Is the cat alive, dead, both or unknown

[Science2Dmax]

my girlfriend is wondering if while shroodingers cat was in the box, we should consider it as both unknown rather than both alive and dead. please shed some light on the subject.

 

[TESL@]

Unknown, or more technically, in the superposition of two states.

 

[Nugatory]

my girlfriend is wondering if while shroodingers cat was in the box, we should consider it as both unknown rather than both alive and dead. please shed some light on the subject.

You'll find a bunch of threads on Schrodinger's cat here if you search. The mainstream answer is also the commonsense one: The cat is either alive or dead, just as a tossed coin is either heads or tails even before we look.

I should add that that's pretty much always been the standard answer. When Schrodinger posed his famous though experiment almost a century ago, it wasn't because he or anyone else was seriously suggesting that the cat would somehow be "both alive and dead" or "in a superposition of alive and dead". He was pointing out a problem in the then-current understanding of quantum mechanics: nothing in the mathematical formalism clearly explained why the cat would be either dead or alive but not something in between.

 

[atyy]

Unknown. It "is" in a superposition of two states, but we don't now what that means. Quantum mechanics is not about what "is", but about what we can predict about what we will observe.

 

[rootone]

Unknown, but we DO know the probability of the cat being either alive or dead.
The thought experiment involves a radioactive atom, which when it decays triggers the mechanism which kills the cat.
The atom type has a known half life, and after this amount of time has passed the probability of the cat being alive or dead is 1:1.
If the cat is left in the box for a longer time the probability of it being dead increases and given sufficient time it become a near certainty.

 

[OCR]

Unknown. It "is" in a superposition of two states, but we don't now what that means.

my girlfriend is wondering if while shroodingers cat was in the box, we should consider it as both unknown rather than both alive and dead.

So never, never, put a dead cat in "the box", at the beginning... such an action would have a probability of

creating fundamental disturbances in the Force, or at the vary least, a minor "tremor"...

 

[Nugatory]

Unknown, or more technically, in the superposition of two states.

"Unknown" and "in the superposition of two states" are not the same thing.

If toss a coin, it's either heads or tails but I don't know which until I look at it. That's "unknown".

A spin-1/2 particle with its spin aligned up along the z axis is not in an unknown state. It's in the up eigenstate of the $S_z$ operator and that's a complete and unambiguous specification of its state that leaves nothing unknown. However, that state is also a superposition of spin-up along the x-axis and spin-down along the x axis.

 

[bhobba]

"Unknown" and "in the superposition of two states" are not the same thing.

Indeed.

Technically its the difference between a superposition and a mixed state. If you don't know the difference look it up.

Thanks
Bill

 

[Nugatory]

Technically its the difference between a superposition and a mixed state.

What Bhobba said.
You have to use the density matrix formalism to see the difference. Googling for "quantum density matrix" will find some good links - it's unfortunate that this is not covered by some intro textbooks.

 

[TESL@]

Thanks for the correction.

 

[atyy]

Indeed.

Technically its the difference between a superposition and a mixed state. If you don't know the difference look it up.

Thanks
Bill

What Bhobba said.
You have to use the density matrix formalism to see the difference. Googling for "quantum density matrix" will find some good links - it's unfortunate that this is not covered by some intro textbooks.

But since this is the density matrix before the measurement outcome, it could be an improper mixture, which is a superposition.

 

[bhobba]

But since this is the density matrix before the measurement outcome, it could be an improper mixture, which is a superposition.

Improper mixtures are not superpositions from the very definition of a mixture. Its called improper because its physical origin is different to a proper one - not that its not a mixture - which it obviously is.

Thanks
Bill

 

[atyy]

Improper mixtures are not superpositions from the very definition of a mixture. Its called improper because its physical origin is different to a proper one - not that its not a mixture - which it obviously is.

Improper mixtures are superpositions which is why they are not proper. A superposition refers to a pure state, which is what an improper mixture is.

 

[bhobba]

Improper mixtures are superpositions which is why they are not proper. A superposition refers to a pure state, which is what an improper mixture is.

An improper mixture is NOT a superposition.

Outside the system it remains in superposition - inside it isn't. That is the key difference - see the section 1.2.3:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

It is removing system B from our control by tracing over the environment that does it.

Thanks
Bill

 

[atyy]

An improper mixture is NOT a superposition.

