Schroedinger's cat: half-alive and half-dead

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ZapperZ

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I do not think that knowledge has anything to do with it. Finding something weird is an attitude not knowledge.

I do not find it weird at all. Clearly we are not smart enough to understand it. So I find it incomprehencible but not weird.

To call something weird because we do not understand it is a cop out IMHO.
I'm using it in the sense of describing the "pedestrian" view of it. I personally do not find it weird, because as I've said many times, one is trying to force a square peg into a round hole. There's nothing here that says that the "weirdness" isn't due to our insistance that our classical idea of physical quantities such as position and momentum and energy should have the same well-defined concepts at the quantum scale.

Besides, even if it IS weird, it doesn't necessarily be a bad thing. As scientists, we LOOK for weird stuff, because it means that there's new physics in it that we don't understand yet. That is the whole reason why we are employed.

Zz.
 
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vincentm

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Awesome discussion, thanks ZapperZ

Edit:

I've found this paper today, not sure what to make of it, my understandings QM is very novice.

Authors: Hiroaki Terashima, Masahito Ueda
Comments: 20 pages, 2 figures

It is shown that a large class of weak disturbances on the Schrodinger cat state can be canceled by a reversing operation on the system. We illustrate this for spin systems undergoing an Ising-type interaction with the environment and demonstrate that both the fidelity to the original cat state and the purity of the amended state can simultaneously be increased by the reversing operation. A possible experimental scheme to implement our scheme is discussed.
 
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But it is RIDICULOUS if you try to apply it IN THE CONTEXT of our classical world, where two properties that are different are now intermixing simultaneously! He wasn't ridiculing QM, nor superposition! Talk about taking things out of context! And since when did Schrodinger wrote in English?!
It's a translation into English. Here's the whole paper. See section 5 titled "Are the variables really blurred?"

http://www.tu-harburg.de/rzt/rzt/it/QM/cat.html

He not only calls the half-dead cat ridiculous. He calls acceptance of a "'blurred model' for representing reality" naive. If you want, you can explain what he means here. "It's weird" is not an explanation. He doesn't seem to be saying "it's weird".

But really, this is besides the point. We ALL know (don't we?) that quantum behavior IS "weird". That's the whole point of all of these demonstrations and thought experiments. Einstein tried to do that with EPR, and Schrodinger tried to show how weird it is using his Cat experiment. I will against tell you right away that if he had used H2 molecule as an example, you won't be so captivated by it and we won't be having this conversation. It is AS "ridiculous" when applied to the H2 molecule where an electron occupies two different locations simultaneously.
I don't know what "weird" means in this context. Schrodinger was not trying to show "weirdness" with his thought experiment. He was ridiculing a "weird" interpretation. The quantized energy levels of hydrogen don't seem weird to me. The shape of the electron "clouds" ([tex]\Psi*\Psi[/tex]) don't seem weird to me. That each cloud does not radiate does not seem weird to me. That a transition from one of these states to another radiates a quantum doesn't seem weird to me. I simply take this description for granted.

All of this is what is meant by the wavefunction having a linear superposition of ORTHORGONAL basis states! This is what is "ridiculous" as far as classical mechanics is concerned.
There is nothing weird about decomposing a function into components along orthogonal basis functions. Any piecewise continuous function whatsoever can be expressed as a superposition of sines and cosines of discrete frequences, precisely because these functions form an orthonormal basis. This superposition is the Fourier series expansion of the function. Many other sets of functions also form an orthogonal basis for various function spaces. The eigenstates of a quantum mechanical system seem to have some physical significance as well. I'd like to understand this physical significance better.

First of all, what is a "half-dead cat"? If you LOOK at the cat, the cat will either be DEAD, or ALIVE. The "observable" for "deadness" and "aliveness" is NEVER "half-dead". The same thing with the 2-slit. The position observable if you measure it, will detect only a photon passing through the left slit, or the right slit, never "half-right" or "half-left".
A "half-dead cat" is what Schrodinger ridicules in the thought experiment. He says, "The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts." If you don't like "living and dead cat ... smeared out in equal parts", you agree with Schrodinger as I do.

So already you are either consciously, or unconsciously causing an immediate confusion. So if you care so much about the exact "words" that Schrodinger used (assuming you TRUST the translation and that you put more emphasis on the "words" rather than the mathematics), then you have already used phrases that have vague meanings.
I'm trying to clarify rather than confuse. If you have some reason to distrust the translation, explain the reason. The translator is John Trimmer. It appeared Quantum Theory and Measurement edited by John Wheeler and published by Princeton University Press. Wheeler was a professor of physics at Princeton and UT Austin. His grad students include Feynman and Kip Thorne.

Let's settle this once and for all.

1. Would you say that this is an example of a quantum wavefunction that one would get by solving a schrodinger equation, where the u's are orthornormal basis functions?

