Why exactly cannot cat be in a superposition state?

[Genady]

Just this question.

[J.C.MacSwell]

A full cat? My understanding is that it is highly unlikely...approaching but not reaching zero probability. (unlike the possibility that my understanding is wrong possibly approaching and reaching 100%)

Edited January 27, 2022 by J.C.MacSwell

[Genady]

Yes, like this:

|cat〉 = (1/√2)|dead〉 + (1/√2)|alive〉

[Markus Hanke]

Because a system the size of a cat cannot be isolated from its environment by any practical means. When you scale up a quantum system, you also scale up the degree by which it will undergo decoherence due to interactions with its environment. For a system the size of a cat, decoherence happens so quickly that any quantum effects become entirely negligible almost instantaneously (not that you could even establish such a superposition in the first place!). Colloquially put, the system’s quantumness - if there is any to begin with - bleeds out into the environment, and this happens the more quickly the bigger the system is.

In principle it is possible for such a superposition to exist, if you could somehow find a way to completely prevent the cat from interacting with its environment; in practice this is not possible by any conceivable means. Even superpositions in very small systems - like on atomic scales - are difficult to maintain for any length of time for this same reason; this is eg one of the fundamental issues in quantum computing.

[geordief]

5 minutes ago, Markus Hanke said:

Because a system the size of a cat cannot be isolated from its environment by any practical means. When you scale up a quantum system, you also scale up the degree by which it will undergo decoherence due to interactions with its environment. For a system the size of a cat, decoherence happens so quickly that any quantum effects become entirely negligible almost instantaneously (not that you could even establish such a superposition in the first place!). Colloquially put, the system’s quantumness - if there is any to begin with - bleeds out into the environment, and this happens the more quickly the bigger the system is.

In principle it is possible for such a superposition to exist, if you could somehow find a way to completely prevent the cat from interacting with its environment; in practice this is not possible by any conceivable means. Even superpositions in very small systems - like on atomic scales - are difficult to maintain for any length of time for this same reason; this is eg one of the fundamental issues in quantum computing.

Does the cat (any system) also  interact with itself ?

So you would have to seal off (compartmentalise)  every part of itself with every other part of itself before you could even consider isolating  it from its external  environment. 

 

Is any system not already its own environment?

[Genady]

1 hour ago, Markus Hanke said:

Because a system the size of a cat cannot be isolated from its environment by any practical means. When you scale up a quantum system, you also scale up the degree by which it will undergo decoherence due to interactions with its environment. For a system the size of a cat, decoherence happens so quickly that any quantum effects become entirely negligible almost instantaneously (not that you could even establish such a superposition in the first place!). Colloquially put, the system’s quantumness - if there is any to begin with - bleeds out into the environment, and this happens the more quickly the bigger the system is.

In principle it is possible for such a superposition to exist, if you could somehow find a way to completely prevent the cat from interacting with its environment; in practice this is not possible by any conceivable means. Even superpositions in very small systems - like on atomic scales - are difficult to maintain for any length of time for this same reason; this is eg one of the fundamental issues in quantum computing.

I am very happy to hear that in principle cat can be in a superposition state.

Next, I'd like to understand where / how a superposition state, e.g. (1/√2)|dead〉 + (1/√2)|alive〉, becomes an eigenstate, e.g. either |dead〉 or |alive〉.

I don't see a difficulty to establish such a superposition state in the first place, like this:

A photon source emits a single photon aimed at a beam-splitter, whereupon the photon’s state splits into a superposition of 2 parts, e.g. (1/√2)|left〉 + (1/√2)|right〉. In one of these, the photon encounters a detector, triggering a murderous weapon that kills the cat; in the other, the photon escapes and the cat lives. Unitary evolution results in a superposition of a dead and a live cat, (1/√2)|dead〉 + (1/√2)|alive〉.

Then the question becomes, what happens to such superposition next?

[studiot]

11 hours ago, Genady said:

Just this question.

Comments.

1)

An average cat has a mass of 4kg.
Most of this is water which has a molecular mass of 18g
Using this and applying a factor of 90% to account for the otherr, heavier molecules making up the cat we have the number of moles making up the cat as

[math]\frac{{4*{{10}^3}}}{{18}}*\frac{{90}}{{100}} = 200[/math]

Multiplying this by avogadro's number we have the number of molecules in the cat to be

[math]200*6*{10^{23}} \approx {10^{26}}[/math]

This means that to calculate a superposition we must have a system of simultaneous wavefunction equations of the order of 10²⁶ in number.

