Understanding the Cat in a Box Paradox

[StatusX]

I'm talking theorists, who have used this pragmatic approach for many years,

The problem with the Copenhagen approach from a theoretical point of view is that the act of "measurement" is not well-defined. There are various attempts at nailing this concept down, but none that seem obviously correct.

The difference with the many worlds view, and the reason I favor it, is that there is no collapse, and so the measurement problem disappears. In fact, that's the only real difference between it and the Copenhagen view: there are no extra assumptions, just one less. From simply denying this process and applying the idea of decoherence (which is not an assumption, but a consequence of QM common to all interpretations), the unitary schrodinger equation alone gives rise to phenonmena macroscopic beings would almost certainly interpret as wavefunction "collapse". That's too nice a fact to ignore.

And yes, the Schrodinger Cat issue, in my opinion, has nothing to do with either classical or quantum mechanics. Rather it's about biology and standard probability theory.

I'm taking it you don't consider the wavefunction to be real, but only some kind of representation of the experimenter's knowledge. If this is the case, I can understand your position.

 

[Anonym]

It's been the best game in town for a long, long time -- no one, as yet, has come up with a better alternative.

I am. And I do not need to convince anyone that it is so. It is obvious, since my roots are: Galileo, Newton, Huygens, Hamilton, Faraday, Maxwell, Einstein, Schrödinger, Dirac, Wigner, Yang and many others. It is General Theory of Fields.

The linear superposition is not violated in the classical physics, it is not observed. It is the problem of measurements when the measurement apparatus obey laws of the macroscopic physics. Therefore, it is the classical physics that must provide the natural explanation (solution) of it and not QT.

It is a serious problem; therefore, one should find a serious solution. As usual, it is invention of the previously unknown and unused mathematical framework. In that specific case, it is Real Hilbert Space. When I finished work and finished even to write paper, suddenly I remembered that I did not check whether it is not already done. The literature said that it is or trivial or not enough investigated. I entered Google and typed: Real Hilbert space. I got list of more than 3 000 000 publications. Then I typed Real Hilbert space+classical mechanics+dispersion free. Then I got zero.

If you accept that the hydrogen atom is not a physical system made out of the single electron and the single proton, I have no problem with that. If you accept that the single elementary particle may do statistic with itself, I have no problem with that either.

Regards, Dany.

 

[Demystifier]

The difference with the many worlds view, and the reason I favor it, is that there is no collapse, and so the measurement problem disappears. In fact, that's the only real difference between it and the Copenhagen view: there are no extra assumptions, just one less. From simply denying this process and applying the idea of decoherence (which is not an assumption, but a consequence of QM common to all interpretations), the unitary schrodinger equation alone gives rise to phenonmena macroscopic beings would almost certainly interpret as wavefunction "collapse". That's too nice a fact to ignore.

But this is not enough for the consistency of the many-world interpretation. Decoherence alone does not explain why only one of the possibilities is seen by the observers. See e.g.
http://xxx.lanl.gov/abs/quant-ph/0312059 (Rev. Mod. Phys. 76, 1267-1305 (2004))

 

[Fra]

I am. And I do not need to convince anyone that it is so. It is obvious, since my roots are: Galileo, Newton, Huygens, Hamilton, Faraday, Maxwell, Einstein, Schrödinger, Dirac, Wigner, Yang and many others. It is General Theory of Fields.

(Sorry for jumping into the discussion)

Dany, do you have any yet finished papers where your personal ideas are elaborated?
I'm curious.

/Fredrik

 

[ZapperZ]

But this is not enough for the consistency of the many-world interpretation. Decoherence alone does not explain why only one of the possibilities is seen by the observers. See e.g.
http://xxx.lanl.gov/abs/quant-ph/0312059 (Rev. Mod. Phys. 76, 1267-1305 (2004))

It probably just might! Read, for example, H. Ollivier et al., PRL v.93, p.220401 (2004). In it, they showed how "preferred pointer states" of the system affects what is being observed, resulting in what we see classically as an objective observation.