[tex]|\Psi> = a_1|u_1> + a_2|u_2> + a_3|u_3> + ... a_N|u_N>[/tex]
I recognize the notation, but it's less common in mathematics than in physics. You don't specify the functions { u_i }, so I don't know whether they form an orthogonal basis. I can tell you how to know that a set of vectors is an orthogonal basis. I know that <f,g> typically denotes an inner product of vectors, and I understand vector spaces, inner products and orthogonal bases. I understand that we can view certain functions as vectors in an infinite dimensional vector space, and I understand the inner product in this sense.

2. If you do, then do you accept one of the postulates of quantum mechanics that states that such wavefunction, in principle, describes ALL the properties of that system upon a measurement of an observable?
The wave function describes the state of the system. It tells you what the theory says you can know about the system after an observation. The same function can be decomposed along many different sets of orthogonal basis functions. I understand that eigenstates have a particular physical significance in Quantum Mechanics, but I'm not a great authority on the physics, as I acknowledged eariler.

3. If you accept #1 and #2, tell me what happened if you make a single measurement of an observable that is an eigen-operator of the basis function represented by the u's.
I'm not sure what you're asking me here. The outcome of a measurement is physical information regardless of the mathematical formalism. You're the physicist. I'm curious to know how the operator associated with an observable is determined.

4. Assuming you have completed #3, compare what you got with the ORIGINAL description of the system, which is [itex]|\Psi>[/itex]. Now tell me, in your own words, not Schrodinger's, the difference between the two.
If you want to explain this notation to me, that's fine. I've already acknowledged that my background is more mathematical than physical, and I've already acknowledged your greater expertise in physics, so I'm not sure what your test is supposed to settle once and for all. I would be happy for you to share some of your expertise with me.
 
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I do not think that knowledge has anything to do with it. Finding something weird is an attitude not knowledge.

I do not find it weird at all. Clearly we are not smart enough to understand it. So I find it incomprehencible but not weird.

To call something weird because we do not understand it is a cop out IMHO.
I agree. I don't find it entirely incomprehensible, but it can be counter-intuitive until one develops an intuition for it. Classical physics can be too for that matter.
 

ZapperZ

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It's a translation into English. Here's the whole paper. See section 5 titled "Are the variables really blurred?"

http://www.tu-harburg.de/rzt/rzt/it/QM/cat.html

He not only calls the half-dead cat ridiculous. He calls acceptance of a "'blurred model' for representing reality" naive. If you want, you can explain what he means here. "It's weird" is not an explanation. He doesn't seem to be saying "it's weird".



I don't know what "weird" means in this context. Schrodinger was not trying to show "weirdness" with his thought experiment. He was ridiculing a "weird" interpretation. The quantized energy levels of hydrogen don't seem weird to me. The shape of the electron "clouds" ([tex]\Psi*\Psi[/tex]) don't seem weird to me. That each cloud does not radiate does not seem weird to me. That a transition from one of these states to another radiates a quantum doesn't seem weird to me. I simply take this description for granted.



There is nothing weird about decomposing a function into components along orthogonal basis functions. Any piecewise continuous function whatsoever can be expressed as a superposition of sines and cosines of discrete frequences, precisely because these functions form an orthonormal basis. This superposition is the Fourier series expansion of the function. Many other sets of functions also form an orthogonal basis for various function spaces. The eigenstates of a quantum mechanical system seem to have some physical significance as well. I'd like to understand this physical significance better.



A "half-dead cat" is what Schrodinger ridicules in the thought experiment. He says, "The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts." If you don't like "living and dead cat ... smeared out in equal parts", you agree with Schrodinger as I do.



I'm trying to clarify rather than confuse. If you have some reason to distrust the translation, explain the reason. The translator is John Trimmer. It appeared Quantum Theory and Measurement edited by John Wheeler and published by Princeton University Press. Wheeler was a professor of physics at Princeton and UT Austin. His grad students include Feynman and Kip Thorne.



I recognize the notation, but it's less common in mathematics than in physics. You don't specify the functions { u_i }, so I don't know whether they form an orthogonal basis. I can tell you how to know that a set of vectors is an orthogonal basis. I know that <f,g> typically denotes an inner product of vectors, and I understand vector spaces, inner products and orthogonal bases. I understand that we can view certain functions as vectors in an infinite dimensional vector space, and I understand the inner product in this sense.



The wave function describes the state of the system. It tells you what the theory says you can know about the system after an observation. The same function can be decomposed along many different sets of orthogonal basis functions. I understand that eigenstates have a particular physical significance in Quantum Mechanics, but I'm not a great authority on the physics, as I acknowledged eariler.



I'm not sure what you're asking me here. The outcome of a measurement is physical information regardless of the mathematical formalism. You're the physicist. I'm curious to know how the operator associated with an observable is determined.



If you want to explain this notation to me, that's fine. I've already acknowledged that my background is more mathematical than physical, and I've already acknowledged your greater expertise in physics, so I'm not sure what your test is supposed to settle once and for all. I would be happy for you to share some of your expertise with me.
It appears that from the way you responded to my series of questions, I would have to TEACH you quantum mechanics, something which I have no patience to do on here since students spend a year in school to grasp such a thing.

