Undergrad About nature of superposition of states

[gentzen]

Apologies to everyone for insisting on this thread. I would like to shed some light on this point.
...
How can the phrase "both dead and alive" be a synonym for "a superposition of two states, dead or alive"? Is the inherent formulation of this thought experiment correct? And what role does superposition play?

Thanks, now I see where you see the connection between mixed states and Schroedinger's cat.

After I learned about partial coherence in optics and how to handle it (as part of my job), I started to suspect that this might be the key for me personally to make sense of all those "the ψ-function represents knowledge" explanations of the Copenhagen interpretation. Which was not wrong, but in the end it was also my job that later forced me to really learn QM. It is a monumental time investment and constant source of frustration, because there is just so much stuff to learn.

 

[HighPhy]

The important point is that an electron is not a cat. And "alive" and "dead" are not fundamental quantum properties like spin. In the sense that, within reason, simply observing a cat doesn't cause the cat to assume a state of alive and dead.

I reformulate. Many sources I read said that the superposition means that the cat is both alive "and" dead. But AFAIK, the addition in the wave function doesn't mean "and". The way I learned it, it means a sort of "or", so the superposition should say that the cat is dead or alive, with the appropriate probabilities. Is this correct? I'd like to figure out if and where I'm going wrong.

I've also read that " Schroedinger was wrong because quantum mechanics does imply that such superpositions are totally allowed and must be allowed and this fact can be experimentally verified – not really with cats but with objects of a characteristic size that has been increasing". And that "macroscopic objects have already been put to similar "general superposition states" and from a scientifically valid viewpoint, the thought experiment shows that superpositions are indeed always allowed – it is a postulate of quantum mechanics – even if such states are counterintuitive." Is this point of view correct?

This is the source of my confusion. Many sources say that "the cat is in a state that is a superposition of our "life states" alive and dead" means "the cat is both alive and dead" until we open the box.

Other sources say that Schrodinger's cat is not both dead and alive any more than an electron simultaneously exists at every point in space, also because a system cannot be in multiple states at once. So Schrodinger's cat would be always in a single state: there would be an equal probability of us "measuring" the cat to be either alive or dead once we open the box. Therefore, "the cat is in a state that is a superposition of our "life states" alive and dead" would not mean that "the cat is both alive and dead" until we open the box, because is in a single state, and this state is described as a superposition of life states.

I'm not speculating on any theory, I am just very confused. I'm describing some of the interpretations I read because I would like to see more clearly about which one is the most appropriate and reliable.

All this I say despite the fact that I am still aware that the cat represents a classical system. Therefore it does not behave like an electron. My question was not addressing so much Schroedinger's purpose (criticizing the Copenhagen interpretation) and the absurdity to which he wants to lead us. It was directed at the interpretation of "both alive and dead" and "superposition."

The reason that the same formalism does not applies to cats

If we have a pure spin-1/2 state $\vert \hat n\rangle$, then we can always find some linear combination of spin operators $\sigma_{\hat n}$ with $\vert \hat n\rangle$ as an eigenvector. Thus, it makes perfect sense to think of $\vert \hat n\rangle$ as a single state, which can be expanded in a basis of eigenstates of $\sigma_z$ so that
$$
\vert \hat n\rangle = \cos\left(\textstyle\frac{\theta}{2}\right)\vert +\rangle_z + e^{i\phi}\sin\left(\textstyle\frac{\theta}{2}\right)
\vert -\rangle_z\, , \tag{1}
$$
for some $\theta$ and $\phi$. Whether one chooses to describe $(1)$ as a state that is spin-up and spin-down (with suitable probabilities) until one makes a measurement with $\sigma_z$, or as a single quantum state expanded on two basis states is a matter of semantics: both description will lead to the same results. If we measure $\sigma_z$: some of the time the outcome will be spin-up, some of the time the outcome will be spin-down. Moreover, if we measure in the direction $\hat n$, there will be a single outcome.

