----- Original Message -----
From: Robert Shaw <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Thursday, March 15, 2001 1:07 AM
Subject: Re: Kant QM
>
> From: "Dan Minette" <[EMAIL PROTECTED]>
> > >
> >
> > > For a quantum system we can calculate the wavefunction to arbitrary
> > accuracy.
> > >
> >
> > We can, until the wavefunction collapses. Then we can calculate no
> further
> > until we determine which eigenstate it collapsed into.
> >
> Wavefunction collapse is an arrtifact of the Copenhagen interpretation.
> It works when doing calculations but, as Schrodinger's cat shows, it
> is not really sound.
>
Well, you can call it what you will. First the wave function is is
superposition of a number eigenstates, then it exists in an eigenstate or a
smaller number of eigenstates. I suppose you can say there is the creation
of a plethora of universes at that point instead of a collapsing
wavefunction.
Schrodinger's cat didn't necessarily show that this wasn't sound. It
certainly is at odds with common sense metaphysics, but that doesn't make it
unsound. Fairly well respected people, like Wigner, took that very
seriously. I had the chance to briefly talk with Wigner, BTW, about this
stuff before he died.
> Decoherence is an approach that suggets the wavefunction doesn't
> actually collapse, it's just that for classical systems all trace of
> interfeerence is washed out by interactions with the rest
> of the universe.
I understand why the off diagnal terms go away, that makes sense. The
remaining question is why there is only one term that is on the diagonal
that is selected.
> > I think we really did misscommunicate here. We do know the probability
> of
> > finding the balls, but we cannot predict where the balls will be. After
> 10
> > seconds, a minute for sure, all we can say is that the balls will be on
> the
> > table (assuming the table is, say, 5 meters by 5 meters).
>
> You are not asking a meaningful question.
I'm a plumber. I ask questions that can be answered experimentally. Let me
restate it clearly:
If we have instruments that can measure the position and momentum of the
balls to within theoretical limits at time t, and then again at time t+dt,
what is the maximum value of dt such that we can predict the measured
position at time t+dt to better than 1 cm? That's a pretty simple question.
One thing that may be lost in the consideration of QM formalism, is that we
are asking questions that are answered experimentally.
> You can either do a fully classical calculation, in which case the
positions
> are theoretically predictable, or you can do a fully quantum calculation,
> in which case the probablity distribution of the position can be predicted
> to arbitary accuracy.
Yes, and so? The probability distributions will tell us where the billard
balls may be found: somewhere on the table. The point is that their
position will be indeterminate.
>
> Either way events are theoretically predictable to arbitary accuracy.
No, they are not. Events are things that happen Predictable means you will
know what will happen. Think about what answer you will get for a totally
quantum description of the positions of the balls after 1 minute: it will
be very close to uniform probability of them being anywhere on the table.
That tells me that we cannot predict the position of the ball on the table.
Its not just me, about a year ago someone point out a website that described
this for a single bouncing ball.
Dan M.