If you truly believe that your classical model is analogous to the Schrodinger-Cat type experiment, then as I've said before, submit it to AJP and prove me wrong.

I'm leaving this thread because I notice no progress that any of my explanation has gotten through.

Zz.
 
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I don't know what "weird" means in this context.
It means counter intuitive.

Schrodinger was not trying to show "weirdness" with his thought experiment. He was ridiculing a "weird" interpretation.
What do you mean by "weird" in this context ?

There is nothing weird about decomposing a function into components along orthogonal basis functions. Any piecewise continuous function whatsoever can be expressed as a superposition of sines and cosines of discrete frequences, precisely because these functions form an orthonormal basis. This superposition is the Fourier series expansion of the function. Many other sets of functions also form an orthogonal basis for various function spaces. The eigenstates of a quantum mechanical system seem to have some physical significance as well. I'd like to understand this physical significance better.
But it is exactly the "physical significance " that is "weird". This is exactly what you want to understand and that is very normal. If it were so intuitive, you would not have asked this question.

A "half-dead cat" is what Schrodinger ridicules in the thought experiment. He says, "The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts." If you don't like "living and dead cat ... smeared out in equal parts", you agree with Schrodinger as I do.
Did Schrödinger actually talked about a half dead cat ? What is that ? How did he define that ? I have never met this terminology, though i use QM every day for my work. What have i missed ?

I recognize the notation, but it's less common in mathematics than in physics.
this is untrue. Besides, the actual formula is mathematics, nothing more.

You don't specify the functions { u_i }, so I don't know whether they form an orthogonal basis.
But Zz wrote they are orthogonal by definition. This is very correct. You don't need to know the actual function or what it represents (they can represent ANYTHING) because Zz wanted to outline the formalism.

I can tell you how to know that a set of vectors is an orthogonal basis. I know that <f,g> typically denotes an inner product of vectors, and I understand vector spaces, inner products and orthogonal bases.
But this is irrelevant. All mathematical requirements for orthogonality are respected by definition. Just accept that these functions are orthogonal.

It tells you what the theory says you can know about the system after an observation.
What is that supposed to mean ?

The same function can be decomposed along many different sets of orthogonal basis functions. I understand that eigenstates have a particular physical significance in Quantum Mechanics, but I'm not a great authority on the physics, as I acknowledged eariler.
Well, the eigenstates correspond exactly to the orthogonal functions that Zz was talking about. Actually this is what he eventually wanted to say to you.


I'm not sure what you're asking me here. The outcome of a measurement is physical information regardless of the mathematical formalism.
There is only ONE formalism : QM

You're the physicist. I'm curious to know how the operator associated with an observable is determined.
This is basic QM stuff. You really should know that before engaging into this kind of discussions. A lot of your misconceptions would have already been cleared out. Don't take this the wrong way, please, BUT IT IS TRUE !

marlon
 
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I agree. I don't find it entirely incomprehensible, but it can be counter-intuitive until one develops an intuition for it.
Semantics...

Classical physics can be too for that matter.
Are you saying that classical physics is counter intuitive in the same way as QM ? If so, you really must have missed out on some basic points of the QM's formalism.

marlon
 
It appears that from the way you responded to my series of questions, I would have to TEACH you quantum mechanics, something which I have no patience to do on here since students spend a year in school to grasp such a thing.

If you truly believe that your classical model is analogous to the Schrodinger-Cat type experiment, then as I've said before, submit it to AJP and prove me wrong.

I'm leaving this thread because I notice no progress that any of my explanation has gotten through.

Zz.
I don't pretend to know everything there is to know about Quantum Mechanics, but I do have a grasp of it. If you aren't here to share what you know about it, I'm not sure why you are here.
 
Are you saying that classical physics is counter intuitive in the same way as QM ? If so, you really must have missed out on some basic points of the QM's formalism.

marlon
No, I didn't say it.
 
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Hmmm, at least I'm getting a lot of replies...

I'm not sure if we actually got to the right answer to my original question, or are heading there once the debate is resolved. I don't understand these equations, but I recognize that mathematics is a more natural language for conferring to for the right answer. The only parts I recognize, myself, are the psi function and the plus sign. Well, like I said, I just wanted to get the ball rolling and introduce my novice brain to all of you.

This seems to be a board with a lot of action. I didn't check from last night to this afternoon and the number of responses went from, like, 17, to, like, 33.

I wrote something that was ignored by the debaters: isn't the cat's state entangled with the radiating atom that triggers the capsule? One of you said entanglement was irrelevant to Schroedinger's cat, and the other one said it was relevant.

Without entanglement, the radiation of the atom would not have anything to do with the life or death of the cat (as it would have to not trigger the poison), and the cat would remain a classical system, right? Or, no? The cat is a macroscopic object and it's own Heisenberg Uncertainty value would be low according to it's large mass (which would confer to momentum, although I'm not sure about the velocity...)
 

