Schrödinger's Cat and radioactive atom

[entropy1]

Particles can be made to be in superposition of their states. Concerning Schrödingers cat, if the cat is in superposition of being dead and alive, does that mean that the atom that drives the narcotic is in superposition of having decayed and not having decayed? And does that mean that any radioactive atom is always in that superposition?

 

[anuttarasammyak]

Yes, they are in corresponding superposition states.

 

[phinds]

Concerning Schrödingers cat, if the cat is in superposition of being dead and alive,

The cat is never in superposition of being dead and alive. It's always either dead or alive.

Schrödinger 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.

https://www.wtamu.edu/~cbaird/sq/2013/07/30/what-did-schrodingers-cat-experiment-prove/

And here on PF:
https://www.physicsforums.com/threads/quantum-cat-question.798022/

 

[StevieTNZ]

The cat is never in superposition of being dead or alive. It's always either dead or alive.

https://www.wtamu.edu/~cbaird/sq/2013/07/30/what-did-schrodingers-cat-experiment-prove/

And here on PF:
https://www.physicsforums.com/threads/quantum-cat-question.798022/

Please explain how this OR case comes about.

 

[phinds]

Please explain how this OR case comes about.

Do you mean you want me to explain why pop-science presentations, which are not actual physics but rather are entertainment, will always say that the cat is alive OR dead?

Get a textbook.

 

[StevieTNZ]

Do you mean you want me to explain why pop-science presentations, which are not actual physics but rather are entertainment, will always say that the cat is alive OR dead?

Get a textbook.

Which textbook do you suggest? And actually answer my question. Is that how you got your SA badge? By telling people to Google for answers or get "a textbook" without being specific, instead of being knowledgeable yourself about the subject and answering accordingly? What a joke PF has become.

EDIT: tagging @Greg Bernhardt into this post so something can be done once and for all.

 

[phinds]

Which textbook do you suggest?

It depends on your level and just how deep you want to dive in. There are a number of theads here discussing what books are best. Here's a good one to check out
https://www.physicsforums.com/threads/good-textbook-for-qm.238397/

 

[StevieTNZ]

Threads like this -- https://www.physicsforums.com/threads/macroscoptic-quantum-entanglement.1009354/ -- become rather pointless seeing you dismiss the idea of superposition states for macroscopic objects. Your reasoning, I don't know.

 

[phinds]

And actually answer my question.

Your question boils down to "why do people who do not know what they are talking about, not know what they are talking about". I don't have a good answer for that in general but in this particular case it's likely because they are getting THEIR information from pop-science presentations instead of from textbooks.

Unfortunately the cat thing is one of many items in physics that have been grossly misrepresented in the popular press, usually starting not long after the time the concept is first discovered and continuing all the way up to the present.

 

[StevieTNZ]

Your question boils down to "why do people who do not know what they are talking about, not know what they are talking about". I don't have a good answer for that in general but in this particular case it's likely because they are getting THEIR information from pop-science presentations instead of from textbooks.

Unfortunately the cat thing is one of many items in physics that have been grossly misrepresented in the popular press, usually starting not long after the time the concept is first discovered and continuing all the way up to the present.

You are simply misguided. At no point in the linear Schrödinger equation does 'collapse of the wave function' occur. How does a superposition state (AND) suddendly become OR? Answer me that.

 

[phinds]

Hm ... I thought I was addressing the OP. Sorry about that.

 

[phinds]

@StevieTNZ are you saying that you believe there IS a state in which the cat is both dead and alive?

 

[StevieTNZ]

@StevieTNZ are you saying that you believe there IS a state in which the cat is both dead and alive?

Indeed I am. It follows from the fundamental Schrödinger equation; decoherence does nothing to depart from that view as its simply entanglement with the environment. While interference is supressed, its present in principle. However, taking all systems together and doing a double slit will show interference.

 

[StevieTNZ]

I actually suggest you read "Sneaking a Look at God's Cards", the book most referenced here as a good source of information on quantum theory for the layman. It seems you don't have the appropriate qualifications in physics to deal with this subject. I'm not trying to sound harsh, but it might illuminate the quantum world for your information.

 

[phinds]

@StevieTNZ are you saying that you believe there IS a state in which the cat is both dead and alive?

Indeed I am.

Well, I have no answer to that other than to suggest you read the links I provided and a few hundred others here on PF which all show in various ways why the cat is not, and cannot be, both dead and alive at the same time.

 

[PeterDonis]

At no point in the linear Schrödinger equation does 'collapse of the wave function' occur.

