Schrödinger's Cat and radioactive atom

[akhmeteli]

What is the biggest object that has been put into a state of superpoition? Wasn't it just barely visiible to the naked eye? Is it sufficiently different from a cat to be an exception to quantum mechanical rules?

I don't know if the following is what you need:

U. Delić et al., Science
10.1126/science.aba3993 (2020).
Cooling of a levitated nanoparticle to the motional quantum ground state
Abstract:
"Quantum control of complex objects in the regime of large size and mass provides opportunities for sensing applications and tests of fundamental physics. The realization of such extreme quantum states of matter remains a major challenge. We demonstrate a quantum interface that combines optical trapping of solids with cavity-mediated light matter interaction. Precise control over the frequency and position of the trap laser with respect to the optical cavity allows us to laser-cool an optically trapped nanoparticle into its quantum ground state of motion from room temperature. The particle comprises of ##10^8## atoms, similar to current Bose-Einstein condensates, with the density of a solid object. Our cooling, in combination with optical trap manipulation, may enable otherwise unachievable superposition states involving large masses."

Can conclusions obtained in experiments with such systems be extended to cat-size objects? Opinions on the results of unperformed experiments may differ.

 

[gentzen]

Baird says: "Schrodinger constructed his imaginary experiment with the cat to demonstrate that simple misinterpretations of quantum theory can lead to absurd results which do not match the real world." So what does Baird mean? That Schrödinger believed in 1935 that this prediction of quantum mechanics is wrong? Then I agree with Baird.

In the quoted sentence, Baird is pretty clear that this prediction results from a simple misinterpretation of quantum theory, and that Schrödinger believed in 1935 that this prediction is wrong. Baird later makes it clear that the "simple misinterpretation" in question here is "that quantum particles only collapse to a single state when viewed by a conscious observer".

quantum mechanics predicts macroscopic superpositions;

"the universal validity of unitary dynamics and the superposition principle has been confirmed far into the mesoscopic and macroscopic realm in all experiments conducted thus far;"

"all observed restrictions can be correctly and completely accounted for by taking into account environmental decoherence effects;"

experiments with cat-sized objects have never been performed with proper measures to prevent decoherence.

Which of these statements do you dispute?

I dispute the first statement, namely that QM would predict superpositions for systems that are not sufficiently small such that one can produce and manipulate them in more or less arbitrary quantities. Of course, some interpretations like MWI do "believe" that, but many other interpretations are either agnostic about that point, or even explicitly reject it, like for example A. Neumaier's thermal interpretation:

One cannot superpose whole universes. In any case I do not know how one could prepare such a situation. ... The superposition principle only applies to systems that are sufficiently small that one can produce and manipulate them in more or less arbitrary quantities. Macroscopic systems are definitely not in this category!

For the second statement, the claim about "macroscopic realm" would need some qualifications:

Steven Weinberg in "Lectures on Quantum Mechanics" in section "8.3 Broken Symmetry" seems to "suggest" that often even molecules won't be in strange superpositions of states (even if that superposition would constitute the minimal energy eigenstate), if some related timeinterval far exceeds the lifetime of the universe.

I certainly agree with the third statement in the sense that no observations so far have hinted at any need to modify quantum theory (like collapse theories a la Penrose or Ghirardi). The fourth statement is pointless, and I disagree with the implicit suggestion that "proper measures to prevent decoherence" exist even in principle for "experiments with cat-sized objects".

 

[CoolMint]

I don't know if the following is what you need:

U. Delić et al., Science
10.1126/science.aba3993 (2020).
Cooling of a levitated nanoparticle to the motional quantum ground state
Abstract:
"Quantum control of complex objects in the regime of large size and mass provides opportunities for sensing applications and tests of fundamental physics. The realization of such extreme quantum states of matter remains a major challenge. We demonstrate a quantum interface that combines optical trapping of solids with cavity-mediated light matter interaction. Precise control over the frequency and position of the trap laser with respect to the optical cavity allows us to laser-cool an optically trapped nanoparticle into its quantum ground state of motion from room temperature. The particle comprises of ##10^8## atoms, similar to current Bose-Einstein condensates, with the density of a solid object. Our cooling, in combination with optical trap manipulation, may enable otherwise unachievable superposition states involving large masses."