JesseM

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It's provable the Bohm's interpretation never leads to any different interpretations than the Copenhagen interpretation for nonrelativistic QM. In Bohm's interpretation each particle has a definite position at all times, particles in the double-slit experiment definitely go through one slit or the other, so I would think this would extend to macroscopic superpositions, implying that the cat would be in a definite state according to Bohm's interpretation. Since there's no experimental way to test which of these interpretations is right (or if another interpretation is right, like the many-worlds interpretation), it seems to me that the question of whether the cat is "really" neither alive nor dead must be a metaphysical one, not a question of physics.
 
It means counter intuitive.
Thanks for clearing that up.

What do you mean by "weird" in this context ?
What Schrodinger calls "ridiculous" and "naive". I quoted his description of the thought experiment earlier.

But it is exactly the "physical significance " that is "weird". This is exactly what you want to understand and that is very normal. If it were so intuitive, you would not have asked this question.
That solutions of a particular differential equation have physical significance does not seem weird to me, per se.

Did Schrödinger actually talked about a half dead cat ? What is that ? How did he define that ? I have never met this terminology, though i use QM every day for my work. What have i missed ?
Yes, he did. I quoted him more precisely earlier. Someone started this thread to discuss the thought experiment. I joined it later.

this is untrue. Besides, the actual formula is mathematics, nothing more.
I know the formula is mathematical. As I said, I have a masters in applied mathematics with a 4.0 GPA exhausting material at the phd level at the graduate school I attended, and I rarely used this notation specifically though I studied vector spaces extensively. Psi specifically and the bra-ket notation is more common in quantum mechanics than in the theory of vector spaces and orthogonal bases more generally. Dirac invented the notation, and Dirac was a physicist and an architect of Quantum Mechanics specifically. I've never seen a Fourier expansion written this way, but a Fourier expansion is the representation of a function in similar terms; however, as I said, I do understand the notation.

But Zz wrote they are orthogonal by definition. This is very correct. You don't need to know the actual function or what it represents (they can represent ANYTHING) because Zz wanted to outline the formalism.
I know what he wrote. I explained to him that I understand the mathematical formalism.

But this is irrelevant. All mathematical requirements for orthogonality are respected by definition. Just accept that these functions are orthogonal.
I'm willing to accept an assumption.

What is that supposed to mean ?
I don't know what isn't clear to you.

Well, the eigenstates correspond exactly to the orthogonal functions that Zz was talking about. Actually this is what he eventually wanted to say to you.
Right. I made my understanding of this point clear when I compared eigenstates to other basis functions and said that eigenstates specifically have physical significance. You quote me in this regard above.

There is only ONE formalism : QM
QM is one formalism. ZapperZ asked, "tell me what happened if you make a single measurement of an observable". He seemed to be asking about the outcome of an experiment rather than something about the formalism, so I asked for clarification. I understand that a quantum mechanical system is observed in an eigenstate. Suggesting an intuition for understanding this expectation is the point of my first post. As I say above, the eigenstate is a time-invariant, steady state solution to Schrodinger's equation associated with a discrete energy. It is a non-radiating state, like the discrete orbits in Bohr's model.

This is basic QM stuff. You really should know that before engaging into this kind of discussions. A lot of your misconceptions would have already been cleared out. Don't take this the wrong way, please, BUT IT IS TRUE !
I don't pretend to know everything there is to know about Quantum Mechanics. I'm happy for you to share your expertise with me.
 
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marlon, I found classical mechanics to be counter-intuitive

I think the comparison is intended in a more limited sense than to equate QM counter-intuitiveness to classical counter-intuitiveness.

For instance, during an optics lecture, my high school physics teacher had said before (or perhaps I read it in a Relativity book) that light always travels at the same speed. This turned out to be wrong: light can slow down in mediums other than a vacuum (a medium? anyways...) Not only that, but it bends in water, thus providing an optical illusion as to the actual position of a long object like a stick. I saw this for myself during the lab, where the class measured the position of thumb tacks in water or something, viewed from the side. Animals that live above water, such as cranes, have to deal with this visual distortion without knowing the classical physics behind it.

(At least, I hope optics counts as classical physics, photon/light waves and all.)

Another weird classical phenomenon is the Doppler effect on sound that I hear everytime the train goes by. A moving object emmitting sound waves bunches them up in the forward direction and elongates the waves in the rearward direction. This experience is counter-intuitive to most children (not me, though; heh) and again, perhaps to animals as well.

Perhaps this is what Martin Brock meant. His example of the rotating bar was a little hard to follow, and I had to read it carefully several times. It's not a perfect classical analogy to the quantum phenomenon of Schroedinger's cat, as has been noted, but I would prefer not to take sides in the debate going on here. I just try to read all the posts with much interest and eagerness.

o| Hiram
 

JesseM

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I'm using it in the sense of describing the "pedestrian" view of it. I personally do not find it weird, because as I've said many times, one is trying to force a square peg into a round hole. There's nothing here that says that the "weirdness" isn't due to our insistance that our classical idea of physical quantities such as position and momentum and energy should have the same well-defined concepts at the quantum scale.