Of course, things are different for a cat. There is no "cat" operator $\sigma_{\hbox{cat}}$ with eigenstate
$$
\vert\hbox{cat}\rangle= \cos\left(\textstyle\frac{\theta}{2}\right)\vert \hbox{dead}\rangle + e^{i\phi}\sin\left(\textstyle\frac{\theta}{2}\right)
\vert \hbox{alive}\rangle\, . \tag{2}
$$
The sense of the superposition $(2)$ as a single quantum state eigenstate of a non-existent $\sigma_{\hbox{cat}}$ operator, and thus analog of $\vert \hat n\rangle$ is rather abstract, but maybe the sense of the superposition of alive and dead cat could be clear as a generalization of the right hand side of $(1)$ (??).

Does this description fit?

 

[PeroK]

@HighPhy it would be better if we understood where you are learning QM? Are you a university student?

 

[HighPhy]

@HighPhy Are you a university student?

Yes.

 

[PeroK]

Yes.

Then, forget Schrodinger's cat and learn the QM you need for your course. IMO, you need to immerse yourself in QM and forget the macroscopic world for the time being. The objective is to retrain your understanding of nature to include non-classical concepts. The more you focus on the macroscopic world, the less you focus on QM.

I would treat all popular sources as a distraction.

 

[Nugatory]

Many sources I read said that the superposition means that the cat is both alive "and" dead. But AFAIK, the addition in the wave function doesn't mean "and". The way I learned it, it means a sort of "or", so the superposition should say that the cat is dead or alive, with the appropriate probabilities. Is this correct? I'd like to figure out if and where I'm going wrong.

You are going wrong in your choice of sources.
If you want to understand the cat, your source should either be Schrodinger - the cat is just one paragraph in a longer paper - or one that presents the cat with the necessary historical context. Any popularization that fails to make clear that Schrodinger's cat is of more interest to historians than physicists is misleading and should be ignored. There are serious foundational problems in quantum mechanics, but apparent predictions of dead/alive cats are no longer one of these.

Some of the difficulty with the popular discussions of superposition is that they're trying to substitute natural language for the mathematical formalism, and natural language just is not up to the task. You are right that "and" is a poor description but "or" is no better - one way of seeing this is that "neither...nor" is no less reasonable than "and" or "or", as in "the cat is neither alive nor dead" instead of "the cat is both alive and dead" or "the cat is either alive or dead".

That last statement - "either alive or dead" - does fairly describe a mixed state, one that we now understand will be reached by decoherence as the wave function evolves. That resolves Schrodinger's challenge to the 1920's-vintage Copenhagen interpretation but it doesn't do anything for the popular understanding of superimposed states - it's not the result of addition in the wave function.

 

[PeterDonis]

This seems to me a misrepresentation of this thought experiment, typical of bad pop-science.

It is, but not for the reason you give. The reason it is a misrepresentation is that the cat will decohere itself, so that it is "either dead or alive" and not "a superposition of dead and alive" long before you open the box. But even that isn't really correct; see further comments below on the limitations of ordinary language.

How can the phrase "both dead and alive" be a synonym for "a superposition of two states, dead or alive"?

No phrase in ordinary language is really a good representation of the state of the cat after the radioactive atom decays but before decoherence takes place. That's why physicists use math.

what role does superposition play?

"Superposition" is actually a misnomer in this case. The key property is entanglement: the cat is entangled with the radioactive atom, so that neither one has a definite state at all; only the joint system containing both of them does. Mathematically, the joint state looks like (ignoring normalization):

$$
\ket{\text{atom decayed}} \ket{\text{cat dead}} + \ket{\text{atom not decayed}} \ket{\text{cat alive}}
$$

Many pop science sources will describe the cat as being "in a superposition of dead and alive", but that is not really correct. The cat is entangled with the atom; that is the correct description (or at least the best you can do in ordinary language). The ordinary language phrase "superposition of dead and alive" would describe a cat state that looked like this (again ignoring normalization):

$$
\ket{\text{cat dead}} + \ket{\text{cat alive}}
$$

In other words, not entangled with anything else, just not an eigenstate of the "dead/alive" operator.

