How can Schrödinger's Cat be both alive and dead?

[stevendaryl]

A proper mixture is one created by supplying a randomly selected pure state to be observed. It leads to a mixed state operator. The same operator results from decoherence but it was not physically created the same way.

I'm not sure that there is a big distinction here. How does one randomly select something? If you use quantum randomness (for example, using decay times, or spin measurements, or whatever), then you're just entangling the state with something else, just as with decoherence (except it's done on purpose). On the other hand, if you classical randomness, such dice, then it's not truly random.

 

[stevendaryl]

I personally hold to the ensemble interpretation - but as you can see it's not generally agreed it solves the measurement problem.

I don't understand what the ensemble interpretation means for quantum mechanics. Well, if we're talking about mixed states, it makes sense, but is the ensemble interpretation supposed to be useful for pure states as well?

For pure states, what bothers me about the ensemble interpretation is the question of what VARIES from one element of the ensemble to another. In the ensemble interpretation of classical statistical mechanics, you have an ensemble of systems, all of which have the same macroscopic state (specified by temperature, volume, number of particles, etc.) but differ in microscopic state (positions and momenta of particles). So when we try to reason about our actual system, we don't know the details, so it could be any system in the ensemble. So out of ignorance, we can only make statistical statements about our system.

I just don't see how the ensemble approach is supposed to be applied to quantum uncertainty. If you prepare an electron with spin-up in the z-direction, then its spin in the x-direction is uncertain. But if we try to create an ensemble model for this uncertainty, what do you do? Do you have one system in the ensemble with spin-up in both the x-direction and the z-direction, and one system in the ensemble with spin-down in the x-direction and spin-up in the z-direction? You can't do that, because they are incompatible observables.

So what varies from one member of the ensemble to another?

 

[bhobba]

I'm not sure that there is a big distinction here. How does one randomly select something?

Easy - imagine you are given a system to observe that someone has randomly selected. That's the standard interpretation of a mixed state. If they are eigenstates of the observable you are measuring then no collapse occurs and its in that state prior to observation.

Thanks
Bill

 

[bhobba]

I don't understand what the ensemble interpretation means for quantum mechanics. Well, if we're talking about mixed states, it makes sense, but is the ensemble interpretation supposed to be useful for pure states as well?

What don't you understand about the idea of decoherence converting a pure state to a mixed state of eigenstates of what you are observing?

So what varies from one member of the ensemble to another?

The eigenstates of the observable you are measuring.

Thanks
Bill

 

[stevendaryl]

What don't you understand about the idea of decoherence converting a pure state to a mixed state of eigenstates of what you are observing?

There's a lot I don't understand about it, but the specific issue is: What does that have to do with ensembles? Decoherence seems to be a mechanism for getting an effective mixed state in a case where there is no ensemble involved.

The eigenstates of the observable you are measuring.

So the ensemble is determined by which experiment you perform? I don't see what the ensemble is doing for you, in that case.

 

[audioloop]

ah wow, excellent link. they give a nice introduction and description of this collapse problem, and ideas that have been put forward to explain it.

yes, put objects on ground states, decoherence free.
the issues of decoherence is that preserves all the superpositions:

http://arxiv.org/pdf/1001.3391v1.pdf

"Our second observation has to do with the quantum measurement problem. As is known,
during such a measurement, the quantum system makes a transition from being in a superposition of eigenstates of the measured observable, to being in one of the eigenstates, and the probability of any given outcome is proportional to the square of the amplitude for the wave function to be in that state. If we assume that this transition happens within the framework of standard linear quantum mechanics, then it is explained by the phenomenon of decoherence, in conjunction with the Everett many worlds interpretation. Decoherence destroys interference amongst the various superposed alternatives, while still preserving their superposition. However, since we observe only one of the alternatives in an outcome, we must invoke also the branching of the Universe into many worlds, at the time of a measurement, so that the quantum system, apparatus, and observer, all split into dierent branches, one branch for every alternative."
.