Besides, even if it IS weird, it doesn't necessarily be a bad thing. As scientists, we LOOK for weird stuff, because it means that there's new physics in it that we don't understand yet. That is the whole reason why we are employed.

Zz.
I would say that QM is more fundamentally weird, than, say, curved spacetime in general relativity (which is certainly not very intuitive or easy to picture), because unless you add some additional assumptions as in the various "interpretations" of QM, it does not give you any objective description of the universe as a self-contained system; this is a problem in formulating quantum cosmology, for example. You can only get the probabilities for how a given system behaves by plugging in the choice of variables to measure, and when the measurement is made, by hand--if you try to describe the measuring-system itself using the rules of QM in order to predict when and what it measures, then to get any definite probabilities you need some second measuring system whose measurements must be put in by hand, and so on. You can't describe the dynamics of the entire universe, measuring systems and all, using some fundamental mathematical rules and initial boundary conditions, as you can in other theories of physics.
 
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Then what did you mean by saying "Classical physics can be too for that matter" ?

marlon
I meant that classical physics can be confusing too until one understands it. I nowhere state that classical physics is counterintuitive "in the same way" that Quantum Mechanics is counterintuitive. The quoted words are yours, not mine.

Centuries ago, that the Earth circles the Sun was counterintuitive to most people. That the Earth is a sphere was also counterintuitive.
 
Perhaps this is what Martin Brock meant. His example of the rotating bar was a little hard to follow, and I had to read it carefully several times. It's not a perfect classical analogy to the quantum phenomenon of Schroedinger's cat, as has been noted, but I would prefer not to take sides in the debate going on here. I just try to read all the posts with much interest and eagerness.

o| Hiram
It's a system with two stable states that when excited returns to one of the two states, though we can't easily know which one. It absorbs or emits a quantum of energy during its transition from one state to the other. We can expect to find the system in one of the two stable states, because other states always decay into one of these states, but we know which state to expect only in terms of probabilities.

If you understand why the system fits this description, you understand most of the point of the analogy. [If you can suggest improvements in the presentation, please do.] Though we don't know the state of the system after excitation without observing it, the act of observing the system does not drive it into a stable state. Observation doesn't cause the system to enter a discrete state. Observation reveals a discrete state. Our ignorance of a particular state collapses.

Schrodinger's cat dies when a Quantum Mechanical system changes state thus emitting a quantum of energy (a photon). This photon kills the cat by triggering the release of poison. No one needs to observe the Quantum Mechanical system for this state change and photon release to occur. I don't believe the Copenhagen Interpretation implies that anyone must observe the system for the state change to occur.

If we open the door to find a dead cat, the cat has been dead since the radioactive decay occured, whenever that was. What changes as we open the door is our knowledge of the state of the system. Before opening the door, we might know the probability of finding a dead cat, if we know the probability of a decay since we closed the door. When we open the door, our knowledge of the actual state of the cat replaces this probability.

How weird or mysterious is that?

A quantum mechanical system can exist in an intermediate or indeterminate or mixed state or a superposition of states (any state other than an eigenstate, however you want to describe it). This fact is a separate issue. A mixed state is analogous to the spinning state of the classical system. A Quantum Mechanical system between eigenstates is emitting or absorbing a quantum of energy. An eigenstate is precisely a state in which the system's energy is not changing. The time-invariant Schrodinger equation has solutions only for discrete values of E (the energy of the system). These discrete values characterize the solutions. They are the system's characteristic values (eigenvalues).

So I learned it. If you get a clearer explanation from someone else, you should run with it.

Johann Balmer's story might interest you.

http://en.wikipedia.org/wiki/Johann_Balmer
 
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JesseM

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Schrodinger's cat dies when a Quantum Mechanical system changes state thus emitting a quantum of energy (a photon). This photon kills the cat by triggering the release of poison. No one needs to observe the Quantum Mechanical system for this state change and photon release to occur. I don't believe the Copenhagen Interpretation implies that anyone must observe the system for the state change to occur.
But what if you consider the cat and photon as a single entangled system, isolated from the outside world? (You can imagine a simulation of a 'cat' on a quantum computer to make this slightly more realistic.) In the case of the double-slit experiment, one way of looking at the idea that you can't assume the particle definitely went through one slit or another is that if you calculate the probability of the particle hitting the detector at a particular location by doing a path integral where you integrate over paths that go through both slits, you'll get a different answer than if you calculated (probability particle hits detector when you integrate over only paths going through first slit) + (probability particle hits detector when you integrate over only paths going through the second slit). This is different from a classical situation like a ball going through one of two slits and hitting a wall, where you could indeed assume the probability the ball hits the wall at a particular spot is given by (probability ball hits that spot if it goes through first slit) + (probability ball hits that spot if it goes through second slit).

