Double Slit and Shroedinger's Cat

[Weeping Rupee]

I'm not a physics major and I have only a minimal/mild understanding of physics at best, and I have a question.

I've heard and read a lot of people say that using the phrase "observation collapses the wave function" is very misleading, and that it should more accurately be said that "measurement collapses the wave function."

I realize that the detector is interacting with the particle and that the experiment as a whole does not mean anything like "consciousness determines the way the universe behaves" necessarily (as so many self help doctrines have used to justify ideas similar to "the secret")

BUT! I'm wondering then; what is the point/justification for the cat existing in two states until observed in the Schrodinger's Cat analogy? Is it just an analogy used to describe how certain very very small things act in QM or is the argument that for objects of our size this is a reality? If the latter is true, is there some other experiment or principal that shows this is the case?


thanks in advance.

 

[Nugatory]

BUT! I'm wondering then; what is the point/justification for the cat existing in two states until observed in the Schrodinger's Cat analogy? Is it just an analogy used to describe how certain very very small things act in QM or is the argument that for objects of our size this is a reality? If the latter is true, is there some other experiment or principal that shows this is the case?

The cat doesn't exist in two states at once, and no one has ever seriously suggested otherwise (some mischievous Copenhagenistas will point out that we have no way of proving that the cat is not in two states at once, but that's not the same thing as saying that it is in two states at once).

Schrodinger proposed this famous thought experiment not because he thought the cat was really in two states at once, but to point out a problem in the then-current understanding of quantum mechanics. As it was formulated then, QM didn't have any satisfying explanation for why the cat wouldn't be in two states at once. Only many decades later did the discovery of decoherence (google for "quantum decoherence", but I have to caution you that some of it is pretty heavy going) start to answer this question.

There's a pretty decent book written for laymen, entitled "Where did the weirdness go" that explains this at a hand-wavy no-math level.

 

[PeterDonis]

The cat doesn't exist in two states at once

No, but it *can* be in a state that looks nothing at all like a classical state. Before the cat is measured, it's in a superposition of |alive> and |dead>. This superposition is not "being in two states at once", true; but it *is* being in a single state that is nothing like the classical states |alive> and |dead> that we're used to seeing.

Only many decades later did the discovery of decoherence (google for "quantum decoherence", but I have to caution you that some of it is pretty heavy going) start to answer this question.

Decoherence does not say that superpositions don't exist. All it does is show why superpositions like the cat's above (of |alive> and |dead>), involving systems with many, many quantum particles interacting with an environment, can't last very long. In the case of the cat thought experiment, decoherence tells you that the cat won't stay in a superposition of |alive> and |dead> until you open the box; just the presence of air molecules inside the box, interactions with the box walls, etc. is sufficient to quickly decohere the cat's state after the radioactive atom inside the box decays, so that the cat is either |alive> or |dead> well before we open the box to look.

But that doesn't mean the cat is never in a superposition; it just means that the superposition only lasts for a very short time. In principle, if we could isolate the cat well enough from all environmental interactions, we could keep it in a superposition of |alive> and |dead> indefinitely; but the level of isolation this would take for a system like a cat is far beyond our technology now or in the foreseeable future, whereas we know how to do it for atoms and small molecules today.

 

[Nugatory]

Decoherence does not say that superpositions don't exist. All it does is show why superpositions like the cat's above (of |alive> and |dead>), involving systems with many, many quantum particles interacting with an environment, can't last very long.

Right - the problem with 1930-vintage QM is that it had no explanation for why macroscopic superpositions couldn't persist indefinitely and be observed. Decoherence explains the lack of observed macroscopic weirdness not by saying that superpositions don't exist, but rather that they disappear so quickly as to be macroscopically irrelevant.

Interestingly, experimenters are managing to produce ever-larger superimpositions by carefully isolating systems and measuring them in ways that minimize decoherence. The largest superimposed systems created so far are however still many many orders of magnitude smaller than a cat (or even an oyster) and the superimposition is very fragile.

 

[bhobba]

No, but it *can* be in a state that looks nothing at all like a classical state. Before the cat is measured, it's in a superposition of |alive> and |dead>.

In standard Copenhagen that's not the case. It is assumed the world is divided into classical and quantum. Observations appear here in the classical world and in Schroedinger's cat that happens at the particle detector. From that point on everything is classical. The cat is never in a superposition, it is alive or dead whether the box is opened or not.

The same with other interpretations as well - such as Ensemble or Ignorance Ensemble.

The purpose of Schroedinger's cat was to bring home the problem with this arbitrary division. No one seriously thought the cat was in a superposition. QM is the fundamental theory of the world around us so should be expected to explain that world. Its a bit hard to do that when the existence of that world is assumed to begin with. What was needed was a purely quantum theory of measurement. A lot of progress has been made to that end in recent times, but a few issues such as the so called factoring problem do remain.

The cat doesn't exist in two states at once, and no one has ever seriously suggested otherwise (some mischievous Copenhagenistas will point out that we have no way of proving that the cat is not in two states at once, but that's not the same thing as saying that it is in two states at once).

I wish more people realized that.

Thanks
Bill

 

[bhobba]

Decoherence does not say that superpositions don't exist.

Of course.

What it explains is how 'apparent' collapse occurs ie a superposition is converted to an improper mixed state that is observationally equivalent to a proper one ie you can assume, and there is no way to tell the difference, that the cat is alive or dead whether the box is opened or not.

In effect this puts the Von Neumann cut just after decoherence which in Schroedinger's cat occurs at the particle detector. Again everything is common sense from that point on.

