Quantum Cat: Is the Wave Collapsed if Box Isn't Opened?

[maline]

How can the cat be alive unless it interacts with air outside the body?

put it in a pressurized suit and tell it to hold its breath?

Come again. Coherence simply means the off diagonal terms of the density matrix in the observational basis is not zero.

Am I wrong in saying that a good rule of thumb for intuiting when you will have coherence is that interference is possible- i.e. there must be a possible measurement that might yield the identical a posteriori state for "both alternatives" of the "superposition"?

 

[bhobba]

put it in a pressurized suit and tell it to hold its breath?

Then how is it going to be killed by the cyanide?

Am I wrong in saying that a good rule of thumb for intuiting when you will have coherence is that interference is possible- i.e. there must be a possible measurement that might yield the identical a posteriori state for "both alternatives" of the "superposition"?

I personally am weak on this intuition stuff. Coherence has a specific meaning to do with pure and mixed states:
http://pages.uoregon.edu/svanenk/solutions/Mixed_states.pdf

A decohered state is a mixed state where each element of the mixed state is a possible outcome of the observation - its actually an operator which contrasts to a pure state that can be considered an element of a vector space. Pure states are of the form |u><u|. Mixed states are of the form ∑pi |ui><ui| where pi is the probability of observing the system to be in state |ui><ui|. If the |ui><ui| are the possible outcomes of the observation then the mixed state is said to be decohered. One way to get a mixed state is to randomly present pure states for observation. If such was the case we would have no measurement problem - we are observing what's there beforehand - no collapse - no nothing. Such states are called proper mixed states. However mixed states are not usually prepared that way - there is no way to tell the difference - but the fact is they are not prepared that way and that is the modern essence of the measurement problem.

Thanks
Bill

 

[maline]

Then how is it going to be killed by the cyanide?

We are not dealing with how you get to the "superposition" state, only whether the state itself is meaningful. Do you agree that such a state cannot possibly be coherent?

 

[bhobba]

Do you agree that such a state cannot possibly be coherent?

Are you asking if a superposition of a live and dead cat is in principle meaningful?

If so, then in principle - yes it's meaningful. The live cat is in state |a>. The dead cat state |b>. By the axioms of QM 1/root 2*|a> + 1/root 2 |b> is in principle possible - that is more or less implied by the strong principle of superposition that is usually assumed - often without stating it as an assumption. If it can be achieved in practice is another matter. You won't achieve it in Schroedinger's Cat set-up.

Thanks
Bill

 

[maline]

Are you asking if a superposition of a live and dead cat is in principle meaningful?

If so, then in principle - yes it's meaningful. The live cat is in state |a>. The dead cat state |b>. By the axioms of QM 1/root 2*|a> + 1/root 2 |b> is in principle possible

I am asking whether such a state is physically meaningful -that is, in principle distinguishable from a proper mixed state.

 

[bhobba]

I am asking whether such a state is physically meaningful -that is, in principle distinguishable from a proper mixed state.

Yes it is - in principle.

Thanks
Bill

 

[maline]

Very well, I concede defeat
My criticism of the Sci Am article is still valid though.

 

[bhobba]

Very well, I concede defeat My criticism of the Sci Am article is still valid though.

I don't know what you are admitting defeat of. Its IN PRINCIPLE - in practice you can't achieve a superposition of a live and dead cat. Its simply for the axioms of QM to be consistent it needs to be possible in principle.

I have read the Scientific American article and can't see anything wrong with it - but I think that requires a separate thread.

Thanks
Bill

 

[maline]

I don't know what you are admitting defeat of. Its IN PRINCIPLE

That's what I was discussing with RUTA. He said the cat experiment won't work b/c of enviromental decoherence, and I was claiming that the state itself is not coherent, i.e. it's already a mixed state. I don't see why I'm wrong but I'll take your word for it.

I say the Sci Am article is badly written because it perpetuates the myth that decoherence has to do with our ability to know something.