So the question is, suppose you open the box containing Schroedinger's cat after some time, and you want to know the probability you'll find it in some exact quantum state A: can you assume the probability of finding it in this state is given by (probability system is in state A when you sum over paths where photon was emitted and cat died) + (probability system is in state A when you sum over paths where photon was not emitted and cat lived)? It may be that if you open it shortly after the photon was or wasn't emitted, then no matter what happened you'll be able to tell unambiguously whether it was or wasn't in retrospect (because the cat clearly was or wasn't poisoned), so you can indeed sum the probabilities that way just like you could in the double-slit experiment if you had a detector which made an unambiguous measurement of which slit the particle went through. But suppose you waited a billion years to open the box, and that by the time you opened it the matter making up the cat and poison had gone to a state of maximum entropy, so there was no record of whether the cat had or hadn't been poisoned? In this case I think you really would need to sum over all possible paths to get the probability that you'd find it in some particular quantum state A, so you couldn't say that the cat had definitely either been poisoned or not poisoned all those years ago, just like you couldn't say which slit the particle went through in the double-slit experiment when you had no measuring-device at the slits (at least, not in the Copenhagen interpretation; as I said in a previous post, I think Bohm's interpretation would say there was a definite answer to these questions, even though you couldn't determine it).
 
I wrote something that was ignored by the debaters: isn't the cat's state entangled with the radiating atom that triggers the capsule? One of you said entanglement was irrelevant to Schroedinger's cat, and the other one said it was relevant.
I said that entanglement is relevant to experiments involving a SQUID, which is a superconducting ring in which Quantum Mechanical states (not a classical analogy) can be observed macroscopically. I withdrew this claim, because I don't know the SQUID experiments cited. I'm not sure anyone has said that Quantum Mechanical entanglement is irrelevant to Schrodinger's Cat.

Without entanglement, the radiation of the atom would not have anything to do with the life or death of the cat (as it would have to not trigger the poison), and the cat would remain a classical system, right? Or, no?
I might agree with you here, but I'm not sure Schrodinger would. The fates of the atom and the cat are entangled, but I'm not sure this is literally "Quantum Mechanical entanglement".

The cat is a macroscopic object and it's own Heisenberg Uncertainty value would be low according to it's large mass (which would confer to momentum, although I'm not sure about the velocity...)
Many pairs of observables have Heisenberg Uncertainty principles, not only position and momentum. I'll say this. The radioactive decay occurs regardless of the cat and regardless of anyone opening the door. The cat dies only if the radioactive decay occurs. Someone knows the cat is dead only by opening the door. The resolution is no more mysterious than this.
 
But what if you consider the cat and photon as a single entangled system, isolated from the outside world? (You can imagine a simulation of a 'cat' on a quantum computer to make this slightly more realistic.) In the case of the double-slit experiment, one way of looking at the idea that you can't assume the particle definitely went through one slit or another is that if you calculate the probability of the particle hitting the detector at a particular location by doing a path integral where you integrate over paths that go through both slits, you'll get a different answer than if you calculated (probability particle hits detector when you integrate over only paths going through first slit) + (probability particle hits detector when you integrate over only paths going through the second slit).
I have no problem with the wave going through both slits. We see the interference lines.

This is different from a classical situation like a ball going through one of two slits and hitting a wall, where you could indeed assume the probability the ball hits the wall at a particular spot is given by (probability ball hits that spot if it goes through first slit) + (probability ball hits that spot if it goes through second slit).
Yes, it is.

So the question is, suppose you open the box containing Schroedinger's cat after some time, and you want to know the probability you'll find it in some exact quantum state A: can you assume the probability of finding it in this state is given by (probability system is in state A when you sum over paths where photon was emitted and cat died) + (probability system is in state A when you sum over paths where photon was not emitted and cat lived)? It may be that if you open it shortly after the photon was or wasn't emitted, then no matter what happened you'll be able to tell unambiguously whether it was or wasn't in retrospect (because the cat clearly was or wasn't poisoned), so you can indeed sum the probabilities that way just like you could in the double-slit experiment if you had a detector which made an unambiguous measurement of which slit the particle went through. But suppose you waited a billion years to open the box, and that by the time you opened it the matter making up the cat and poison had gone to a state of maximum entropy, so there was no record of whether the cat had or hadn't been poisoned? In this case I think you really would need to sum over all possible paths to get the probability that you'd find it in some particular quantum state A, so you couldn't say that the cat had definitely either been poisoned or not poisoned all those years ago, just like you couldn't say which slit the particle went through in the double-slit experiment when you had no measuring-device at the slits (at least, not in the Copenhagen interpretation; as I said in a previous post, I think Bohm's interpretation would say there was a definite answer to these questions, even though you couldn't determine it).
I can't observe the billion year scenario at all, so I'll stick with my intuition (and Schrodinger's) that the radioactive decay occurs when it occurs and the cat dies when the radioactive decay occurs regardless of any formalism of any kind. I don't know Bohm's interpretation, but I'm happy for you to explain it.

Particles are theoretical fictions. Even classical particles are theoretical fictions. Matter does not exist at a point and isn't realistically described with only six degrees of freedom in three dimensions. An electron is not a particle, and it is not a classical wave either. It is neither of these and something else. When a cathode ray passes through double slits, we get an interference pattern we expect from a wave, but the same ray behaves like a stream of charged particles in an electric field.

