# Does Schrodinger's Cat Paradox Suck?

• yuiop
Hey Rap, sorry if you feel that way, but honestly not my intent

LOL - read the whole sentence - I'm thanking you for the reasoned attack.

So no more pestering you on this topic - honest. Have a nice stress-free day!

Thanks, you too. But your "pestering" revealed a problem regarding Wigner's friend that is just the kind of thing I was looking for.

A more accurate statement would be "until then the wave function for the box and contents will consist of a superposition of moved and not moved regarding the position of the box".
According to your earlier definitions there is no such thing as "the wave function for the box and contents" independent of a observer. For example do you mean the wave function according to the cat, according to the observer outside the box or according to the friend in a box inside the SC box? You have stated that the wave function is not an absolute entity, but an observer dependent entity, so like in Special Relativity when we say the velocity of an object is v, this has no meaning until we add a qualifier such as "according to observer x at rest with respect to reference frame S". Is that really how wave functions are defined in QM?

I am not positing that human observation must happen. Any entity making symbolic quantum mechanical calculations and capable of modifying those calculations in light of new information (i.e. a measurement) will respond to this new information in the quantum mechanical way - collapsing the wave function that it is using to describe the system.
Let us say we have two almost identical experiments but one is "open box" and one is "closed box". For each experiment we have a radioactive source, a Geiger counter, a paper chart with a constant drive and a recording pen. The Geiger system is connected in such a way that a voltage signal from the detector causes a blip on the chart. There are no microprocessors or other logic devices built into the system and I doubt no one would describe the Geiger counter and recording chart as a "sentient system". Now we run the experiments a million times but one experiment is in an open box closely monitored by scientists skilled in the art of making quantum calculations and the other is run in a closed box. After each run, the paper chart is removed from the closed box and put in a safe without anyone looking at it. After a million test runs, we remove the test charts from the safe and compare them with the results from the observed "open box" runs. Do you expect there to be any statistically significant difference between the open box and closed box results. If there is any difference we repeat the experiment a million times again and collate the statistical average of the tests. Does observation by intelligent beings make any difference to the two cases? (I say no, what do you say?). Are the paper charts in the locked safe in a superposed state until someone opens the safe and looks at them?
I am not positing that human observation must happen. Any entity making symbolic quantum mechanical calculations and capable of modifying those calculations in light of new information (i.e. a measurement) will respond to this new information in the quantum mechanical way - collapsing the wave function that it is using to describe the system.
I still think you are using wave function to mean the predictions of humans with limited information rather than the state of the system itself.
I object to the many worlds idea because it is unverifiable, you can make no measurement to verify or refute it, and therefore it is not scientific.
While that may well be true, there are many interpretations of what is going on in QM systems, but they are all equally valid. There is equally no measurement to verify or refute the Copenhagen Interpretation versus the other interpretations. It comes down to personal taste or philosophy. It is a bit like the difference between LET and SRT in relativity. The mathematical predictions are the same, but the philosophical interpretations are different. Personally I find the MWI distasteful, because it requires many worlds/universes and a sort of book keeping system to correctly sort them, when there are other interpretations that only require a single universe and non-local interaction at the quantum level.
This is a "hidden variables" approach to QM which has been shown to be wrong.
Bell's inequalities do not by themselves demonstrate that hidden variables "are wrong". They demonstrate that theories that explain the EPR experiment results must be either non-local or unrealistic (or both). A theory that contains hidden variables is not excluded as long as it is non-local or unrealistic.

P.S. Dr Chinese. Have you seen/considered https://www.physicsforums.com/showpost.php?p=3118570&postcount=63"?

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Let us say we have two almost identical experiments but one is "open box" and one is "closed box". For each experiment we have a radioactive source, a Geiger counter, a paper chart with a constant drive and a recording pen. The Geiger system is connected in such a way that a voltage signal from the detector causes a blip on the chart. There are no microprocessors or other logic devices built into the system and I doubt no one would describe the Geiger counter and recording chart as a "sentient system". Now we run the experiments a million times but one experiment is in an open box closely monitored by scientists skilled in the art of making quantum calculations and the other is run in a closed box. After each run, the paper chart is removed from the closed box and put in a safe without anyone looking at it. After a million test runs, we remove the test charts from the safe and compare them with the results from the observed "open box" runs. Do you expect there to be any statistically significant difference between the open box and closed box results. If there is any difference we repeat the experiment a million times again and collate the statistical average of the tests. Does observation by intelligent beings make any difference to the two cases? (I say no, what do you say?). Are the paper charts in the locked safe in a superposed state until someone opens the safe and looks at them?

The fundamental thing here is that the closed box is an isolated system, the open box is not. For the closed box, the calculations of the wave function may be carried out using only the results of our measurements on it when we closed it. The open box is open to the universe, and being affected by the universe, and unless we have the universe (without the scientist) isolated, we cannot do QM calculations on it. We cannot even do classical calculations on it, unless it is classically isolated, which is much easier. Suppose we have a container of gas which is at equilibrium and classically isolated - thermally insulated, constant volume, opaque, etc. whose temperature and pressure we measure. Then we can predict the future for that system - its pressure and temperature will remain constant. Suppose we kick the container off the edge of the grand canyon. We know that it will be dented or broken on the way down but we cannot predict its future, unless we know the position of every rock on the way down, the momentum and position after we kicked it, etc. We have opened it to the universe, and lost the ability to predict its future. Quantum systems must be VERY isolated in order to do wave function calculations. You cannot do quantum calculations on an open box because you cannot know all the variables that are affecting it: its effectively been kicked off the edge of the grand canyon. The minute you open one of the closed boxes, you can no longer do quantum calculations on it. But the contents of the box may be treated classically, its a classical cat. If you open it, and the readings on the tape are are not significantly changed by the environment (and unless you open the box in a burning building or something, they will not be), then the results will be valid, altho they cannot be treated quantum mechanically. So I believe there will be no statistical difference in the results, and no, the tapes cannot be treated quantum mechanically, as being in a superposition of states when they are stored in the safe, because the prerequisites for a quantum mechanical treatment (complete isolation of your experiment) have been violated.

I still think you are using wave function to mean the predictions of humans with limited information rather than the state of the system itself.

If by "limited information" you mean "quantum-limited information" (e.g. Heisenberg uncertainty), then yes, I am doing exactly that with the wave function, but the wave function IS the "state of the system itself". I am not trying to use a wave function outside of an isolated system. I wouldn't try to do a classical analysis of a problem if it were not practically isolated from the rest of the universe. If I flip a coin and cover it with my hand before looking at it, that is a classical problem, the coin is made of metal, and is isolated from severe classical perturbations, so we can treat it as a classical probability problem. No quantum analysis is possible, the system is not isolated enough. If I fully isolate the coin and a flipping machine, then I can use quantum mechanics to describe the state of the system and once the coin is flipped, I will describe it as being in a superposition of flipped and not flipped. Now I am using quantum uncertainty to describe the situation. Decoherence theory says that I will not get radically different results when I open the box, because the coin is, as already noted, a classical system. When decoherence theory is applicable, quantum uncertainty translates to classical uncertainty.

While that may well be true, there are many interpretations of what is going on in QM systems, but they are all equally valid. There is equally no measurement to verify or refute the Copenhagen Interpretation versus the other interpretations.

The Copenhagen interpretation is different. It does not postulate anything beyond measurement. So what you are saying is that there is no measurement to verify or refute the idea that there is nothing beyond measurement, which is ... well, you see my point.

Bell's inequalities do not by themselves demonstrate that hidden variables "are wrong". They demonstrate that theories that explain the EPR experiment results must be either non-local or unrealistic (or both). A theory that contains hidden variables is not excluded as long as it is non-local or unrealistic.

I think you are right, but we are dealing with quantum mechanics as it is presently understood, not as it might be some day when such a theory is developed.

If by "limited information" you mean "quantum-limited information" (e.g. Heisenberg uncertainty), then yes, I am doing exactly that with the wave function, but the wave function IS the "state of the system itself".
You are again being self inconsistent here. You have many times stated that there is no such thing as the wave function of the "state of the system itself", but only the wave function according to the cat in the box or according to the observer outside the sealed box or according to Wigner's friend, so by your definition, the wave function is an observer dependent function that is totally incompatible with statements like the wave function IS the "state of the system itself"

I think the difference in our positions is well described by this quote by Mermin http://arxiv.org/PS_cache/quant-ph/pdf/9609/9609013v1.pdf: [Broken]
(1) The theory should describe an objective reality independent of observers
and their knowledge.
The maddening thing about the wave–function is the way in which it manages to mix
up objective reality and human knowledge. As a clear indication of this murkiness note that even
today there is coexistence between those who maintain that the wave–function
is entirely real and objective
— notably advocates of Bohmian mechanics or seekers of a
modiﬁed quantum mechanics in which wave–function collapse is a ubiquitous real physical
phenomenon—and those who maintain, unambiguously with Heisenberg and presumably
with Bohr, that the wave–function is nothing more than a concise encapsulation of our
knowledge.

