"Langley, Rob" wrote:

>	I would be very grateful if someone could help me on this, please: 1. is there a difference between 'correlated' and 'entangled' states, and

I expect you mean superposition and entangled. Superposition "has to do" with single qubits and entangled "has to do" with multiple qubits. A different word for entangled is also entertwined.

One quantum operation is called Hadamard. If I understand this operation correct than if you perform that operation on 3 Qubit Register than as a result of that operation the 8 possible states are entangled. There should not be any correlation between the individual states.

>	2. if so, how and how often do they occur in nature, please?

I expect you mean does superposition and entangled occur in nature. To answer that question you must first know what each mean (which is your question 1) Unfortunate I do not know what the exact definition is.

To indicate how difficult this is consider a Schrodinger Cat experiment with the cat at centre stage surrounded by a circle of 10 observers each in a small room. Only one observer can see the cat at the same time through a window that means when one observer sees the cat the other windows are closed.

During the setup of the experiment all the windows are closed. The first observer is randomly selected. The next observer is clock wise. Each observer when the cat is alive will turn on a green light OR when the cat is dead a red light. At the end some (consecutive) lights will be green and some (consecutive) will be red.

The question is now if it is true that EACH observer can claim that before his or her observation the cat is in a superposition of states of both being alive and dead ?

(IMO that does not make much sense, but my opinion is of no importance)

Nick.

Nicolaas Vroom wrote in message news:...

>	"Langley, Rob" wrote:

> >	I would be very grateful if someone could help me on this, please: 1. is there a difference between 'correlated' and 'entangled' states, and

>	I expect you mean superposition and entangled.

Why? Correlated states are different from entangled states. Consider the mixture 1/2(|00><00|+|11><11|). Here, the two qubits are perfectly correlated and completely unentangled.

(Actually, as I understand it, you only get mixtures when you project entangled states onto a subspace of the system. If you consider the entire universe, it's in a single pure state because there's nothing else for it to get entangled with. In the example I gave above, it could well be that I've got two out of three qubits in a GHZ state, which is pure and completely entangled, but without that other qubit I have no way of finding out.)

-- Mike Stay http://www.xaim.com/staym

Mike Stay wrote:

>	Nicolaas Vroom wrote in message news:...

> >	I expect you mean superposition and entangled.

>	Why? Correlated states are different from entangled states. Consider the mixture 1/2(|00><00|+|11><11|). Here, the two qubits are perfectly correlated and completely unentangled.

I agree.

I expect the same situation exists if you perform the Schrodinger Cat experiment "twice" in parallel.

The state of the two cats is unentangled but the outcome of the two experiment is highly correlated if you start the experiment at the same time and if you observe at the same time.

The question is if the original poster Bob has this in mind when he raised the question.

Nick.

Nicolaas Vroom wrote:

>	To indicate how difficult this is consider a Schrodinger Cat experiment with the cat at centre stage surrounded by a circle of 10 observers each in a small room.

SNIP

>	The question is now if it is true that EACH observer can claim that before his or her observation the cat is in a superposition of states of both being alive and dead ?

You can also ask the question if EACH observer can claim that at the moment when he or she makes an observation each time there is a collapse of the wave function.

Again IMO that does not make much sense,

>	(but my opinion is of no importance)

Nick.

Nicolaas Vroom wrote in message news:...

>	"Langley, Rob" wrote:

> >	I would be very grateful if someone could help me on this, please: 1. is there a difference between 'correlated' and 'entangled' states, and

>

I expect you mean superposition and entangled. Superposition "has to do" with single qubits and entangled "has to do" with multiple qubits. A different word for entangled is also entertwined. One quantum operation is called Hadamard. If I understand this operation correct than if you perform that operation on 3 Qubit Register than as a result of that operation the 8 possible states are entangled. There should not be any correlation between the individual states.

> >	2. if so, how and how often do they occur in nature, please?

>

I expect you mean does superposition and entangled occur in nature. To answer that question you must first know what each mean (which is your question 1) Unfortunate I do not know what the exact definition is. To indicate how difficult this is consider a Schrodinger Cat experiment with the cat at centre stage surrounded by a circle of 10 observers each in a small room. Only one observer can see the cat at the same time through a window that means when one observer sees the cat the other windows are closed. During the setup of the experiment all the windows are closed. The first observer is randomly selected. The next observer is clock wise. Each observer when the cat is alive will turn on a green light OR when the cat is dead a red light. At the end some (consecutive) lights will be green and some (consecutive) will be red. The question is now if it is true that EACH observer can claim that before his or her observation the cat is in a superposition of states of both being alive and dead ? (IMO that does not make much sense, but my opinion is of no importance) Nick.

