So the AI thinks it collapsed the wave function whether it actually did or not, why do we then think we can collapse the wave function?

Isn't there always a higher order wave function still waiting to be collapsed?

My conclusion is that the collapse of the wave function is just a short hand for "now we, right here, right now, know" and whether this is the final collapse of "the" wave function, we will never know.

Even the empty room without AI within it collapses the unhappy cat. The problem of AI is self-consciousness that it [ or maybe (s)he :) ] is what has caused cat's accident. A quantum automaton seems to be able to possesses self-consciousness (see the attachments).

von Neumann is the most overrated author on this topic.  I remember my adviser in grad school saying "von Neumann answers all" here with great reverence.  Not that he ever read his book, just that he was a shill for the established famous dead people.  I think a similar method the many worlds approach give a long lasting bifurcation of the space for any kind of measurement that is independent of any notion of consciousness.  To plug my exposition:

Article Quantum Measurement and Classical States

Thank you to the initial participants.  I read the answers this morning, and it seems to me the various positions are represented and "staked out" so to speak.  

• Only Olof seems to me to have grasped the "new" dilemma present in this reformulation of Schrodinger's cat.  
• Charles correctly points out we don't know why the probability propagates as a wave, however the quantum wave will produce an interference pattern which the classical probabilities will not.  They are simply additive, i.e. no phase component.
• Vasil comes functionally close to a line of thought I was pursuing a few years ago, but for possibly different reasons.  I was using quantum uncertainty vs. momentum to collapse the wave function based on mass, not "quantum consciousness."  But the idea is the collapse happens continually in various situations where the objects are just slightly larger than quantum scales.
• Clifford appears to suggest it is related to the many worlds hypothesis.  That it is, but in the example, assuming the state function behaves as the question supposes (I have no certain knowledge of course) then the possibilities of the many worlds exist in the state function, but they aren't physical.

So, to build on Olof's answer (correct me Olof if you meant something different), the many worlds seem to be present in the state function still as possibilities, not as bifurcated physical entities the way most people speak of many worlds.

Instead of traveling between worlds, we have the problem of a reference position in the state function, i.e. which part of the state am I a member of?  Traveling is equivalent to jumping to a different part of the state function, and remembering it, which is self-contradictory.

The AI, presumed non-conscious (trust me, I can write a computer program now that would do what is required, it wouldn't be that long, and you'd never get the impression it was conscious), is a stand-in for ourselves.  But with consciousness removed to avoid the sort of "mystical" arguments von Neumann proposes.  The purpose is just to point out we don't actually know whether the state function is collapsed, not by any of our current experiments.  

Just because we no longer see an interference pattern, that only means we have become entangled with the state function.  The interference pattern may still be observable to a meta-observer.  But we cannot communicate with the meta-observer without becoming entangled with him or her, in which case each possible state we are in sees only its context, not the whole state function, and therefore not the interference.

It is difficult to wrap your head around.  Now with a more full explanation, who sees the dilemma, and who thinks I'm hallucinating and why?  More important, can we make a theory of collapse that does not have this problem?

Pioneering QM is a fantastic theory describing Nature to an unsurpassed exactitude. Nevertheless it is based on the idealization of isolated systems leading to conceptual difficulties like the collapse of the wave function. For instance Mandelstam's indirect measurement process provides a more realistic alternative to the measurement problem.

In general, however, such a hypothesis must be followed up by a rigorous formulation that incorporates appropriate (quantum-thermal) correlations between the system and the apparatus.

To account for dead and alive cats as well as Wigner's friend one would also need a theory of consciousness that also involves the brain of the cat. If the cat could communicate with Wigner's friend he/she would convey if he/she is still alive – at any rate the cat would be more intelligent than the AI as far as surviving dangers and catching mouse involving the evolution of the species denoted as cats.

@Robert Low & Erkki, I had not heard of "Wigner's friend," and didn't look it up until the second mention, but I see it is the same question I've posed.  This is described briefly in a Wiki article https://en.wikipedia.org/wiki/Wigner%27s_friend which supposes that while a material object may be in a superposition of states, a consciousness may not.

