
I'll take a much closer look at QM measurent to see what's wrong with my
assumptions.

> Since you seem to
> want to give things a psychological cast, say that a happy man will
> react to a certain piece of news with laughter, a sad man with tears,
> and that pure laughter or tears are the only possible observations. A
> whimsical man will react to the same news with laughter or tears
> according to some probabilities, but this doesn't mean he is in a
> superimposed state of laughter and tears before receiving the news.
>
Ok, I see something here.
Your system is reacting to the observation process, yielding out one or
another value.
Though the "cause" for yielding these values is hidden, QM has a way to
predict the probabilities of the possible "reactions".

Now, how come a system behave like this I wouldn't know, but I suspect this
is what I'm after.

> It happens that the precursor states of laughter and tears in our
> model are vectors in the same space and that the last state is a
> linear superimposition (combination) of these states, being a third
> distinct state in the given space. This use of "superimposition" in
> the space of precursor states which happen to live in a vector space
> confuses the unwary into thinking we are taking a superimposition of
> the outcome of various measurments applied to these states.
>
Exactly as I was confused.
Was I hope :-)

So when we say that the system is in a "combined state" of the form "aX+bY"
we're essentially just expressing mathematically the prediction about the
possible outcome of an observation as X or Y, right?

So in physics, the "state" of something is not "it's cause of reaction" (as
I was largely assuming), but rather the "reaction spectrum" as pictured
under some prediction scheme.

> > Le me see: you say that we need the addition of the collapse
> postulate to
> > explain
> > why if we make another measure inmeditely we see the same outcome.
> > (without the postulate the system could rerandomize inmediately)
> > Right?
>
> Things are not entirely unlike that.
>
OK

>
> I am uncomfortable making weightly absolute sounding pronouncements:
> but I perhaps can make things, if not entirely unweird, no weirder
> than necessary.
>
:-) which is all I can ask for at this point

Thanks

Fernando Cacciola

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