In your set up of the Schrodinger Cat experiment, the cat will either be killed, or it won't. There is a 50% chance of either result. Which ever happens, everyone will either see a live cat or dead cat. There's no way you could have some people see a live cat, and other people see a dead cat.

Jeffery Winkler

http://www.geocities.com/jefferywinkler

Mike Stay wrote:

>	Nicolaas Vroom wrote in message news:...

>>	"Langley, Rob" wrote:

>> >	I would be very grateful if someone could help me on this, please: 1. is there a difference between 'correlated' and 'entangled' states, and

>>	I expect you mean superposition and entangled.

>	Why? Correlated states are different from entangled states. Consider the mixture 1/2(|00><00|+|11><11|). Here, the two qubits are perfectly correlated and completely unentangled.

Right. Let me just (for the sake of completenes) give the definition of "entangled". We uusually thinks of three different "degrees" of correlation; for simplicity, I will only talk about the case of two parties (Alice and Bob), which have quantum systems in the (total) state rho, and reduced states rho_A = tr_B rho (for Alice) and rho_B = tr_A rho (for Bob).

1. no correlations = product states: rho = rho_A \otimes rho_B
Here \otimes means the tensor product.

2. separable states: states rho which can be written as a convex combination of product states, i.e.
rho = \sum_i p_i rho_A^(i) \otimes rho_B^(i)
with non-negative p_i's which sum up to unity.

The mixture above is clearly of this form.

3. entangled states: states which are not separable.

Product states show no correlations at all (and are trivially always separable), separable states are only correlated classically (they can be produced by distant parties using local operations and classical communication alone), and entangled states are, well, the things which are "special". One could also add

4. states which violate a Bell inequality

States of the form (4) are always entangled, but entangled states do not necessarily violate a Bell inequality.

>	(Actually, as I understand it, you only get mixtures when you project entangled states onto a subspace of the system.

You mean "trace out one part of the system", right? Anyway, one can never empirically prove (or better: falsify) such statements; for this reason some people call this statement "the First Principle of the Church of the Pure State". Not speaking as a physicist, however, I also adhere to this principle...

Hans

Jeffery wrote:

>	Nicolaas Vroom wrote in message news:...

> >

To indicate how difficult this is consider a Schrodinger Cat experiment with the cat at centre stage surrounded by a circle of 10 observers each in a small room. Only one observer can see the cat at the same time through a window that means when one observer sees the cat the other windows are closed. During the setup of the experiment all the windows are closed. The first observer is randomly selected. The next observer is clock wise. Each observer when the cat is alive will turn on a green light OR when the cat is dead a red light. At the end some (consecutive) lights will be green and some (consecutive) will be red. The question is now if it is true that EACH observer can claim that before his or her observation the cat is in a superposition of states of both being alive and dead ?

>	In your set up of the Schrodinger Cat experiment, the cat will either be killed, or it won't. There is a 50% chance of either result. Which ever happens, everyone will either see a live cat or dead cat.

In principle you are right.
If that is the case you should take that there is a time delay dt when the next window is opened and the previous is closed.
If dt is large enough than you have a reasonable chance that at least the first observer will see the cat alive and the last observer will see the cat dead.
However remember no observer knows during one experiment if he or she is the first or the last.

If observer 3 sees that the cat is alive than he knows that the cat will die later.
If observer 3 sees that the cat is dead he knows that the cat has died earlier.
Observer #4 does not know either before he or she makes an observation.
The question is can observer 4 claim that the cat is in a superposition of states of both being alive or dead before doing an observation. ?

What is the physical meaning of such a claim ?

Can observer 4 claim that when he or she looks there is a collapse of the wave function ?

Can each observer claim that ?

>	There's no way you could have some people see a live cat, and other people see a dead cat.

I disagree. Remember all observe the cat in the box at a different moment.

Nick

Nicolaas Vroom wrote in message news:<3F0FFE92.E90D0D2D@pandora.be>...

>	Jeffery wrote:

> >	Nicolaas Vroom wrote in message news:...