A satisfactory interpretation should be unambiguous about what has objective reality
and what does not, and what is objectively real should be cleanly separated from what is
“known”. Indeed, knowledge should not enter at a fundamental level at all.

I wouldn't try to do a classical analysis of a problem if it were not practically isolated from the rest of the universe. If I flip a coin and cover it with my hand before looking at it, that is a classical problem, the coin is made of metal, and is isolated from severe classical perturbations, so we can treat it as a classical probability problem. No quantum analysis is possible, the system is not isolated enough. If I fully isolate the coin and a flipping machine, then I can use quantum mechanics to describe the state of the system and once the coin is flipped, I will describe it as being in a superposition of flipped and not flipped. Now I am using quantum uncertainty to describe the situation. Decoherence theory says that I will not get radically different results when I open the box, because the coin is, as already noted, a classical system. When decoherence theory is applicable, quantum uncertainty translates to classical uncertainty.
The Copenhagen interpretation is different. It does not postulate anything beyond measurement. So what you are saying is that there is no measurement to verify or refute the idea that there is nothing beyond measurement, which is ... well, you see my point.

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For me, the most obvious problem with the thought experiment lies in the fact that the Geiger counter is perfectly sufficient in collapsing the wave function of the decay particle, and superposition ends there, does it not?

Not necessarily, the only way to know anything at all in this universe(reality) is through a mind. A Geiger counter is just a tool. This point is very obvious if you trust the experiements that highlight the role that potential knowledge plays on collapsing wavefunction.

No. A human observer does not have to be present for a measurement to take place.

The Geiger counter is a classical system. That is the key. The measurement occurs when the quantum system interacts with a classical system. It is this interaction that causes the decoherence phenomenon which collapses the entire composite system, the cat+Geiger counter+ decaying atom into a classical, non superimposed state.

No human intervention or reading of the Geiger counter is necessary to collapse the system.

The human observers uncertainty about the measurement is classical, and does not correspond to a quantum superposition.

I am sure many people will disagree on the split into classical and quantum systems(Bohr was of this opinion) but i'd point out that environmentally induced decoherence doesn't explain the transition from mixed states to single outcomes. Some form of measurement/observation/split-ala-MWI is mandatory. The idea that the environment does all the selection 'work' through some deterministic(realist) process is just wishful thinking.

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You are again being self inconsistent here. You have many times stated that there is no such thing as the wave function of the "state of the system itself", but only the wave function according to the cat in the box or according to the observer outside the sealed box or according to Wigner's friend, so by your definition, the wave function is an observer dependent function that is totally incompatible with statements like the wave function IS the "state of the system itself"

You are absolutely right, I never should have said that without explanation, knowing as I do that your definition of "the state itself" is different than mine. I think you define the state as an objective reality, while I define a state as the sum of my knowledge, properly expressed in terms of whatever theory I am making my calculations with. In thermodynamics, for example, if you have a container of gas, its "macrostate" or thermodynamic state is defined e.g. by its temperature and pressure. In classical statistical mechanics, its "microstate" is defined by the position and momentum of every gas molecule in the container. In quantum mechanics the wave function is also known as the "state vector" in the Hilbert space that is being used to describe the set of all possible wave vectors that could exist for a system. I will not use the term "state" without explanation in the future.

I think the difference in our positions is well described by this quote by Mermin http://arxiv.org/PS_cache/quant-ph/pdf/9609/9609013v1.pdf: [Broken]

Yes, that is an excellent quote. I only object to the word "maddening". I used to be maddened by it until I realized that my idea of "objective reality" is encoded in my brain by my DNA which has evolved to survive in a classical Newtonian world, and had no need to deal with quantum uncertainty, just as my brain is wired to deal with Galilean relativity and the absolute nature of time, rather than Einsteinian relativity where space and time get all mixed up. If the equations work, I will take it as providing true clues as to how the world works, and not demand that they make intuitive sense to my Cro-magnon brain.

You say you are a Copenhagen Interpretation sympathiser and as I understand it in that interpretation it is only what we measure that counts. This implies you can not say things like "in a superposition of flipped and not flipped" because you do not have any knowledge of what is going on between measurements.

I think you are trying to assign objective reality to a superposed wave function. A superposed wave function is not describing the (unmeasureable) objective reality of the system, it is simply encoding what we know about it based on previous measurements. You get a superposed wave function by measuring a system, which gives a non-superposed wave function, then you let Schroedinger's equation tell you how that wave function changes, and it will change into a superposed wave function. Thats how you know it is a superposed wave function.

The wave function is a vector in Hilbert space. Any vector can be expressed as a weighted sum of N base vectors. You can pick any bunch of base vectors you want, as long as they are linearly independent (i.e. not pointing in the same direction). If you have an electron, it can be spin up (i.e. "flipped") or spin down (i.e. not flipped). These are two base vectors <up> and <down> in the 2-d Hilbert space, and any other wave function (vector) can be expressed as A1 <up>+A2 <down>. If A1=1, A2=0 you have spin down, A1=0, A2=1, you have spin up. If you have A1=1/2, A2=1/2, then you have a superposition of spin up and spin down. This superposed wave function is a precisely defined wave function that tells you that if you now measure the spin of that electron, half the time you will measure spin up, half the time spin down. I do not have any knowledge of what is going on between measurements, but I do know exactly what the wave function is, and it reflects my uncertainty about what my result will be if I measure the spin of the electron.

You flip the coin and cover it with your hand. When you uncover the coin you find you have "heads". One interpretation is that when the coin was covered, it was either heads or tails but not both but we because we do not have certain knowledge we can only assign a probability to the state of heads or tails which simply reflects our lack of certain knowledge. Another interpretation is that the coin under your hand is in a superposition of both heads and tails.

No - the coin is not in an isolated system, we cannot do quantum mechanics on it until it is part of an isolated system.

However, according to the CI, we can say nothing about the coin until we uncover it and find we have heads, so saying it is in a superposition before before the uncovering is against the spirit of the CI because you are saying you know something about the coin (i.e. it is a state of superposition" without making any objective measurement to prove it is a superposition.)

Suppose I have an electron in a weak magnetic field along the x axis, and I measure its z-spin to be "up". If I plug <z-up> into Schroedingers equation, Schroedingers equation will show how the wave function changes in time, until at a certain time T later, it is in a superposition of z-up and z-down. My "proof" that it is a superposed state at time T is my measurement that it was <z-up> at time zero and my use of Schroedinger's equation to predict the superposed state at time T.

Lets take another example. Let us say we have source of light that is unpolarised, i.e. if we place a polarising filter in the path we always get 50% transmission in accordance with Malus's law. Now there are two (maybe more) possible interpretations for what is going on here. One is that a given photon has a definite polarisation state before the polariser and if it orientated between -45 and +45 degrees of the polariser it passes through, giving a 50% chance. Once the photon has passed through the filter it is aligned with the filter and and information and the orthogonal component of its polarisation is lost. The other interpretation is that the photon has no definite polarised state before the filter and is in a superposition of vertical and horizontal polarisation. On arriving at the polariser, the photon flips a coin and has 50% chance of passing through. Now Malus's law simply says that the photon has probability of 50% of passing through and does not postulate whether the photon was in a superposed state before the polariser or not. The CI on the other hand goes beyond Malus's law and its own remit, by claiming to know that the photon was in a superposed state before the measurement, so it is not adhering to the "Shut UP and Calculate Interpretation", but offering an explanation or assumption of what is happening before measurement, by stating the photon is superposed before measurement. If the CI adheres strictly to not postulating anything beyond measurement, then the CI should say "we do not know whether the photon is superposed or in a definite state before measurement, all we know is that the measurements will statistically agree with the predictions of Malus's law."

The idea that a photon must have a polarization within 45 degrees of the polarizer before passing thru does not work. If I pass a beam of randomly polarized photons thru a polarizer oriented at zero degrees, then I guess we could say the polarization of the photons coming out are evenly distributed between +45 and -45. Next we pass them thru a polarizer at 45 degrees. Half of the ones out of the first polarizer will be between 0 and 45 degrees, and only these will make it thru the second polarizer, since they are between 45-45=0 and 45+45=90 degrees. Now we pass these thru a polarizer at 90 degrees - none will make it thru, because there are none in the beam that are between 90-45=45 and 90+45=135 degrees. In actual fact, something like 20 percent of the original photons make it thru all three polarizers.