 

[bhobba]

So the ensemble is determined by which experiment you perform? I don't see what the ensemble is doing for you, in that case.

I will go through it one more time, but if you still don't get it I will have to leave it up to someone else.

A proper mixed state is when by some process, such as someone presenting it to you, a randomly selected state is given for observation. The randomness is modeled by an ensemble of states containing the states that can be presented for observation. Now suppose those randomly selected states are all eigenstates of what you are observing. The observation does not change the state - no collapse occurs. What you observe is there before observation, and the observation simply reveals what is already there. No collapse, no measurement problem, objective reality exists out there independent of observation, much, if not all quantum weirdness disappears.

Now the mathematics of such a situation is described by mixed states and that is precisely what decoherence does - transforms a pure to a mixed state where the components of that mixed state are eigenstates of what you are observing. If it was a proper mixed state - measurement problem solved. However it is only mathematically, not physically, the same. And that's where issues arise.

Thanks
Bill

 

[stevendaryl]

I will go through it one more time, but if you still don't get it I will have to leave it up to someone else.

I still don't get it, so could someone else explain how ensembles do anything for you
in terms of interpretations of quantum mechanics? It doesn't make any sense to me.

Yes, if a system is prepared in such a way that it is a mixture of eigenstates of whatever it is you're trying to measure, then you can think of your measurement classically, and use the classical notion of ensembles. But what if it was not prepared to be a mixture of eigenstates of the observable you're trying to measure? Quantum mechanics still gives the same statistical predictions, although the ensemble view doesn't seem to make any sense, in such a case.

So it seems to me that the ensemble interpretation of probability makes no sense for quantum mechanics. Not in any obvious way, anyway (without invoke weird measures, or nonlocal interactions, or something else).

 

[bhobba]

the issues of decoherence is that preserves all the superpositons:

That is exactly what decoherence does NOT do.

Nor does decoherence require the MWI.

A pure state in superposition is transformed to a mixed state by becoming entangled with the environment and measurement apparatus, and one of the components of the mixed state is selected by observation.

What remains in superposition is the environment, measuring apparatus, and system being observed as a whole - not the system being observed or observational apparatus which are now entangled. In fact the modern view of measurement is it is nothing but entanglement - which is the view given in Susskinds lectures I linked to before.

Thanks
Bill

 

[audioloop]

That is exactly what decoherence does NOT do.

Nor does decoherence require the MWI.

A pure state in superposition is transformed to a mixed state by becoming entangled with the environment and measurement apparatus, and one of the components of the mixed state is selected by observation.

What remains in superposition is the environment, measuring apparatus, and system being observed as a whole - not the system being observed or observational apparatus which are now entangled. In fact the modern view of measurement is it is nothing but entanglement - which is the view given in Susskinds lectures I linked to before.

Thanks
Bill

i disagree, decoherence does not solve the measurement problem.

 

[bhobba]

i disagree, decoherence does not solve the measurement problem.

Well seeing that's not what I said, and I even posted it didn't, why you posted that is - well - puzzling.

Thanks
Bill

 

[jambaugh]

"Our second observation has to do with the quantum measurement problem. As is known,
during such a measurement, the quantum system makes a transition from being in a superposition of eigenstates of the measured observable, to being in one of the eigenstates, and the probability of any given outcome is proportional to the square of the amplitude for the wave function to be in that state. If we assume that this transition happens within the framework of standard linear quantum mechanics, then it is explained by the phenomenon of decoherence, in conjunction with the Everett many worlds interpretation. Decoherence destroys interference amongst the various superposed alternatives, while still preserving their superposition. However, since we observe only one of the alternatives in an outcome, we must invoke also the branching of the Universe into many worlds, at the time of a measurement, so that the quantum system, apparatus, and observer, all split into dierent branches, one branch for every alternative."