Outside the system it remains in superposition - inside it isn't. That is the key difference - see the section 1.2.3:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

It is removing system B from our control by tracing over the environment that does it.

Thanks
Bill

There is no difference because the entire system is still in a superposition. Everything you do on the improper mixture has a counterpart in the full system.

 

[StevieTNZ]

Bernard d'Espagnat makes the distinction between an improper mixture v a proper mixture in his book "On Physics and Philosophy". atyy is correct in stating an improper mixture refers to a superposition (pure) state.

 

[bhobba]

There is no difference because the entire system is still in a superposition. Everything you do on the improper mixture has a counterpart in the full system.

Of course. But we are talking about inside the system. That's what tracing over the environment does.

Thanks
Bill

 

[bhobba]

Bernard d'Espagnat makes the distinction between an improper mixture v a proper mixture in his book "On Physics and Philosophy". atyy is correct in stating an improper mixture refers to a superposition (pure) state.

It can't - by the definition of a mixed state. You have traced over the environment to do it.

Thanks
Bill

 

[bhobba]

Just to expand further on the issue, Lubos has done an excellent post giving the detail - if I was to write something it would basically be what he wrote:
http://physics.stackexchange.com/qu...ake-the-partial-trace-to-describe-a-subsystem.

What's going on is you have the whole system A+B - that will be assumed to be a pure state |p><p| - here I have used the operator description of a pure state to avoid confusion later. The mixed state comes about because we are only interested in observations on A. But its entangled with B. Its that entanglement that leads to it being a mixed state because you need to do a partial trace over B due to only A being observed. It is this only observing A when it entangled with B that's the cause ie you are observing inside the system ie the state is (trace over B |p><p|) - which, lo and behold, turns out to be a mixed state - see equation 1.2.3 in the paper I linked to before. Outside the system its a pure state |p><p|, hence a superposition of all sorts of things, and remains in superposition, until, of course, it becomes entangled with something else. But because of the partial trace inside the system, since you are observing only A, its a mixed state.

Thanks
Bill

 

[harrylin]

"Unknown" and "in the superposition of two states" are not the same thing.

If toss a coin, it's either heads or tails but I don't know which until I look at it. That's "unknown".

A spin-1/2 particle with its spin aligned up along the z axis is not in an unknown state. It's in the up eigenstate of the $S_z$ operator and that's a complete and unambiguous specification of its state that leaves nothing unknown. However, that state is also a superposition of spin-up along the x-axis and spin-down along the x axis.

This thread is not about the radioactive atom, but about the cat which will be killed when that atom decays. The question is if the special state that the atom is in according to the theory, necessarily affects the cat because we don't know about it. It was Schrödinger's intention to ridicule that idea by means of his cat example.
- https://en.wikipedia.org/wiki/Schrödinger's_cat#The_thought_experiment

 

[atyy]

Just to expand further on the issue, Lubos has done an excellent post giving the detail - if I was to write something it would basically be what he wrote:
http://physics.stackexchange.com/qu...ake-the-partial-trace-to-describe-a-subsystem.

What's going on is you have the whole system A+B - that will be assumed to be a pure state |p><p| - here I have used the operator description of a pure state to avoid confusion later. The mixed state comes about because we are only interested in observations on A. But its entangled with B. Its that entanglement that leads to it being a mixed state because you need to do a partial trace over B due to only A being observed. It is this only observing A when it entangled with B that's the cause ie you are observing inside the system ie the state is (trace over B |p><p|) - which, lo and behold, turns out to be a mixed state - see equation 1.2.3 in the paper I linked to before. Outside the system its a pure state |p><p|, hence a superposition of all sorts of things, and remains in superposition, until, of course, it becomes entangled with something else. But because of the partial trace inside the system, since you are observing only A, its a mixed state.

Thanks
Bill

The link you give itself shows that the the partial trace is equivalent to observing $L_{A} \otimes \bf{1}$ on the full system which is in a pure state. So the distinction you are making is rather arbitrary. In particular, with respect to your comment in on Nugatory's 'If toss a coin, it's either heads or tails but I don't know which until I look at it. That's "unknown".' - that refers to a proper mixture, not an improper mixture.

 

[bhobba]

Ok - maybe what I said was a bit general so I will do a simple specific example and we can see exactly what's going on.