Can conclusions obtained in experiments with such systems be extended to cat-size objects? Opinions on the results of unperformed experiments may differ.

Maybe people have trouble with the notion of a quantum cat. If one accepts the notion that the cat is entirely quantum and all the quantum rules apply to the cat as well, maybe they can come to different conclusions?
If the cat is not quantum, then what is it made of?

 

[PeterDonis]

quantum mechanics predicts macroscopic superpositions

Since this claim, according to the quote you give a little bit later in your post, depends on the universal validity of unitary dynamics, the claim is only valid under an interpretation of QM such as the MWI, in which the universal validity of unitary dynamics is accepted. Other interpretations, such as collapse interpretations, do not accept that.

Note that experimentally we do not know that unitary dynamics is universally valid. We only know it's valid when quantum coherence is maintained. Once decoherence comes into play, we can no longer verify that the dynamics is unitary.

Note also that the restriction I just stated is not a restriction on the size of the system for which we can verify unitary dynamics. If we could somehow figure out how to keep a cat from decohering, we could in principle test to see if the cat's dynamics were unitary. The problem is that there are so many internal interactions within the cat that it decoheres itself.

 

[PeterDonis]

experiments with cat-sized objects have never been performed with proper measures to prevent decoherence.

How would you propose performing such an experiment?

 

[akhmeteli]

In the quoted sentence, Baird is pretty clear that this prediction results from a simple misinterpretation of quantum theory, and that Schrödinger believed in 1935 that this prediction is wrong. Baird later makes it clear that the "simple misinterpretation" in question here is "that quantum particles only collapse to a single state when viewed by a conscious observer".I dispute the first statement, namely that QM would predict superpositions for systems that are not sufficiently small such that one can produce and manipulate them in more or less arbitrary quantities. Of course, some interpretations like MWI do "believe" that, but many other interpretations are either agnostic about that point, or even explicitly reject it, like for example A. Neumaier's thermal interpretation:For the second statement, the claim about "macroscopic realm" would need some qualifications:I certainly agree with the third statement in the sense that no observations so far have hinted at any need to modify quantum theory (like collapse theories a la Penrose or Ghirardi). The fourth statement is pointless, and I disagree with the implicit suggestion that "proper measures to prevent decoherence" exist even in principle for "experiments with cat-sized objects".

As for Baird, he also writes: "Careful analysis reveals that the Schrodinger Cat "experiment" would play out in the real world as follows: as soon as the radioactive atom interacts with the Geiger counter, it collapses from its non-decayed/decayed state into one definite state. The Geiger counter gets definitely triggered and the Cat gets definitely killed. Or the Geiger counter gets definitely not triggered and the cat is definitely alive. But both don't happen." This statement is controversial in the best case. It is not clear why the system containing the atom, the cat, and the Geiger counter cannot be in a superposition.

So you dispute my first statement, but you seem to agree that the statement is within main stream. I agree that there are interpretations disputing such statement, such as the objective collapse interpretation, but predictions of such interpretations are not supported by experimental results (yet). As for Neumaier's thermal interpretation, I have not seen his peer-reviewed articles on his interpretation; if you know such articles, please advise. I know he issued a book, but I am not sure about the status of the book.

As for the second statement, it contains the words "in all experiments conducted thus far", so Weinberg's words do not seem to "qualify" it as his words self-qualify with "if some related time interval far exceeds the lifetime of the universe".

I don't understand why the fourth statement is pointless, and I don't feel comfortable with discussing "implicit suggestions".