>

> > >

To indicate how difficult this is consider a Schrodinger Cat experiment with the cat at centre stage surrounded by a circle of 10 observers each in a small room. Only one observer can see the cat at the same time through a window that means when one observer sees the cat the other windows are closed. During the setup of the experiment all the windows are closed. The first observer is randomly selected. The next observer is clock wise. Each observer when the cat is alive will turn on a green light OR when the cat is dead a red light. At the end some (consecutive) lights will be green and some (consecutive) will be red. The question is now if it is true that EACH observer can claim that before his or her observation the cat is in a superposition of states of both being alive and dead ?

> >	In your set up of the Schrodinger Cat experiment, the cat will either be killed, or it won't. There is a 50% chance of either result. Which ever happens, everyone will either see a live cat or dead cat.

>

In principle you are right. If that is the case you should take that there is a time delay dt when the next window is opened and the previous is closed. If dt is large enough than you have a reasonable chance that at least the first observer will see the cat alive and the last observer will see the cat dead. However remember no observer knows during one experiment if he or she is the first or the last. If observer 3 sees that the cat is alive than he knows that the cat will die later. If observer 3 sees that the cat is dead he knows that the cat has died earlier. Observer #4 does not know either before he or she makes an observation. The question is can observer 4 claim that the cat is in a superposition of states of both being alive or dead before doing an observation. ? What is the physical meaning of such a claim ? Can observer 4 claim that when he or she looks there is a collapse of the wave function ? Can each observer claim that ?

> >	There's no way you could have some people see a live cat, and other people see a dead cat.

>	I disagree. Remember all observe the cat in the box at a different moment. Nick

Let's say the cat will be killed anytime in a 5 minute interval, and 5 different observers look in the box, one each minute. Those that look in the box during the beginning of the interval see a live cat. Those that look in the box towards the end of the interval see a dead cat. If they get together and discuss their observations, they can determine during which minute the cat died. You can describe that completely classically without mentioning quantum mechanics.

Now, from the quantum mechanics point of view, if you ask when did the wavefunction collapse, there are different ways of describing it. The way the Schrodinger's cat experiment is usually formulated, you set up the experiment, before you open the box, the cat is in a superposition of states, and then you open it and it collapses the wavefunction. You could imagine your thought experiment as five separate traditional Schrodinger's cat experiment, one after another. Whenever someone opens the box, it collapses the wavefunction, but when they close it, a new superposition of states is set up, since the outside world is again in a state of ignorance as to whether the cat is alive or dead, and that continues until the experiment is over, and the box is opened for the last time.

A stranger way of describing it is to say whether the cat is in a superposition of states depends on the individual. According to that, from the point of view of the observers who have already looked in the box, the wavefunction has already collapsed and the cat is not in a superposition of states, while at the exact same time, from the point of view of the observers who have not yet looked in the box, the cat is still in a superposition of states. Then whether or not the cat is in a superposition of states, depends on the observer, and can be different for different observers.

Jeffery Winkler

http://www.geocities.com/jefferywinkler

In article <325dbaf1.0307130950.73ef26d2@posting.google.com>, Jeffery wrote:

[About a Schrodinger's cat experiment in which five people successively observe the cat's state.]

>

Now, from the quantum mechanics point of view, if you ask when did the wavefunction collapse, there are different ways of describing it. The way the Schrodinger's cat experiment is usually formulated, you set up the experiment, before you open the box, the cat is in a superposition of states, and then you open it and it collapses the wavefunction. You could imagine your thought experiment as five separate traditional Schrodinger's cat experiment, one after another. Whenever someone opens the box, it collapses the wavefunction, but when they close it, a new superposition of states is set up, since the outside world is again in a state of ignorance as to whether the cat is alive or dead, and that continues until the experiment is over, and the box is opened for the last time.

I just want to point out that this is now what the "standard" Copenhagen interpretation of quantum mechanics says. In the Copenhagen interpretation, the first guy collapses the wavefunction. From then on, the cat is either alive or dead; it doesn't revert to a superposed alive/dead state.

-Ted -- [E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

"I think the burden is on those people who think he didn't have weapons of mass destruction to tell the world where they are." --Ari Fleischer

"Ted Bunn" schreef in bericht news:bf1uoa$hao$1@lfa222122.richmond.edu...

>	In article <325dbaf1.0307130950.73ef26d2@posting.google.com>, Jeffery wrote: [About a Schrodinger's cat experiment in which five people successively observe the cat's state.]