Suppose we have the following superposition |p> = 1/√2|b1>|a1> + 1/√2|b2>|a2>. This is obviously an entangled system where system A is entangled with system B. It's a pure state. It remains in a pure state until observed ie until its interacted with.

But now we will do an observation on just system A with the observable A.

E(A) = <p|A|p> = 1/2 <a1|<b1|A|b1>|a1> + 1/2 <a1|<b1|A|b2>|a2> + 1/2 <a2|<b2|A|b1>|a1> + 1/2 <a2|<b2|A|b2>|a2>

Now here is the kicker - since you are only observing system A the observable A has no effect on the B system or its states. So we have:

<p|A|p> = 1/2 <Aa1|<b1|b1>|a1> + 1/2 <Aa1|<b1|b2>|a2> + 1/2 <Aa2|<b2|b1>|a1> + 1/2 <Aa2|<b2|b2>|a2> = 1/2 <a1|A|a1> + 1/2 <a2|A|a2>
= Trace((1/2|a1><a1| + 1/2|a2><a2|) A) = Trace (p' A)

Here p' is the mixed state 1/2|a1><a1| + 1/2|a2><a2|. Thus observing system A is equivalent to observing a system in the mixed state p' - which by definition is the state from |p> by doing a partial trace over B. The observation will of course give |a1> or |a2> and the entanglement will be broken so that if you get |a1> system B will be in |b1> and conversely. We still have collapse if you like that language - but now it has a different interpretation - you are not observing a pure state - but a mixed one. Its not a proper mixed state because its not prepared the way a proper mixed state is prepared - but the state is exactly the same. Any observable A will not be able to tell the difference. This means we, in a sense, can kid ourselves and say, somehow, its a proper mixed state. If it was a proper mixed state then prior to observation it is in state |a1> or state |a2> with probability of half. Prior to observation its in superposition - after it isnt. Until observed it continues in superposition - its simply because of the entanglement it can now be interpreted differently. By observing 'inside' the system - ie only observing system A - it is in a mixed state - not a proper one - but still a mixed state. Because of that it allows a different and clearer interpretation that avoids a lot of problems.

I really can't explain it better - so if its still unclear then there isn't much more I can do.

Thanks
Bill

 

[atyy]

Ok - maybe what I said was a bit general so I will do a simple specific example and we can see exactly what's going on.

Suppose we have the following superposition |p> = 1/√2|b1>|a1> + 1/√2|b2>|a2>. This is obviously and entangled system where system A is entangled with system B. It's a pure state. It remains in a pure state until observed ie until its interacted with.

But now we will do an observation on just system A with the observable A.

E(A) = <p|A|p> = 1/2 <a1|<b1|A|b1>|a1> + 1/2 <a1|<b1|A|b2>|a2> + 1/2 <a2|<b2|A|b1>|a1> + 1/2 <a2|<b2|A|b2>|a2>

Now here is the kicker - since you are only observing system A the observable A has no effect on the B system or its states. So we have:

<p|A|p> = 1/2 <Aa1|<b1|b1>|a1> + 1/2 <Aa1|<b1|b2>|a2> + 1/2 <Aa2|<b2|b1>|a1> + 1/2 <Aa2|<b2|b2>|a2> = 1/2 <a1|A|a1> + 1/2 <a2|A|a2>
= Trace((1/2|a1><a1| + 1/2|a2><a2|) A) = Trace (p' A)

Here p' is the mixed state 1/2|a1><a1| + 1/2|a2><a2|. Thus observing system A is equivalent to observing a system in the mixed state p' - which by definition is the state from |p> by doing a partial trace over B. The observation will of course give |a1> or |a2> and the entanglement will be broken so that if you get |a1> system B will be in |b1> and conversely. We still have collapse if you like that language - but now it has a different interpretation - you are not observing a pure state - but a mixed one. Its not a proper mixed state because its not prepared the way a proper mixed state is prepared - but the state is exactly the same. Any observable A will not be able to tell the difference. This means we, in a sense, can kid ourselves and say, somehow, its a proper mixed state. If it was a proper mixed state then prior to observation it is in state |a1> or state |a2> with probability of half. Prior to observation its in superposition - after it isnt. Until observed it continues in superposition - its simply because of the entanglement it can now be interpreted differently. By observing 'inside' the system - ie only observing system A - it is in a mixed state - not a proper one - but still a mixed state. Because of that it allows a different and clearer interpretation that avoids a lot of problems.

