Re: collapsing quantum wave function

2005-06-12 Thread Stathis Papaioannou


Russell Standish writes:

[quoting Norman Samish]
 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?

Yes and no. In a 3rd person description of the situation, the
Multiverse has decohered into 10 distinct universes at the moment the
robot decides which ball it picks up. What about the 1st person
description? According to the interpretation I follow, the observer is
in fact superposed over all 10 branches, and only collapses into a
single branch the moment the observer becomes aware of the robot's
record.

A more conventional physics interpretation would have the conscious
observer as belonging to a definite branch since the Multiverse
decohered, but not knowing which. I understand that David Deutsch
holds this interpretation, for example.

There is certainly no 3rd person experiment that can be done to
distinguish between these two interpretations, and the only 1st person
experiment I can think of relates to tests of quantum immortality. I
find it hard to believe the no cul-de-sac conjecture would hold in
the latter case.


If you accept that it makes no first person difference whether there is one 
or many instantiations of the same observer moment - that it is all one 
observer moment - then it becomes meaningless to ask whether the observer 
belongs to just one or to a superposition of all of the instantiations. How 
would QTI distinguish between the two interpretations?


--Stathis Papaioannou

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Re: collapsing quantum wave function

2005-06-12 Thread Russell Standish
On Sun, Jun 12, 2005 at 09:14:11PM +1000, Stathis Papaioannou wrote:
 There is certainly no 3rd person experiment that can be done to
 distinguish between these two interpretations, and the only 1st person
 experiment I can think of relates to tests of quantum immortality. I
 find it hard to believe the no cul-de-sac conjecture would hold in
 the latter case.
 
 If you accept that it makes no first person difference whether there is one 
 or many instantiations of the same observer moment - that it is all one 
 observer moment - then it becomes meaningless to ask whether the observer 
 belongs to just one or to a superposition of all of the instantiations. How 
 would QTI distinguish between the two interpretations?
 
 --Stathis Papaioannou
 

I think the latter interpretation would see that there _is_ a
difference between identical instantiations. Since I tend to follow
the first interpretation, as do you by the sounds of things, the
second interpretation looks a little inconsistent, and smacks of
hidden variables. However I note it, as not everyone sees the world in
the same way I do.

-- 
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A/Prof Russell Standish  Phone 8308 3119 (mobile)
Mathematics0425 253119 ()
UNSW SYDNEY 2052 [EMAIL PROTECTED] 
Australiahttp://parallel.hpc.unsw.edu.au/rks
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Re: collapsing quantum wave function

2005-06-10 Thread Patrick Leahy


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


Re: collapsing quantum wave function

2005-06-10 Thread Eugen Leitl
On Thu, Jun 09, 2005 at 04:09:15PM -0700, Norman Samish wrote:

 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? 

In QM, it is not possible to distinguish featureless balls (systems in the
same quantum state). Storing labels in an external system (robot) would
perturb the systems, stopping them being featureless and/or precisely
localized. Experimental limitations currently prevent experiments with system
sizes much larger than a buckyball, IIRC.

If you're talking about entangling several such systems (qubits),
manipulating them by the robot should cause collapse of the total
wavefunction -- you need to do it in QC to be able to read the 
result. IANAP, though, so above may be wrong.

-- 
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Re: collapsing quantum wave function

2005-06-10 Thread Norman Samish
Thank you for the fascinating quantum analogue of my ten ball experiment, 
where you use electrons instead of steel balls.  You destroy the electron in 
the third Penning trap and then point out that electron number 3 was NOT 
destroyed, because electrons are not individuals.  Instead, (If I interpret 
correctly) we have 9 electrons distributed among ten Penning traps, with 
equal probability in their distribution.

If we now examine each of the Penning traps for the existence of an 
electron, what do we find?  My guess is that we would find nine electrons in 
the ten traps, and one empty trap.  The identity of the empty trap would 
presumably be unpredictable.

Is my guess correct?

I don't dispute this, but you are certainly correct when you say This may 
sound ridiculous. . .   This vividly demonstrates quantum weirdness.

Norman Samish


- Original Message - 
Patrick Leahy wrote:

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 



Re: collapsing quantum wave function

2005-06-10 Thread scerir
From: Norman Samish 
 This reminds me of my problems trying to understand 
 the collapsing quantum wave function.  

Einstein was very interested in collapsing wave functions
(see Solvay Congr. 1927) and developed many experiments
about it (well before the EPR paper). One of these
experiments was Einstein's 'gun powder' experiment
(which then became the poor Schroedinger's cat).
Another one was Einstein's boxes (then it bacame
de Broglie's boxes). 

In the briefcase of Straycat 
http://briefcase.yahoo.com/straycat_md 
you can find the 'Travis Norsen's boxes paper' folder,
which has two very interesting papers (pdf) about 'collapse',
and 'alternative' collapse (factorizable superpositions), 
one written by Travis, one by Shimony.

Interesting also the other side, when 'collapse' is 
forbidden. A good paper might be this one by Michael
http://research.imb.uq.edu.au/~m.gagen/pubs/thesis.html 


s.

Can a dog collapse a state vector?
-Christopher Alan Fuchs





Re: collapsing quantum wave function

2005-06-10 Thread scerir
 In the briefcase of Straycat 
 http://briefcase.yahoo.com/straycat_md 
 you can find the 'Travis Norsen's boxes paper' folder,
 which has two very interesting papers (pdf) about 'collapse',
 and 'alternative' collapse (factorizable superpositions), 
 one written by Travis, one by Shimony.

One of the papers above is also at
http://www.arxiv.org/abs/quant-ph/0404016



Re: collapsing quantum wave function

2005-06-09 Thread Russell Standish
On Thu, Jun 09, 2005 at 04:09:15PM -0700, Norman Samish wrote:
 
 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? 

Yes and no. In a 3rd person description of the situation, the
Multiverse has decohered into 10 distinct universes at the moment the
robot decides which ball it picks up. What about the 1st person
description? According to the interpretation I follow, the observer is
in fact superposed over all 10 branches, and only collapses into a
single branch the moment the observer becomes aware of the robot's
record.

A more conventional physics interpretation would have the conscious
observer as belonging to a definite branch since the Multiverse
decohered, but not knowing which. I understand that David Deutsch
holds this interpretation, for example.

There is certainly no 3rd person experiment that can be done to
distinguish between these two interpretations, and the only 1st person
experiment I can think of relates to tests of quantum immortality. I
find it hard to believe the no cul-de-sac conjecture would hold in
the latter case.

Cheers

-- 
*PS: A number of people ask me about the attachment to my email, which
is of type application/pgp-signature. Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.


A/Prof Russell Standish  Phone 8308 3119 (mobile)
Mathematics0425 253119 ()
UNSW SYDNEY 2052 [EMAIL PROTECTED] 
Australiahttp://parallel.hpc.unsw.edu.au/rks
International prefix  +612, Interstate prefix 02



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