> >

Now, from the quantum mechanics point of view, if you ask when did the wavefunction collapse, there are different ways of describing it. The way the Schrodinger's cat experiment is usually formulated, you set up the experiment, before you open the box, the cat is in a superposition of states, and then you open it and it collapses the wavefunction. You could imagine your thought experiment as five separate traditional Schrodinger's cat experiment, one after another. Whenever someone opens the box, it collapses the wavefunction, but when they close it, a new superposition of states is set up, since the outside world is again in a state of ignorance as to whether the cat is alive or dead, and that continues until the experiment is over, and the box is opened for the last time.

>	I just want to point out that this is now what the "standard" Copenhagen interpretation of quantum mechanics says. In the Copenhagen interpretation, the first guy collapses the wavefunction. From then on, the cat is either alive or dead; it doesn't revert to a superposed alive/dead state.

Does the Copenhagen interpretation then suppose the wave function does exist independent of the observer?

If the wave function is supposed to represent what the observer knows then evidently for five observers which know different things you need five wave functions, one for each observer.

>	-Ted -- [E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.] "I think the burden is on those people who think he didn't have weapons of mass destruction to tell the world where they are." --Ari Fleischer

ebunn@lfa221051.richmond.edu wrote in message news:...

>	In article <325dbaf1.0307130950.73ef26d2@posting.google.com>, Jeffery wrote: [About a Schrodinger's cat experiment in which five people successively observe the cat's state.]

> >

Now, from the quantum mechanics point of view, if you ask when did the wavefunction collapse, there are different ways of describing it. The way the Schrodinger's cat experiment is usually formulated, you set up the experiment, before you open the box, the cat is in a superposition of states, and then you open it and it collapses the wavefunction. You could imagine your thought experiment as five separate traditional Schrodinger's cat experiment, one after another. Whenever someone opens the box, it collapses the wavefunction, but when they close it, a new superposition of states is set up, since the outside world is again in a state of ignorance as to whether the cat is alive or dead, and that continues until the experiment is over, and the box is opened for the last time.

>	I just want to point out that this is now what the "standard" Copenhagen interpretation of quantum mechanics says. In the Copenhagen interpretation, the first guy collapses the wavefunction. From then on, the cat is either alive or dead; it doesn't revert to a superposed alive/dead state. -Ted

In Nickolaas Vroom's thought experiment, the cat isn't out of the woods just because the first person opened the box. The cat might still yet be killed. When you close the box, it goes back into a superposition of states, because you don't know if it was killed after the box was closed. You are essentially performing several traditional Schrodinger cat experiments in linear chronological succession. Of course, if the cat is dead when you first open the box, then it obviously does not go back into a superposition of states. Just because it's alive now, doesn't mean it won't be dead one second from now, but if it's dead now, it will definitely never be alive again.

Jeffery Winkler

http://www.geocities.com/jefferywinkler

Jeffery wrote in message news:325dbaf1.0307212224.75b0aa8b@posting.google.com...

>

In Nickolaas Vroom's thought experiment, the cat isn't out of the woods just because the first person opened the box. The cat might still yet be killed. When you close the box, it goes back into a superposition of states, because you don't know if it was killed after the box was closed. You are essentially performing several traditional Schrodinger cat experiments in linear chronological succession. Of course, if the cat is dead when you first open the box, then it obviously does not go back into a superposition of states. Just because it's alive now, doesn't mean it won't be dead one second from now, but if it's dead now, it will definitely never be alive again.

And so the quantum fun continues. For the sake of argument let's say that the diabolical killing device is triggered by the decay of a radioactive element with a half life of one hour. After an hour the probability of the cat being alive is fifty percent. Observer one finds the cat alive at this point. What is the probability of the cat being found alive by observer number two a half an hour later?

Ed Keane III wrote:

>	For the sake of argument let's say that the diabolical killing device is triggered by the decay of a radioactive element with a half life of one hour. After an hour the probability of the cat being alive is fifty percent.

How do we know this ?
Yes by performing experiments, many experiments. (Meten is weten)
In each experiment you should measure with a stop watch the duration when your radioactive element decays.

>	Observer one finds the cat alive at this point. What is the probability of the cat being found alive by observer number two a half an hour later?