Zz.

 

[Demystifier]

It probably just might! Read, for example, H. Ollivier et al., PRL v.93, p.220401 (2004). In it, they showed how "preferred pointer states" of the system affects what is being observed, resulting in what we see classically as an objective observation.

I do not understand this paper. Can you explain, in simple terms, how objective observation emerges without a collapse? Or give a link where such a simple explanation is given?

 

[ZapperZ]

I do not understand this paper. Can you explain, in simple terms, how objective observation emerges without a collapse? Or give a link where such a simple explanation is given?

Er.. where does it say these things occurs without a collapse? Isn't "decoherence", by definition, implied a gazillion interactions (and thus, collapse) of the system?

I was responding to your claim that decoherence can't explain why only one outcome is seen by an observer. This paper laid out how decoherence (which, by definition, implies an interaction already with an environment) can in fact results in a "preferred" outcome, leading to a reproducible, objective observation that we see at the classical level.

Zz.

 

[Fra]

It probably just might! Read, for example, H. Ollivier et al., PRL v.93, p.220401 (2004). In it, they showed how "preferred pointer states" of the system affects what is being observed, resulting in what we see classically as an objective observation.

Quite Interesting paper. Thanks for the link! I like parts of it and, but I have doubts about some details, in particular their choice of information measures and the conditions posed, which from a quick reading seems closely related to what I'd consider to be "near information equilibrium", in the sense that they are effectively considering perturbations around an equilibrium state and may not be valid in a general case and I suspect that to make this consistent time has to be brought into the picture. It seems to have some similarities to my preferred thinking, and I think I can relate to what they are trying to do but I need to read it properly when I've got time, the page count was quite reasonable.

/Fredrik

 

[Demystifier]

Zz, as I understood, the paper you mentioned explains objective existence not simply by using decoherence, but by combining decoherence with the Zurek's existential (quantum Darwinism) interpretation of quantum mechanics. This interpretation is not the same as MWI. What I look for is a simple explanation of the existential (quantum Darwinism) interpretation of quantum mechanics.

In the meantime, I have found this:
http://www.advancedphysics.org/forum/showthread.php?t=1791
Apparently, I am not the only one who does not understand the Zurek's interpretation of QM.
Maybe we should open a separate thread.

 

[ZapperZ]

Zz, as I understood, the paper you mentioned explains objective existence not simply by using decoherence, but by combining decoherence with the Zurek's existential (quantum Darwinism) interpretation of quantum mechanics. This interpretation is not the same as MWI. What I look for is a simple explanation of the existential (quantum Darwinism) interpretation of quantum mechanics.

I didn't say that it is the same as MWI. I don't think the authors were trying to do that. However, they have tried to show that by invoking decoherence, you CAN get back the classical "certainty" that we know and love. I thought this was a very good first step, at least, in trying to figure out why our classical world has a definite objectivity, meaning you get a definite ONE outcome when you make a classical measurement. That's what they have tried to show.

Zz.

 

[Anonym]

Dany, do you have any yet finished papers where your personal ideas are elaborated?

The paper I referred to in my post above is quant-ph/0606121 entitled “On the connection between classical and quantum mechanics”. It will be published in the HAIT JSE special issue devoted to memory of Prof. I.D.Vagner.

The related papers are:

1)physics/0504008 entitled “On the problem of Zitterbewegung of the Dirac electron”, HAIT JSE, 1 (3), 411,(2004);
2)“Quantum mechanics of non-abelian waves I”, Hadronic Journal,6, 801(1983).

The first is the corrected version of Ch. IX and the second is Ch.VIII of my Ph.D thesis entitled “Quantum Mechanics of Non-Abelian Waves”, Tel-Aviv University, 1982, unpublished.
Ch. III – Ch.VII was published as the paper written by L.P.Horwitz and L.C. Biedenharn, Ann. Phys., 157, 432 (1984).