I really can't explain it better - so if its still unclear then there isn't much more I can do.

Thanks
Bill

How is observing A inside the system any different from observing A $\otimes$ I on the full system?

Anyway, the important point is that the improper mixed state does not correspond to Nugatory's definition of unknown - that is a proper mixed state.

 

[Buzz Bloom]

Note the following well known quote by Richard Feinman"
"I think it is safe to say that no one understands Quantum Mechanics."
See http://www.spaceandmotion.com/quantum-mechanics-richard-feynman-quotes.htm .

 

[Buzz Bloom]

Please see:

http://www.spaceandmotion.com/quantum-mechanics-richard-feynman-quotes.htm

 

[Buzz Bloom]

Please see
http://www.spaceandmotion.com/quantum-mechanics-richard-feynman-quotes.htm

I don't understand why I have these dupicate posts but I don't seem to be able to delete all but one. When I try to delete one, all vanish.

 

[bhobba]

Note the following well known quote by Richard Feinman" "I think it is safe to say that no one understands Quantum Mechanics."

Everyone knows Feynmans quotes. But as you learn more about QM you understand plenty of people understand QM - what he meant was understanding it in usual everyday terms.

In particular you need to get used to the idea the primitive of the theory is observations.

Thanks
Bill

 

[atyy]

Let me see if I can use two different definitions of "unknown" to explain more clearly the point of view in which an improper mixture and a superposition are the "same thing".

In one definition of "unknown", the quantum system is in a definite state of reality, but we don't know what it is. All classical randomness is "ignorance interpretable" in this sense. In the quantum mechanical formulation, this most closely (but not exactly) corresponds to a measurement, followed by wave function collapse and the formation of a proper mixture. (I believe Nugatory gave this answer in post #3.)

In the definition of "unknown" that is the typical answer to the OP's question, the quantum system is in a definite state, but we don't know what that means because we don't understand whether the quantum state is real. It is in this sense that the pure state and the improper mixture are the "same thing", in that the randomness produced by each is not "ignorance interpretable". (This was my answer in post #4.)

Although there are two different definitions of "unknown" that are used to reply to the OP, it is known in some cases how to make the second definition into the first without wave function collapse, ie. give the quantum system a definite state of reality - by using nonlocal hidden variables.

At our current stage of technology, if nonlocal hidden variables do exist, we are not able to control them. So the second answer is more currently practical, in the sense that as long as we don't have enemies who are able to control such nonlocal hidden variables, then we can use quantum mechanics to produce "true" randomness for secure codes. Of course, if our enemies are much more technologically advanced than we are and can control the hidden variables, then quantum mechanics will not produce "true" randomness, and the enemies can use the determinism to break our codes.

 

[Buzz Bloom]

Everyone knows Feynmans quotes. But as you learn more about QM you understand plenty of people understand QM - what he meant was understanding it in usual everyday terms.

Hi bhobba:

I am not a physisist.

From other material of Feyman's that I have read, I have come to believe that he had a more profound interpretation in mind than the one you give in your post. Unfortunaely, I can't at this time find any other relevant quotes of his I can post.

I think Feynman meant that the interpretive relationship between the QM math and the real physical world was, at the time of his quote, outside the realms of both math and physics. The relationship was (and may still be) entirely philosophical. That is, all the interpretations about this relationship that had been put forth by the best minds in physics soon after were seen to be apparent philosophical paradoxes. A relativelty recent example of this is the "action at a distance" interpretation of entanglement.

A physisist friend introduced me to an interpretation (one that I have been unable to find on the internet anywhere) that so far seems to me to be free of paradoxes, but it would require a somewhat lengthy exposition. As a brief overview, I offer: The interpretation of probability states involves multiple contingent parallel universes (not to be confused with any real parallel universes or multiverses). The instant of an observation (between the past and the future) constrains the collection of contingent universes to become a single real universe.

Regarding the cat: When the experiment has been set up, and the particle that will determine fate of the cat is emitted, two contigent universes are created, one in which tha cat will survirve, and the other in which the cat will soon after die. When the obsever opens the lid, one of these two contingent universes becomes the real universe in which the observer continues to exist.