A cat is not like this.
 

JesseM

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Particles are theoretical fictions. Even classical particles are theoretical fictions. Matter does not exist at a point and isn't realistically described with only six degrees of freedom in three dimensions. An electron is not a particle, and it is not a classical wave either. It is neither of these and something else. When a cathode ray passes through double slits, we get an interference pattern we expect from a wave, but the same ray behaves like a stream of charged particles in an electric field.

A cat is not like this.
But the Schroedinger's cat experiment is only a thought-experiment in the first place--if you're concerned about realism, then you should just point out that decoherence makes it impossible in practice to isolate the cat from the outside environment even briefly. But this is a bit like saying that since we can't do experiments at the planck scale, we should just ignore the whole issue of quantum gravity. Theorists are interested in how nature works in the most fundamental way, so the question of whether the cat would be alive or dead if it were possible to fully isolate it from the outside world (a practical impossibility at present, but not a theoretical impossibility) is of interest to them. And if you conclude the cat wasn't alive or dead in the scenario where you wait a billion years, then unless you believe the cat's state can somehow "anticipate" how soon you'll open the box, you should be forced to conclude it wasn't alive or dead in the scenario where you opened the box more quickly.

Anyway, as I suggested above, if large quantum computers ever become possible, one could probably design an experiment analogous to the "waiting for the cat to go to maximum entropy" experiment--an experiment where the outcome of a single event such as the photon emission has a large-scale effect on some other complex entangled system simulated by the computer, but where if you wait a certain time before measuring the system then it will no longer contain a "record" of the event.
 
But the Schroedinger's cat experiment is only a thought-experiment in the first place--if you're concerned about realism, then you should just point out that decoherence makes it impossible in practice to isolate the cat from the outside environment even briefly.
Realism is not the issue. Schrodinger developed his theory to describe quantum mechanical systems like the hydrogen atom, not cats. A cat is not a system confined to discrete energy states. A cat does not absorb or emit quanta. It's not a quantum mechanical system at all. The whole idea of applying Schrodinger's theory to this scenario is ridiculous, according to Schrodinger.

But this is a bit like saying that since we can't do experiments at the planck scale, we should just ignore the whole issue of quantum gravity. Theorists are interested in how nature works in the most fundamental way, so the question of whether the cat would be alive or dead if it were possible to fully isolate it from the outside world (a practical impossibility at present, but not a theoretical impossibility) is of interest to them.
It's not a scientific question. No one can perform your billion year experiment, but I can close a cat in a box with a geiger counter and the rest and open the box an hour later. If the cat is dead, I may conclude that a decay occured sometime before I opened the box. This conclusion does not offend Schrodinger, and it doesn't violate his Quantum Mechanics.

And if you conclude the cat wasn't alive or dead in the scenario where you wait a billion years, then unless you believe the cat's state can somehow "anticipate" how soon you'll open the box, you should be forced to conclude it wasn't alive or dead in the scenario where you opened the box more quickly.
I conclude that I don't know whether the cat is alive or dead before opening the box in the scenario where I open the box more quickly. I can reach the same conclusion without waiting a billion years.

Anyway, as I suggested above, if large quantum computers ever become possible, one could probably design an experiment analogous to the "waiting for the cat to go to maximum entropy" experiment--an experiment where the outcome of a single event such as the photon emission has a large-scale effect on some other complex entangled system simulated by the computer, but where if you wait a certain time before measuring the system then it will no longer contain a "record" of the event.
If you say so.
 

JesseM

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Realism is not the issue. Schrodinger developed his theory to describe quantum mechanical systems like the hydrogen atom, not cats. A cat is not a system confined to discrete energy states. A cat does not absorb or emit quanta. It's not a quantum mechanical system at all. The whole idea of applying Schrodinger's theory to this scenario is ridiculous, according to Schrodinger.
If one is a reductionist, then the behavior of macroscopic systems should just be the product of all the interactions between its component particles. Most physicists are reductionists in this sense. Would you propose new fundamental laws to describe the behavior of large systems? Where would the cutoff be? Would there be a maximum number of particles that can be in a system and have it still obey the laws of quantum mechanics, and adding a single extra particle would cause it to stop obeying these laws?
Martin Brock said:
It's not a scientific question. No one can perform your billion year experiment
Are you really arguing that experiments which are not practical to perform today cannot be the subject of science? Is the the question of what happens to an observer falling into a black hole "not a scientific question", for example? I don't think you would find many theorists who'd agree with this philosophy.
JesseM said:
And if you conclude the cat wasn't alive or dead in the scenario where you wait a billion years, then unless you believe the cat's state can somehow "anticipate" how soon you'll open the box, you should be forced to conclude it wasn't alive or dead in the scenario where you opened the box more quickly.
Martin Brock said:
I conclude that I don't know whether the cat is alive or dead before opening the box in the scenario where I open the box more quickly. I can reach the same conclusion without waiting a billion years.
You misunderstood, when I said "if you conclude the cat wasn't alive or dead in the scenario where you wait a billion years", I wasn't talking about whether you know if the cat was alive or dead, I was talking about the question of whether the cat was ever in a single definite state at all, analogous to the question of whether the particle in the double-slit experiment ever went through one of the slits (which is a separate question from whether, even if it did, you know which one it went through). Again, the conclusion of the billion-year thought-experiment was that you couldn't assume it had been definitely alive or definitely dead in the past, because when you open the box and measure the system inside, the probability it is in a given quantum state A would not be equal to the sum (probability system is in state A when you sum over paths where photon was emitted and cat died) + (probability system is in state A when you sum over paths where photon was not emitted and cat lived). As always, in the thought-experiment the inside of the box is perfectly insulated from the outside world so there is no environmental decoherence, the system inside would be described by a single complicated entangled pure state. Few physicists would say the laws of physics fundamentally forbid such an experiment, even if it's far beyond our practical abilities.
 