There is a prevalent language problem exemplified by this author which seeps into ones attempt to understand the issues. Let me key specifically on
"the quantum system makes a transition from being in a superposition of eigenstates of the measured observable, to being in one of the eigenstates"

This transition is not physical --in and of itself-- in that the qualities of "being in a superposition of eigenstates" vs "being in one eigenstate" are not observable properties of the system. Of course "being in a specific eigenstate" is exactly the statement that the system has been observed but the comparison between "spooky superposition" vs "sensible objective non-superposition" is not a physical distinction. To say a system is in superposition of states of one observable one must specify effectively that the system is in a specific "sensible objective non-superposition" eigen-state of another (complementary) observable.

The system is always in in the eigen-state of some observable when we are describing it with wave-functions or more generally Hilbert space vectors.

Everyone contemplating quantum mechanics should focus and meditate on this one point until it is clear, superposition is not a physical property of a system, it is a relationship between observables, the fact that they are not compatible but rather complementary.

Get this clear and then re-parse the Schrodinger Cat experiment, asking yourselves a question at the point in the narrative where the cat is hypothesized to be in a superposition.

Of what complementary observable is the cat then in an eigenstate?

To attempt to answer this question we must and may go back and describe the observable for which the original decaying atom was in an eigenstate when asserted to be in a superposition of whole and decayed. It is out there just not easy to describe in terms of laboratory procedures. One would then take the dynamics and evolve this complementary observable forward in time to find its future equivalent. But in expanding the system to describe atom plus cat you are left with the impossibility of describing a living cat in a sharp initial state. The very concept of "alive" precludes the absolute zero temperature and zero entropy assumption when using a sharp description.

We must thus invoke a density operator format.

Now as to density operators and decoherence... let me point out that at one end you have a density operator constructed (mathematically) using classical probabilities. It thus has the same semantic status as a classical probability distribution in that it is not describing/modeling the system's state of reality but rather potential behavior when subject to an act of observation. I can speak of the outcome of a coin flip (before the flip!) as a 50%-50% "classical superposition" of heads vs tails and we all know the coin is not physically in a "cloud of probability" but rather that --languagewise-- I am speaking in the hypothetical mode. Now understanding that as the semantic meaning of the density operator at the end of the decoherence process, it is improper for us to change that semantic meaning along the described dynamic evolution. We must for the purposes of being consistent and clear, maintain that semantic interpretation of the density operator at the beginning when it is e.g. equivalently (to a hilbert space vector) expressing a system in a sharp "state". (Hence a better word is "sharp mode" as in mode of system production.)

Note that this does not argue that the sharp modes cannot be given alternative, metaphysical interpretation (though I assert this with other facts does imply such) it does however tell us that this is not the interpretation, the semantic meaning of the density operator and hence the quantum mechanics of the Schodinger's cat experiment and parallel thought experiments. And that my dears, plus the above hinted at assertion that no additional metaphysical interpretation is meaningful, is Copenhagen in a (moderately large) nutshell.

With CI there is no "measurement problem" or "Schrodinger's Cat" problem. Decoherence is de-coherence as in it is not iterpretationally distinct from classical "decorrelation". No other (metaphysical) interpretation can resolve the Schrodinger's Cat scenario any better than does CI. CI's explanation is the only explanation because no explanation can properly ignore this need for consistent unchanging meaning of the density operator when it is invoked in this instance nor deny the classical meaning of probabilities as limiting relative frequencies for non-actualized potential outcomes. One is committed to remaining in the hypothetical mode for the duration of the exposition.* "IF we measure A, we see a1 with probablity p1 and ..."

(* or one must present a very explicit and very rigorous treatment of the transition to actual mode. I think this is best done by using a wholly distinct set of words/symbols. Something like \hat{\psi} for a "metaphysical" wave function and \tilde{\psi} for a "statistical" wave function, if these are what you want to invoke.)

 

[BruceW]

But in expanding the system to describe atom plus cat you are left with the impossibility of describing a living cat in a sharp initial state. The very concept of "alive" precludes the absolute zero temperature and zero entropy assumption when using a sharp description.

We must thus invoke a density operator format.