 

[akhmeteli]

Since this claim, according to the quote you give a little bit later in your post, depends on the universal validity of unitary dynamics, the claim is only valid under an interpretation of QM such as the MWI, in which the universal validity of unitary dynamics is accepted. Other interpretations, such as collapse interpretations, do not accept that.

Note that experimentally we do not know that unitary dynamics is universally valid. We only know it's valid when quantum coherence is maintained. Once decoherence comes into play, we can no longer verify that the dynamics is unitary.

Note also that the restriction I just stated is not a restriction on the size of the system for which we can verify unitary dynamics. If we could somehow figure out how to keep a cat from decohering, we could in principle test to see if the cat's dynamics were unitary. The problem is that there are so many internal interactions within the cat that it decoheres itself.

You seem to agree that the claim of universal validity of unitary dynamics is at least main stream. If so, I don't have to accept phinds' categorical statements on impossibility of Schrödinger's cat. I keep repeating: maybe the cat can be both dead and alive, maybe not, but at this stage we just cannot be sure.

As for "many internal interactions", we discussed this earlier. I mentioned that molecules containing thousands of atoms and numerous degrees of freedom were experimentally shown to interfere.

 

[akhmeteli]

How would you propose performing such an experiment?

Experimentalists have hard time trying to prevent decoherence even with much smaller systems, so I cannot give a recipe to eliminate decoherence for cat-size objects. However, experimentalists keep making progress in this direction, showing what kind of measures should be taken to prevent decoherence.

 

[PeterDonis]

You seem to agree that the claim of universal validity of unitary dynamics is at least main stream.

No, I don't. As I said, the claim is interpretation dependent, so since there is no single QM interpretation that is "mainstream", the claim that unitary dynamics is universally valid is not "mainstream".

I keep repeating: maybe the cat can be both dead and alive, maybe not, but at this stage we just cannot be sure.

In the sense that we do not have a single QM interpretation that is "mainstream", this is correct, since the cat would only be "both dead and alive" on certain interpretations, such as the MWI. (And one then has to be careful in interpreting what "both dead and alive" actually means.)

As for "many internal interactions", we discussed this earlier. I mentioned that molecules containing thousands of atoms and numerous degrees of freedom were experimentally shown to interfere.

"Numerous" is a relative term. Molecules containing thousands of atoms still have some ##10^{25}## or more fewer degrees of freedom than a cat.

Also, the molecules in question have very simple, homogeneous structures, and are cooled down during experiments to the point where only a few degrees of freedom with energy levels sufficiently close to the ground state are excited. You cannot do that with a cat, at least not if you want it to remain a cat. An object with the same atoms as a cat in which only a few degrees of freedom with energy levels sufficiently close to the ground state were excited would not even be a dead cat; it would be a mixture of various simple elements and compounds with no significant structure. What makes a cat a cat, even a dead one, is that it has an extremely complex structure in which many, many degrees of freedom are constantly excited, so many that it is impossible to keep track of them all. That is why a cat decoheres itself, and cannot be prevented from doing so without completely destroying its structure and making it not even a dead cat any more.

 

[akhmeteli]

No, I don't. As I said, the claim is interpretation dependent, so since there is no single QM interpretation that is "mainstream", the claim that unitary dynamics is universally valid is not "mainstream".In the sense that we do not have a single QM interpretation that is "mainstream", this is correct, since the cat would only be "both dead and alive" on certain interpretations, such as the MWI. (And one then has to be careful in interpreting what "both dead and alive" actually means.)"Numerous" is a relative term. Molecules containing thousands of atoms still have some ##10^{25}## or more fewer degrees of freedom than a cat.

Also, the molecules in question have very simple, homogeneous structures, and are cooled down during experiments to the point where only a few degrees of freedom with energy levels sufficiently close to the ground state are excited. You cannot do that with a cat, at least not if you want it to remain a cat. An object with the same atoms as a cat in which only a few degrees of freedom with energy levels sufficiently close to the ground state were excited would not even be a dead cat; it would be a mixture of various simple elements and compounds with no significant structure. What makes a cat a cat, even a dead one, is that it has an extremely complex structure in which many, many degrees of freedom are constantly excited, so many that it is impossible to keep track of them all. That is why a cat decoheres itself, and cannot be prevented from doing so without completely destroying its structure and making it not even a dead cat any more.

