I Why don't we bury Schrodinger's Cat?

[PeterDonis]

In which interpretation does 'transition' belong?

Any interpretation that says that collapse of the wave function is a real, physical process.

 

[NickMDal]

More precisely, entanglement has been tested for explicitly in controlled experiments in this range. But that doesn't mean entanglement doesn't exist outside that range. Entanglement is the normal result of any interaction between quantum systems.

I believe the merit of the Schrodinger's cat metaphor hinges entirely on this. What evidence is there that entanglement exists between the ejected photon and the cat itself? Saying that entanglement exists between "any" interactions is way to inclusive and is without evidence.

 

[PeterDonis]

What evidence is there that entanglement exists between the ejected photon and the cat itself?

Nobody has actually done the experiment so how could there be any actual evidence?

QM predicts that there will be entanglement, based on the Schrodinger Equation, and since such predictions have turned out to be correct in every experiment that has actually been done, it seems reasonable to explore their implications in this case.

 

[NickMDal]

Nobody has actually done the experiment so how could there be any actual evidence?

QM predicts that there will be entanglement, based on the Schrodinger Equation, and since such predictions have turned out to be correct in every experiment that has actually been done, it seems reasonable to explore their implications in this case.

QM predicts that there will be entanglement, based on the Schrodinger Equation, and since such predictions have turned out to be correct in every experiment that has actually been done, it seems reasonable to explore their implications in this case.

There are no experiments that prove entanglement continuity between consecutive macro objects to a single particle. Whether or not this is eventually proven to be possible, you can't make it the basis for your argument that the cat is in an entangled state. We have no evidence at all saying this is possible. So you might hypothesize but it does not give any new credence to the cat in a superposition.

 

[PeterDonis]

you can't make it the basis for your argument that the cat is in an entangled state

I have already said that I am not basing the argument on evidence, since there is none. I am basing it on standard QM, using the same framework whose predictions have already been verified in countless other experiments. This kind of extrapolation of a theory is commonplace in science. You are of course free to stick your fingers in your ears and refuse to pay attention, but scientists are going to continue to do it whether you like it or not. As long as the distinction is clear between a theoretical prediction, studied in order to explore its implications, and a claim of actual evidence, which is not the case here as has already been said, there is no problem with such theoretical extrapolations. If you refuse to accept this, then please stop posting in this thread since you are adding no value to this particular discussion.

 

[NickMDal]

No need to be sensitive. We are addressing the very question the OP asked.

 

[PeterDonis]

No need to be sensitive.

I'm not being sensitive. I'm giving you valuable information about the rules and norms of this forum. Please take heed.

We are addressing the very question the OP asked.

I don't see how your posts are relevant to that question, since if everyone took your attitude Schrodinger's Cat would never have become a subject of discussion in the first place, let alone still be one after almost nine decades, and the OP certainly wouldn't have had to ask why it hasn't been buried yet.

 

[bob012345]

TL;DR Summary: Why would something think a cat, living or dead, is in a quantum state. Isn't the physical process of measurement happening all the time in a cat, living or dead, effectively starting a new quantum state?

What’s with Schrodinger’s Cat?

I seem to be missing something. I keep on hearing about Schrodinger’s cat. Why? Why would anyone think that a cat, alive or dead, is in a quantum state?

Schrödinger meant it as a critique of the Copenhagen interpretation of quantum mechanics, to show how absurd, ridiculous and nonsensical he thought the Copenhagen interpretation was.

 

[bhobba]

To answer the original question, it is an Einstein-type thought experiment highlighting an essential concept in QM - entanglement. Of course, we know if an actual experiment was done because the cat is decohered by the environment it requires to live (eg air); it is alive or dead. I often point this out, but that is not the point of the thought experiment; it is to get people to think about entanglement, etc. It is also an excellent way to introduce pure and mixed states when analysing entangled systems. I seem to recall Susskind in his book doing it this way.

As a teaching tool, it is interesting. Students often don't understand decoherence and entangled states when first encountering it. In analysing it, those concepts emerge, and then you realise a real cat would be decohered by its environment.

Thanks
Bill

 

[bob012345]

Of course, we know if an actual experiment was done because the cat is decohered by the environment it requires to live (eg air); it is alive or dead.

If that was the case, wouldn't the cat just decohere itself? And if the cat was always in a state of decoherence, how then could it ever be entangled with anything? Then what's the point of bothering to put it in the (mental) box in the first place?