Now as to density operators and decoherence... let me point out that at one end you have a density operator constructed (mathematically) using classical probabilities.

yes, agreed. If we only know about the cat as a mixed state, then there is no problem, since we can blame the collapse on the fact that we have used classical probabilities. But what if I could write down the pure quantum state of the cat? Then we could no longer blame classical probabilities. So this comes back to the question "is it possible in principle to know the pure quantum state of a cat?". This is out of our grasp technology-wise, which is why it is kind of a moot point. But on the other hand, to say that we cannot in principle write down the pure quantum state of a cat, leaves us with an unsatisfactory theory. I say that, because there is no clear answer for what we can write down as a pure quantum state and what we can't. But of course, in many cases (i.e. the cat), it doesn't really matter, because we are not practically any where near to being able to write down it's pure quantum state anyway. Also, I'm not saying that any other interpretation is better than CI, I'm just saying they are all unsatisfactory.

edit: when I say "being able to write down the pure quantum state of the cat", you know what I mean, like what we can do with an atom. Doing a diffraction experiment with a cat would also answer the same question (and would also be ridiculously difficult experimentally).

 

[nitsuj]

I don't see any sense in this picture. We just don't know about the state, that's it. If I have a dice and you know that I will kill the cat if I play the dice and have a 6 then I am with a chance of 1/6 a cat killer and the cat is with a chance of 1/6 dead.
That's all. This does not produce any superpositions of killers or not-killers and cats being dead or alive. It's only quantum mechanics where we don't know about the outcome of a situation, it is nothing but that we don't know when something will happen but we know from experience that it will happen earlier or later (not me, I won't kill a cat).
We see quantum entanglement but this has nothing to do with superstates of a cat or whatever. Einstein wrote, in translation more or less "God does not play dices". He might have been wrong but it might be the same way wrong to overstress something simple given: Uncertainty.

Im glad this thread come back up again, I wouldn't have read this other wise.

I totally agree with your sentiment on this. "Uncertainty" has always been strange to me from a physical perspective. Your description is from the correct perspective. The "story/interpretation" from microscopic to macroscopic Is just bizarre. Especially if a retort is along the lines of well, it's true for a particle, then it's how the macroscopic world works. We already have started from macroscopic and for a very very good reason. Tech pops up (well math/ experiments) and suddenly the majority "switch" to that perspective of analysis.

As if the mechanics of physics "cares" about the distinction we have between the macro & micro. In other words there is no "this precedes that" from a scale perspective. (I don't mean "precede" from a dimensional sense, just a logic sense; for all I know, temporally "micro" precedes "macro, my point is one view is not "superior" to the other logically...less the nonsense part )

The "story/interpretation" of QM is nonsense imo. Never should we have to throw out axiom type logic for the sake of even the "most successful" theory.

I don't know QM well enough to say what I think is true, but it is what I think as a "general public person".

In other words, less "it's what the math predicts and what the experiment results confirm" and more story telling. I think that was given up on part way through GR...poor Albert :(

Confirm the "story" with experiments, not confirm the mathematics with experiments.

Anyways glad to see there are others out there with a sane physics perspective too, and if that's ignorance, well too bad for the "enlightened".

 

[jambaugh]

Then we could no longer blame classical probabilities. So this comes back to the question "is it possible in principle to know the pure quantum state of a cat?".

Firstly to speak of a cat being "in a pure quantum state" you must cool it to absolute zero which precludes the validity of "alive" vs "dead" as a meaningful definition... the cat is dead by assumption from the beginning. Now to observe the phenomena of quantum superposition one will also need to perform a large number of experiments so you in effect need a beam of frozen cats so one can see say an interference pattern in the distributions of frequencies for some cat observable. [BTW This "frozen beam of cats" scenario is not mine, I heard it from my thesis advisor who may likewise not be the original source.]

But if one could produce a device emitting a beam of identically prepared frozen cats sufficiently identical to describe the device using a sharp wave-function, then one could indeed perceive superposition phenomena at such a scale. But as mentioned achieving such is pragmatically intractable, very very very much so.