Quantum mechanics gives the right answer, but you have to be sure and distinguish between a bunch of photons in a superposition of up and down, and a bunch of randomly polarized photons. The first involves a quantum uncertainty about the polarization of the photons, the second implies further lack of information about the polarization which is not included in the wave function. You can have two kinds of uncertainty - Heisenberg uncertainty encoded in a well-defined wave function, and then uncertainty about the wave function itself. If you flip a coin with your hand, you have uncertainty about the wave function itself, because its not a system that is isolated enough to do quantum mechanics.

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I am sure many people will disagree on the split into classical and quantum systems(Bohr was of this opinion) but i'd point out that environmentally induced decoherence doesn't explain the transition from mixed states to single outcomes. Some form of measurement/observation/split-ala-MWI is mandatory. The idea that the environment does all the selection 'work' through some deterministic(realist) process is just wishful thinking.
Yes, there are really three stages to the cat paradox, not two the way it is normally explained. There is the true superposition of the entire closed system, there is its unitary evolution that projects into a mixed-state subspace (via decoherence) constituting the physical parameters that we (the physicists) are actually tracking (which suffice to tell us if a cat is alive or dead), and there is the observational outcome which "actualizes" only one substate from that mixed substate. Which of those steps is the "collapse", and which is most paradoxical? Many people would choose different answers to those two questions, so until that landscape is navigated clearly, we are spinning our wheels. It might also help to recognize that the fundamental difference between MWI and Copenhagen is how they construct the flow of priority in those steps-- MWI appeals to an "outside-in" ordering of priorities just as it was stated above, which is essentially a temporal ordering, and Copenhagen uses an "inside-out" ordering of priorities, which starts with the physicist and builds outward, essentially in reverse to the temporal order described above. That, in turn, boils down to whether you think physics gives rise to physicists (MWI), or physicists give rise to physics (Copenhagen).

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You can have two kinds of uncertainty - Heisenberg uncertainty encoded in a well-defined wave function, and then uncertainty about the wave function itself. If you flip a coin with your hand, you have uncertainty about the wave function itself, because its not a system that is isolated enough to do quantum mechanics.
Yes, that is true, but remember that one can always recover the superposition state by embedding the coin into a larger system that is effectively isolated (like the whole Earth or some such thing). The cat paradox is often erroneously stated that the cat is in a superposition state, but that is simply wrong quantum mechanics. It is never the cat that is in a superposition state, because just as you say, the cat is not isolated. It is only the larger isolated system, including the amplifier and decaying nucleus, that is in a superposition state. Projecting that onto the cat will always yield a mixed state, so there's no paradox in that projection at all. The paradox doesn't come until we (the observers using the physics) observe the cat, and take a combined isolated system that contained dead-cat substates and alive-cat substates, and get just one or the other. That's the Wigner's friend version of the paradox, which is the real issue-- the quantum mechanics part only seems like a paradox if it is done wrong. (The same goes for the issue of whether or not a wave function is a description of the reality or just a description of our knowledge-- I agree with you that it is always the latter, but that doesn't resolve the real cat paradox, only the wrong one.)

In other words, when you flip a coin and cover it, you would not describe that coin with a superposition state, because that would just be wrong quantum mechanics, and for just the reasons you've described. But someone else, say an alien on a distant planet interested in not just the coin but everything happening on the Earth, might indeed use a superposition state that includes you, the coin, the room, etc.. The tension between those two different but correct uses of quantum mechanics is really what the "cat paradox" is, and it is a very good paradox for bringing out those distinctions. I would conclude the resolution is that not only is the wave function determined by our knowledge and what questions we are trying to answer, but the reality itself is also so dependent. There is no such thing as "reality" beyond what we have decided we want to know about reality, and so the reality that Mermin is searching for, and requiring our physics to describe, simply does not exist (or at least, we can't get at it with physics, so should not make that a requirement of physics). I believe that is also what Bohr was saying.

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Yes, there are really three stages to the cat paradox, not two the way it is normally explained. There is the true superposition of the entire closed system, there is its unitary evolution that projects into a mixed-state subspace (via decoherence) constituting the physical parameters that we (the physicists) are actually tracking (which suffice to tell us if a cat is alive or dead), and there is the observational outcome which "actualizes" only one substate from that mixed substate. Which of those steps is the "collapse", and which is most paradoxical? Many people would choose different answers to those two questions, so until that landscape is navigated clearly, we are spinning our wheels. It might also help to recognize that the fundamental difference between MWI and Copenhagen is how they construct the flow of priority in those steps-- MWI appeals to an "outside-in" ordering of priorities just as it was stated above, which is essentially a temporal ordering, and Copenhagen uses an "inside-out" ordering of priorities, which starts with the physicist and builds outward, essentially in reverse to the temporal order described above. That, in turn, boils down to whether you think physics gives rise to physicists (MWI), or physicists give rise to physics (Copenhagen).

I read a quote from Callen (Thermodynamics and statistical physics, p 15), that said "'Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory.'' LOL. Sounds like a Copenhagen guy to me. I believe the idea that you cannot have physics without a theory, wrong or right, and physicists are the ones who come up with that theory. But a wrong theory is just wrong, and in that sense, physics gives rise to physicists.

Anyway, decoherence isn't some kind of change in the physics of the situation, it is an approximation that becomes valid. Sort of like the thermodynamic limit is not a change in the physics of the situation (i.e. N-particle problem), it is an approximation that becomes valid. Both constitute a loss of information when the approximation is made. This means that you can, in principle, analyse a problem using pure QM wave functions, or you can make the decoherence approximation, just like you can, in principle, analyse a container of gas as an N-body problem, or you can make the thermodynamic approximation, and treat it as a much simpler thermodynamic system. If you do the SC problem as pure QM, then when you open the box, the wave function will collapse into a superposition of all the alive wave functions or a superposition of all the dead wave functions, which is all the scientist is really measuring upon opening the box. Decoherence says you can approximate the wave function before opening the box as a bunch of classical possibilities with classical probabilities, one of which the scientist observes when opening the box. Decoherence does not deny the validity of the pure wave function treatment. Once you make the classical approximation of decoherence theory, you are no longer doing pure QM, and the rules change, but the results are the same (if the decoherence assumption is valid).

I believe the idea that you cannot have physics without a theory, wrong or right, and physicists are the ones who come up with that theory. But a wrong theory is just wrong, and in that sense, physics gives rise to physicists.
That is what I would call the "literal school" for dealing with "laws of physics," the idea that we are really finding out laws, and although we might not get them exactly right, there are laws there and we are trying to find them. Presumably this is based on the idea that if there weren't laws, our search for them would be fruitless. But I find that argument unconvincing-- we have no idea why the search is fruitful, it does not have to be because there actually are laws. In my opinion, the whole idea of a "law" is a construct of our intelligence, so constructed for all the same reasons that intelligence evolved: it works. But why it works is not necessarily because there actually are laws-- instead, we observe that there are various patterns and consistencies, but we have no idea why, and we never really get any idea why. We just penetrate deeper into the mystery, the mystery never goes away. So that puts me in the "physicists give rise to physics" school.
Anyway, decoherence isn't some kind of change in the physics of the situation, it is an approximation that becomes valid.
It is a function of the use of substates to do quantum mechanics, which is not well explained in my opinion. So much of quantum mechanics is based on the evolution of the state, it is easy to overlook that a large part of it has nothing to do with state evolution, it has to do with judicious substate projections. The physicist decides what projections are judicious, and it gives us the ability to recognize an alive or dead cat from a hopelessly complex array of atomic wave functions and entanglements.
Sort of like the thermodynamic limit is not a change in the physics of the situation (i.e. N-particle problem), it is an approximation that becomes valid. Both constitute a loss of information when the approximation is made.
All true, but that's in a sense the easy part-- the part that gets overlooked is the choice of a projection in the first place. The same holds for thermodynamic equilibrium-- in literal terms, there is never any system that is anywhere close to full thermodynamic equilibrium, we only get even approximate validity when we ignore certain differences we don't care about (like a particle here versus a particle there, which we don't care about when we are doing volume averages).
This means that you can, in principle, analyse a problem using pure QM wave functions, or you can make the decoherence approximation, just like you can, in principle, analyse a container of gas as an N-body problem, or you can make the thermodynamic approximation, and treat it as a much simpler thermodynamic system.
Yes, the physicist is making those choices, the physicist is doing the physics-- and all based on what questions they are trying to address.
If you do the SC problem as pure QM, then when you open the box, the wave function will collapse into a superposition of all the alive wave functions or a superposition of all the dead wave functions, which is all the scientist is really measuring upon opening the box.
I would take issue there, the way I would say it is, when you open the box, you are necessarily treating a projected subspace, because you will never include yourself in the physics there. Thus, you simply never have a superposition state at all when you open the box and look at the cat-- it would be wrong quantum mechanics to claim the state of what you see is a superposition state in regard to the history of that system (i.e., its unitary evolution). It would be all right to say that is a superposition state going forward-- as a boundary condition to some new calculation which will involve closing up the system again and following some new evolution. Decoherence never applies to the full wave function, it is a treatment of projections onto subspaces that are not isolated, and are chosen by the physicist. The theme in all this is how involved the choices of the physicist are.

in literal terms, there is never any system that is anywhere close to full thermodynamic equilibrium.