If you perform this experiment 100 times you will get a list with 100 durations.
Next you rearrange this list in order of increasing duration. The duration of experiment 50 in this new list should be the value of 60 minutes, which is the starting assumption in your posting.

There should also be a duration close to 90 minutes.
If this is experiment 93 than you know that the answer on your question (observer 2 etc) is approx. 7%.
If the highest value is less than 90 minutes than you know that the chance is 0%.

If you perform the experiment 1000 times you can get a more accurate answer.

For some more information see: http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&selm=XYysa.72030%24t_2.6538%40afrodite.telenet-ops.be or http://groups.google.com/groups?hl=en&lr=&ie=ISO-8859-1&q=%22Nicolaas+Vroom%22+sci.physics+Schrodinger%27s+cat+paradox&btnG=Google+Search Search: "Nicolaas Vroom" sci.physics Schrodinger's cat paradox

Nick.

ebunn@lfa221051.richmond.edu wrote:

>	In article <325dbaf1.0307130950.73ef26d2@posting.google.com>, Jeffery wrote:

> >

before you open the box, the cat is in a superposition of states, and then you open it and it collapses the wavefunction. You could imagine your thought experiment as five separate traditional Schrodinger's cat experiment, one after another. Whenever someone opens the box, it collapses the wavefunction

>	I just want to point out that this is now what the "standard" Copenhagen interpretation of quantum mechanics says.

Who or which group of scientists discusses and or decides what is now the "standard" Copenhagen interpretation? Is that done each year in some form of meeting?

[Moderator's note: No. The word "now" was a typo for "not", as the following text makes clear. - jb]

>	In the Copenhagen interpretation, the first guy collapses the wavefunction. From then on, the cat is either alive or dead; it doesn't revert to a superposed alive/dead state.

In the Schrodinger Cat experiment you have the experimenter who sets up the experiment and who places the cat in the box and you have observer 1 who opens the box and who looks inside the box. This is what I call experiment 1. Now suppose observer 1 sees that the cat is still alive keeps silent and closes the box and asks observer 2 to see what is inside the box. This is what i call experiment 2. Is in experiment 2 observer 1 not equivalent with the experimenter as in experiment 1? Accordingly to the standard interpretation this is not the case. Accordingly to the "standard" interpretation only when observer 1 observes there is a collapse of the wave function but not when observer 2 observes. Why is observer 1 not the experimenter in experiment 2?

To make it more difficult why is the experimenter in experiment 1 also not an observer ?

Suppose when the experimenter after he places the cat in the box and closes the box immediate there after opens the box to see if the cat is still alive... (Which ofcourse the cat is) Does that simple act collapses the wave function ? At the same time does the cat not revert to a superposed alive/dead state when the experimenter again closes the box ? And do those simple actions invalidate experiment 1 ?

IMO ......

Nick https://www.nicvroom.be/

Ed Keane III wrote:

>

And so the quantum fun continues. For the sake of argument let's say that the diabolical killing device is triggered by the decay of a radioactive element with a half life of one hour. After an hour the probability of the cat being alive is fifty percent. Observer one finds the cat alive at this point. What is the probability of the cat being found alive by observer number two a half an hour later?

With all that diabolical radiation outside the box ?

In message , Chris Jacobs writes

>>	I just want to point out that this is now what the "standard" Copenhagen interpretation of quantum mechanics says. In the Copenhagen interpretation, the first guy collapses the wavefunction. From then on, the cat is either alive or dead; it doesn't revert to a superposed alive/dead state.

>	Does the Copenhagen interpretation then suppose the wave function does exist independent of the observer? If the wave function is supposed to represent what the observer knows then evidently for five observers which know different things you need five wave functions, one for each observer.

I think it is fair to say that Copenhagen stops short of actually answering this question, which is one reason it is inadequate. However I agree with you. If you take that off shoot of Copenhagen which says that the wave function describes knowledge of reality rather than reality itself (and I do), then you should have different wave functions for observers with different knowledge.

Regards

-- Charles Francis

Nicolaas Vroom wrote:

>	ebunn@lfa221051.richmond.edu wrote:

> >	I just want to point out that this is now what the "standard" Copenhagen interpretation of quantum mechanics says.

>

In my ongoing struggle to understand the Schrodinger Cat Experiment I have two questions.

Let me first explain the experiment. The experiment is very much as described in http://www.faqs.org/docs/qp/chap08.html with certain modifications.
"There is a 50% chance that the radioactive substance decays in one hour."