Taking the experiment less literally one is again asking about the transition from quantum probabilities to macroscopically classical ones and again one is either committing the mistake of changing semantics mid stream or one is dealing with a non problem. The resolution is to always understand that quantum descriptions are statistical descriptions and the idea of "a pure quantum state (of reality)" is just plain wrong. One has a pure quantum mode of system production about which one is describing probabilities for potential observations. If one is being operationally meaningful one is never talking about anything else. If one is talking about something else one has moved beyond operationally meaning and is hypothesizing as far outside empirical science as invisible angels dancing on pinheads (which is to say all the way outside).

Also, I'm not saying that any other interpretation is better than CI, I'm just saying they are all unsatisfactory.

Then you are wrong! They may all be unsatisfactory but not equally so and saying so begs the question of satisfactory by what criterion. CI is THE interpretation of the meaning of the quantum language with the additional caveat that one should not attempt a metaphysical (i.e. ontological) interpretation. It is that last part that some find "unsatisfying". Most competing interpretations are attempts at restoring ontology. Still others are practically equivalent (to CI) e.g. Von Neumann's ensemble interpertation is letting the unactualized potential systems described by a wave function become an actualized (and thus large but finite) set of systems. But note again that von Neumann's reality of the ensemble cannot be reduced to an ensemble of realities for each component. There is no more reality in the ensemble interpretation than is in CI.

One must step back and understand that the bias of "realities" is a bias of classical physics which is inappropriate to QM, one then can be satisfied, and indeed enriched by the CI... or so I assert!

Meditate on the distinction between "objective reality" vs "independent actuality". (what is vs what happens). That is the transition of paradigm one must make to understand quantum physics without invoking the mystical in some form or other.

[Final qualifier, by CI I mean Bohr's, it is clear in some expositions of CI that the speaker understands some critical points differently, so that while what they say is technically correct, that is so only if you take what they say as distinct from what they obviously mean. E.g. that fact that the observer creates reality is true provided one understands that any "reality" is a mental construct, a conceptual model supposed to conform to an independent actuality which is there whether observed or not. And hence wave functions do "collapse in reality", but this collapse is none-the-less conceptual and not physical because "objective reality" is truly conceptual and not physical. To better see this ask yourself how you tell if a cat is really alive.

BTW I am thinking of Schrodinger, as and example of someone presenting CI and saying something distinct from what they mean when he cooked up this though experiment as a supposed counter argument to CI. In effect I'm saying Schrodinger misunderstood CI as Bohr understood it. Otherwise he would have seen that his cat paradox as vindicating CI rather than weakening it in that CI resolves the paradox by pointing out the antnomy (not the element, rather the semantic contradiction) we find behind all such paradoxes.]

 

[nitsuj]

Meditate on the distinction between "objective reality" vs "independent actuality". (what is vs what happens). That is the transition of paradigm one must make to understand quantum physics without invoking the mystical in some form or other.

Never should we have to throw out axiom type logic for the sake of even the "most successful" theory.

I've never thought (meditated lol) of/on this, is there really a distinction? The "mystical" part is the part that must be "thrown" out, and really how mystical is common sense at this level?. At least that's what I see.

There doesn't seem to be "continuity" of the "physics story". Logic and concepts cannot change part way through a story; if it's to make sense at that level (concepts & logic).

We have to introduce things like I have a brain, or lasers shooting out replicated frozen cats?

I suppose there is still some non-zero chance some genius will come along and rescue QM from the depths of common sense nonsense.

I really like that capitalism quote in your signature!

 

[BruceW]

Then you are wrong! They may all be unsatisfactory but not equally so and saying so begs the question of satisfactory by what criterion.

What is it about CI that you think is unsatisfactory?

 

[bhobba]

The "story/interpretation" of QM is nonsense imo. Never should we have to throw out axiom type logic for the sake of even the "most successful" theory.

Can't follow you there.

QM is weird - but nonsense is another matter.