Well, I would disagree with that. Using Callen's approach, that would be tantamount to saying the equations of thermodynamics never come anywhere close to working

I would take issue there, the way I would say it is, when you open the box, you are necessarily treating a projected subspace, because you will never include yourself in the physics there. Thus, you simply never have a superposition state at all when you open the box and look at the cat-- it would be wrong quantum mechanics to claim the state of what you see is a superposition state in regard to the history of that system (i.e., its unitary evolution). It would be all right to say that is a superposition state going forward-- as a boundary condition to some new calculation which will involve closing up the system again and following some new evolution. Decoherence never applies to the full wave function, it is a treatment of projections onto subspaces that are not isolated, and are chosen by the physicist. The theme in all this is how involved the choices of the physicist are.

Yes, I agree - once you open the box, QM no longer can be used, the box is not isolated. But I don't understand the phrase "you are necessarily treating a projected subspace". What does that mean?

Well, I would disagree with that. Using Callen's approach, that would be tantamount to saying the equations of thermodynamics never come anywhere close to working
Sure, I was then not using Callen's pragmatic approach, but rather the theoretical definition of thermodynamic equilibrium. In other words, I was supporting Callen's approach to thermo and Bohr's approach to QM by showing they are the only approaches that can actually be used in practice: they are both best seen as how physicists do physics, rather than "laws of nature" that don't need physicists. They appear as simplifications that emerge only once the physicist has decided what he/she cares about, whereas nature has to "care about" everything-- it's nature.

Yes, I agree - once you open the box, QM no longer can be used, the box is not isolated. But I don't understand the phrase "you are necessarily treating a projected subspace". What does that mean?
The state of the cat must be viewed as a substate of the whole system, it is a projection that does not obey the Schroedinger equation. That equation applies to the closed system on the Hilbert space, not open substates that are projections onto subspaces of the Hilbert space. The subspaces do not preserve the postulates of quantum mechanics (in particular, they evolve into mixed states under decoherence, not superposition states), and this is the source of a lot of misunderstanding about the cat paradox.

Indeed, that is perhaps the key difference between a micro system and a macro system, it is the meaning of the Heisenberg divide: a micro system, as a substate, can recover its status as a pure state by measuring it and isolating it-- even though it remains a substate of something larger, it can be treated as a pure state going forward (and exhibit interference and so on). But a macro system, once evolved into a mixed state via external interactions, can never recover its pure state status, it is forever a substate of something larger, and will never exhibit interference. It is just wrong to say that baseballs don't give two-slit patterns because their wavelengths are too small, they are simply not in pure states period. That is also what you said, focusing on the need for isolation, so what I'm saying can be cast as the remark that macro systems like cats can never be sufficiently isolated from their own histories to be treated as systems that obey the Schroedinger equation as the unitary evolution of a state vector in a Hilbert space-- it's just wrong quantum mechanics to describe them that way.

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Indeed, that is perhaps the key difference between a micro system and a macro system, it is the meaning of the Heisenberg divide: a micro system, as a substate, can recover its status as a pure state by measuring it and isolating it-- even though it remains a substate of something larger, it can be treated as a pure state going forward (and exhibit interference and so on). But a macro system, once evolved into a mixed state via external interactions, can never recover its pure state status, it is forever a substate of something larger, and will never exhibit interference. It is just wrong to say that baseballs don't give two-slit patterns because their wavelengths are too small, they are simply not in pure states period. That is also what you said, focusing on the need for isolation, so what I'm saying can be cast as the remark that macro systems like cats can never be sufficiently isolated from their own histories to be treated as systems that obey the Schroedinger equation as the unitary evolution of a state vector in a Hilbert space-- it's just wrong quantum mechanics to describe them that way.
Seems to me this puts in proper language what I had been groping at in #41. Assuming cat and everything else forming the closed box system is perfectly isolated, freezing box and all within to near perfect absolute zero would allow interference (but since the cat is now dead...), otherwise essentially classical behavior? Same for the baseball (obviously only temporal here, until it 'thawed')?
BTW - how do you understand the claims made in the link in #70 http://www.nature.com/news/2010/100317/full/news.2010.130.html "Next, the researchers put the quantum circuit into a superposition of 'push' and 'don't push', and connected it to the paddle. Through a series of careful measurements, they were able to show that the paddle was both vibrating and not vibrating simultaneously...The environment is this huge, complex thing," says Cleland. "It's that interaction with this incredibly complex system that makes the quantum coherence vanish.""
And you would interpret this how - hype (more research funds please), misguided realism (they only imagine it to be actually in two states at once), or something else?

Well in my opinion it shouldn't be labeled as a paradox but as an example how things can be in a superposition of states UNTIL someone or something makes an observation that breaks down the superposition.

For me all the cats of planet Earth that i don't or can't observe are in a superposition of states, i know that for any cat there is probably someone else (different for each cat) other than me observing that cat and he knows the state of the cat, but since he doesn't communicate with me to inform me, for me the cat is in superposition. I think when we intuitevely conclude that a cat can't be in superposition of dead and alive we kind of think of an invisible universal observer that knows the state of the cat, but that kind of observer doesn't necessarily exists.

Aren't all entities on the planet including you and the cats connected trough something like a butterfly effect?If so,than you are in contact with the cats and observing them.It doesn't matter if the information enters your brain,you are having contact anyway,right?And we can also assume this whole planet is one observer to the rest of the universe,since we are all surrounded by atoms just like the atoms that bind the parts of the body,making you a whole.There's a lot of imagination in there :D

The idea that a photon must have a polarization within 45 degrees of the polarizer before passing thru does not work. If I pass a beam of randomly polarized photons thru a polarizer oriented at zero degrees, then I guess we could say the polarization of the photons coming out are evenly distributed between +45 and -45. Next we pass them thru a polarizer at 45 degrees. Half of the ones out of the first polarizer will be between 0 and 45 degrees, and only these will make it thru the second polarizer, since they are between 45-45=0 and 45+45=90 degrees. Now we pass these thru a polarizer at 90 degrees - none will make it thru, because there are none in the beam that are between 90-45=45 and 90+45=135 degrees. In actual fact, something like 20 percent of the original photons make it thru all three polarizers.
Actually it more like 25% make it through, but you are correct that the actual result is non zero and the model does not work if you assume "the polarization of the photons coming out are evenly distributed between +45 and -45". However, if you assume that photons passing through the polariser are randomised so that they come out with a percentage distribution between any two angles a and b, described by:

$$100* \int_{\theta = a}^{\theta =b}cos(2*\theta)$$

then the percentage of photons that exit the first polariser and pass through a second polariser with an angle of $\theta$ relative to the first would be given by:

$$100* \int_{\theta-\pi/2}^{\pi/2}cos(2*\theta)$$

This agrees with Malus's law. I am not saying that this is what happens and it certainly not the conventional explanation, but I am just trying to demonstrate that there can often be more than one way of explaining a given observation.

Some popular accounts of polarisation describe the component of the polarisation parallel to the polariser axis passing through and the component of the polarisation orthogonal to the polarisation axis being chopped off. This sorts of work on average for millions of photons, but when photons pass through one by one it unlikely that that they are sliced and diced like this as they pass through a polariser. It is more likely that they either pass through, or do not pass through, in a binary fashion with a probability of cos(theta)^2, so that individual photons have the same energy before and after passing through. After thinking about this way, I am coming round to that photons exiting a polariser do have a polarisation axis exactly equal to the last polariser they passed through.

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Seems to me this puts in proper language what I had been groping at in #41. Assuming cat and everything else forming the closed box system is perfectly isolated, freezing box and all within to near perfect absolute zero would allow interference (but since the cat is now dead...), otherwise essentially classical behavior? Same for the baseball (obviously only temporal here, until it 'thawed')?
BTW - how do you understand the claims made in the link in #70 http://www.nature.com/news/2010/100317/full/news.2010.130.html "Next, the researchers put the quantum circuit into a superposition of 'push' and 'don't push', and connected it to the paddle. Through a series of careful measurements, they were able to show that the paddle was both vibrating and not vibrating simultaneously...The environment is this huge, complex thing," says Cleland. "It's that interaction with this incredibly complex system that makes the quantum coherence vanish.""
And you would interpret this how - hype (more research funds please), misguided realism (they only imagine it to be actually in two states at once), or something else?
I imagine that they do not make both measurements at the same time, but rather perform one measurement that demonstrates it is not vibrating and then at a later time perform a different kind of measurement that demonstrates it is is vibrating. In an analogous situation when we carry out out the double slit experiment (one kind of measurement) the photons behave like waves, but when we cover one slit so that we know which slit it passed through (another kind of measurement) then they appear to act a bit like particles. It seems we can not make measurements of location and momentum at the same time of a given individual photon (HUP). Having said that, the ingenious experiment of Afshar using a double slit, a lens and a grid of wires, has raised some controversy over this issue.