 

[bhobba]

Regarding the cat: When the experiment has been set up, and the particle that will determine fate of the cat is emitted, two contigent universes are created, one in which tha cat will survirve, and the other in which the cat will soon after die. When the obsever opens the lid, one of these two contingent universes becomes the real universe in which the observer continues to exist.

Ok.

A question then.

In that thought experiment the particle detector clicks or not and that is what determiners if the cat lives or dies.

What has the lid opening got to do with anything?

The reason I ask is there is a lot of confusion about it and what it means. I could explain it, but I think its usually better if you think it through for yourself - and beside I may be wrong.

Thanks
Bill

 

[carllooper]

The state of the cat before opening the box can be regarded as no different from the state of the cat after opening the box.

Before opening the box we can say the cat is alive or dead.

And after opening the box? Well we find the cat is ... as described ... alive or dead.

C

 

[write4u]

Would it be correct to say that Schrodingers cat is in a state of superimposed potentials?

 

[Buzz Bloom]

What has the lid opening got to do with anything?

Hi Bill:

(I notice you signed your post "Bill", I so I assume that's your name rather than bhobba.)

As I undesrand the various philosophical views about this ambiguous point, it remains controversial regarding what constitutes an observation. There seem to be a spectrum of views. The two extrremes are:

1. Any physical interaction constitutes an "observation" that (in what I remember as being the old Copenhagen terminolgy) collapses the superimposed potentials into a single state. (In my terminology, it would be the conversion of the collection of contingent parallel universes into a single real universe. This is the simplified "brief overview" explanantion. A more complete explanantion would consider the collection to be a combination all all of the contingient universes for all of the particles for which there are unresolved superimposed potentials. In some more complicated thought experiments, multiple particles might involve a joint collection of superimposed potentials.)

2. It requires a conscious mind to make an observation that will accomplish the "collapse".

In my example, the opening of the lid is based on the second extreme.

Thanks for your post.
Buzz

 

[bhobba]

In my example, the opening of the lid is based on the second extreme.

That is one view, but a very very backwater view these days because of the severe problems it poses. For example imagine we did a Schroedinger's Cat with a robot opening the lid that recorded the result to computer memory. We then made billions of copies and scattered each copy across the cosmos. A million years later someone reads the contents of one of those copies - it would be a very very weird view of the world that's when it collapsed - and all of those copies collapsed. You could probably formulate a consistent view of the world along those lines - but - like solipsism - most would reject it as unnecessarily contrived.

The point I was trying to make is in the standard Copenhagen interpretation QM is a theory about observations that occur here in an assumed common-sense classical world. In Schroedinger's Cat that observation occurs at the particle detector - everything from that point on in common-sense classical - the cat is alive or dead regardless of if the box is opened or not.

Thanks
Bill

 

[bhobba]

Would it be correct to say that Schrodingers cat is in a state of superimposed potentials?

No. Its entirely classical. The observation occurred at the particle detector.

Thanks
Bill

 

[bhobba]

A more complete explanantion would consider the collection to be a combination all all of the contingient universes for all of the particles for which there are unresolved superimposed potentials. In some more complicated thought experiments, multiple particles might involve a joint collection of superimposed potentials.)

The modern version of that view is after decoherence each part of the resultant mixed state is a separate world. You can find the full detail in David Wallaces book:
http://users.ox.ac.uk/~mert0130/books-emergent.shtml

Thanks
Bill

 

[write4u]

write4u said: ↑
Would it be correct to say that Schrodingers cat is in a state of superimposed potentials?

No. Its entirely classical. The observation occurred at the particle detector.
Thanks, Bll

Sorry, but that answer makes no sense, in context of the question. The superposition is before we make the observation. The experiment does not ask if the cat is dead or alive (or both), it asks when the cat is dead or alive. Until the uncertain trigger moment has arrived neither potential is explicate in reality and are superposed. We can only know when the trigger moment occurred (if at all), by looking at the particle detector (inside the box).
Until we look we cannot be certain which potential was expressed and for our purposes are superposed., IMHO. .

 

[carllooper]

Sorry, but that answer makes no sense, in context of the question. The superposition is before we make the observation. The experiment does not ask if the cat is dead or alive (or both), it asks when the cat is dead or alive. Until the uncertain trigger moment has arrived neither potential is explicate in reality and are superposed. We can only know when the trigger moment occurred (if at all), by looking at the particle detector (inside the box).
Until we look we cannot be certain which potential was expressed and for our purposes are superposed., IMHO. .

