Re: collapsing quantum wave function

From: Patrick Leahy <jpl.domain.name.hidden>
Date: Fri, 10 Jun 2005 12:31:15 +0100 (BST)

On Thu, 9 Jun 2005, Norman Samish wrote:

> Jonathan Colvin wrote: "If I take a loaf of bread, chop it half, put one
> half in one room and one half in the other, and then ask the question "where
> is the loaf of bread?", we can likely agree that the question is ill-posed."
>
> Depending on definitions, this may indeed be an ill-posed question. On the
> other hand, with appropriate definitions, the question might be answered by
> "The loaf is half in one room and half in the other," or "The loaf no longer
> exists."
>
> This reminds me of my problems trying to understand "the collapsing quantum
> wave function." I've heard of Schrödinger's Cat, which I'm told is half
> alive - half dead until the box is opened and the cat is observed. This
> observation "collapses the quantum wave function," and the cat at that point
> is either alive or dead.
>
> Here's a variation. Is my interpretation correct?
>
> Suppose we take ten apparently identical ball bearings and put stickers on
> each with the identifiers "1" through "10." We leave the room where the
> balls with stickers are, and a robot removes the stickers and mixes the
> balls up so that we don't which ball is which. However, the robot remembers
> which sticker belongs on which ball. We come back into the room and pick
> one ball at random to destroy by melting it in an electric furnace. If at
> this point we ask "What is the probability that the destroyed ball is ball
> '3'?" we can truthfully answer "My memory tells me that the destroyed ball
> has a one in ten probability of being '3.' "
>
> However, by reviewing the robot's record we can see that "6" was, in fact,
> the one destroyed.
>
> Does this mean that the quantum wave functions of all ten balls collapsed at
> the moment we viewed the record and observed what happened to "6"? Or did
> the wave function never exist, since the robot's record always showed the
> identity of the destroyed ball, irrespective of whether a human observed
> this identity or not?

No this is not a quantum problem at all. The wavefunction does not encode
ordinary lack-of-information uncertainty. Even if there was no robot, ball
bearings are complicated enough that no two of them are genuinely
identical, so there is always a fact of the matter about which was
destroyed.

Quantum "uncertainty" is better thought of as "both at once" rather than
"either or". Here's a quantum analogue of your experiment.

Take ten electrons held in a row of "Penning traps" (magnetic "bottles"
that can hold single electrons) labelled 1 to 10 (the label is attached to
the trap). Introduce an anti-electron into trap number 3, causing an
annihilation, so we now have 9 electrons, held in traps 1, 2 and 4 to 10.

Does this mean that electron number 3 was destroyed?

No, because since electrons *are* genuinely identical, they are not
individuals. The wavefunction for any group of electrons is always a
perfect mixture of all possible "identity assignments", e.g. electron 1 in
trap 1, 2 in trap 2 etc plus electron 2 in trap 1, 1 in trap 2 etc.

This may sound ridiculous, but without this feature matter as we know it
simply wouldn't exist, since it underlies the Pauli exclusion principle
and hence the structure of atoms and all chemical properties.

Paddy Leahy
Received on Fri Jun 10 2005 - 07:37:02 PDT