 

[bhobba]

Schroedinger rightly mocked the people propagating the Copenhagen interpretation with his thought experiment.

Rightly? The experiment is about entanglement, the math of QM and decoherence. Schrodinger may have meant it to do that, but QM explains it - there is no mystery.

As an aside, I am not a fan of Copenhagen - but that is for a separate thread. I hold to the Ensemble interpretation if an actual interpretation is needed, which it usually is not. Both Copenhagen and the Statistical Interpretation account for Schrodinger's Cat - as it must - since they agree on the math of QM, only differing in what it means. There are variations of Copenhagen, but in Bohr's version, he thought it complete. That is what Schrodinger, I believe, was trying to challenge. Instead, it is an instructive tale about entanglement and decoherence.

Thanks
Bill

 

[bob012345]

Rightly? The experiment is about entanglement, the math of QM and decoherence. Schrodinger may have meant it to do that, but QM explains it - there is no mystery.

How does QM explain decoherence?

 

[bhobba]

If that was the case, wouldn't the cat just decohere itself?

A live cat can't exist without an environment eg air. A dead cat can exist without air, so I suppose one can imagine a situation where it is not interacting with an environment - even if it's just the CMBR. But knowing anything about such a cat is another issue. It's like Hyperion:

https://www.preposterousuniverse.com/blog/2008/10/23/quantum-hyperion/

I don't know how long a dead cat would last as a cat if isolated entirely from the environment.

Thanks
Bill

 

[bhobba]

How does QM explain decoherence?

See:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

Some say it solves the measurement problem; others say it solves it for all practical purposes. I think it is a pseudo-problem personally because of Gleason's theorem, but that is another story. If interested, start a new thread about Gleason's Theorem and the Measurement Problem.

Thanks
Bill

 

[bob012345]

See:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

Thanks. When it comes to quantum mechanics, I have more issues with coherence than decoherence.

 

[Algr]

Schrödinger meant it as a critique of the Copenhagen interpretation of quantum mechanics, to show how absurd, ridiculous and nonsensical he thought the Copenhagen interpretation was.

That's right. People are supposed to reject the idea of a decohered cat, just like Bushmonk did:

TL;DR Summary: Why would something think a cat, living or dead, is in a quantum state. Isn't the physical process of measurement happening all the time in a cat, living or dead, effectively starting a new quantum state?

Why would anyone think that a cat, alive or dead, is in a quantum state?

The purpose of the cat is to demonstrate a weakness in QM: There isn't a clear description of how the quantum world transitions into the world we experience. If the cat doesn't count as an observer, why would a human? People who start seeing decoherence in their daily lives are not going to provide practical solutions to anything.

 

[vanhees71]

How does QM explain decoherence?

By standard quantum dynamics. You couple the "system" to an "environment", e.g., by describing the latter as a "heat bath". Then you consider only the "reduced state" of the "system". There's a huge community of quantum physicists dealing with such "open quantum systems". My favorite approach are the "Kadanoff-Baym equations" which guarantee to a certain extent the obedience of conservation laws and thermodynamical consistency (particularly that the "system" equilibrates to the given temperature of the heat bath in the long-time limit). For a very simple example, see

https://arxiv.org/abs/2308.07659

 

[WernerQH]

By standard quantum dynamics.

I think you are slightly disingenuous here. For most people there exist two strictly separate types of quantum evolution: unitary evolution according to Schrödinger's equation and "measurements". The nice feature of the Schwinger-Keldysh fornalism is that it combines these two types of evolution in one formalism, Schrödinger's equation is seamlessly joined with the Born rule.

Quantum theory is more than about wavefunctions. The Schwinger-Keldysh method permits direct calculation of probabilities (not probability amplitudes), i.e. observable quantities.

 

[vanhees71]

There is no separate types of quantum evolution. That's the main problem I have with Copenhagen (particularly Bohr). Indeed, the Schwinger-Keldysh real-time formalism is about the time evolution of the general quantum state, i.e., statistical operators, not only for the special case of pure states. However, they describe the unitary time evolution for closed systems and no distinct "evolution" due to measurements. Measurements are nothing else than interactions between the system and a measurement device, which obey the same "quantum rules" as any other interaction.

