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

[bland]

OK here's a hypothetical situation in order to tease out a query that is bugging me...

We have a cat, this cat has a bomb in it that is wired to it's brain and when brain death is detected, the cat explodes (you probably see already where I'm going with this). Unknown to the experimentalists, this cat has been substituted for the cat they were going to use in the thought experiment they were setting up with the box, the cyanide and the radio active atom plus detector and switch.

In the room are only the scientists who do not know the cat has been switched, outside the room in a sound proof cubicle are some other scientists who do know the cat has been switched.

Obviously if the cat is dead there's going to be exploded cat and no one is going to have to actually peer into the box to collapse the wave.

What is the situation here, with regards to the superposition of the dead and alive cat, where the box has not exploded and those in the room don't know about the bomb, and how does it change if someone who does know walks into the room.

 

[Nugatory]

You have been victimized by one of the more common misstatements in popularizations of quantum mechanics.

The cat is never in a superposition of dead and alive. It is always either dead or alive, and which it is has nothing to do with whether or not a conscious observer has made an observation. When Schrodinger first proposed his cat experiment involving the cat and the cyanide and the radioactive decay, he was not suggesting that the cat might be in a superposition. Instead, he was pointing out a problem: Although there was never any doubt that the cat would always be either dead or alive (just as a tossed coin is either heads or tails even if we don't look at it), in the then-current (75-odd years ago) understanding of QM there was no reason why it had to turn out that way.

The explanation only became clear some decades later with the discovery of quantum decoherence (google for that term, but be warned that the math is a bit daunting - you may also want to try a layman-friendly book entitled "Where does the weirdness go?"). Unfortunately, by then the notion of the cat with an uncollapsed wave function, both dead and alive at the same time, had taken root in the broader culture.

 

[bhobba]

Just to expand on Nugatory's excellent answer the reason conciousness came into this thing is an early analysis of the measurement process done by Von-Neumann in his classic Mathematical Foundations of Quantum Mechanics. QM is basically a theory about observations that appear in a common-sense classical world. What Von-Neumann showed is the quantum classical cut can be placed pretty much anywhere. With no place better than any other he decided to place it at the only place that was different - human conciousness.

While this an issue in principle, in practice it never is eg in the Schroedinger's cat experiment the obvious place the observation occurs is at the particle detector - everything is classical from that point on and the cat is dead or alive.

Still we have the in principle issue and further research was required to resolve it. The resolution is in decoherence:
http://www.ipod.org.uk/reality/reality_decoherence.asp

These days the cut is usually assumed to be just after decoherence. This also allows a fully quantum definition of what a observation is - it's when decoherence happens. The reason for conciousness introduction was no longer valid and it's now a very backwater idea.

Thanks
Bill

 

[bland]

Ok thanks for those excellent replies.

These days the cut is usually assumed to be just after decoherence.

I presume this is referring to Heisenberg's 'schnitt'

I have been listening to Amir Aczel's 'Entanglement', Manjit Kumar's 'Quantum' and Louisa Gilder's 'Age of Entanglement' and I see that I may be stuck in that era. I will most certainly now focus on this 'decoherence' business. Thanks for the heads up.

PS, that ipod.org site looks like I've struck gold.

 

[bhobba]

I presume this is referring to Heisenberg's 'schnitt'

Its also known as the Von-Neumann cut. I suppose its who you were most influenced by determines what you call it. My background is math so its Von-Neumann in my case.

I will most certainly now focus on this 'decoherence' business. Thanks for the heads up.

It doesn't resolve the measurement problem which is surprisingly subtle and has a number of parts. Some parts, such as what is called the preferred basis problem it resolves. Others, such as the problem of outcomes (it the main one - colloquially called why do we get any outcomes at all - technically how does an improper mixed state become a proper one) it leaves untouched.

If you want to pursue it further THE textbook is the following:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

In particular see section 2.5.

A freely available cut down version is the following:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

Thanks
Bill

 

[RUTA]

You have to be careful when talking about the cat in a superposition state. If it's truly in a superposition of dead and alive, then it can't be interacting with the environment, i.e., the floor, the box, the air in the box, etc. That's where decoherence comes in, as mentioned above. However, decoherence doesn't solve the measurement problem, which is the non-unitary evolution from the superposition state to a definite outcome. You have to add something to decoherence to make that happen. http://arxiv.org/pdf/quant-ph/0112095v3.pdf

 

[maline]

RUTA, you can't kill a cat while avoiding decoherence. The air etc. is not relevant.

 

[RUTA]

If you assume the cat is in a superposition state of live and dead, then you've "killed it" and "not killed it" before decoherence. I think it was in this experiment that air-caused decoherence was an issue for example, Gerlich, S., et al.: Quantum interference of large organic molecules. Nature Communications 2, 263 doi: 10.1038/ncomms1263 (2011).

 

[maline]

The "live" and "dead" states are by definition not in coherence.