I discuss ideas here at PF. All mentioned papers discuss mathematical results only. They use fairly advanced extensions of the functional analysis.

Not yet finished papers are:

1) On the “eigenschaften” operators in QM; finished, not written;
2) The squeezed states, the coherent states, etc.; perhaps finished, not written;
3) On relativistic QM; not finished, not written.

I understand that you are interesting in the problems of statmech. I do not believe that I will ever consider the description of more than N=3 states.

Regards, Dany.

 

[StatusX]

But this is not enough for the consistency of the many-world interpretation. Decoherence alone does not explain why only one of the possibilities is seen by the observers. See e.g.
http://xxx.lanl.gov/abs/quant-ph/0312059 (Rev. Mod. Phys. 76, 1267-1305 (2004))

I haven't gone through the paper ZapperZ mentioned, but my understanding is roughly as follows. Look at the state after observation:

|happy scientist>|alive cat> + |sad scientist>|dead cat>

If we denote the first term by |A> and the second by |B>, then decoherence says that |A> and |B> are incoherent, which roughly means that for any observable O we might measure, <A|O|B>\approx0. But as I described in post 33, this means the system is behaving essentially like a classical probabilistic ensemble, and so the results we get by continuing to apply Schrodinger's equation without collapse is the same as if we did assume collapse, ie, where we assume the cat is in a well-defined classical state, just one which we don't initially know.

In particular, |A> and |B> evolve independently: |happy scientist> evolves into |scientist picking up and hugging the cat>, while |sad scientist> independently evolves into |scientist quietly putting cat into a box>. Yes, a superposition still exists, but the two states in the superposition carry on as if it didn't, essentially because the incoherence of the states means there are no interference effects.

The question still remains: what determines which of the outcomes you experience. Evidently, you experience one, and someone else with an equal claim to be called "you" experiences the other. This is really strange, and I haven't heard any satisfying explanation that incorporates consciousness.

But for now, we can carry on noting that if you were to querry any of the different scientist-copies after he's carried out several quantum experiments, chances are very high that he'll have a memory of a world where the laws of quantum probability were closely followed, so the predictions of the theory are solid (in the probabiliistic sense which is the only sense in which QM can be verified).

 

[nrqed]

The problem with the Copenhagen approach from a theoretical point of view is that the act of "measurement" is not well-defined. There are various attempts at nailing this concept down, but none that seem obviously correct.

The difference with the many worlds view, and the reason I favor it, is that there is no collapse, and so the measurement problem disappears. In fact, that's the only real difference between it and the Copenhagen view: there are no extra assumptions, just one less. From simply denying this process and applying the idea of decoherence (which is not an assumption, but a consequence of QM common to all interpretations), the unitary schrodinger equation alone gives rise to phenonmena macroscopic beings would almost certainly interpret as wavefunction "collapse". That's too nice a fact to ignore.

I am trying to understand the next to last sentence in this paragraph. I thought that the MW interpretation and decoherence were very different beasts. Are you saying that one implies the other? I thought that MW did not make use of decoherence and vice versa.

Thanks for the interesting points.

 

[nrqed]

Er.. where does it say these things occurs without a collapse? Isn't "decoherence", by definition, implied a gazillion interactions (and thus, collapse) of the system?

I am a bit confused by the last statement. Interactions are equivalent to collapse?? I thought that interactions in the context of decogherence meant entanglement of states and that no collapse ever took place. Maybe I missed completely the point?

 

[ZapperZ]

I am a bit confused by the last statement. Interactions are equivalent to collapse?? I thought that interactions in the context of decogherence meant entanglement of states and that no collapse ever took place. Maybe I missed completely the point?

I wanted to say "loss of coherence" after so many interactions with the surrounding, but then I'm only saying what "decoherence" is. I would consider an "interaction" as a "collapse", because such interaction can in fact tell you the state of a system.

Zz.