I think Bill is making a distinction between the system describing the atomic system and the cat. One can (pursuing silences in Copenhagen) enlarge the scope of that system to include the cat, the robot who opens the box, etc. Or one can contain it to the atomic system.

One can also (pursuing a different tack from Copenhagen) say that there is no dividing line. The atomic system, the cat, the entire universe is always in a superposition of states, regardless of observations.

Even when we look inside the box (or even the atomic system), there is no additional certainty, or decrease in uncertainty. When we look inside the box the cat (as a direct analogy of the atomic system) will be no different from if we didn't.

The cat will be alive or dead. A particle detection will be here or there.

To put it another way, in answer to the question: "is the cat alive or dead", regardless of whether the box is open or closed, the answer is yes.

C

 

[Quotidian]

'What did you do to the cat, Erwin? It looks half dead' ~ Mrs Schrodinger.

 

[Swamp Thing]

'What did you do to the cat, Erwin? It looks half dead' ~ Mrs Schrodinger.

Or maybe it was Scroedinger's Girlfriend, who famously accompanied him on that mountain hiking trip where he figured out his Equation.

Interestingly, it was the OP's GF who inpired this discussion

my girlfriend is wondering if while shroodingers cat was in the box, we should consider it as both unknown rather than both alive and dead. please shed some light on the subject.

 

[bhobba]

Sorry, but that answer makes no sense, in context of the question. The superposition is before we make the observation.

Its obvious the observation is made at the particle detector and occurs before the cat becomes involved or the box is opened.

My suspicion is you are confused by the term 'observation' thinking it involves a conscious observer. That is not its meaning in QM.

No one ever took seriously that the cat was in some weird live or dead superposition - in fact the prevailing Copenhagen interpretation said it wasn't, because it's obvious the observation occurred at the particle detector. The issue was the theory didn't force you to put the observation there - which was what the thought experiment highlighted. The other related issue is, since QM is a theory about observations that occur in a an assumed common-sense classical world, exactly how does that theory explain such a world - in reality everything is quantum. None of this invalidates the theory, or the standard interpretation - but its a blemish that's best done away with.

A lot of progress has been made in resolving it with a much better understanding of decoherence. But still a few issues remain. If you want to delve deeper into it, at the lay level here is the book to get:
https://www.amazon.com/dp/0465067867/?tag=pfamazon01-20

Also Lubos has written a rather good article on it:
http://motls.blogspot.com.au/2011/05/copenhagen-interpretation-of-quantum.html

Thanks
Bill

 

[Quotidian]

As a student of history, culture and ideas, I would say the significance of Schrodinger's remark is not something that can be simply papered over so that we can all go back to thinking that normalcy is restored. 'Move right along folks, nothing to see here', is what a lot of physicists seem to want to say. In actual fact, I'm with whoever said that reality is 'queerer than we can suppose'. We ought to live on the cusp of that, rather than persuading ourselves that everything simply adds up, especially in light of the enormity of the known philosophical and epistomological issues confronting physics.

(Incidentally I read Lindley's book previous work on http://amzn.com/1400079969, and whilst I thought it was a reasonable historical account, I thought it failed to grasp the depth of the philosophical issues at stake.)

 

[bhobba]

I would say the significance of Schrodinger's remark is not something that can be simply papered over so that we can all go back to thinking that normalcy is restored.

If by remark you mean the thought experiment, then I think you have to judge it by the appraisal of physicists about it. What they say, at least in modern times, is not what popularisations say, nor is it what philosophers sometimes say.

Technically its a variation of the argument I gave before in post 22 where the cat has been entangled with the atomic particle by the set-up. System A will be the cat and system B the atomic nucleus. We will take state |b1>|a1> as particle not emiited by nucleus, and cat alive, |b2>|a2> particle emitted and cat dead. We observe the cat - not the particle.

Now chugging through exactly the same math you get the mixed state 1/2|a1><a1| + 1/2|a2><a2|. This is NOT a superposition. Its a mixed state - the cat is either alive or dead. It comes about because of the set-up - we observe the cat - not the total system which is particle and cat.