 

[RUTA]

I use Schrodinger's Cat to introduce the measurement problem (which is not solved by decoherence alone), the lack of a Schnitt, and counterfactual indefiniteness. It's not about humans knowing something, it's about experimental configurations which allow for information about the cat to be obtained. Changing the configuration to keep that from happening (quantum eraser) restores the quantum behavior. Those are the points I was trying to make because at the time I entered the thread, all that I saw being pointed out was the mundane/obvious fact that we don't have the technology to screen off a cat. Schrodinger's Cat is a pedagogical prop for me, certainly nothing to be taken literally.

 

[Derek Potter]

Decoherence does not suspend Schrodinger evolution, it scrambles the phase relationships between different states. So Schrodinger's original picture was incomplete. But's that's hardly surprising as it was designed to illustrate the absurdity of the prevalent idea that systems are fuzzy at the microscopic level. Schrodinger probably didn't even think about decoherence.

But the picture is an excellent way to test a concept. It just needs a patch. Agreed that the cat does not remain in a superposition very long, but if we include the environment then [cat plus environment] does remain in superposition indefinitely. Decoherence does not get rid of the Many Worlds aspect of quantum mechanics, it just ensures that macroscopic systems behave, well, macroscopically. You still need explicit collapse to get rid of the unwanted worlds, assuming you actually want to get rid of them. And then you have to find a place to put the collapse where it won't affect the predictions of no-collapse quantum mechanics. That might be seen as making it an untestable, superfluous hypothesis but perhaps I am being subversive in saying so. :)

 

[Derek Potter]

The cat is made up something like $10^{29}$ particles, and the Hilbert space that spans the states of all these is of <understatement>rather large</understatement> dimension. There's no $|live\rangle$ and $|dead\rangle$ that spans that Hilbert space

Isn't there? Why can't we separate out all those states that we call "live" from all those that we call "dead"? The two subspaces then form the basis for spanning the original space.

 

[maline]

Decoherence does not get rid of the Many Worlds aspect of quantum mechanics, it just ensures that macroscopic systems behave, well, macroscopically. You still need explicit collapse to get rid of the unwanted worlds, assuming you actually want to get rid of them.

Only if you assume the quantum state is something real. Most physicists do not assume this.

 

[Derek Potter]

Actually, MW does not insist on the worlds* being real, states have exactly the same ontological status as the wavefunction itself. Real and physical in some interpretations, abstract calculating devices in others. What matters is that, real or otherwise, the wavefunction evolves linearly under the Schrodinger equation and tells us everything there is to be told about the world of real observations. So, my statement stands: you need to introduce wavefunction collapse otherwise QM tells us there will be co-existing phenomenal worlds. If states are not real it just makes wavefunction collapse all the more mysterious - why should a perfectly good calculating device suddenly go so spectacularly wrong?

edit: * worlds in the sense of states, that is.

 

[AlexCaledin]

... it just makes wavefunction collapse all the more mysterious - why should a perfectly good calculating device suddenly go so spectacularly wrong?

Why, it's the situation of a computer game. Richard Feynman said,

"Suppose that physics, or rather nature, is considered analogous to a great chess game with millions of pieces in it, and we are trying to discover the laws by which the pieces move. The great gods who play this chess play it very rapidly, and it is hard to watch and difficult to see. However, we are catching on to some of the rules, and there are some rules which we can work out which do not require that we watch every move."

Why not suppose that the chessboard (the "calculating device") is the universal wavefunction and the moves are collapses?

 

[Derek Potter]

I do not believe God plays chess with the universe.

 

[Nugatory]

Why not suppose that the chessboard (the "calculating device") is the universal wavefunction and the moves are collapses?

Feynman clearly states that he is making an analogy. Furthermore, this analogy isn't to how the universe works but rather to the way we make inferences about how it works. You can rework that analogy to use a computer game but it doesn't stretch into being a testable claim about how the universe works.

We have drifted far enough from the original question and from science into philosophy, that it is time to close this thread.