So we at least seem to agree that "maybe the cat can be both dead and alive, maybe not, but at this stage we just cannot be sure", that is good enough for me.

As for molecules being "cooled down during experiments to the point where only a few degrees of freedom with energy levels sufficiently close to the ground state are excited", I wrote previously:

"In Nature Physics volume 15, pages 1242–1245(2019), they don't seem to cool anything at all. They say: "The delocalized molecules in our experiment are each roughly the mass of the green fluorescent protein25 (27 kDa) or a small BEC, while exceeding the temperature of a BEC by more than nine orders of magnitude. High-contrast quantum interference persists despite the thousands of excited vibrational levels and billions of structural and conformational isomers present in the molecular beam."

 

[Morbert]

Statements about the past cannot in general be made in quantum-mechanical (QM) language. The wave-function doesn’t allow statements like “The radioactive atom has decayed or not at this or that time.” Quantum mechanics differs from classical physics because the assumption that one of the answers is "objectively" realized in between observations or measurement is simply impossible.

"The wavefunction doesn't allow statements..." is too strong imo. Say we have a wavefunction ##\Psi## and we take a measurement in the present. If we can identify an observable ##O = \sum \lambda_i E_i## whose possible measurement results correlate with possible (mutually exclusive) past events ##\{C_i\}## , such that [1] $$\mathrm{Re}\langle\Psi|E_i C_j |\Psi\rangle \approx 0, i\neq j$$ then a measurement of ##O## would, under the appropriate interpretation, let us infer time-information about events in the past.

Quantum probabilities are not the probabilities that the radioactive atom has decayed or not at a certain instant of time. It’s the probabilities that an observer will find it decayed or not at a certain instant of time. That’s all what QM has to say.

The projectors for decayed and not decayed are ##\Pi_D## and ##\Pi_N## respectively. Say the time interval between the preparation of the experiment at ##t_0## and now is divided into ##N## smaller intervals ##T_i = \left[t_{i-1},t_i\right)##. Let's also say the decay is registered by a detector that can register time of decay with pointer states ##0,1,2,3,\dots,N## represented by projectors ##E_0,E_1,E_2,E_3,\dots,E_N##, with the state ##0## denoting the "ready" or "no detection" state. Maybe the detector is a time-of-death reading on the cat's collar. These pointer states record time of decay if $$\mathrm{Re}\langle \Psi|E_i \Pi_D(t_{j})\Pi_N(t_{j-1})|\Psi\rangle\approx 0, i\neq j$$In which case an observer can infer a past event from a present clock reading.

This description is of course interpretation-laden, and for the 2nd part of this post I am assuming a Von Neumann style partition of measured system (particle) + measurement device (detector in the box) + observer (physicist who opens the box)

[1] https://arxiv.org/pdf/1608.04145.pdf

 

[Halc]

The cat is never in superposition of being dead and alive. It's always either dead or alive.
...
And here on PF:
https://www.physicsforums.com/threads/quantum-cat-question.798022/

I want to throw in my $0.02. I don't want to post to the topic linked above due to its age and its presence in quantum physics instead of interpretations like this one, but it is heavy with talk of this quantum-classical 'cut' (by various names). This cut seems to be a feature of (and only of) Copenhagen interpretation. Much of the discussion in that topic seems overly interpretation dependent in my opinion.

I lay no claim to being an expert, so just let me paraphrase what I've been reading in this thread. There seems to be two different meanings of 'superposition' being used, resulting in people talking past each other.