You don't need "collapse of the wave function" to have a cat state that is not a coherent superposition of dead and alive. All you need is decoherence. Even the many worlds interpretation recognizes that, once the "dead" and "alive" branches of the wave function have decohered, they will never interfere with each other, and without interference, there is no way to ever demonstrate experimentally that both branches of the superposition are there.

 

[entropy1]

You don't need "collapse of the wave function" to have a cat state that is not a coherent superposition of dead and alive. All you need is decoherence. Even the many worlds interpretation recognizes that, once the "dead" and "alive" branches of the wave function have decohered, they will never interfere with each other, and without interference, there is no way to ever demonstrate experimentally that both branches of the superposition are there.

So, don't we then have superposition without interference, in this case the cat dead AND alive but in different world threads? (Although that might be semantics)

 

[entropy1]

If a radioactive atom is continuously in superposition of not having decayed and having decayed, has it or hasn't it? What can actually be said about it?

 

[Lord Jestocost]

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.

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.

 

[Lord Jestocost]

The cat is never in superposition of being dead and alive. It's always either dead or alive.

The formalism of quantum mechanics doesn’t change one whit between the microscopic and macroscopic levels. Thus, with all due respect, statements like “the cat is always either dead or alive” make physically no sense and merely reflect classical wishful thinking. One cannot make a quantum theoretical thought experiment using a living organism as its integrating part, but on the other hand do not take seriously the application of quantum theory, i.e., here simply the concept of probability, to the organism.

 

[entropy1]

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.

, there is no way to ever demonstrate experimentally that both branches of the superposition are there.

So does that mean that we can only find ourselves observing the cat being either alive or dead, and that it means the cat is either alive or dead? Or is the reality that QM actually does not make a choice between those? (And that might mean the observed world is pretty much "an illusion", and that some other notion, like the wave function is ontic)

 

[AlexCaledin]

If I remember correct, James Hartle says that the actual decoherent history (which we find ourselves observing) is ontic, it's determined by the "quantum dice throwing" - so we can use the QM to calculate the probabilities, so the cat superposition is merely a thinking tool...

 

[WernerQH]

If a radioactive atom is continuously in superposition of not having decayed and having decayed, has it or hasn't it? What can actually be said about it?

There's a widely held conviction that "every physical system is described by a wave function". Yet through reductio ad absurdum Schrödinger himself disproved this idea with his (in)famous cat experiment. Surprisingly many physicists think that it ought to be meaningful to speak of a cat that is both dead and alive at the same time, but Schrödinger chose the example of a cat precisely because he considered it too absurd even to contemplate.

The superposition of photon states is well defined and meaningful, e.g. $\frac 1 {\sqrt 2} |\text{horizontal}\rangle + i × \frac 1 {\sqrt 2} |\text{vertical}\rangle$ represents circular polarization. But the "analogous" state $\frac 1 {\sqrt 2} |\text{undecayed}\rangle + i × \frac 1 {\sqrt 2} |\text{decayed}\rangle$ for an unstable nucleus is without any operational meaning. An undecayed atom that has been sitting there for one half-life is experimentally indistinguishable from another atom that is "freshly prepared". The decay happens in a fraction of a second, on a timescale much shorter than the half-life. To insist that the first atom is in a different state that should be represented by $\frac 1 {\sqrt 2} |\text{decayed}\rangle + \frac 1 {\sqrt 2} |\text{undecayed}\rangle$ is to attribute more reality to the wave function than to reality itself.

 

[PeterDonis]

don't we then have superposition without interference, in this case the cat dead AND alive but in different world threads?

In the many worlds interpretation, yes. But there are other interpretations in which that is not the case.

If a radioactive atom is continuously in superposition of not having decayed and having decayed, has it or hasn't it?

Neither.

What can actually be said about it?

That it is in a superposition of not having decayed and having decayed.

So does that mean that we can only find ourselves observing the cat being either alive or dead, and that it means the cat is either alive or dead?

Remember, the comment of mine you responded to here was specifically about the MWI. In the MWI, the cat has no definite state because it is entangled. Only the joint system of radioactive atom plus cat has a definite state. That is a general property of entangled systems: neither system alone has a definite state, only the joint total system does.

Or is the reality that QM actually does not make a choice between those?

This is too vague to be meaningful.

(And that might mean the observed world is pretty much "an illusion", and that some other notion, like the wave function is ontic)

In the MWI, yes, the wave function is ontic, and it is the only thing that is ontic.