 

[RUTA]

The assumption is an entangled state of live and dead, as I understood the OP. If it's merely a matter of not having checked for evidence, then it's an epistemic problem, not a quantum problem.

 

[MichaelSB]

i always say this when i come across this topic...the cat is dead when the experiment takes longer than say 8 minutes.

 

[maline]

RUTA, my point is that such a state is a contradiction in terms, except in Collapse models, where superposition can be meaningful post-decoherence.

 

[RUTA]

But, if there is truly no way to know whether the cat is alive or dead, e.g., no evidence exists because the cat is not interacting with anything -- air, floor, box, etc, then quantum mechanics says it's neither alive nor dead. Keep in mind this is not a claim about the knowledge of observers, this is a claim about interactions of the cat with its environment that could be used to ascertain its true state, regardless of whether or not anyone chooses to do so.

 

[RUTA]

So, for example, if you set up twin-slit interference with electrons then scatter photons off the electrons and collect the scattered photons to discern the electrons' paths, the electron interference pattern is destroyed. But, if you hide the results of that photon scattering, say with a lens in front of the photon detector that ruins the which way information, then the electron interference pattern is restored. Having the information available at the photon detector (before you destroy it with a lens) destroys the electron interference pattern whether or not any conscious entity chooses to look at the photon detector.

 

[maline]

That's not correct. Quantum mechanics does not say anything at all about states that cannot be observed. There are only two ways to correctly talk about superposition in physics:
1. Before decoherence, where the elements of the state can potentially interact and affect future observations.
2. If you specify that you are working in a psi-ontic model, and that you are interested in the philosophical rather than the physical implications of superposition. This only really works in collapse models, because in hidden variable models there are no superpositions, whereas in MWI the two states are in different "worlds" following decoherence.

Scattering photons off electrons will almost always cause decoherence and ruin interference patterns, even without a photodetector. "Information available" is not important.

 

[maline]

Actually, there may be an exception: I believe that Roger Penrose, in his Objective Reduction scheme, intended superpositions to have physical effects even post- decoherence through some sort of gravitational influence. I can't provide a reference for this and I also don't think a model for it has ever been developed.

 

[RUTA]

See page 95 of this Sci Am article on quantum eraser for the electron-photon reference http://www.arturekert.org/quantum-eraser.pdf

 

[RUTA]

We're not talking about a state that cannot be observed. We're talking about a state prior to "observation" (no consciousness needed -- see quantum eraser article in previous post, all that matters is that the experimental apparatus allows for the information).

 

[maline]

Sorry, badly written article. That's yellow science for you. As for the specific case of scattering off electrons, I don't know, there may be a clever way to do it with one electron and one photon; that's why I wrote "almost always". But if that article is your only source I'd assume it's their mistake.
The important thing to realize is that decoherence has nothing to do with knowledge, potential or actual. It basically means that the state is too complicated to create interference.

 

[bahamagreen]

Just for fun...

"Seems Schrodinger demonstrated a keen sense of humor picking the cat, anticipating difficulty of experimental preparation using the only creature with nine lives (a hidden variable), the uncertainty principle enjoining certain knowledge which of its lives the cat would be living during the experiment, thus confounding the "catlapse of the wave function", and therefore with great foresight anticipating the "Many Cats" interpretation of QM, long before Everett, Dewitt, et al... "

 

[RUTA]

Paul Kwiat was a co-author on that paper. He's good, the article is correct. Not knowledge, information as created by measurement. What I said is correct.

 

[Nugatory]

RUTA, my point is that such a state is a contradiction in terms, except in Collapse models, where superposition can be meaningful post-decoherence.

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, so no way to describe the state of the cat as a superposition of live and dead, nor of the cat's wave function collapsing into one one or the other state.

 

[RUTA]

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, so no way to describe the state of the cat as a superposition of live and dead, nor of the cat's wave function collapsing into one one or the other state.

QM doesn't have a size limit as to what can be screened off (behave as a quantum entity). Molecules with 60 atoms have been screened off (as evidenced by interference patterns). Are you proposing an upper limit?

 

[bhobba]

Just a comment.

We seem to be stuck on the cat here. The observation occurs way before then - at the particle detector. Everything is common-sense classical from that point on and is the obvious place to put the observation. The issue is while obvious there is nothing in QM that says it must be put there. But with our knowledge of decoherence the place to put it is just after decoherence which occurs at the detector.

That said, as Nugatory said, for a macrospic object like a cat for it not to behave in a classical way you must screen it ENTIRELY of from the environment for it not to be decohered and that would at a minimum require being very close to absolute zero which most definitely is NOT the thought experiment.

If anyone want to propose an alternative set-up be my guest.

Thanks
Bill

 

[bhobba]

QM doesn't have a size limit as to what can be screened off (behave as a quantum entity). Molecules with 60 atoms have been screened off (as evidenced by interference patterns). Are you proposing an upper limit?