 

[WernerQH]

However, they describe the unitary time evolution for closed systems

It's strange that you insist on describing a "closed system" and assume a heat-bath in your paper at the same time. Of course you can imagine the heat-bath arbitrarily large while still separated from the rest of the universe, but concerning the application of the formalism I find the distinction rather pointless.

 

[vanhees71]

In the paper we describe of course an open system, because we couple the particle to a heat bath, but the underlying equations are quantum time evolution. There's nothing "classical" in this approach! In other words, I don't like Copenhagen precisely because of the "Heisenberg cut" and (some flavors of it) assuming a "collapse of the quantum state" when measuring something on the system. There's no such thing, and it's also not necessary.

 

[PeterDonis]

wouldn't the cat just decohere itself?

Yes. In other words, even in the absence of external interactions, the cat still has a huge number of degrees of freedom, most of which cannot be individually tracked, so it will continually be decohering itself.

And if the cat was always in a state of decoherence, how then could it ever be entangled with anything?

Decoherence does not prevent entanglement. The cat can decohere itself but its individual atoms can still be entangled with each other. Similar remarks apply to entanglement with other things.

 

[Algr]

That's right. People are supposed to reject the idea of a decohered cat, just like Bushmonk did:

Am I using "decohered" wrong up there? PeterDonis seems to be using it in the opposite way. Maybe I mean "quantum superimposed" cat. To me decohered -> incoherent.

 

[PeterDonis]

To me decohered -> incoherent

Not really, no.

Basically, decoherence means that quantum interference becomes negligible. In the case of the cat, it means that quantum interference between "alive" and "dead" becomes negligible. Which in turn means that the entanglement between the cat and the apparatus inside the box, which either gets triggered by a quantum event and kills the cat, or doesn't get triggered and leaves the cat alive, will also show no interference between the cat being alive and dead.

However, that does not mean that there is no entanglement at all. The cat is still entangled with the apparatus, so their joint state will be the one I wrote down in post #26. What happens next is interpretation dependent, as has been discussed in previous posts.

 

[bob012345]

Decoherence does not prevent entanglement. The cat can decohere itself but its individual atoms can still be entangled with each other. Similar remarks apply to entanglement with other things.

But the scenario does talk of the cat being entangled with the atom which it can't as a whole. Suppose we replace the cat with a 1MT nuclear device. Are we to suppose the atom/device is in an entangled state till we open the box and see if it decayed (and triggered the device)? Somehow, I think we'd know if the atom decayed or not without opening the box.

 

[PeterDonis]

the scenario does talk of the cat being entangled with the atom which it can't as a whole

Sure it can. Yes, initially the effects of the atom being triggered will not interact with every single atom of the cat, but since all of the atoms of the cat interact with each other, any interaction with any part of the cat will quickly affect the state of all the atoms in the cat. That, in fact, is part of the process of decoherence--the effects of interactions that initially involve only a few degrees of freedom, spreading among a very large number of degrees of freedom that are not individually trackable.

Are we to suppose the atom/device is in an entangled state till we open the box and see if it decayed (and triggered the device)? Somehow, I think we'd know if the atom decayed or not without opening the box.

This is a quibble. The key point is not exactly what it takes for an external observer to tell whether the cat is alive or dead. The key point is that the state that the Schrodinger Equation predicts is the entangled state I have been describing, which is not a state in which the cat, by itself, is either alive or dead. It is entangled, and subsystems that are entangled do not have definite quantum states at all; only the overall joint system does. But we never observe such odd states with things like cats. That was Schrodinger's original point: either our observations are grossly misrepresenting "actual reality", or the Schrodinger Equation, by itself, cannot be a complete theory.

 

[bob012345]

That was Schrodinger's original point: either our observations are grossly misrepresenting "actual reality", or the Schrodinger Equation, by itself, cannot be a complete theory.

Thanks. Which of these two do you hold?

 

[Nugatory]

But the scenario does talk of the cat being entangled with the atom which it can't as a whole. Suppose we replace the cat with a 1MT nuclear device. Are we to suppose the atom/device is in an entangled state till we open the box and see if it decayed (and triggered the device)? Somehow, I think we'd know if the atom decayed or not without opening the box.

The discussion so far has considered the cat/atom system as isolated within the box - until the box is opened there is negligible interaction between the contents of the box and the outside. That's how Schrodinger could suggest (as a sort of straw man) a coherent superposition of dead and alive, and how decoherence can (more seriously) predict a cat that is dead or alive but we don't know which until we open the box.