Frankly, my reaction to that is that the idea is rubbish.  Basically it supposes that all physicists and mathematicians are religious in the extreme, believing that there is something about consciousness that is not materially describable.  It may be so, but it is not the standard assumption of science, nor is it acceptable.

It is my purpose to suggest that we should be assuming consciousness is a material object until conclusively proven otherwise.  This would not have been an automatic assumption in the first half of the 20 century, and would have been heresy before, but I think it is reasonable now.  Perhaps we should start by voting on that question, the reasonableness of discarding consciousness as non-material?

I think many worlds gets dismissed as unphysical because the notion seems just another ad hoc interpretation designed to reproduce the same results.  I showed that, given the rather restricted set of wavefunctions that describe physical objects one has such results arise as a consequence of Schrodinger dynamics (but including photons).  These split off spaces are not permanently separated and I suggest some low mass experiments where these results begin to interfere again.  It is not so absolute, permanent or ad hoc and many worlds.  It has resolved all the paradoxes I have ever constructed with such constructed and nested/coupled observers.  Of course, since it is not an equivalency, the question is if it is right. 

Charles, thanks for clarification on the wave propagation.

With regard to Wigner, according to the Wiki, the friend was only in the lab not the box.  It proceeds exactly as I've described with the friend in place of the AI.  All I have done is take issue with consciousness.

As far as Wigner being "in the box" (not literally, but more "in the wave function" i.e. entangled with it), I agree it must be so, and this is critical, Wigner must be unaware of his own duplicity and under the illusion he has made a measurement.

So, this is my "answer."  There is no basis in the theory that I'm aware of (my formal exposure is only a 1 semester course, but fairly wide reading on "the measurement problem") for postulating that measurement exists in reality.  

I.e. I suppose we can always find (or postulate) another observer outside the box any given experimenter is in, and for that meta observer, superposition and interference remain.  

PROPOSED EXPERIMENT

As I initially state this, it will seem infeasible.  But I believe not theoretically so.  It remains only for someone to re-imagine the experiment with smaller entities, and we might be able to settle this empirically.

We examine the superposed states one at a time by preparing particles (test subjects) in the same way, and running the experiment repeatedly.  We need only design an experiment with a hierarchy of experimenters.  We must make at least one of the experimenters simple and small enough we can run it-him-her through a double slit type of experiment, yet complex enough that it can make and record a measurement.  But I will describe it with objects that are a little too complex and invite viewers of the thread to suggest simplifications.

LEVEL 1, experimenter A creates an ensemble of cat-in-box experiments, and throws them at an interferometer, which we suppose instead of killing the cat (actually it'll kill most of them, as most photons don't really make it through either slit but impact the slit structure, but we suppose some make it through) allows them to stack up in an interference pattern.  This proves to A that the cat-box is really a superposition of states (aka "wave").

LEVEL 1b, same experimenter A "peeks" in the box before sending them through the inteferometer, and the interference pattern disappears, suggesting to A that peeking collapses the wave function.

LEVEL 2, experimenter B creates and ensemble of A's at the point where A looks to see if after a few thousand iterations an interference pattern has formed.  Specifically, all the A's in B's ensemble have been doing the 1b version, and none of them see an interference pattern.  

Assume B keeps A and A's cat-in-box experiment all in a bigger box, and does NOT peek, and does not know whether a LIVE or DEAD cat is present at any particular time.  Further B does NOT WAIT for A to complete A's ensemble for any one element of B's meta-ensemble.  B sends the instances through one at a time.

What is the QM prediction?

I am thinking it will be that since B does not know whether the cat is live or dead in each case, it will be an interference pattern indicating superposition.  BUT, if this group is sub-sampled for just the samples belonging to ONE of the A ensembles, then there will not be an interference pattern because A didn't see one.

This might be a little more tricky to formulate equations for than Wigner's friend.  What do you think?

PS, @Clifford, by allowing the many worlds to recombine, I think that means effectively they are only "states" and so we are saying the same thing.