I imagine that they do not make both measurements at the same time, but rather perform one measurement that demonstrates it is not vibrating and then at a later time perform a different kind of measurement that demonstrates it is is vibrating. In an analogous situation when we carry out out the double slit experiment (one kind of measurement) the photons behave like waves, but when we cover one slit so that we know which slit it passed through (another kind of measurement) then they appear to act a bit like particles. It seems we can not make measurements of location and momentum at the same time of a given individual photon (HUP). Having said that, the ingenious experiment of Afshar using a double slit, a lens and a grid of wires, has raised some controversy over this issue.
Not being able to 'freely' access the detailed paper, I'd say you're probably right yuiop about non-simultaneous measurements. It does say in the link given "Using a sequence of careful measurements...". Point though is these guys are adamant such shows simultaneous coexistence of two states in a macroscopic system. And there are many similar assumed superposed systems that have or are being studied in eg. quantum qubit circuits. I'm of the impression assumptions about things actually going on have to be made to make sense of behavior in such. I agree Afshar experiment is very interesting. Maybe the most interesting aspect is the wide disagreement amongst Afshar's many critics: "A number of scientists have published criticisms of Afshar's interpretation of his results. They are united in their rejection of the claims of a violation of complementarity, while disagreeing amongst themselves as to precisely why Afshar is wrong.", under 'Specific critiques' at http://en.wikipedia.org/wiki/Afshar_experiment. Wait some more and see approach from me.

Seems to me this puts in proper language what I had been groping at in #41. Assuming cat and everything else forming the closed box system is perfectly isolated, freezing box and all within to near perfect absolute zero would allow interference (but since the cat is now dead...), otherwise essentially classical behavior? Same for the baseball (obviously only temporal here, until it 'thawed')?
Yes, it does seem possible to "freeze" a previously macro system into its quantum ground state, though I don't know about the technical challenges there. It isn't the number of particles that make something "macro", it is the number of accessible modes or states for those particles. One might, for example, imagine a laser beam of a huge number of coherent photons all with the same polarization, which could exhibit interference even though there was a spectacular number of particles there, so would be fundamentally quantum mechanical because all those particles still had access to a very limited number of states across the laser bandwidth.

What I worry about is degeneracy-- it would seem that if the individual particles in some seemingly macroscopic paddle were in their ground states, the whole system still does not have a unique "ground state", as there can be any phase relationship among the parts, even before you account for the identical particle multiple wavefunctions. It would seem to generate a huge manifold of equal-energy "ground states" for the whole system, so if you started out with a mixture of those before you "froze" it, you'd still have a mixture after freezing it-- not a pure state. That might not affect its behavior as it evolves as in its frozen condition, but when you later interact it with something, or heat it up, one might imagine the mixed state would "pop out" again, like magnetic domains. For some kinds of interactions that might not matter, but for others it might, and it would still not be literally a superposition, it would be a mixture of ground states with great similarities.
BTW - how do you understand the claims made in the link in #70 http://www.nature.com/news/2010/100317/full/news.2010.130.html "Next, the researchers put the quantum circuit into a superposition of 'push' and 'don't push', and connected it to the paddle. Through a series of careful measurements, they were able to show that the paddle was both vibrating and not vibrating simultaneously...
I can believe it, it depends on what those "careful measurements" were and what they mean by vibrating and not vibrating. It's not real coherent language, a more technical understanding of what they did would probably generate more precise terms. Anyway, I'm still not sure they got the paddle into a pure state, it might have been a mixture of degenerate ground states that nevertheless interacted with the quantum circuit so as to not destroy the distinction between "push" and "don't push." There's just not enough detail. I'll bet most of the coherences were destroyed, but maybe there's an energy mode in there that is preserved over the entire mixture, like how the "sweet" is preserved when you mix sugar and corn syrup.
And you would interpret this how - hype (more research funds please), misguided realism (they only imagine it to be actually in two states at once), or something else?
Hype is too harsh, it sounds like they are faithfully reporting what they did, but the language seems imprecise. I'm not even crazy aboug that language for clearly quantum mechanical systems, like the idea that a photon "goes through both slits", when instead it seems more economical to simply assert no opinion on anything that sounds like a photon path through the slits at all. So I wouldn't say the paddles was both vibrating and not vibrating at the same time, I would just say the classical notions of vibration or no vibration does not encompass the behavior of the paddle.

What I worry about is degeneracy-- it would seem that if the individual particles in some seemingly macroscopic paddle were in their ground states, the whole system still does not have a unique "ground state", as there can be any phase relationship among the parts, even before you account for the identical particle multiple wavefunctions. It would seem to generate a huge manifold of equal-energy "ground states" for the whole system, so if you started out with a mixture of those before you "froze" it, you'd still have a mixture after freezing it-- not a pure state. That might not affect its behavior as it evolves as in its frozen condition, but when you later interact it with something, or heat it up, one might imagine the mixed state would "pop out" again, like magnetic domains. For some kinds of interactions that might not matter, but for others it might, and it would still not be literally a superposition, it would be a mixture of ground states with great similarities.
Interesting. My crude analogy here would be 'glass' vs 'crystal' - the former has an intrinsic disorder entropy even at absolute zero, the latter in principle may not (not sure here about isotope mix or nuclear spin ordering). So I guess an ultra deep frozen cat would be more 'glass' than 'crystal' in the quantum states sense. At another level, I take it then a macroscopic super-current at relatively high temp (say in a so-called high temperature superconductor) could be described as in a coherent ground state but not a pure state?
...I would just say the classical notions of vibration or no vibration does not encompass the behavior of the paddle.
OK this is no doubt your pure CI coming out!

The state of the cat must be viewed as a substate of the whole system, it is a projection that does not obey the Schroedinger equation. That equation applies to the closed system on the Hilbert space, not open substates that are projections onto subspaces of the Hilbert space. The subspaces do not preserve the postulates of quantum mechanics (in particular, they evolve into mixed states under decoherence, not superposition states), and this is the source of a lot of misunderstanding about the cat paradox.

Indeed, that is perhaps the key difference between a micro system and a macro system, it is the meaning of the Heisenberg divide: a micro system, as a substate, can recover its status as a pure state by measuring it and isolating it-- even though it remains a substate of something larger, it can be treated as a pure state going forward (and exhibit interference and so on). But a macro system, once evolved into a mixed state via external interactions, can never recover its pure state status, it is forever a substate of something larger, and will never exhibit interference. It is just wrong to say that baseballs don't give two-slit patterns because their wavelengths are too small, they are simply not in pure states period.

Ok, I think I understand, and I see that I was wrong to say that what is observed in opening the box is a superposition of e.g. dead microstates. Let me rephrase and see if I get what you are saying: What the scientist observes when opening the box is not a well defined wave function that is some superposition of all the e.g. dead states, but rather an observation that can be attributed to some ill-defined wave function that lies somewhere in the space spanned by the e.g. dead microstates. Is that the "projected subspace" you refer to?

That is also what you said, focusing on the need for isolation, so what I'm saying can be cast as the remark that macro systems like cats can never be sufficiently isolated from their own histories to be treated as systems that obey the Schroedinger equation as the unitary evolution of a state vector in a Hilbert space-- it's just wrong quantum mechanics to describe them that way.

I'm not sure I understand this - What I read is that a macro system cannot be treated quantum mechanically, and I disagree with that, just as I would disagree that a classical macrosystem cannot be treated as an N-body problem, at least in principle.

Interesting. My crude analogy here would be 'glass' vs 'crystal' - the former has an intrinsic disorder entropy even at absolute zero, the latter in principle may not (not sure here about isotope mix or nuclear spin ordering). So I guess an ultra deep frozen cat would be more 'glass' than 'crystal' in the quantum states sense.
That sounds like either a reasonable or an excellent analogy, I can't really tell which without much deeper analysis.
At another level, I take it then a macroscopic super-current at relatively high temp (say in a so-called high temperature superconductor) could be described as in a coherent ground state but not a pure state?
That's an interesting question, it might be a bit like the laser. A laser is highly coherent, but not exactly coherent, and I'm really not sure if it is more accurate to say we have a pure state that has a bandwidth, or if the bandwidth is also expressing a mixed character to the state. When doing laser spectroscopy, the bandwidth is treated as a mixed state of plane waves, but it's probably more coherent than that. But I doubt it is a pure state either, where every photon has the same definite wavefunction.
OK this is no doubt your pure CI coming out!
No doubt! But I would argue this goes beyond interpretation-- it is just correct quantum mechanics, and even MWI would say the same thing. None of the interpretatons know how to reconcile the language of the quantum mechanical wave function of the closed system with the language that applies to whatever piece we actually observe from our vantage point as part of the system. The only one that can navigate that is Bohmian, and it comes with all kinds of excess baggage-- and claims the paddle must be either vibrating or not vibrating, possibly sequentially one or the other, but never both.