As for decoherence, that is what limits the entangled state I wrote above to only two terms; in other words, it eliminates terms like $\ket{\text{atom decayed}} \ket{\text{cat alive}}$ and $\ket{\text{atom not decayed}} \ket{\text{cat dead}}$. Terms like that are often called "interference terms" and decoherence is said to eliminate interference.

 

[PeroK]

And the first step for a physics student is to really understand how quantum interference works. There are a couple of recent threads in the homework forum where a student was wrestling with this for the first time. In the context of the simple, idealised infinite square well. There's no substitute for seeing non-classical behaviour emerge from the basic premises and mathematics of QM. You can't burrow down to QM by starting with cats and seeing QM through the lens of classical behaviour. You have to learn the basics of QM and then start to see classical behaviour though the lens of QM.

 

[HighPhy]

Some of the difficulty with the popular discussions of superposition is that they're trying to substitute natural language for the mathematical formalism, and natural language just is not up to the task. You are right that "and" is a poor description but "or" is no better - one way of seeing this is that "neither...nor" is no less reasonable than "and" or "or", as in "the cat is neither alive nor dead" instead of "the cat is both alive and dead" or "the cat is either alive or dead".

I completely agree. I couldn't have said it better myself.

I'd like to share my understanding as to whether I am going in the right direction or not. I may be wrong: that is why I'm asking you to correct me.

I had said that "both dead and alive" is wrong, and that "dead or alive" is better for two reasons.

1) AFAIK, it is not true that both states exist and influence the evolution of the system. Instead, it is unknown which properties the cat has. When the cat is measured to be dead, it follows that the orthogonal state "alive" is gone and has never influenced anything at all: the possibility didn't exist at all.

2) The word "or" is a preposition and it in no way implies any "objective sense" or classical physics. Prepositions like "or" only have a logical sense - they're tools to create composite propositions that have a truth value. But the truth value isn't objective. According to quantum mechanics, it depends on the things that are assumed - the previous observations of the observer. The translation of such propositions to mathematics must be done carefully and in quantum mechanics, one must specify the relative phases etc. which aren't determined by the sentence with "or".

How close did I come to the truth?

 

[HighPhy]

And the first step for a physics student is to really understand how quantum interference works. There are a couple of recent threads in the homework forum where a student was wrestling with this for the first time. In the context of the simple, idealised infinite square well. There's no substitute for seeing non-classical behaviour emerge from the basic premises and mathematics of QM. You can't burrow down to QM by starting with cats and seeing QM through the lens of classical behaviour. You have to learn the basics of QM and then start to see classical behaviour though the lens of QM.

What you say is reasonable and is very good advice. In my defense, however, I can say that QM is just for fun; it is not yet the subject of my studies.

 

[Nugatory]

How close did I come to the truth?

About as close as you can get with natural language, as opposed to writing down a density matrix.

But that's not very close. When we use "or" to describe a superposition state we lose the distinction between that state and a mixed state and with it any sense of what a superposition is.

 

[PeterDonis]

AFAIK, it is not true that both states exist and influence the evolution of the system.

That depends on which QM interpretation you use. In the MWI, for example, there is no collapse, so both branches of the wave function, the "dead" branch and the "alive" branch, exist and continue to evolve.

 

[HighPhy]

"Superposition" is actually a misnomer in this case. The key property is entanglement: the cat is entangled with the radioactive atom, so that neither one has a definite state at all; only the joint system containing both of them does. Mathematically, the joint state looks like (ignoring normalization):

$$
\ket{\text{atom decayed}} \ket{\text{cat dead}} + \ket{\text{atom not decayed}} \ket{\text{cat alive}}
$$

Many pop science sources will describe the cat as being "in a superposition of dead and alive", but that is not really correct. The cat is entangled with the atom; that is the correct description (or at least the best you can do in ordinary language). The ordinary language phrase "superposition of dead and alive" would describe a cat state that looked like this (again ignoring normalization):

$$
\ket{\text{cat dead}} + \ket{\text{cat alive}}
$$

In other words, not entangled with anything else, just not an eigenstate of the "dead/alive" operator.