Does anyone know the largest set ever solved ?

 

2)

A superposition is not a single state since it does not have a unique solution.

So in asking for a defined state, what you are really asking is like asking for particular line parallel to a given one, without providing the necessary information to know which one.

 

3) Your calculation of probabilities is flawed.

Edited January 27, 2022 by studiot

[swansont]

In addition to studiot's observation above, is there a connection between the quantum states of the individual atoms and the condition of being alive or dead? 

[studiot]

Just now, swansont said:

In addition to studiot's observation above, is there a connection between the quantum states of the individual atoms and the condition of being alive or dead? 

 

Yes that is why I said the probability calculation is flawed.

I apologise for my first edit, but I see I am not the only one getting the quote instead of the edit by mistake.
I have put that right now.

 

Schrodinger's original question was

At the moment of opening the box is the cat alive or dead ?

Now there are actually more than 2 possibilities.

!) The cat is alive and well.

2) the cat is dying.

3) The cat is dead.

Which comes back to my system of  10²⁶ equations, which if linear could have 10²⁶ solutions.

Some of these would be assigned to each of the above situations.

So your comment on correlation is hugely pertinent when trying to assess/assign probabilities.

[Genady]

19 minutes ago, swansont said:

In addition to studiot's observation above, is there a connection between the quantum states of the individual atoms and the condition of being alive or dead? 

I am not sure. If it is dead because of a hole in its head, for example, I don't think a connection to the quantum states of the individual atoms is important.

[swansont]

3 minutes ago, Genady said:

I am not sure. If it is dead because of a hole in its head, for example, I don't think a connection to the quantum states of the individual atoms is important.

Superposition state implies quantum mechanics. Is being dead, or alive, a quantum state? 

[geordief]

34 minutes ago, swansont said:

Superposition state implies quantum mechanics. Is being dead, or alive, a quantum state? 

How much of the cat can be dead and the cat can still  be said to be alive?

 

(Wouldn't it be interesting  if deadness and aliveness could actually be modeled as an on/off quantum  state ?-if that makes sense)

[Genady]

50 minutes ago, swansont said:

Superposition state implies quantum mechanics. Is being dead, or alive, a quantum state? 

I think so. I don't see why not.

We could go into more details of the system, if we want to. We could consider a state of the photon P after the beam splitter, P left or right. And, a state of the detector, D yes or no. And, the weapon, W on or off. And the cat, C dead or alive. They are entangled and the state of the system is (dropping the normalization for simplicity):

|P left, D yes, W on, C dead〉 + |P right, D no, W off, C alive〉

Projection of this state onto the two-dimensional space of the cat states gives:

|C dead〉 + |C alive〉

Regardless of how much detail we add, the state remains a superposition state. What would make it into one of the basis states, |C dead〉 or |C alive〉 ?

[joigus]

8 hours ago, geordief said:

Does the cat (any system) also  interact with itself ?

Yes.

8 hours ago, geordief said:

So you would have to seal off (compartmentalise)  every part of itself with every other part of itself before you could even consider isolating  it from its external  environment. 

Mmmm. Maybe you would have to do that. Which makes @Markus Hanke's accurate comment "in practice," if anything, even more compelling.

You can always subdivide the cat into the cat's head, and the cat's rest of the body. With the head registering some crucial condition about "rest of the body," and conversely,

\[ \left|\textrm{cat}\right\rangle =\frac{1}{\sqrt{2}}\left|\textrm{cat's head wrong}\right\rangle \left|\textrm{cat's body wrong}\right\rangle +\frac{1}{\sqrt{2}}\left|\textrm{cat's head OK}\right\rangle \left|\textrm{cat's body OK}\right\rangle \]

With any interference terms of the kind \( \left|\textrm{cat's head wrong}\right\rangle \left|\textrm{cat's body OK}\right\rangle \) and \( \left|\textrm{cat's head OK}\right\rangle \left|\textrm{cat's body wrong}\right\rangle \) being erased due to decoherence. That goes to reflect in the quantum formalism that a cat's head cannot be alive of its own.

Ultimately these states are macroscopic (made up of a huge amount of microscopic states consistent with statements like "the head knows the body is dead" and "the body knows the head is dead." Understanding "knows" as "has registered." IOW, microstates of the cat don't change the argument.

Any "living states" of the cat's head immediately decohere with "dead states" of the rest of the body. And so on: (left part of the head vs right part...)