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Let me rephrase and see if I get what you are saying: What the scientist observes when opening the box is not a well defined wave function that is some superposition of all the e.g. dead states, but rather an observation that can be attributed to some ill-defined wave function that lies somewhere in the space spanned by the e.g. dead microstates. Is that the "projected subspace" you refer to?
Exactly-- the wave function is ill defined because the scientist is now part of it, and cannot attribute their own involvement, so must instead treat a projection that will end up looking like a mixed state. So decoherence can happen in a closed system that does not include an observer, but it will still be unitary evolution-- the paradoxical elements only appear when we have a different flavor of decoherence, the kind that involves untraced noise modes within the observer themself, for that hopelessly derails the concept of a pure state wavefunction, or at least any chance of getting that language to connect with the answers a physicist actually wants in an experiment. That's classic Bohr-- physics is done by macro brains.
I'm not sure I understand this - What I read is that a macro system cannot be treated quantum mechanically, and I disagree with that, just as I would disagree that a classical macrosystem cannot be treated as an N-body problem, at least in principle.
The problem is worse than just complexity. I agree with you that in principle, formal Hilbert-space quantum mechanics should apply to any closed system, no matter how complex, if it can be shown that the system starts off in a pure state when it gets closed. But that's just what cats won't be-- you can put a cat in an isolation booth, but you can't isolate it from its own history, it is already in a mixed state because you can only put the cat in the booth, not everything the cat has ever interacted with. In particular, you aren't putting yourself in the booth with it, but at some point you would have had to interact with it to tell that it is a cat in the first place. This is different from putting a "spin up" particle in an isolation booth, because there really isn't anything else there to know about the particle that is relevant to its behavior. That right there is the crux of the Heisenberg divide, a concept that seems to get little play any more but still seems profoundly relevant to me.

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Exactly-- the wave function is ill defined because the scientist is now part of it, and cannot attribute their own involvement, so must instead treat a problemjection that will end up looking like a mixed state. So decoherence can happen in a closed system that does not include an observer, but it will still be unitary evolution-- the paradoxical elements only appear when we have a different flavor of decoherence, the kind that involves untraced noise modes within the observer themself, for that hopelessly derails the concept of a pure state wavefunction, or at least any chance of getting that language to connect with the answers a physicist actually wants in an experiment. That's classic Bohr-- physics is done by macro brains.

But how can we ever observe a pure state? Every pure state is connected to a macroscopic measuring device, which a macroscopic scientists observes. The connection between the device and the scientist is classical, so the effect of the scientist on the device is negligible as far as its readings are concerned. We are not trying to determine the wave function of the device, only the system it is measuring. The interaction between the scientist and the box upon opening can be minimal, like some kind of heartbeat detector which turns on a laser beam which emits a few photons per second when the cat's heartbeat stops. Opening the box is equivalent to opening an aperture and detecting or not detecting a stream of photons.

The problem is worse than just complexity. I agree with you that in principle, formal Hilbert-space quantum mechanics should apply to any closed system, no matter how complex, if it can be shown that the system starts off in a pure state when it gets closed.

But it applies for a mixed state as well. A mixed state is just a set of pure wavefunctions spanning the space, each multiplied by a probability. Each wave function can then be propagated using e.g. the Schroedinger equation.

But that's just what cats won't be-- you can put a cat in an isolation booth, but you can't isolate it from its own history, it is already in a mixed state because you can only put the cat in the booth, not everything the cat has ever interacted with. In particular, you aren't putting yourself in the booth with it, but at some point you would have had to interact with it to tell that it is a cat in the first place. This is different from putting a "spin up" particle in an isolation booth, because there really isn't anything else there to know about the particle that is relevant to its behavior. That right there is the crux of the Heisenberg divide, a concept that seems to get little play any more but still seems profoundly relevant to me.

I don't understand "isolate it from its own history". In principle, I could close the box knowing the cat's pure wave function. Or, I can get more realistic, and say its in a mixed state - probabilities of live wave functions are, I don't know, equal a priori, probabilities of dead are zero. Then I propagate both using the Schroedinger equation. Just before I open the box, I have a superposition of live and dead in the first case, and a mixed state combination of live and dead in the second. Now I "open the box". Just as I could in principle specify the pure state when I closed the box, I can in principle determine the pure state when I open it. Yes, practically, that's not likely, but not in principle impossible. Or, if I started with a pure case, but open the box and just observe a dead cat, I can say that my observation yields a mixed state which contains none of the alive components of the pure state I calculated before opening. I would call that a "collapse" of the wave function, but I am not adamant about that terminology. If I start with a mixed case, I can propagate that, then open the box, and again the mixed state collapses to a mixed state of dead cat only. Again, the interaction between the scientist and the box upon opening can be minimal for the mixed case measurement.

But how can we ever observe a pure state? Every pure state is connected to a macroscopic measuring device, which a macroscopic scientists observes.
We don't observe pure states. In fact, we don't observe states at all-- we observe outcomes of observations. States, be they pure or mixed, are theoretical devices we use to understand what we actually do observe. Now, if we observe that a particle has "spin up", then we are allowed to treat the particle as being in a pure spin state going forward, because there's nothing else there to know-- there isn't unknown information being glossed over (if spin is what we care about). This is in contrast to the state of ourselves and the observational device we used that gave spin up-- those contain all kinds of unknown information we are indeed glossing over. So there we have a case where the substate (the particle) is in a pure state going forward into a new isolated environment where we can treat it as a closed system, or an environment with known attributes (like fields) which alter the Hamiltonian. The point is, there we can use the postulates of quantum mechanics going forward (but not backward) in time. The larger system that includes us and our instrument, however, cannot be so treated-- it is not a pure state, owing to all that untracked information and relevant history.

The problem with the usual rather bogus way of introducing the cat paradox is that the alive or dead status of the cat is treated like the spin state of the particle, which is just wrong quantum mechanics, because of all that untreated information that goes into an alive or dead cat (not present in a spin state of a particle). So the question is not if the cat can be in a superposition state, we already know the cat cannot be in a superposition state. The question is, can the system that includes the cat be in a pure state, and if it is, how can there be an alive and a dead cat tangled up in that pure state somewhere? That's the right way to describe the paradox, and it suggests what I think is the right answer-- the Bohr answer, the concept of an alive or dead cat is not a description of a global quantum mechanical system, it is a description of a projection onto a subspace, and projections like that are routinely going to be mixed states.

So there's no paradox as to why the cat is in a mixed state of alive or dead, that's just correct quantum mechanics. The paradox doesn't appear until we open the box and become part of the closed quantum mechanical system. We cannot perceive the quantum mechanical system because we are just a part of it and that's not how our brains work anyway, our brains work by throwing out most of the information there and concentrating on a subspace (like one that distinguishes the cat from ourselves instead of the holistic treatment of the full wave function of the closed system). Then we get the real question here: how does the subspace we are concentrating on get actualized into a set with specific attributes,keeping a set that is consistent with our information and throwing away all that isn't? This has to be answered in the language of information processing, it has to be something about how we do physics itself, not something involving any particular law of physics like quantum mechanics, which is necessarily subject to how we do physics.
But it applies for a mixed state as well. A mixed state is just a set of pure wavefunctions spanning the space, each multiplied by a probability.
But that isn't a quantum mechanical wave function, it is a mixture of wave functions. A mixture of things that obey quantum mechanical formalism is not something that obeys quantum mechanical formalism, but we know how to do quantum mechanics on it (density matrices and so forth). In particular, it produces no cat paradox, the cat paradox requires us to have a pure state in which there is an alive or dead cat in there somewhere, and that requires the state of the whole system.
I don't understand "isolate it from its own history". In principle, I could close the box knowing the cat's pure wave function.
No, that is just exactly what you could never do, not even in principle. Because the only way to know that would be to do measurements on the cat, but that would involve a measuring device, so immediately the cat becomes a subspace of the thing that is a pure state. Unlike measuring the spin of a single particle, where there is no information being ignored, if you measure an "entire cat", there is vast amounts of information you could never get a handle on, like herding cats (literally). There's no measurement like that which even in principle could result in complete information about the cat's wave function that could be treated as a closed system going forward, too much of the data (all the phase coherences) that would need to be tracked is going to be entangled with the instruments doing the measuring, not to mention the brain processing that information.