 

[StatusX]

I am trying to understand the next to last sentence in this paragraph. I thought that the MW interpretation and decoherence were very different beasts. Are you saying that one implies the other? I thought that MW did not make use of decoherence and vice versa.

Here's a quote that explains the gist of it:

However, decoherence by itself may not give a complete solution of the measurement problem, since all components of the wave function still exist in a global superposition, which is explicitly acknowledged in the many-worlds interpretation. All decoherence explains, in this view, is why these coherences are no longer available for inspection by local observers. To present a solution to the measurement problem in most interpretations of quantum mechanics, decoherence must be supplied with some nontrivial interpretational considerations (as for example Wojciech Zurek tends to do in his Existential interpretation). However, according to Everett and DeWitt the many-worlds interpretation can be derived from the formalism alone, in which case no extra interpretational layer is required.

Basically, Everett and DeWitt reason that decoherence alone leads to what "local observers" (eg, one of the copies of the scientist) would interpret as irreversible wavefunction collapse. In other words, you could still enforce collapse, but it would be redundant (except from an ontological point of view, where it removes worlds that aren't practically accessible to us). Although decoherence is now widely accepted as a real effect, the validity of DeWitt's argument that it implies MW is still controvertial.

 

[cesiumfrog]

good post, X.

When I was first taught of MW, I was given the impression that the branching of worlds was a very random ad hoc alternative to nondeterministic collapse. Now I wonder whether historically it was first proposed with decoherence already in mind.

 

[nrqed]

a) You don't read what I say. So, let me repeat. The cat cannot be both dead and alive, it is a logical contradiction. Still, it can be in a superposition of dead and alive. In this case, it is neither dead nor alive. Sometimes we say for such a state that the cat is "both dead and alive", but it is simply an incorrect (or imprecise) language.

b) I say it is in the superposition of head and tail (recall that I am still talking within the 1. paradigm, despite the fact that I actually prefer 2.)

By the way, this is my 666th post.

as I am rereading this thread, I want to say that I agree with Demystifier.

This part of the thread was about whether a linear superposition of two states (dead or alive) should be described as "both dead and alive" or "neither dead nor alive". At thi spoint I think that everybody agrees that the most (and maybe only) accurate description is to say that the system is a linear superposition, period. But if one insists on using everyday language, it seems impossible to accurately convey what a quantum linear superposition means. Then it becomes subjective, to a point, what language is used. Still, I personally think that "both dead an alive" is misleading. It would imply that once the measurement is made, and let`s say the outcome is "alive", that the cat "ceased to be dead" since it was both dead and alive before the measurement.

I find the "neither dead nor alive" at the same better and quite unsatisfying.

I would suggest the following as the best description. A cat in the linear superposition of dead and alive is a cat which has the potential of being alive and he potential of being dead.

Just my two cents...

 

[ZapperZ]

as I am rereading this thread, I want to say that I agree with Demystifier.

This part of the thread was about whether a linear superposition of two states (dead or alive) should be described as "both dead and alive" or "neither dead nor alive". At thi spoint I think that everybody agrees that the most (and maybe only) accurate description is to say that the system is a linear superposition, period. But if one insists on using everyday language, it seems impossible to accurately convey what a quantum linear superposition means. Then it becomes subjective, to a point, what language is used. Still, I personally think that "both dead an alive" is misleading. It would imply that once the measurement is made, and let`s say the outcome is "alive", that the cat "ceased to be dead" since it was both dead and alive before the measurement.

I find the "neither dead nor alive" at the same better and quite unsatisfying.

I would suggest the following as the best description. A cat in the linear superposition of dead and alive is a cat which has the potential of being alive and he potential of being dead.

Just my two cents...

So an electron that is in an H2 molecule is neither near one H atom, nor the other.

Where is the electron that somehow has formed the bonding or antibonding? It has formed it, but it isn't here nor there!

And you found this to be "better"?

Zz.