Why didn't Schroedinger recognise this? Like I said decoherence wasn't as well understood in those days. And an issue still remains - its the difference between a proper and an improper mixed state - but that really requires another thread.

Thanks
Bill

 

[atyy]

Now chugging through exactly the same math you get the mixed state 1/2|a1><a1| + 1/2|a2><a2|. This is NOT a superposition. Its a mixed state - the cat is either alive or dead. It comes about because of the set-up - we observe the cat - not the total system which is detector and cat.

That is not correct. This mixed state is improper - it is not "ignorance interpretable".

 

[bhobba]

That is not correct. This mixed state is improper - it is not "ignorance interpretable".

Atty - you know as well as I do an improper mixed state is still a mixed state and is not a superposition. The reason its not a superposition is we are observing the cat and not the cat and particle emitted by the nucleus. The cat is entangled with it and observing the total setup is not the thought experiment - we observe the cat. Because of that it's a mixed state - not a superposition. The set-up precludes it.

Now if you want to discuss the difference between a proper and improper mixture we can do that - but I think it's better done in a separate thread.

Thanks
Bill

 

[atyy]

Atty - you know as well as I do an improper mixed state is still a mixed state and is not a superposition. The reason its not a superposition is we are observing the cat and not the cat and particle emitted by the nucleus. The cat is entangled with it and observing the total setup is not the thought experiment - we observe the cat. Because of that it's a mixed state - not a superposition. The set-up precludes it.

Now if you want to discuss the difference between a proper and improper mixture we can do that - but I think it's better done in a separate thread.

But that is the key point - the reason it is not ignorance interpretable is because the state is in some sense a superposition.

Also, the ignorance interpretability is the key point of this thread. Classical probability is always ignorance interpretable, which is why one never asks such bizarre questions in classical probability as whether the cat is alive or dead. In quantum mechanics (without BM or MWI), for either answer - superposition or improper mixed state - it is not ignorance interpretable, so cannot say that the cat is either alive or dead.

 

[Tristan C]

my girlfriend is wondering if while shroodingers cat was in the box, we should consider it as both unknown rather than both alive and dead. please shed some light on the subject.

The whole point of Schrodingers cat is that it is like a variable. This is obvious but if you think about it quantum Physics is about being able to figure it out without needing to see it. Algebra can teach us to solve for a variable. So is the cat dead or alive, it is uncertain but we can conclude that if it has nothing in the box with it it has died, because we can observe the y to get the x. All organisms die in time. The cat will die, but is it dead right now...that is our x.

 

[julcab12]

... In the Box experiment. It is usually 50/50. Details and summary. https://www.physicsforums.com/threads/clarifying-the-meaning-of-random-in-quantum-physics.819719/ #17.

 

[write4u]

I think Bill is making a distinction between the system describing the atomic system and the cat. One can (pursuing silences in Copenhagen) enlarge the scope of that system to include the cat, the robot who opens the box, etc. Or one can contain it to the atomic system.

One can also (pursuing a different tack from Copenhagen) say that there is no dividing line. The atomic system, the cat, the entire universe is always in a superposition of states, regardless of observations.

Even when we look inside the box (or even the atomic system), there is no additional certainty, or decrease in uncertainty. When we look inside the box the cat (as a direct analogy of the atomic system) will be no different from if we didn't.

The cat will be alive or dead. A particle detection will be here or there.

To put it another way, in answer to the question: "is the cat alive or dead", regardless of whether the box is open or closed, the answer is yes.

Yes, I was not so much looking at it through the lens of QM, but rather from that what comes before QM, Potential. The superposition of Implicates, before they are expressed in reality.

 

[bhobba]

But that is the key point - the reason it is not ignorance interpretable is because the state is in some sense a superposition..

That is the key point - you are observing one part of an entangled system so its NOT a superposition. Look at the actual superposition:
|p> = 1/√2|b1>|a1> + 1/√2|b2>|a2>

It's entangled and neither system is in an actual pure state. System A is not in superposition. System B is not in superposition. But what the argument shows is if you just observe system A then it is in a mixed state.

I often discuss decoherence and I sometimes get the feeling a key point is being missed by some. This seems to be it. In entangled systems each system is not in a pure state - in fact the concept makes no sense at all in such a situation. However if you observe one part of the combined system it is in a mixed state.

Thanks
Bill