We have one experimenter or operator. The experimenter sets up the experiment in a laboratory or stadium. Only the operator is allowed to open the "box" i.e. is allowed to go inside the laboratory. The operator starts the experiment.

There are 10 observers, each in a separate room, in a circle around the stadium. Each observer can see the inside of the laboratory through a window and observe if the cat alive or dead. Maximum only one window is open. That means only one observer at a time can see inside for a two minute interval in a rotation fashion.

The first observer will see the inside of the laboratory after 50 minutes of the start of the experiment. (Before that time all windows are closed) The whole experiment finishes after 50 + 10*2 = 70 minutes.

Because each observer can see the inside for two minutes he or she can see the following.
1. The cat is alive.
2. First the cat is alive. The poisonous gas is released and the cat dies.
3. The cat is dead.

The two questions are:
1. In this setup is there in any way superposition (or superimposed) involved ?
2. Is there collapse of the wave function involved.

Please, current opinions. I am not so much interested what the Standard Copenhagen Interpretation has to say Remember observers can only see inside the box. They don't have to open the box. (Any way this is dangerous because the poisonous gas can be released)

There is also a different arrangement possible. The only difference is that between the radioactive atom and the poison device there is a big metal screen which captures the alpha particle such that the gas will not be released.
Each observer will see the same: 1. The cat is alive.

Again the same two questions are:
1. In this setup is there in any way superposition (or superimposed) involved ?
2. Is there collapse of the wave function involved.

Nick https://www.nicvroom.be/

Charles Francis wrote in message news:...

>	In message , Chris Jacobs writes

> >>	I just want to point out that this is now what the "standard" Copenhagen interpretation of quantum mechanics says. In the Copenhagen interpretation, the first guy collapses the wavefunction. From then on, the cat is either alive or dead; it doesn't revert to a superposed alive/dead state.

> >	Does the Copenhagen interpretation then suppose the wave function does exist independent of the observer? If the wave function is supposed to represent what the observer knows then evidently for five observers which know different things you need five wave functions, one for each observer.

>

I think it is fair to say that Copenhagen stops short of actually answering this question, which is one reason it is inadequate. However I agree with you. If you take that off shoot of Copenhagen which says that the wave function describes knowledge of reality rather than reality itself (and I do), then you should have different wave functions for observers with different knowledge.

I agree but wouldn't that be modeled as a single wave function that is a superposition of the different wave functions if one were to want to use it to make predictions? It seems to me that the superpositions of a wave function should be said to collapse when an interactionction takes place. In this case that would be when the killing device measures the decay of the particle. The wave function would not collapse until an observer actually stopped the experiment after making an observation. Should an observer who continuously watches through a window but takes no action cause a wave function to not exist? What about an observer that is given a result of A or B and not told until later that A means alive and B means bye-bye kitty?

It seems to me that there are two things represented by a wave function that are represented by the same formula but that are different in principle. One would be information about a potential for something to happen and the other is unknown information about something that has happened. I think that the concept of a particle somehow being in more than one place until measured has an element of reality. Extending this to the idea that all possible unknown results of a measurement once made really exist at the same time seems unwarranted.

A problem with what I have said might be defining when the collapse of the superposition occurs. Is it when the particle decays or is it when that decay is measured? It seems that the collapse of the wave function can occur whenever you want to define it to after this.

-Ed Keane III

Ed Keane III wrote:

>

I agree but wouldn't that be modeled as a single wave function that is a superposition of the different wave functions if one were to want to use it to make predictions? It seems to me that the superpositions of a wave function should be said to collapse when an interactionction takes place. In this case that would be when the killing device measures the decay of the particle. The wave function would not collapse until an observer actually stopped the experiment after making an observation. Should an observer who continuously watches through a window but takes no action cause a wave function to not exist? A problem with what I have said might be defining when the collapse of the superposition occurs. Is it when the particle decays or is it when that decay is measured? It seems that the collapse of the wave function can occur whenever you want to define it to after this.

If you read my latest posting in this thread (27/08/03) then you will see that I struggle with this same problem. (That why I introduced this big metal screen)

When you study the Schrodinger Cat Paradox there are three events involved: FIRST there is radio active decay. that means there is an alpha particle "created" (equivalent to an electron emits a photon) SECONDLY the alpha particle is "destroyed" either captured by the container which contains the poisonous gas or by a big metal shield. (equivalent to an electron captures/annihilates a photon) THIRDLY an observer who observes and sees something. this is also called who takes a measurement.