 

[StatusX]

When I was first taught of MW, I was given the impression that the branching of worlds was a very random ad hoc alternative to nondeterministic collapse. Now I wonder whether historically it was first proposed with decoherence already in mind.

Yea, until a few months ago I just assumed it was someone getting carried away with their imagination and the weirdness of QM. Then I read some more about it and realized it's actually the simplest interpretation, in terms of number of assumptions, and more or less resolves the measurement problem. I'm surprised it isn't more popular than it is (I believe it's second to the Copenhagen interpretaion, depending on the kind of physicists you ask)

 

[Alan J.]

From my years of playing poker and trying to determine my opponents hand via looking for "tells" or ways to figure out if his hand is good or not based on my opponents behavior and the current environment(other information I've gathered such as the cards in my hand and other cards shown or showing). This is indeed the same problem. We can determine if the cat is alive or dead by making simple observations about it's environment whether it being atmospherical or physical. Is the box moving? Is the box shaking? Is the box warm in a particular spot? Is there air in which the cat can breathe?Is the box emitting sound? These are ways to determine if the cat is alive or not.

The same thing is, in theory, true for particle movement just we have not yet found these observations or what to look for regarding the particles environment.
And another question comes in where if 2 particles were entangled across the universe. Would the entanglements affect other traveling particles and entanglements?

 

[ueit]

Yea, until a few months ago I just assumed it was someone getting carried away with their imagination and the weirdness of QM. Then I read some more about it and realized it's actually the simplest interpretation, in terms of number of assumptions, and more or less resolves the measurement problem. I'm surprised it isn't more popular than it is (I believe it's second to the Copenhagen interpretaion, depending on the kind of physicists you ask)

Did you find out how MWI accounts for the observed probabilities (Born rule)?

 

[Fra]

Some comments.

I read that paper again last night, and while the general idea that any system will attain some level of correlation with the environment, and that there is a selective mutual pressure between environment and the system is right on...

...but like others say, I wouldn't say it solves the collapse as such, beucase OTOH the collapse isn't an issue for me becuse IMO it's simply sort of a bayesian revision due to the limited measurement resolution and finite complexity of memory - I suspect Alan who is a poker will know what I mean - I like the poker analogy too. I see no way around this. Unless you of course reformulate the problem, but the care should be taken because then we might not ask the same question.

Also, if we are consider an observer B that observes a system + observer A, then clearly we are working in two different descriptions. Observer A has not use of B:s information. Sure they can communicate, but then we add time. In my thinking (spacetime aside!) one can't transfer arbitrary amounts between two records arbitrarily. I think the information transfer is part of defining time which implies a locality in terms of information. I am eventually working on an explicit formalism for this but it a lot of things to do left.

Also, I think the assumption that there is strong correlation between the environment and the system in the first place is valid only it they are close to equilibrium - ie that the system is already "stabilized" i the environment. I figure that this is not a valid assuption in the general case. Also if one is to talk about the actual stabilisation process, this takes time, and then the argumentation gets more complicated. Information that is available in the future, is not available now. I see no sense in that argumentation.

I think the paper is interesting in a sense but it does not get rid of the collapse. The fact that C may observe the correlation between A and B the system, and sees a resolution to the collapse problem is an observation with the wrong condition. The fact that A sees a collapse, doesn't mean that everybody sees a collapse. I don't see a problem with that at all.

I think there is an intrinstic limit due to information capacity, which limits the maximum possible entanglement! and this constraint may impose collapses. I think part of the problem is that all the players have incomplete information, and it's NOT due to flawed or incompetent strategies, it's due to the limiting structures to hold correlation information and due to TIME that correlations are a dynamical thing, if you are thrown into a new environment, then you need some time to equilibrate with the environment, which is btw, mutual.

/Fredrik

 

[Alan J.]

Some comments.