As for decoherence, that is what limits the entangled state I wrote above to only two terms; in other words, it eliminates terms like $\ket{\text{atom decayed}} \ket{\text{cat alive}}$ and $\ket{\text{atom not decayed}} \ket{\text{cat dead}}$. Terms like that are often called "interference terms" and decoherence is said to eliminate interference.

This explanation is excellent.

So, is it fair to say that the cat is in an "entangled superposition of dead and alive" until the box is opened; that is, for as long as it remains closed? And that when the box is opened, is the cat dead or alive?

What I didn't understand is the role of the collapse of the wave function. Why should collapse occur when the box is opened?
And in general, what role does the collapse of the wave function play in this thought experiment?

 

[mattt]

This explanation is excellent.

So, is it fair to say that the cat is in an "entangled superposition of dead and alive" until the box is opened; that is, for as long as it remains closed? And that when the box is opened, is the cat dead or alive?

What I didn't understand is the role of the collapse of the wave function. Why should collapse occur when the box is opened?
And in general, what role does the collapse of the wave function play in this thought experiment?

Because there's no way to get from:

(Atom decayed)x(cat dead) + (atom not decayed)×(cat alive)

to:

(Atom decayed)x(cat dead)

Or from:

(Atom decayed)x(cat dead) + (atom not decayed)×(cat alive)

to:

(atom not decayed)×(cat alive)

by means of Schrodinger Equation.

 

[PeterDonis]

is it fair to say that the cat is in an "entangled superposition of dead and alive" until the box is opened; that is, for as long as it remains closed?

Not if you then say this...

And that when the box is opened, is the cat dead or alive?

As far as the basic math of QM is concerned, once decoherence has happened, the measurement has a result. You might not know what the result is until you open the box, but that doesn't mean the result doesn't happen until you open the box. It happens as soon as decoherence happens (and the decoherence time for an object like a cat is very, very short).

What different interpretations of QM disagree on is what "the measurement has a result" means. Collapse interpretations say it means the wave function has actually, physically collapsed to a single result: i.e., the two terms in the decoherent entangled superposition of dead and alive have become one, either the dead term or the alive term.

No collapse interpretations, such as the MWI, say that both results happen, just in different branches of the wave function. What happens when you open the box in these interpretations is that you now become part of the entangled superposition; a ket representing your observation becomes part of each term.

So on a no collapse interpretation, your first statement quoted above would be true, but your second would be false: the entangled superposition doesn't go away when you open the box. On a collapse interpretation, your second statement quoted above would be true, but your first one would be false: the entangled superposition goes away as soon as decoherence happens, because a collapse interpretation says that the actual, physical collapse happens when decoherence happens.

In other words, there is no interpretation under which both of your quoted statements are true.

 

[HighPhy]

Not if you then say this...


As far as the basic math of QM is concerned, once decoherence has happened, the measurement has a result. You might not know what the result is until you open the box, but that doesn't mean the result doesn't happen until you open the box. It happens as soon as decoherence happens (and the decoherence time for an object like a cat is very, very short).

What different interpretations of QM disagree on is what "the measurement has a result" means. Collapse interpretations say it means the wave function has actually, physically collapsed to a single result: i.e., the two terms in the decoherent entangled superposition of dead and alive have become one, either the dead term or the alive term.

No collapse interpretations, such as the MWI, say that both results happen, just in different branches of the wave function. What happens when you open the box in these interpretations is that you now become part of the entangled superposition; a ket representing your observation becomes part of each term.

So on a no collapse interpretation, your first statement quoted above would be true, but your second would be false: the entangled superposition doesn't go away when you open the box. On a collapse interpretation, your second statement quoted above would be true, but your first one would be false: the entangled superposition goes away as soon as decoherence happens, because a collapse interpretation says that the actual, physical collapse happens when decoherence happens.

In other words, there is no interpretation under which both of your quoted statements are true.

I'll try to fix my mistake.