If one is a reductionist, then the behavior of macroscopic systems should just be the product of all the interactions between its component particles. Most physicists are reductionists in this sense. Would you propose new fundamental laws to describe the behavior of large systems? Where would the cutoff be? Would there be a maximum number of particles that can be in a system and have it still obey the laws of quantum mechanics, and adding a single extra particle would cause it to stop obeying these laws?
The cat obeys Quantum Mechanics. Any uncertainty in the cat's position and momentum, for example, is negligible. If I open the door and find the cat dead, the only Quantum Mechanical system of any significance is a decaying atom. Opening the door has nothing to do with the atom's decay. The atom either has decayed or it hasn't, and the cat is either fully dead or fully alive, before I open the door. I don't know the state of the atom or the cat before opening the door. Opening the door removes the uncertainty, but it doesn't cause any change in the state of the relevant quantum mechanical system. Opening the door changes the state of my knowledge of the system.

Are you really arguing that experiments which are not practical to perform today cannot be the subject of science?
These experiments are fair game for theoretical speculation. You described an experiment that is fundamentally impossible to perform ever, because I must wait a billion years to conclude the experiment. I'm happier discussing some other experiment. Call me an obsessive experimentalist.

Is the the question of what happens to an observer falling into a black hole "not a scientific question", for example?
It's not a scientific question at this point, because I can't falsify anything you say about it. We can talk about observers outside of black holes observing things falling into black holes, and we can speculate about observers falling into black holes if we enjoy the pastime.

I don't think you would find many theorists who'd agree with this philosophy. You misunderstood, when I said "if you conclude the cat wasn't alive or dead in the scenario where you wait a billion years", I wasn't talking about whether you know if the cat was alive or dead, I was talking about the question of whether the cat was ever in a single definite state at all, analogous to the question of whether the particle in the double-slit experiment ever went through one of the slits (which is a separate question from whether, even if it did, you know which one it went through).
I'm talking about whether I know if the cat is alive or dead.

Again, the conclusion of the billion-year thought-experiment was that you couldn't assume it had been definitely alive or definitely dead in the past, because when you open the box and measure the system inside, the probability it is in a given quantum state A would not be equal to the sum (probability system is in state A when you sum over paths where photon was emitted and cat died) + (probability system is in state A when you sum over paths where photon was not emitted and cat lived).
You're right. I can't know that the cat dies of radioactive decay induced poisoning (rather than starvation) if I wait a billion years. What I know is that either it did or it didn't. I don't need to wait a billion years to reach this indeterminate conclusion. A few weeks is sufficient. I can monitor the cat's heart from outside the box and only look at the monitor after a few weeks without opening the box to reveal the state of the geiger counter and poison. This scenario leaves me in the same state of uncertainty as your scenario. Can you tell me specifically what path integral to perform to reach this conclusion? Don't worry about confusing me with the mathematics.

As always, in the thought-experiment the inside of the box is perfectly insulated from the outside world so there is no environmental decoherence, the system inside would be described by a single complicated entangled pure state. Few physicists would say the laws of physics fundamentally forbid such an experiment, even if it's far beyond our practical abilities.
The laws of physics forbid me to wait for the heat death of the universe to complete an experiment. My descendants can't complete it for me either, because their fate is the same as the cat's, according to Solomon.

I declare categorically that my classical system is far more illustrative of the essential elements of Schrodinger's thought experiment than anything we're discussing now. I wish Schrodinger himself could comment, but unfortuately, his fate is also the same as the cat's.
 
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ZapperZ

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I declare categorically that my classical system is far more illustrative of the essential elements of Schrodinger's thought experiment than anything we're discussing now. I wish Schrodinger himself could comment, but unfortuately, his fate is also the same as the cat's.
And I declare categorically that your classical system has NOTHING to do with the Schrodinger Cat/Superposition illustration of QM. Again, if you believe that it is so, submit it to AJP or EJP for publication. If not, I consider this as a misinformation. We have allowed this "discussion" to go on long enough. If you wish to further pursue this on PF, please do so in the Independent Research forum, per our guidelines.

Zz.
 

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