So no more pestering you on this topic - honest. Have a nice stress-free day!
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?
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 still think you are using wave function to mean the predictions of humans with limited information rather than the state of the system itself.
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.
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.
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 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. 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. 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.) Can you prove that if after you remove your hand the coin showed "heads" that it was not in a state of "heads" while it was covered by your hand? So when you say "The Copenhagen interpretation is different. It does not postulate anything beyond measurement." that is not entirely true, because it is postulating that something is in a superposed state before measurement. Let's 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."
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).
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.)
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.
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.
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).
Yes, the physicist is making those choices, the physicist is doing the physics-- and all based on what questions they are trying to address.
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.
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.
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.
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')?
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:
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.
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.
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.
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.
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?
OK this is no doubt your pure CI coming out!
That sounds like either a reasonable or an excellent analogy, I can't really tell which without much deeper analysis.
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.
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.OK this is no doubt your pure CI coming out!
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.
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.
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.
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.
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.
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 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.
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.
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.
Absolutely true-- but only because you are talking about a classical situation through and through.
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.
That is the purpose of thought experiments.
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.
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.
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.
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.
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.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.