Re: QM Measurement Problem

In article <27ad8097-7a65-4dea-be09-866700d5b6b0@
41g2000hsc.googlegroups.com>, dougsweetser@xxxxxxxxx says...
Hello Gerry:

Yet a solid structure built out of identical atoms behaves classically, and even
individual atoms in such a structure can behave in some ways
classically. Suppose you took a flat facet of an iron crystal and used
a scanning tuneling microscope to place iron atoms on it so they spelt
your name. Those iron atoms will be persistent; they can be imaged
repeatedly; they don't do anything crazy at all. They behave
classically, at least insofar as their position is concerned.

I don't see the point. It looks like you are alluding to the
uncertainty principle, which is not about measuring the certainty of
position. Rather the uncertainty is about measuring the position of
two conjugate measurements, say position and momentum, and recognizing
a constraint on the variation of both measurements. That would apply
to this iron crystal. If this is a well ordered crystal, you probably
could collect data on the photo electric effect. The same collection
of atoms knows how to do both classical and quantum mechanics.

I was responding to your proposal that cats were special because they
were made up of non-identical parts which could swap position if we were
not looking. As pointed out above, collections of identical parts can
behave classically too, so long as the parts are sufficiently entangled
with each other or the environment in general.

And yes - the uncertainty principle does apply to the crystal. But the
interesting thing is that it does not apply, at least naively, to the
individual atoms. A particular atom, say the one creating the top serif
of the 'D', can consistently be observed to be in the same place, and it
is not moving anywhere. There is a real sense in which its position is
known exactly, and its momentum is zero. It is living in the classical
world, precisely because of its entanglement with the other atoms.

The difference, of course, is that the atoms aren't in a 'cloud'; they
are in a solid, and their interaction with their environment is such as
to lead to rapid decoherence. They are entangled with each other in
such a fashion that the probability of observing a superposition state
is infinitesimal.
If I read a little into this (in other words, you did not say this
directly, so I apologize in advance if needed), it sounds like the
'cloud' does not have information. In quantum mechanics, the
probability distribution represented by the wave function is the best
and most complete information one can have about a system. It is the
sum of all possible paths. The superposition cannot be seen because
it is a composition of data that can be measured.

I didn't say anything like that. I do not know how to phrase what I did
say better. The atoms in the solid are strongly entangled with others
in their environment - the electrons in your vaguely-described 'cloud',
presumably, are not.

This also, obviously, applies to a cat. And cats also generate entropy,
which can be considered a measure of the number of measurements carried
out and recorded by the system. So while you might, if you handled the
system very carefully, be able to observe some quantum superposition
properties of the iron atoms, you have no chance with the cat.

Entropy is not relevant to this discussion.

It is, IMO. It is another special feature of cats which brings them
further away from the quantum world.

I created the
superposition of a live and dead cat here:

http://picasaweb.google.com/dougsweetser/Superposition/photo#5168676570581305906

That's not what a quantum superposition state of Schrodinger's cat would
look like. That is two possible classical states superimposed. (Two
very distinct states, in fact, selected from a myriad possibilities.)

You could semi-plausibly have a superposition state that looked like a
cat that you could not tell was alive or dead. It would instantly
collapse into one or the other, or more likely into a very sick cat.

You can make a case that a picture of all classical possibilities
superimposed describes the wave function of the cat at a particular
time. But this wave function has *already* in the process of its own
evolution decohered into an ensemble of non-interfering, effectively
classical states. Opening the box just continues this process.

I assume you are not actually taking a picture of each cat, which would
correspond to an observation, negating the point of the experiment.

No, that is incorrect. We have a system that produces about 50% dead
Siamese cats clones every time we have investigated. One time, we
make all these observations, collect all the data, and from that data,
construct the superposition. We have a system that can repeatably
generate indistinguishable collections of dead cats.

So you are taking the classical results observed after opening each box,
and superimposing them. Just what I said. No picture of an observed
superposition state. No indication of interference between dead and
alive states.

It appears like you are using the phrase "classical result" for what
might also be referred to as the collapse of the wave function. I
don't like either term, both sounding to active.

Classical result = what you get when you open the box and see a dead cat
or a live cat. Nothing more.

So your picture corresponds to an ensemble of expected classical results.
I don't see where quantum statistics come into it.

I am only trying to get at superposition, not even and odd spin
statistics.

So am I. I am not talking about spin statistics. The point is that
quantum superposition states imply interference between the different
possible results. Superimposing a lot of non-interfering classical
states does not give such a state.

I feel you are missing the point here. Your combined image isn't a
picture of a quantum superposition state; it is a picture of 1000
classical states, classically superimposed on each other (with additive
probability).

(And you also can't make the boxes indistinguishable, for reasons
similar to those already discussed.)

I don't recall in classical physics where folks deal with the
information of superpositions of states.

But everyone who deals with probability produces diagrams similar in a
sense to your superimposed diagrams. If you want to analyse a dice
game, for example, you start by (notionally) drawing a picture of all
the different ways the dice might land. There's nothing non-classical
here. Classical thermodynamics involves similar scenarios.

That sounds far more like
quantum mechanics than classical mechanics, where one has the video of
the cat, either live or dead, but certainly not both. In my
superposition photo, the cat is unambiguously live and dead, an idea
that is suppose to be too odd to understand. I get it. I also
understand why you don't accept that I get it, so we can politely
disagree.

"Unambiguously live and dead"? What do you mean by that? You could say
that both live and dead cats exist in Everett's 'multiverse', and that
your diagram is a picture of the multiverse, I suppose. What it is not
is a superposition state in the sense of the word that is normally used.
- Gerry Quinn



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