The cat is in an entangled superposition of dead and alive until decoherence occurs. From then on, the cat is either dead or alive, and although we cannot know, the measurement has a definite result. When we open the box, we observe the result of the measurement: the cat is either alive or dead.

From this I can also infer that the view proposed by many pop-science journalistic articles that the collapse of the wave function occurs as soon as we open the box is false.

Is my view now correct?

Finally, I wanted to point out a kind of discomfort. AFAIK, the phenomenon of decoherence was not known in 1935 (when Schroedinger thought up this thought experiment). My question arises: apart from Schroedinger's intent (to expose the absurdity of CI), had Schroedinger designed the experiment so that the cat was in an "entangled superposition of dead and alive" until the box was opened, and at that moment the cat could have been either dead or alive?

 Please correct me if I'm going wrong.

 

[PeterDonis]

The cat is in an entangled superposition of dead and alive until decoherence occurs. From then on, the cat is either dead or alive, and although we cannot know, the measurement has a definite result. When we open the box, we observe the result of the measurement: the cat is either alive or dead.

With the caveats I gave before about what "the measurement has a definite result" actually means for different QM interpretations, yes, this is fine.

From this I can also infer that the view proposed by many pop-science journalistic articles that the collapse of the wave function occurs as soon as we open the box is false.

There are (or perhaps were) interpretations where "collapse of the wave function" is claimed to only be induced by human observers. But such interpretations have very few adherents now. I didn't include them in my survey of interpretations in my previous post.

As far as the basic math of QM goes, where "collapse" is just a mathematical procedure where you update the wave function once you know the result of a measurement, obviously you don't know the result of the measurement until you open the box, so you wouldn't actually make the update to the wave function until then. But that says nothing whatever about any physical process that does or does not happen at any particular time.

The writers of pop science articles most likely are not familiar with any of these nuances, and so it's probably fair to say that whatever they actually have in mind for "collapse" does not correspond to anything in any actual QM model or interpretation.

AFAIK, the phenomenon of decoherence was not known in 1935 (when Schroedinger thought up this thought experiment).

That's correct. Decoherence did not become a recognized area of QM theory until the late 1970s and early 1980s.

apart from Schroedinger's intent (to expose the absurdity of CI), had Schroedinger designed the experiment so that the cat was in an "entangled superposition of dead and alive" until the box was opened, and at that moment the cat could have been either dead or alive?

I don't think you can usefully say anything about the design of Schrodinger's thought experiment without talking about Schrodinger's intent.

 

[Nugatory]

From this I can also infer that the view proposed by many pop-science journalistic articles that the collapse of the wave function occurs as soon as we open the box is false.

Yes, the pop-sci view is wrong. At best, it is decades out of date, invalidated by the discovery of decoherence more than a half-century of ago. And that’s “at best” - there was never a time when many physicists were not deeply skeptical of that notion.
(And I’m running out of ways of saying “The pop-sci is wrong).

My question arises: apart from Schroedinger's intent (to expose the absurdity of CI), had Schroedinger designed the experiment so that the cat was in an "entangled superposition of dead and alive" until the box was opened, and at that moment the cat could have been either dead or alive?

There’s no “apart” here - that’s why he designed the thought experiment the way he did.

 

[HighPhy]

I don't think you can usefully say anything about the design of Schrodinger's thought experiment without talking about Schrodinger's intent.

There’s no “apart” here - that’s why he designed the thought experiment the way he did.

Sorry, I didn't catch the connection.

Could you please explain the connection between the design of Schrodinger's thought experiment and Schrodinger's intent?

 

[PeterDonis]

Could you please explain the connection between the design of Schrodinger's thought experiment and Schrodinger's intent?

Um, that Schrodinger designed the thought experiment the way he did because of his intent? Isn't that what "his intent" means?

 

[Lord Jestocost]

From this I can also infer that the view proposed by many pop-science journalistic articles that the collapse of the wave function occurs as soon as we open the box is false.