I have said it before and I will say it again. In CI Schrodinger's cat is trivial, utterly trivial. Implicit in CI is the assumption and existence of a classical world that follows common sense rules ie is there when you are not looking etc etc. Quantum effects make their presence known when they make their mark in that world. In this case that occurs at the particle detector - that is where the mystery lies - if you want to use that type of language. The cat is never in any kind of superposition - it is alive or dead - period.

What Schrodenger's Cat showed is the need for a fully quantum theory of measurement without this artificial distinction between classical and quantum and since then much work has been done on this with a lot of progress. Some issues still remain such as the so called factoring problem and if people want to discuss that fine. But Schrodinger's cat is simply a non issue. What's going on in CI, the Ensemble Interpretation, MWI, Consistent Histories and the others I know the details of is either very easily handled or utterly trivial.

Thanks
Bill.

 

[jambaugh]

What is it about CI that you think is unsatisfactory?

Me? Not a thing. As I said it is a question of criteria. CI satisfies mine.

 

[BruceW]

what kind of CI are you thinking of? subjective non-unitary collapse, or objective non-unitary collapse? I find the subjective version (which is the more common one) to be completely unsatisfactory as a theory, even though it 'works' in a practical sense. The objective version is fine, but maybe that is not technically 'standard QM', because it gives different predictions, compared to the 'more common' subjective version.

By 'subjective version', I mean that we allow the non-unitary collapse to occur only when doing so will change the predictions of experiment by a 'negligible amount'. And of course, the 'negligible amount' depends on the experiment being done.

And by 'objective version', I mean that the non-unitary collapse is actually some kind of physical process. So in this case, we would potentially be able to measure when the non-unitary collapse occurs.

 

[bhobba]

By 'subjective version', I mean that we allow the non-unitary collapse to occur only when doing so will change the predictions of experiment by a 'negligible amount'. And of course, the 'negligible amount' depends on the experiment being done.

Gee I always thought it was the view, like probabilities, a state is simply an aid to help in calculating the outcomes of observations:
http://en.wikipedia.org/wiki/Copenhagen_interpretation
'The subjective view, that the wave function is merely a mathematical tool for calculating the probabilities in a specific experiment, has some similarities to the Ensemble interpretation in that it takes probabilities to be the essence of the quantum state, but unlike the ensemble interpretation, it takes these probabilities to be perfectly applicable to single experimental outcomes, as it interprets them in terms of subjective probability.'

Thanks
Bill

 

[BruceW]

yes, that is the basic idea. http://en.wikipedia.org/wiki/Copenhagen_interpretation
'Assuming wave functions are not real, wave-function collapse is interpreted subjectively.'
In this version of CI, the wave function is not 'real', so we can add in the non-unitary collapse wherever we want to.

The important part is that when we select this 'subjective wavefunction', we want to place the non-unitary collapse at a time when it makes negligible difference to the predictions of 'standard quantum mechanics'. For example, in most experiments with a cat, we can place the 'subjective non-unitary collapse' as soon as the cat gets entangled with the experiment. But if we were able to make an experiment where a cat is diffracted, then we cannot place the 'subjective non-unitary collapse' so early on, or it would change the predictions of the diffraction experiment. In this case, we must place the subjective non-unitary collapse sometime after, for example, when an even larger, more complicated system has become entangled.

 

[Omega0]

I thought about writing some long text but - without returning to basic statements - I would say:
There is an depency between the outcome of the experiment and the experiment setup.
I agree that it is possible to describe the state of the cat to be something like |dead> between 0 and 1 until it is
measured in a sense that the measurement shows what state comes out in the end.
This is a pure mathematical value.
Perhaps this is the maint point of the discussion: To differentiate between a possible (observable) state (which is physics) and a theoretical state which makes no sense in a logical way...

 

[Nugatory]

This thread has been sleeping quietly for almost two years now... Let's not wake it up now, especially because Schrodinger's Cat has been extensively discussed in other newer threads here.

Thread close.