Those that say that the cat cannot be in superposition of dead and alive are using an empirical definition, saying that even given a hypothetically (and unrealistic) perfect box, there is no way to empirically demonstrate interference between the two states in the box. With this I must agree. I cannot conceive of such a hypothetical box, blocking even undetectable gravitational waves and such. They're enough to cause decoherence with something like a cat. The cat is indeed one or the other, and simply in a unitary unknown state. Also, as PeterDonis points out, the conditions required by the containment would kill the cat before the poison bottle ever came into play. Yes, they've done it with 'macrosopic' objects, but even then the superposition lasted I think under a microsecond. We're needing minutes at least for our cat to be poisoned.

The other meaning of superposition is from the QM theory itself where a wave function of a closed system, unmeasured, which is what the box represents. This meaning says that given the locally impossible perfect box, the cat is indeed in superposition of being both dead and alive. To assert otherwise is to assert a counterfactual, which most interpretations do not support.

While I would not go so far as to qualify my opinion as 'belief', I prefer to frame things in relational terms, per Rovelli. This is a collapse interpretation, and given a simple metal box, relative to the guy that put it in there a short time ago, the cat within is indeed dead or alive and its indeterminate state is purely epistemological. But relative to somebody on Jupiter (a box based on isolation by distance instead of true closed system), the cat state is a temporary (15 minutes?) true counterfactual and is thus in superposition. There's an absolute impossibility to measure that superposition from that distance since any measurement will yield results slower than the decoherence occurs relative to him, so there is no pragmatic meaning to asserting the superposition state except as a descriptive demonstration of the interpretation, which seems to be along the lines of Schrodinger's purposes in bring up the cat, even if different conclusions are reached. Multiple classical states (worlds) were still not an option in those days. Biases take time to fall.

 

[PeterDonis]

I cannot conceive of such a hypothetical box, blocking even undetectable gravitational waves and such. They're enough to cause decoherence with something like a cat.

You don't even need that. As I said in an earlier post, the cat decoheres itself; it has such a huge number of heterogeneous degrees of freedom, most of which cannot be kept track of, that its own interactions with itself are sufficient to decohere it.

 

[CoolMint]

You don't even need that. As I said in an earlier post, the cat decoheres itself; it has such a huge number of heterogeneous degrees of freedom, most of which cannot be kept track of, that its own interactions with itself are sufficient to decohere it.

Is there a peer-reviewed paper that makes this claim?

 

[PeterDonis]

Is there a peer-reviewed paper that makes this claim?

Not directly about a cat, but the literature on decoherence is clear about what the requirements are.

 

[CoolMint]

Not directly about a cat, but the literature on decoherence is clear about what the requirements are.

If this literature is not peer-reviewed, should it be here?

 

[PeterDonis]

If this literature is not peer-reviewed, should it be here?

The literature on decoherence that I referred to is peer-reviewed. There are peer-reviewed papers on it going back to the 1970s.

 

[gentzen]

But relative to somebody on Jupiter (a box based on isolation by distance instead of true closed system), the cat state is a temporary (15 minutes?) true counterfactual and is thus in superposition. There's an absolute impossibility to measure that superposition from that distance since any measurement will yield results slower than the decoherence occurs relative to him, so there is no pragmatic meaning to asserting the superposition state except as a descriptive demonstration of the interpretation, which seems to be along the lines of Schrodinger's purposes in bring up the cat, even if different conclusions are reached.

I like your idea to use relativity for fixing the unrealistic assumptions of the experiment. This reminds me of my reaction to Fuchs' and Peres' assertion:

If Erwin has performed no observation, then there is no reason he cannot reverse Cathy’s digestion and memories. Of course, for that he would need complete control of all the microscopic degrees of freedom of Cathy and her laboratory, but that is a practical problem, not a fundamental one.

This is non-sense, because the description of the experiment given previously was complete enough to rule out any possibility for Erwin to reverse the situation. ... If Erwin had access to a time machine enabling him to realistically reverse the situation, then it might turn out that Cathy and Erwin indeed lived multiple times through both situations (and experienced real macroscopic superpositions), as depicted in movies like “Back to the Future”.