The wave function is mathematically defined in an abstract vector space and not in a real physical space. So to make the collapse of the wave function a real physical process, an abstract vector space would have to be transformed into real physical space.
The wave function collapse is thus not an actual physical event but represents the change that occurs in our knowledge when we become aware of the result of a measurement. It’s completely misleading to assume that the wave function $\Psi$ is a representation of some reality behind the phenomena. $\Psi$ is nothing but a catalog of knowledge that follows from one observed fact and which determines the probabilities for possible future events.

 

[HighPhy]

Um, that Schrodinger designed the thought experiment the way he did because of his intent? Isn't that what "his intent" means?

Sorry, I formulated my concept incorrectly.

What I would like to know are the particular implications of Schroedinger's experiment by virtue of its intent. That is: how is the state of the cat conceived before and after the box is opened (and during the process) by Schroedinger, given the impossibility of resorting to the decoherence principle in 1935? Put another way, I would like to understand in what terms and by what devices Schroedinger wanted to discredit the CI with his experiment, and whether he was in a sense right.

Also because, in the original paper to which @Nugatory referred me, it is said:

It is typical of these cases that an indeterminacy originally restricted to the atomic
domain becomes transformed into macroscopic indeterminacy, which can then be
resolved by direct observation. That prevents us from so naively accepting as valid a
"blurred model" for representing reality. In itself it would not embody anything unclear
or contradictory.

But according to the following:

I've also read that "Schroedinger was wrong because quantum mechanics does imply that such superpositions are totally allowed and must be allowed and this fact can be experimentally verified – not really with cats but with objects of a characteristic size that has been increasing". And that "macroscopic objects have already been put to similar "general superposition states" and from a scientifically valid viewpoint, the thought experiment shows that superpositions are indeed always allowed – it is a postulate of quantum mechanics – even if such states are counterintuitive."

Is this point of view correct?

It would be my interest to understand more deeply the mechanism of superposition in this perspective.

Moreover:

If we have a pure spin-1/2 state $\vert \hat n\rangle$, then we can always find some linear combination of spin operators $\sigma_{\hat n}$ with $\vert \hat n\rangle$ as an eigenvector. Thus, it makes perfect sense to think of $\vert \hat n\rangle$ as a single state, which can be expanded in a basis of eigenstates of $\sigma_z$ so that
$$
\vert \hat n\rangle = \cos\left(\textstyle\frac{\theta}{2}\right)\vert +\rangle_z + e^{i\phi}\sin\left(\textstyle\frac{\theta}{2}\right)
\vert -\rangle_z\, , \tag{1}
$$
for some $\theta$ and $\phi$. Whether one chooses to describe $(1)$ as a state that is spin-up and spin-down (with suitable probabilities) until one makes a measurement with $\sigma_z$, or as a single quantum state expanded on two basis states is a matter of semantics: both description will lead to the same results. If we measure $\sigma_z$: some of the time the outcome will be spin-up, some of the time the outcome will be spin-down. Moreover, if we measure in the direction $\hat n$, there will be a single outcome.

Of course, things are different for a cat. There is no "cat" operator $\sigma_{\hbox{cat}}$ with eigenstate
$$
\vert\hbox{cat}\rangle= \cos\left(\textstyle\frac{\theta}{2}\right)\vert \hbox{dead}\rangle + e^{i\phi}\sin\left(\textstyle\frac{\theta}{2}\right)
\vert \hbox{alive}\rangle\, . \tag{2}
$$
The sense of the superposition $(2)$ as a single quantum state eigenstate of a non-existent $\sigma_{\hbox{cat}}$ operator, and thus analog of $\vert \hat n\rangle$ is rather abstract, but maybe the sense of the superposition of alive and dead cat could be clear as a generalization of the right hand side of $(1)$ (??).

Does this description fit?


However, I realized that the question I asked a few hours ago was simply pointless, poorly worded and at times stupid.
It was late, and tiredness caused me to get ahead of myself. I offer my apologies if I gave the impression that I wasted your time.

 

[gentzen]

And that "macroscopic objects have already been put to similar "general superposition states" and from a scientifically valid viewpoint, the thought experiment shows that superpositions are indeed always allowed

A cat is not just a macroscopic object, but it is also quite hot, compared to absolute zero. Those "macroscopic objects" that have been put to similar "general superposition states" had been cooled to nearly absolute zero.