Precisely what set-up are you proposing?

Its obviously not Schrodinger Cat. And a dust particle can be dechohered from a few stray photons from the CBMR to give it a definite position so that screening off needs to be VERY effective - certainly there would need be no air for the cat to stay alive.

Thanks
Bill

 

[RUTA]

Precisely what set-up are you proposing?

Its obviously not Schrodinger Cat. And a dust particle can be dechohered from a few stray photons from the CBMR to give it a definite position so that screening off needs to be VERY effective - certainly there would need be no air for the cat to stay alive.

Thanks
Bill

I'm proposing a "live cat" "dead cat" source. It doesn't matter how it's made for the purposes of this discussion, it's not ruled out by QM and addresses the question of the OP (assuming the OP was concerned with a true quantum effect).

 

[bhobba]

I'm proposing a "live cat" "dead cat" source.

Scratching head. Certainly a live cat requires air which will decohere it.

Thanks
Bill

 

[RUTA]

Scratching head. Certainly a live cat requires air which will decohere it.

Thanks
Bill

Are you suggesting that the resolution is merely "it can't be done?" When I teach QM I simply use Schrodinger's cat to illustrate two points about QM -- it contains no "Schnitt" and harbors a puzzle concerning counterfactual definiteness.

 

[bhobba]

Are you suggesting that the resolution is merely "it can't be done?"

I am suggesting Schroedinger's Cat brings out an in issue with many interpretations such as Copenhagen and Ensemble - namely exactly where one puts the quantum classical cut (no Schnitt as you say). They assume the existence of a common-sense classical world observations appear in but as Von-Neumann showed that cut is not well defined.

In any set-up it's pretty obvious where you put it eg in Schroedinger's cat its at the particle detector - but the theory doesn't mandate that. Decoherence however suggests placing it just after decoherence which is a purely quantum definition so solves the issue. You don't have to place it there but why make life harder than necessary.

Added Later:
The issue is with our modern understanding of decoherence in Schroedinger's Cat placing the cut anywhere but the detector leads to problems.

Thanks
Bill

 

[RUTA]

I am suggesting Schroedinger's Cat brings out an in issue with many interpretations such as Copenhagen and Ensemble - namely exactly where one puts the quantum classical cut (no Schnitt as you say). They assume the existence of a common-sense classical world observations appear in but as Von-Neumann showed that cut is not well defined.

In any set-up it's pretty obvious where you put it eg in Schroedinger's cat its at the particle detector - but the theory doesn't mandate that. Decoherence however suggests placing it just after decoherence which is a purely quantum definition so solves the issue. You don't have to place it there but why make life harder than necessary.

Added Later:
The issue is with our modern understanding of decoherence in Schroedinger's Cat placing the cut anywhere but the detector leads to problems.

Thanks
Bill

So, your answer to my question is "yes." Given the practical difficulty of screening off a cat, i.e., keeping it from decohering, we can pretty much assume the cat is alive or dead a tiny fraction of second after leaving the source. That's a nice point to make in teaching QM, and I acknowledged that in my first post, but it is orthogonal to the points I was making.

 

[bhobba]

but it is orthogonal to the points I was making.

I think I may have missed something. I thought your earlier post was correctly making the point decoherence doesn't solve the measurement problem.

Can you go over your point again?

Thanks
Bill

 

[maline]

Suppose we somehow avoid all interaction with anything outside the cat's body, as well as the history of how the superposition was formed. Can the state ({cat-alive}+{cat-deat})/sqrt(2) be meaningful in any way? I am making the point that the difference between the states(structural damage to brain cells etc.) is far too large & complex for there to be coherence, that superposition is therefore physically meaningless, and that even ontologically it will only exist in a limited class of nonstandard models. I believe Nugatory was making the same point. RUTA seems to disagree in the idealized case of complete isolation.

 

[maline]

He's good, the article is correct. Not knowledge, information as created by measurement.

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. The statement about information is true, but in the most general & abstract sense of "information": to have quantum coherence you need there to be no difference whatsoever between complete descriptions of the universe that have a probability of resulting from each of the alternatives. If one photon gets absorbed in a wall somewhere, you lost it. Technically you can call that "available information" because ideally you could measure the temperature of the wall, but the reader will not understand that. As for the cat, don't you agree that the structure of the cat's brain cellls (technical definition of death) qualifies as "available information"?

 

[bhobba]

Suppose we somehow avoid all interaction with anything outside the cat's body

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

I think Ruta may have a valid point but its not gelling for me at this stage - I would like him to elaborate.

Thanks
Bill

 

[bhobba]

to have quantum coherence you need there to be no difference whatsoever between complete descriptions of the universe that have a probability of resulting from each of the alternatives.

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

It is one of the successes of decoherence that it explains the preferred basis problem and the off diagonal terms quickly decaying to zero.

What it doesn't explain is why the resulting improper mixed state becomes a proper one.

Thanks
Bill