"Negligible interaction between the contents of the box and the outside" doesn't apply when we replace the cat with a 1MT nuclear device. But that doesn't change the underlying principles, it just means that we need different conditions to achieve the necessary isolation. So let's do the experiment on the far side of the moon and we're back to a valid analogy with the cat and the box - naive 1920s vintage Copenhagen can't explain why we don;t have a coherent superposition of exploded and unexploded, decoherence tells us that either the bomb has exploded or it hasn't and we'll know which when we look.

 

[PeterDonis]

Which of these two do you hold?

I don't "hold" either of them. I think this is still an open area of inquiry.

If I had to guess how the inquiry will eventually turn out, I would guess that we will end up finding that the Schrodinger Equation, or more generally QM in its current form, is not a complete theory. But that's just a guess.

 

[bushmonk]

...every venue that (teaches) introductory physics goes through this same old thought experiment. The Great Courses quantum mechanics lectures describe sitting in three movie theater chairs at once. The lecturer then slogs through Schrodinger's cat. This metaphor just won't die.

This response captures something of my frustration. My experience is that the path towards a decent amateur understanding of QM is educationally inefficient. Much effort for little understanding. The path is obscured by debris, rabbit trails and sometimes rabbit holes.

It would not be a good idea to introduce classical mechanics by stating that according to classical mechanics, I, the teacher, have no choice about what I am about to say, and you, the student, are doomed to pass or fail your first test in the subject. It is all fixed by the prior state of the universe.

No. We start with measurements of time and position so that we an describe simple motions in mathematical terms. We take some ticker tape and try it. We leave determinism to the philosophers.

Likewise, I think it is not a good idea to say to the inquirer that, according to QM you can be in three theatre seats at once, that cats can be alive and dead, or that there are gazillions of copies of both you and the cat in gazillions of worlds. It may be true that there are people wrestling with why such statements are not true or are pressing forward with the idea that they are true, but that is not what we are going to talk about nor why QM is worth understanding.

No. Let's talk about an interferometer. Here is how it works. And so on. There is much to be learned.

Let's learn to balance a chequebook before we worry about Godel's Theorem.

The decoherence viewpoint makes it clear that, once the radioactive atom decays, the cat dies--it doesn't wait to die until you open the box.

Great. We agree on that. So we can bury that part of the cat in the box idea.

I gather that decoherence has opened up the black box of measurement but there are still smaller black boxes inside. I think this progress is great. Mysteries remain. But it doesn't mean that according to QM a cat is both dead and alive. Or that you can sit in three theatre seats at the same time. We just haven't agreed as to why it doesn't. The projection postulate is one idea. Many don't like it. OK. But we're all aiming at the same goal, namely eliminating things that don't happen.

No, it's a state. It doesn't have to be a microstate. A cat has a quantum state, but it's not a microstate.

I don't see why you object to microstate. As in thermodynamics, a microstate is the detailed, unknowable and rapidly changing specification of the microscopic constituents of a large system. "Alive cat" is a crude macroscopic description. For that reason, using a ket with "alive cat" in it is misleading, IMHO. As you said, a live cat is a subspace of Hilbert space.

I stated that the cat was a series of microstates discontinuously and randomly related to each other. Peter responded:

Not at all. If this were the case, cats, and objects generally, would not be describable to a very good approximation using classical physics.

This is a layman's description of the projection postulate in operation. I was using terminology from David Bohm's 1951 "Quantum Theory". The projection postulate is invoked to describe the observation that the quantum state abruptly changes, discards redundant possibilities in a random and discontinuous fashion and renormalizes.

I understand the MWI discards the projection postulate. There is controversy about whether they they have succeeded in explaining what it actually observed. So I don't want to get into it.

But whether they have or they have not, surely they must give an account of why, in this particular cat, an oxygen molecule entered a particular cell, when, by Shrodinger's equation, it could have continued along the bloodstream. Their answer is, if I understand it correctly, that a number of cats were spawned in other worlds to realize the other possibilities. Fine. But that is very different from an electron going through both slits without decoherence. No new electrons in new worlds need be spawned. As long as decoherence is not involved, there is no need to spawn new worlds. A cat is filled to the brim with decoherence. An electron going through a double slit is not. There's a difference, regardless of your interpretive preferences.

That is why I said that some of my statements would need translation into other interpretations.