This is the key point-- the information that goes into determining a wave function is not in the entity being observed, it is in the environment doing the observing and processing that information. Physics is done by physicists, even if we can imagine the action of hypothetical physicists not actually present in the environment. If that environment does include a real brain, it might be able to treat the entity as having a pure-state wavefunction (as for the spin of a particle), but it could never be empowered to treat a cat in a pure-state wavefunction, there would always have to be too much overlooked information (indeed, judicious overlooking of information is more or less the foundational principle of physics). It is only ever the whole system including the observer that could be treated as a pure state, and only if it started out in a pure state, which brings in the issue of history.
Just before I open the box, I have a superposition of live and dead in the first case, and a mixed state combination of live and dead in the second.
But that makes all the difference. If you have a mixed combination, you have no paradox-- you have a purely classical situation, like a coin that is flipped and covered.
Now I "open the box". Just as I could in principle specify the pure state when I closed the box, I can in principle determine the pure state when I open it.
I dispute that, but even if it were possible, you would never get a pure state that is a superposition of an alive cat and a dead cat that way. The very definition of what an alive cat is requires that certain types of information about the cat be processed by a brain (even a hypothetical one) capable of making that determination, but that processing will require coupling the cat to the brain, bringing in all the untracked information in the brain. Again, both physics and language itself are examples of judicious overlooking of unwanted information, completely anathema to a concept of a pure state wavefunction. Quantum mechanics invokes the concept of a pure state expressly for the purposes of later dispelling it, there is no such thing as quantum mechanics involving only pure states. The way I like to put that is, if an electron could think, it wouldn't use quantum mechanics. I believe that is very consistent with Bohr's approach to the role of the mind of the physicist.
Or, if I started with a pure case, but open the box and just observe a dead cat, I can say that my observation yields a mixed state which contains none of the alive components of the pure state I calculated before opening.
Yes, certainly, we invoke mixed states like that all the time, even in classical physics. There isn't any quantum mechanics at the mixed-state level, the quantum mechanics is all what is happening at the pure-state level, and the cat is not described as a pure state in that example. Indeed, a mixture of suitably detailed pure states is exactly the same thing as a classical description. So when what we mean by "an alive cat" has much more to do with the nature of that mixture, than the nature of the pure states that go into it, then we say we have a classical treatment of a cat, not a quantum mechanical treatment.
I would call that a "collapse" of the wave function, but I am not adamant about that terminology.
To say a wave function is collapsed, you must have a wave function in the first place. A mixture is not a wave function, it is a mixture of wave functions. Classically, it is the mixture that matters, not the quantum mechanics of the wave functions-- the evolution of a mixture is a classical evolution, what the individual wave functions are doing gets lost (like a thermodynamic treatment of an ideal gas where we are not a whit for what any given particle is actually doing, only the generic possibilities for what they are allowed to do). When a cat is a super-complicated statistical average of a bunch of possible individual wavefunctions, then it is a classical object, not a quantum mechanical one.
If I start with a mixed case, I can propagate that, then open the box, and again the mixed state collapses to a mixed state of dead cat only. Again, the interaction between the scientist and the box upon opening can be minimal for the mixed case measurement.
Absolutely true-- but only because you are talking about a classical situation through and through.

Nearly eighty years on and this famous experiment is still being discussed.Fair enough but in discussions of this type certain relevant features of the experimental design and set up seem to be overlooked.These features are in connection with the fact that the experiment is a thought experiment,not a real experiment.Thought experiments can be very useful but they must be used with great care and with a consideration of any limitations the experiments may have.The relevant limitations of this experiment can be defined under two headings...Observations and Isolation:

OBSERVATIONS

Schrodinger designed his experiment in such a way that once the box was closed no further relevant observations could be made,not even in principle,until the box was opened again.It becomes pointless to use a theory to make predictions about "happenings" within "hidden" regions(eg the closed box) where,because of the design of the experiment,no evidence can be gained to verify,or otherwise,those predictions.

ISOLATION

A major requirement of the experiment is that whilst the box is closed its contents and all of the surroundings are isolated from each other.If isolation here means "total isolation" then there can be no linkages at all between the contents and all parts of the rest of the universe including no interaction by means of gravitational forces.If it is total isolation that is required then the experiment fails straight away,even as a thought experiment.
Perhaps partial isolation is all that is required and if so before proceeding we would need a definition of "partial isolation".Any takers?

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Actually, neither of those seem like problems to me. I agree with you that we cannot talk about happenings in an unobserved region, but we can talk about how we are treating the state of an unobserved system, and that is all that is needed here. The purpose of language about a state is simply to be able to make the proper predictions of the happenings that are in fact observable given the setup that defines the state. The paradox centers on what treatment we should give to the cat before the box is opened-- it is clear enough how to treat it after it is opened. I claim the real problem with the way the paradox is normally stated is that it is wrong quantum mechanics-- the cat is never in a superposition state, because it is a projected substate of that system, and that generally yields a mixed state not a superposition state. However, that does not make the paradox go away-- the whole system can presumably still be treated as a pure state, even if the whole system must include the entire history of the universe. The key point is, such a system includes the physicist, so it is inescapable that physics is something that is done by physicists, not something that happens to nature.

As for gravity, do you really think the experiment comes out differently, or the quantum mechanical treatment used by the physicist must differ, if done in deep space?

Theories are informed by observations,they must conform to observations and if new predictions are made then for these to gain any credence it must be possible ,even if just in principle,to gain the necessary observations to back these predictions up.Schrodinger designed,perhaps unwittingly,an experiment which disallowed the gaining of such observations.
Deep space.Where's that?Isn't this stretching the thought experiment even further by taking everything to an imaginary place where,I'm guessing, it's assumed that gravitational interactions are vanishingly small.If so in the context of the isolation that is needed for the experiment,when does vanishingly small become zero?

Theories are informed by observations,they must conform to observations and if new predictions are made then for these to gain any credence it must be possible ,even if just in principle,to gain the necessary observations to back these predictions up.Schrodinger designed,perhaps unwittingly,an experiment which disallowed the gaining of such observations.
I agree with your perspective on the interaction between theory and observations, but I don't see how your conclusion follows. It seems to me Schroedinger is asking a simple question-- how should our theory treat the state of the system in that thought experiment to be consistent with all the observations we could make? In particular, the theory says that we can correctly predict observations by treating all pure states as if they evolved according to the Schroedinger equation, which is a unitary evolution that only maps pure states into pure states.

The paradox is the fact that experimental outcomes never represent a mapping of a pure state into a pure state, because the outcome of the experiment never constrains the state of the macro apparatus sufficiently to be able to describe it as a pure state. (Here Schroedinger may err to claim that the cat is ever in a superposition state, but the paradox need not be expressed in that particularly pictorial way.) Hence there is a fundamental disconnect with the postulates of quantum mechanics and the way we do physics. Bohr resolves that simply by saying those are the limitations of the postulates of quantum mechanics, there is no need to take them any more seriously than that. I think he's right.
Deep space.Where's that?Isn't this stretching the thought experiment even further by taking everything to an imaginary place where,I'm guessing, it's assumed that gravitational interactions are vanishingly small.
That is the purpose of thought experiments.

If so in the context of the isolation that is needed for the experiment,when does vanishingly small become zero?
No, vanishingly small means the same thing it always does in physics-- too small to affect the observable outcome of the experiment sufficiently to concern the goals of the physicist.

I am referring to the fact that no observations can be made whilst the box is closed.We can make observations before the box is closed and after it is opened and to explain how the event proceeded during the closed time needs nothing more than a bit of simple forensic investigation,general everyday experience,and common sense.Quantum theory may be able to predict the outcome but it can also be interpreted by some as making weird unproveable predictions such as a simultaneously dead and alive cat.Although it was designed with QM in mind,QM is not needed to explain this particular experiment.
The point I am making about thought experiments is that any limitations they have must be considered.Let me rephrase my question with yet another thought experiment.Assume that the box is at a place where the contents could not be considered as isolated because of their appreciable gravitational interactions with the surroundings.Now let the box go on a journey along a path of reducing gravitational interaction.Where along the path does the interaction fall to such a small value that the box contents become isolated enough to meet the criteria needed by Schroedingers experiment?In other words what exactly is the isolation needed and when can small be considered as zero?
We could go to the limit and take the box to an imaginary place where there are no interactions at all resulting in total isolation but such a place would be separated from the rest of the observeable universe.Yet another thought experiment breakdown.