I think there is an intrinstic limit due to information capacity, which limits the maximum possible entanglement! and this constraint may impose collapses. I think part of the problem is that all the players have incomplete information, and it's NOT due to flawed or incompetent strategies, it's due to the limiting structures to hold correlation information and due to TIME that correlations are a dynamical thing, if you are thrown into a new environment, then you need some time to equilibrate with the environment, which is btw, mutual.

/Fredrik

I'm going to continue with the poker analogy because it's less graphic then a dead cat.

When I sit down to a new table, I do have a set strategy and you are right. There is a time factor here. But if A has basic knowledge of environment A. And then A is thrown into environment B(or a new poker table with new people) with the knowledge of evironment A and we are observing a simular situation of a poker game. Then A would have the potential to make correct predictions on the opponents cards more so then when A started at evironment A.
Then when A is introduced to environment C and is also a simular situation of a poker game. Then A would have the knowledge of Evironments A and B. And so on and so forth until the rules or stakes of the game are changed.
There is a learning curve of player A which could potentially be humans in the future if we can learn more about environments of particles and less about their actions. This is a plausible solution because we no longer care what the particles are doing, thus we are not limited to just quantums observation problems. I.E double slot experiment.

 

[Wonderballs]

If you know the cats state, the box has been opened (even if the box remains closed). So the box will always remain closed. Unless you smell something funky which opens the closed box that is still shut.

 

[Alan J.]

If you know the cats state, the box has been opened (even if the box remains closed). So the box will always remain closed. Unless you smell something funky which opens the closed box that is still shut.

Untrue. The smell is the bi product of the box or cat. Thus making these observations is not directly interferring with the state of the cat(particle). I believe your thinking in more philosophical terms.

 

[Wonderballs]

I may not know much about this stuff, but if you do not know the cats state, the box remains closed restricting the gain of such knowledge. Like lim x --> a .

The funky smell was a joke.

 

[StatusX]

Did you find out how MWI accounts for the observed probabilities (Born rule)?

It's a good question, and I don't think there's a universally accepted answer. One idea would be that if there is a splitting for each quantum microstate of the system, how many of these go one way or the other will be determined by the magntiudes of the different results in the superposition. I don't think this has been rigorously shown though.

 

[ueit]

It's a good question, and I don't think there's a universally accepted answer. One idea would be that if there is a splitting for each quantum microstate of the system, how many of these go one way or the other will be determined by the magntiudes of the different results in the superposition. I don't think this has been rigorously shown though.

I think this is a very serious problem of MWI. It means, in fact, that it cannot explain anything. The obtained experimental results must be introduced by hand without any good reason to do so. Compare this with BM where the probabilities follow naturally. As Einstein said, "make everything as simple as possible, but not simpler."

 

[Anonym]

This part of the thread was about whether a linear superposition of two states (dead or alive) should be described as "both dead and alive" or "neither dead nor alive"... But if one insists on using everyday language, it seems impossible to accurately convey what a quantum linear superposition means.

If one insists on using everyday language, consider 2-dim plane and draw two mutually orthogonal axes on it. Then consider some line belong that plane. That line will contain one of the axes if and only if it is identical to that axis and never both. This is the fundamental property of the metric spaces; otherwise Zz may lock his lab and throw away the keys. Also that “what a quantum linear superposition means”.

So an electron that is in an H2 molecule is neither near one H atom, nor the other.

Where is the electron that somehow has formed the bonding or antibonding? It has formed it, but it isn't here nor there!

And you found this to be "better"?

Yes. Ask Him why. Gmar Hatima Tova!

Regards, Dany.

P.S. Everyday working experience and knowledge of math is required to have instant feeling what is right and what is wrong in the physical theory. If you do not understand something, ask Demy for example or many others here. Your inability to check yourself disturbs me. Why I should believe that you don’t behave similarly in performing your measurements? In addition, we need explanations of the fine features of the experiments in order to understand their true content and neither you nor other experimentalists here do that.

P.P.S. Perhaps, the explanation is: in order the hydrogen atom to be stable. Otherwise, it will be nobody to ask questions.