That's the view of the Ignorance Ensemble interpretation. Its advantage over Copenhagen and Ensemble is it defines an observation independent of a quantum classical cut.

I don't want to get into a drawn out discussion of if decoherence solves the measurement problem. Having been involved in many of those it boils down to semantics. It doesn't solve the measurement problem, but leads to modern interpretations such as MW, Consistent Histories and Ignorance ensemble that do by dint of further assumptions. And they easily solve Schroedinger Cat as well.

But I suspect you know that anyway :thumbs::thumbs::thumbs::thumbs:

Thanks
Bill

 

[bhobba]

Right - the problem with 1930-vintage QM is that it had no explanation for why macroscopic superpositions couldn't persist indefinitely and be observed. Decoherence explains the lack of observed macroscopic weirdness not by saying that superpositions don't exist, but rather that they disappear so quickly as to be macroscopically irrelevant.

Exactly.

I just want to add though the superposition that decays quickly is at the particle detector - not the cat.

Thanks
Bill

 

[PeterDonis]

What it explains is how 'apparent' collapse occurs ie a superposition is converted to an improper mixed state that is observationally equivalent to a proper one ie you can assume, and there is no way to tell the difference, that the cat is alive or dead whether the box is opened or not.

By "observationally equivalent", do you mean equivalent under any possible observations, or only under observations we can make with our current or near future technology? My understanding is it's the latter; that in principle there *are* observations that could be made to distinguish the two cases, but they're much too difficult for us to make now or in the foreseeable future.

In effect this puts the Von Neumann cut just after decoherence which in Schroedinger's cat occurs at the particle detector.

Yes, good point; decoherence is going to occur way before anything gets to the cat.

 

[bhobba]

By "observationally equivalent", do you mean equivalent under any possible observations, or only under observations we can make with our current or near future technology?

Its equivalent from the Born rule.

Take a mixed state of the form P = ∑ pi |bi><bi|. That may be from say some agency presenting the |bi><bi| to be observed with probability pi - in which case its called proper. Or it may be from something else such as decoherence - in which case its called improper.

Regardless the Born rule says if you observe it with any observable O, E(O) = Trace (PO). Since the statistical results are exactly the same its impossible, by any observation, to tell the difference.

That such is the case leads to the so called ignorance ensemble interpretation. Since there is no way to tell the difference I am perfectly entitled to assume its a proper mixed state, meaning it was in the state |bi><bi| prior to observation ie an actual collapse had occurred. Basically I have placed the Von Neumann cut at decoherence.

A discussion of such things can be found here:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

What you may be alluding to is while decoherence occurs very quickly and via tracing over the environment etc etc changes to a state virtually indistinguishable from a mixed state, theoretically it never is exactly that. Future progress may allow us to detect that difference - but it is very very small and gets smaller with time, so I personally would not be confident about that - still one never knows.

Thanks
Bill

 

[StevieTNZ]

I'm reminded of GianCarlo Ghirardi's thought experiment that tests whether collapse occurs at the macroscopic detector or not (whether the system is still in a pure, or now mixed, state), in his book "Sneaking a Look at God's Cards". If QM is correct, collapse does not occur at the macroscopic detector.

 

[bahamagreen]

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... :)

 

[bhobba]

If QM is correct, collapse does not occur at the macroscopic detector.

Von Neumann showed it can occur anywhere - that is called the Von Neumann cut.

The thought experiment you are referring to doesn't show that - its a thought experiment on how to tell the difference between a superposition and a mixed state. Since they are entirely different that is not an Earth shattering revelation.

Just to detail the difference a mixed state is a positive operator of unit trace that is the convex sum of pure states. A superposition simply expresses the vector space nature of pure states. A pure state and a mixed state are totally different so of course you can tell the difference. To be specific p1|u1> + p2|u2> is a superposition of |u1> and |u2> and is a pure state, and an element of a vector space, just like |u1> and |u2> are. But p1 |u1><u1| + p2 |u2><u2| is a mixed state, a positive operator, not a superposition, and not a pure state.

Thanks
Bill

 

[PeterDonis]

What you may be alluding to is while decoherence occurs very quickly and via tracing over the environment etc etc changes to a state virtually indistinguishable from a mixed state, theoretically it never is exactly that. Future progress may allow us to detect that difference - but it is very very small and gets smaller with time

Yes, that's what I was alluding to. The only thing I would add is that the difference will eventually get large again, after a very long time has elapsed (because eventually the various phases involved will all come into sync again), but for any experiment we can perform now or in the near future where decoherence is involved, that time is much longer than the age of the universe, so it's irrelevant in a practical sense.

 

[bhobba]

Yes, that's what I was alluding to. The only thing I would add is that the difference will eventually get large again, after a very long time has elapsed (because eventually the various phases involved will all come into sync again), but for any experiment we can perform now or in the near future where decoherence is involved, that time is much longer than the age of the universe, so it's irrelevant in a practical sense.

Got it.

And I agree.

Thanks
Bill

 

[Demystifier]

Suppose that somehow, with a very advanced technology, we can isolate the cat from the environment thus avoiding decoherence. Even though it seems impossible in practice, the fundamental laws of physics do not seem to forbid it in principle. In this sense, in principle, an interference experiment with a cat is not absolutely impossible. So hypothetically, if we could perform such an interference experiment with a cat, what would it be like to be the cat herself? Here is the answer:
http://lanl.arxiv.org/abs/1406.3221