I am referring to the fact that no observations can be made whilst the box is closed.We can make observations before the box is closed and after it is opened and to explain how the event proceeded during the closed time needs nothing more than a bit of simple forensic investigation,general everyday experience,and common sense.Quantum theory may be able to predict the outcome but it can also be interpreted by some as making weird unproveable predictions such as a simultaneously dead and alive cat.Although it was designed with QM in mind,QM is not needed to explain this particular experiment.
Yes, that is very much Bohr's view-- we use QM for certain things, but not for others, it is our tool not our master. But many theorists find the aesthetic beauty of QM to be compelling as a more fundamental theory that transcends the way we use it and becomes a kind of "actual law" that reality obeys. It sounds like you and I would both agree that this view is elevating physics to a kind of philosophical status that is not justified by the prescriptions of science, but that is in itself a very interesting debate. One thing we cannot ignore is that quantum mechanics obeys the Correspondence Principle-- it never makes a wrong prediction, even when applied on scales where it was not intended, so its problem is that it is unwieldy but not wrong on classical scales. But if it's not wrong on those scales, then if we can get a large enough box around a closed system, it has to evolve according to the Schroedinger equation-- the issue then becomes, what does that evolution mean if it is not what is used by the physicist to make predictions and understand outcomes? That question is what separates the Copenhagen interpretation from the others.
The point I am making about thought experiments is that any limitations they have must be considered.
I would frame that same concern as saying that a thought experiment may be hypothetical, but it must not be magical-- its hypothetical elements have to be included as part of an actual (albeit hypothetical) experiment. So the results have to be framed as experimental outcomes, but we can still ask what states of the system we would use along the way to reach those predictions, and we can ask if those states make sense with what we observe in everyday life. Some say that the cat really is in a superposition state, and we just don't notice it, and others say that what we notice is what physics is all about. I point out that many claims of the superposition state are actually wrong quantum mechanics, because they treat a substate rather than a closed state.
Let me rephrase my question with yet another thought experiment.Assume that the box is at a place where the contents could not be considered as isolated because of their appreciable gravitational interactions with the surroundings.Now let the box go on a journey along a path of reducing gravitational interaction.Where along the path does the interaction fall to such a small value that the box contents become isolated enough to meet the criteria needed by Schroedingers experiment?
If you want to study at what point a system is "closed enough" to be treated as a closed state, you simply carry out the experiment many times, opening it at various gravitational strengths, and see when you start to get the predictions you expect for a closed system. But none of that would get at the issue of the cat paradox, because that paradox already exists for a perfectly closed system-- because when you open it to learn something about the system, at that point it is not closed any more, regardless of whether it was before. So there's always something entering the problem that you are not treating in the "pure state" description of the system, the very way we do physics always assumes we will open the system at the end, and that's where Bohr says the literal interpretation of the postulates breaks down.
We could go to the limit and take the box to an imaginary place where there are no interactions at all resulting in total isolation but such a place would be separated from the rest of the observeable universe.Yet another thought experiment breakdown.
Perhaps we are not that far apart-- I say that experiment breaks down not because it is isolated from the rest of the observable universe, but because it has to return to the observable universe at the point where we use it to test our understanding of it. It is this return that ruins the thought experiment, not the problem with isolation during the unitary evolution of the system.

Having read the last few posts in this thread, there is still some confusion about whether the cat is (1) in superposition of dead AND alive or (2) is definitely either alive or dead but not both, while the box is closed and the observer can make no observations of the state of the cat. Now persons taking either position (1) or (2) are making claims about the state of the cat with absolutely no evidence to support their position because by the definition of the thought experiment no observations can be made, only suppositions.

Now let us say you have introduced a student to quantum physics by way of Schroedinger's cat example and then go on to state that a quantum particle is also in a state of superposition before measurement. A student can then reasonably conclude that "superposition" is just physicists' "mumbo jumbo" for "we do not know what the state of the particle is, simply because we have not yet measured it". If there is a deeper meaning to superposition, then Schroedinger's cat is doing a very poor job of demonstrating what it is.

I agree with much of what you are saying, it sounds like you are making a plea for the value of being able to describe states as theoretical entities without apology, even when no specific observable is specified. This is akin to claims that a wave function is an expression of "everything that could possibly be known" about a system, or maybe even what nature itself "knows" about that system. However, I would say there are equal pitfalls to adopting a stance that nature is a kind of information processor, when in fact it is physicists that are information processors, as there is in adopting language that forces us to treat all theoretical constructs as "mumbo jumbo."

Somehow there is a fine line to walk there, and that line is very much at the heart of the dispute between the Copenhagen interpretation and others. So in that sense, instilling a healthy respect for careful consideration of that "fine line" is very much the point of the cat paradox. To me, walking that line successfully allows us to postulate hypothetical observers (and their brains) without any actually being present, but we are not allowed to postulate hypothetical knowledge of a system without the means for that knowledge to be specified being (hypothetically) present. Thus no experimental outcome has any meaning until we allow that the measuring device (and the brain that interprets it) be present, because its presence is what gives meaning to the outcome in principle-- whether or not the device is actually there in practice.

(Responding to Rap: I don't understand "isolate it from its own history". In principle, I could close the box knowing the cat's pure wave function.)

No, that is just exactly what you could never do, not even in principle. Because the only way to know that would be to do measurements on the cat, but that would involve a measuring device, so immediately the cat becomes a subspace of the thing that is a pure state. Unlike measuring the spin of a single particle, where there is no information being ignored, if you measure an "entire cat", there is vast amounts of information you could never get a handle on, like herding cats (literally). There's no measurement like that which even in principle could result in complete information about the cat's wave function that could be treated as a closed system going forward, too much of the data (all the phase coherences) that would need to be tracked is going to be entangled with the instruments doing the measuring, not to mention the brain processing that information
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If that environment does include a real brain, it might be able to treat the entity as having a pure-state wavefunction (as for the spin of a particle), but it could never be empowered to treat a cat in a pure-state wavefunction, there would always have to be too much overlooked information

So you are saying that even in priciple, we cannot assign a wave function to a macroscopic object because "too much of the data (all the phase coherences) that would need to be tracked is going to be entangled with the instruments doing the measuring". I do not understand this "too much data being entangled with the instrument" effect. I assume this effect is continuous, gets continually worse as the size of the system being investigated contains more and more particles. Can you describe this effect a bit more fully, perhaps with just a few particles which demonstrates the effect, even if the effect is miniscule?

(Responding to Rap: Just before I open the box, I have a superposition of live and dead in the first case, and a mixed state combination of live and dead in the second.)

But that makes all the difference. If you have a mixed combination, you have no paradox-- you have a purely classical situation, like a coin that is flipped and covered.

I would say there is no paradox even if you did have a pure wave function. What is the paradox that occurs in assuming a pure state is known when the box is closed? Is it just the effect you mentioned above - i.e. it cannot be done?

(Responding to Rap: Now I "open the box". Just as I could in principle specify the pure state when I closed the box, I can in principle determine the pure state when I open it.)

I dispute that, but even if it were possible, you would never get a pure state that is a superposition of an alive cat and a dead cat that way. The very definition of what an alive cat is requires that certain types of information about the cat be processed by a brain (even a hypothetical one) capable of making that determination, but that processing will require coupling the cat to the brain, bringing in all the untracked information in the brain. Again, both physics and language itself are examples of judicious overlooking of unwanted information, completely anathema to a concept of a pure state wavefunction. Quantum mechanics invokes the concept of a pure state expressly for the purposes of later dispelling it, there is no such thing as quantum mechanics involving only pure states. The way I like to put that is, if an electron could think, it wouldn't use quantum mechanics. I believe that is very consistent with Bohr's approach to the role of the mind of the physicist.

I'm sorry, I misspoke - if you assume that you have a pure (and of course non-superposed) state when the box is closed, then you can do QM calculations (e.g. Schroedinger's equation) and you will calculate, for some time later (e.g. just before the box is opened), a pure state which is a superposition. This state will tell you the probability of opening the box and seeing the cat dead or alive, pretty much, since there will be little chance that, upon opening the box, the interference of the environment will affect that outcome.

There isn't any quantum mechanics at the mixed-state level, the quantum mechanics is all what is happening at the pure-state level, and the cat is not described as a pure state in that example. Indeed, a mixture of suitably detailed pure states is exactly the same thing as a classical description. So when what we mean by "an alive cat" has much more to do with the nature of that mixture, than the nature of the pure states that go into it, then we say we have a classical treatment of a cat, not a quantum mechanical treatment.

I am not, and I wish to avoid, invoking the decoherence approximation here. A mixture of suitably detailed pure states is NOT EXACTLY the same as a classical description. There IS quantum mechanics at the mixed state level - Upon closing the box, having measured a mixed state, each pure state of the mixture is propagated forward by e.g. the Schroedinger equation. Each pure state propagates to a another pure state, yielding a fully defined propagated mixed state at a time just before the box is opened, which is then used to calculate the probability of finding the cat dead or alive when the box is opened.

Note - when I say "having measured a mixed state", it may be as little as saying "I see a live cat, geiger counter not clicked", and then assigning equal probability to every pure state of the mixture which conforms to this observation, zero to the rest, which is, of course, more than just a measurement.

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