You have to do this, otherwise the decoherence times are simpy too short (to allow to measure anything interesting).

 

[vela]

I think you're suffering from the problem every physics student seems to go through when first encountering quantum mechanics: you're trying to make sense of the theory in terms of everyday, classical ideas. That's a fool's errand since you're supposed to make sense of classical mechanics in terms of quantum mechanics, which is the more general theory.

It's like trying to understand special relativistic effects in terms of Newtonian mechanics. How can there be a maximum speed in the universe? How can two clocks seem to run at different rates? Objects get shorter when they're moving? That can't be right! It must be some sort of illusion! In contrast, if you understand special relativity, it's straightforward to see that Newtonian mechanics is simply what the theory predicts at low speeds.

It's probably best, as @PeroK advised earlier, to forget the Schrödinger's cat nonsense for now and concentrate on learning the basics of quantum mechanics. Or at least, recognize Schrödinger's cat as a fun diversion to think about, but don't put too much effort into trying to make it make sense until you're in a better position to do so.

 

[PeterDonis]

It’s completely misleading to assume that the wave function $\Psi$ is a representation of some reality behind the phenomena. $\Psi$ is nothing but a catalog of knowledge that follows from one observed fact and which determines the probabilities for possible future events.

This depends on which interpretation of QM you adopt. There are interpretations that treat $\Psi$ as a direct representation of physical reality.

 

[PeterDonis]

how is the state of the cat conceived before and after the box is opened (and during the process) by Schroedinger

In other words, you do want to talk about Schrodinger's intent, because Schrodinger's intent was to describe a thought experiment that he believed showed the absurdity of applying the Schrodinger equation to obtain an entangled superposition involving a cat. In other words, he was using the thought experiment to demonstrate that QM had to be an incomplete theory.

 

[PeterDonis]

I've also read that " Schroedinger was wrong because quantum mechanics does imply that such superpositions are totally allowed and must be allowed and this fact can be experimentally verified – not really with cats but with objects of a characteristic size that has been increasing".

"Read" where? Please give specific references.

As a general comment, experiments that are claimed to show "superpositions" of this sort have one crucial feature: maintaining coherence. In other words, these are not decoherent entangled superpositions of the kind we have been discussing and which are involved in a scenario like Schrodinger's cat. They are just scenarios like the double slit experiment, where, if we are very, very careful about shielding the system from decoherence for as long as possible, we can detect interference effects.

 

[PeterDonis]

There is no "cat" operator $\sigma_{\hbox{cat}}$ with eigenstate
$$
\vert\hbox{cat}\rangle= \cos\left(\textstyle\frac{\theta}{2}\right)\vert \hbox{dead}\rangle + e^{i\phi}\sin\left(\textstyle\frac{\theta}{2}\right)
\vert \hbox{alive}\rangle\, . \tag{2}
$$

Says who? One common viewpoint on QM, which you will find even in textbooks, is that in principle every set of mutually orthogonal states are eigenstates of some Hermitian operator. It might just be extremely difficult in practice to physically realize such an operator.

 

[HighPhy]

In other words, you do want to talk about Schrodinger's intent, because Schrodinger's intent was to describe a thought experiment that he believed showed the absurdity of applying the Schrodinger equation to obtain an entangled superposition involving a cat.

Yes. As I said, I badly formulated the previous question and did not properly evaluate the inseparable connection between Schrodinger's intent and experiment design. I apologize again.

"Read" where? Please give specific references.

I read it a few years ago on the online blog of one Lubos Motl (when it was open to the public), an apparently renowned physicist, and jotted it down in my personal notebook because it attracted me.

I thought he might be a reliable source because this physicist also has some ArXiV submissions, but I am fully aware that his narrative might be biased, partial, and not adhering to the facts. That is why I asked in this thread for a judgment from those who know about it.

 

[HighPhy]

Many thanks to all who have contributed to the best of their abilities to enhance my knowledge.