[swansont]

31 minutes ago, Genady said:

I think so. I don't see why not.

We could go into more details of the system, if we want to. We could consider a state of the photon P after the beam splitter, P left or right. And, a state of the detector, D yes or no. And, the weapon, W on or off. And the cat, C dead or alive. They are entangled and the state of the system is (dropping the normalization for simplicity):

|P left, D yes, W on, C dead〉 + |P right, D no, W off, C alive〉

Projection of this state onto the two-dimensional space of the cat states gives:

|C dead〉 + |C alive〉

Regardless of how much detail we add, the state remains a superposition state. What would make it into one of the basis states, |C dead〉 or |C alive〉 ?

Then the next question is what does it take to collapse a wave function thats in a superposition? 

[Genady]

40 minutes ago, swansont said:

Then the next question is what does it take to collapse a wave function thats in a superposition? 

A measurement, I think.

[TheVat]

An adjacent atom can make a measurement.  Schrodinger himself was annoyed that people focused on the cat, when his point was about Copenhagen and its antirealist implications.  And its awkwardness in defining an observer or measurement.  He could just as well have had a box with a sheet of paper and a bottle of ink that's broken if a particle hits the detector.  Would have saved us a lot of pointless fuss about cat consciousness.  Is the paper white or ink spotted?  Same deal.  Decoherence has happened, it's one or the other.

[swansont]

2 hours ago, Genady said:

A measurement, I think.

An interaction counts, I think. I shine a pi/2 pulse on atoms and it puts them in a superposition of states (|g> and |e>), and I shine another pi/2 pulse on them and they end up in one of those two states. I then measure the populations of the two.

It's the second pi/2 pulse that ends the superposition, not the measurement of the populations.

 

[Genady]

46 minutes ago, TheVat said:

An adjacent atom can make a measurement.  Schrodinger himself was annoyed that people focused on the cat, when his point was about Copenhagen and its antirealist implications.  And its awkwardness in defining an observer or measurement.  He could just as well have had a box with a sheet of paper and a bottle of ink that's broken if a particle hits the detector.  Would have saved us a lot of pointless fuss about cat consciousness.  Is the paper white or ink spotted?  Same deal.  Decoherence has happened, it's one or the other.

I did not mention consciousness. "Cat" is just a label for a familiar thought experiment. Saves paper and ink to describe what I refer to.

1 hour ago, swansont said:

An interaction counts, I think. I shine a pi/2 pulse on atoms and it puts them in a superposition of states (|g> and |e>), and I shine another pi/2 pulse on them and they end up in one of those two states. I then measure the populations of the two.

It's the second pi/2 pulse that ends the superposition, not the measurement of the populations.

 

I don't understand this example. Could you please elaborate? It has to do with populations?

[swansont]

52 minutes ago, Genady said:

 I don't understand this example. Could you please elaborate? It has to do with populations?

It's part of how my atomic clocks work. You measure the |g> and |e> state populations of the hyperfine transition, but that's not what collapses the superposition.

[Genady]

5 minutes ago, swansont said:

It's part of how my atomic clocks work. You measure the |g> and |e> state populations of the hyperfine transition, but that's not what collapses the superposition.

OK. How it can be applied to explain that cat is not in a superposition state?

PS. In my opinion, it IS in the superposition state and there is nothing wrong about it. But my opinion will immediately change as soon as I see how it goes out of it, with a math, not words.

[Bufofrog]

51 minutes ago, Genady said:

How it can be applied to explain that cat is not in a superposition state?

It really isn't that hard, an animal cannot be alive and dead at the same time.  No math is necessary to understand this.

[Genady]

1 minute ago, Bufofrog said:

It really isn't that hard, an animal cannot be alive and dead at the same time.  No math is necessary to understand this.

The state |dead〉 + |alive〉 is not the same as the state |alive and dead at the same time〉:

|dead〉 + |alive〉 ≠ |dead〉|alive〉

The latter is impossible, the former is not.

[J.C.MacSwell]

3 hours ago, Bufofrog said:

It really isn't that hard, an animal cannot be alive and dead at the same time.  No math is necessary to understand this.

Not much chance for the reward then...

[joigus]

3 hours ago, Genady said:

The state |dead〉 + |alive〉 is not the same as the state |alive and dead at the same time〉:

|dead〉 + |alive〉 ≠ |dead〉|alive〉

The latter is impossible, the former is not.

The latter actually represents two cats; one dead, the other alive.