 

[PeterDonis]

There's a widely held conviction that "every physical system is described by a wave function". Yet through reductio ad absurdum Schrödinger himself disproved this idea with his (in)famous cat experiment.

Whether or not that is true depends on which interpretation of QM you adopt. This is the interpretations subforum, so it's ok to discuss interpretations, but if you review the ground rules for this forum, you will see that it is not permitted to assert that any particular interpretation is the "correct" one. You have to state which interpretation you are using and make clear that what you are saying is only true for that interpretation. In your case, you are adopting an interpretation in which "collapse of the wave function" is some kind of real process (there are multiple interpretations along these lines, according to what kind of real process "collapse" is claimed to be). But on an interpretation like the MWI, "every physical system is described by a wave function" is indeed correct, and the Schrödinger's cat thought experiment is not a reductio ad absurdum of anything, but just a description of how the MWI describes a scenario in which a cat is involved.

 

[PeterDonis]

If a radioactive atom is continuously in superposition of not having decayed and having decayed

I probably should have commented on this when responding before to this post of yours, but this is not a good description of a radioactive atom in QM. See below.

the "analogous" state $\frac 1 {\sqrt 2} |\text{undecayed}\rangle + i × \frac 1 {\sqrt 2} |\text{decayed}\rangle$ for an unstable nucleus is without any operational meaning.

Which is fine since this state is not a state that figures in any actual analysis of radioactive decay. The actual state of a radioactive atom is one in which the amplitude for decay in some finite period of time is constant in time. Viewing it as being in a superposition like the one you write down (and which is the kind of state @entropy1 appeared to be imagining) is not correct.

 

[entropy1]

Remember, the comment of mine you responded to here was specifically about the MWI. In the MWI, the cat has no definite state because it is entangled. Only the joint system of radioactive atom plus cat has a definite state. That is a general property of entangled systems: neither system alone has a definite state, only the joint total system does.

Do you mean that the superposition of the two world threads (eg $|E_0, v_0 \rangle + |E_1, v_1 \rangle$) is the definite value of the joint system?

 

[PeterDonis]

Do you mean that the superposition of the two world threads (eg $|E_0, v_0 \rangle + |E_1, v_1 \rangle$) is the definite value of the joint system?

I don't know where you're getting the specific superposition you wrote down from, but if we idealize the whole experiment as being isolated from the rest of the universe, then yes, the joint system has a definite state which is entangled, and if you write that state down it will be a sum of two terms (in the case where whatever measurement is being made has two possible outcomes).

 

[Dr Wu]

Interesting discussion! 'Sneaking a Look at God's Cards' has certainly garnered a lot of praise in Amazon's review section, particularly from self-confessed laymen. . . whose ranks include this poster! Unhappily its current price tag is a bit fierce for this pocket, even secondhand (£28) which may be due to it being possibly out of print? I did find 'In Search of Schrödinger's Cat' by John Cribbin an informative and engaging read, likewise the far more recent 'Beyond Weird' by Philip Ball, who I trust is no 'pop' scientist.

 

[akhmeteli]

Well, I have no answer to that other than to suggest you read the links I provided and a few hundred others here on PF which all show in various ways why the cat is not, and cannot be, both dead and alive at the same time.

You provided a link to what looks like a private web-site and referred us, your readers, to PF threads. Those are not reliable sources. If you insist that a cat cannot be both dead and alive, apparently you don't believe that quantum mechanics is correct for macroscopic objects. Nobody performed sufficiently precise experiments with cats, so it is possible that you are right, but it is also possible that you are wrong. Mind you, I am not saying that observer's consciousness plays any role in quantum experiments.

Schrödinger discussed his gedanken experiment in 1935 and argued that a cat being both dead and alive is clearly absurd. However, that was 85 years ago, and since then there has been a lot of progress in experimental physics. You may wish to look at Haroche's Nobel lecture . He mentions Schrödinger's cats and "kittens" without any sarcasm maybe 50 times. He says: "We have realized the non-destructive counting of photons, the recording of field quantum jumps, the preparation and reconstruction of “Schrödinger cat” states of radiation and the study of their decoherence, which provides a striking illustration of the transition from the quantum to the classical world." He says: "The Schrödinger cat experiments in Cavity QED illustrate the fragility of quantum coherences in systems made of increasing number of particles." Fragility, not impossibility! I heard his lecture at 2013 APS March meeting, where he said during the discussion: "There is no fundamental decoherence". (There is a possibility though that I mixed up something and it was not Haroche but Wineland, who presented on the same day). So I would say quantum mechanics predicts superpositions of dead and alive cats and experiments do not disprove that (yet).