IMO the first two events are closely linked with each other. The link is the alpha particle (or a photon) You can also say (I do not know if that is correct) a certain energy transport takes place between those events caused by the alpha particle (or photon) exchange. The second event always takes place after the first event.

The third event is of a complete different nature. This is something that takes place in the brain of the observers and the outcome depents for each observer when the events takes place. (cat alive, cat both alive and dead, cat dead)

If I understand quantum mechanics correct and each particle can be described by a wave function than in event ONE the wave function of both particles involved have changed.
The same for event TWO: two wave functions change. For the alpha particle or photon involved you can call this collapse of its wave function (but I think this is too string wording)

In a next posting I will comment if superposition is involved.

Nick

In message , Ed Keane III writes

>	Charles Francis wrote in message news:...

>>	In message , Chris Jacobs writes:

>> >	Does the Copenhagen interpretation then suppose the wave function does exist independent of the observer? If the wave function is supposed to represent what the observer knows then evidently for five observers which know different things you need five wave functions, one for each observer.

>>

I think it is fair to say that Copenhagen stops short of actually answering this question, which is one reason it is inadequate. However I agree with you. If you take that off shoot of Copenhagen which says that the wave function describes knowledge of reality rather than reality itself (and I do), then you should have different wave functions for observers with different knowledge.

>	I agree but wouldn't that be modeled as a single wave function that is a superposition of the different wave functions if one were to want to use it to make predictions?

No. Stick an observer in the box, with the cat. He observes the wave function in an eigenstate of the "live-dead" operator, but so long as he knows mass and the half life of the isotope his prediction is that the cat has a 50% chance of dying within a given period of time. Unfortunately he doesn't live long enough to observe that eigenstate.

But for another observer outside the box the state is a superposition. His prediction is exactly the same, that the cat has a 50% chance of being found in either eigenstate of "live-dead" when the box is opened after the set period. The wave function is merely a way of saying that he does not know which eigenstate will be found Before the box is opened.

Regards

-- Charles Francis

Read the RIAA Clean Slate Program Affidavit and Description at http://www.riaa.org/ I will be signing an amended Affidavit soon.

Charles Francis wrote in message news:3f669937$3@news.sentex.net...

>	In message , Ed Keane III writes

> >	Charles Francis wrote in message news:...

> >>	In message , Chris Jacobs writes:

> >> >

Does the Copenhagen interpretation then suppose the wave function does exist independent of the observer?

> >>	If you take that off shoot of Copenhagen which says that the wave function describes knowledge of reality rather than reality itself (and I do), then you should have different wave functions for observers with different knowledge.

> >	I agree but wouldn't that be modeled as a single wave function that is a superposition of the different wave functions if one were to want to use it to make predictions?

>

No. Stick an observer in the box, with the cat. He observes the wave function in an eigenstate of the "live-dead" operator, but so long as he knows mass and the half life of the isotope his prediction is that the cat has a 50% chance of dying within a given period of time. Unfortunately he doesn't live long enough to observe that eigenstate. But for another observer outside the box the state is a superposition. His prediction is exactly the same, that the cat has a 50% chance of being found in either eigenstate of "live-dead" when the box is opened after the set period. The wave function is merely a way of saying that he does not know which eigenstate will be found Before the box is opened.

That sounds right. I have thought that the mechanics that predict position after the (presumed) interference of superpositions is the basis of the use of the wave function, or other types of QM, and that the extension of this to every unobserved variable is just a mathematical conveniance.

In describing the cat experiment it is not possible to create separated entangled systems where the alive/dead variable can be measured in both states. It is theoretically, if not practically, possible to create a positional interference pattern if any interaction causing decoherence can be avoided. It could be inferred that the system had been split in two and that the two separated parts would evolve differently and would yield different values if measured in different places and times and so must truly be in a superposition of the two states to interfere with itself. I think it would be more accurate to say that as long as the system contains exactly the same number of particles, having not interacted with any other systems, it does not matter what the configuration of the particles is as far as an interference pattern is concerned and that this is not the same as saying that the particles do not have a configuration until measured.

-Ed Keane III Keane at Westelcom.com

Read the RIAA Clean Slate Program Affidavit and Description at http://www.riaa.org/ I will be signing an amended Affidavit soon.

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