Dear Dr. Shuler,

                             I have a question superimposed on your question and that is If a rocket travelling in space observes an out of focus image of an object on or close to its path of future flight, can we say that it may be a superimposed image as in the Schroedinger cat experiment ? Here it may be noted that relevant space and time are involved. This is meant to be a relevant point in the discussion. Here the Hilbert Space structure of Space is conditioned by the Hilbert Space structure of time by the Laws of  Special Relativity say because of Classical Mechanics in the Closed Box of reference frames. Earl Sir Ashutosh Mukherjee Chair Professor Dr. SKM QC EPS Fellow (In) MES MRES MAICTE

Dear Dr. Shuler,

                             I forgot to mention that in the Schroedinger closed box for the rocket experiment the Hilbert Norm can be replaced by metrics to avoid imaginary numbers provided there is a price characterisation as in econophysics to multiply by a payload factor which is orthogonal to the plane of movement say. On this please refer to my papers on The String Theory of Stock Markets and Haag's Theorem papers on my RG webpage. However I think the Solar Neutrino Field which may act as a Higgs Englert Bosonic Graviton or Magnetic Field with the sun should be factored in spacetime. This chemical potential field I have developed with my son Sandipan Mallick which has been submitted to the members of Nemmers Prize Committee and Nobel Prize Committees separately at different stages of research. However, since we are essentially Econophysicists and Graduate students of  Pharmaceutical Technology I am afraid we may not be able to keep on discussing for long much beyond our immediate Quantum Mechanical Systems. We have invented some new technologies which use Schroedinger Experiments of Quantum Mechanics (my wife's nickname is "Mini" in Bengali, as in Tagore's famous story Kabuliwallah,  which means sweet cat) Thank you. Earl Chair Prof. Dr. SKM QC EPS Fellow (In) MES MRES MAICTE

@Charles, I can only recite what I was taught for the QM case since I have not run single photon experiments, but suppose you throw a die behind a screen by throwing it through a pair of slits.  You throw one at a time, measure its position, and retrieve it.  Classically, the probability of finding a die at any given location is independent of any other.

With the same die, imposing a condition of coherence (difficult to do, and whether it is theoretically possible with macro objects is the object of inquiry in thought exercises such as Schrodinger's cat and Wigner's friend) then the die become not only related by the coherence, but also the probabilities of where they may be found are influenced by this.  There is no classical analogue.

@Soumitra, I presume that the state-space is not directly observable, only one state in which it collapses, so the rocket would not directly observe it.

@All, for your entertainment, as this is more philosophical than physical, I propose to have found the long-sought CONJUGATE of LIVE-DEAD.  Each QM variable must have a conjugate,  If the degree of life-ness does not have, then it cannot be a QM state and the cat experiment is not a superposition, only classical probabilities.

The conjugate seems to be IDENTITY.  You can measure WHICH CAT with some degree of certainty (or UN-certainty).  Maybe the genome compares 99.99%, etc. 

It has several times been proposed to RESURRECT the cat by measuring the conjugate state.  Measuring the conjugate scrambles the original state variable.  You have a probability of getting a live cat out of it.  Repeat until successful.  But until now there is not a convincing idea of the conjugate.  Does my proposal pass this test?

Handily.  After peeking in the box, if the cat is dead, but you lose precise knowledge of the conjugate by making this measurement.  You have opened the box, and the cat may have been quickly switched faster than you could see, etc.  Measure precisely the cat's identity. If it is not the same, you probably can find the original cat alive somewhere.

I don't know about you all, but for months now I conduct a quantum experiment when I click "add your answer."  It works about half the time, and the answer is lost if it doesn't.  Maybe we have found a macro-scale application of QM right under our noses?

Dr. Shuler,

                 There is time involved to go into statistics for the rocket experiment and there is opportunity to experiment so that the flow of time and space will be relevant for the systemic observation. To look at state spaces based on trials and counting is I think too mathematical an understanding. I think as concluded the Arrow of Time postulate is to be added to the Borel Cantelli type of Theorems to Engineer laboratory observations of the Econophysical Field. I hope you won't find these remarks as awaste of your time. Thanks. Earl Sir Ashutosh Mukherjee Chair Prof. Dr. SKM QC EPS Fellow (In) MES MRES MAICTE 

As far as I can see, the essential difference between a coherent superposition of a live and a dead cat is, of course, the phase. Both states

|L> + |D>

and

|L> - |D>

with  obvious notation and the 1/sqrt2 normalisation suppressed, represent a 50% probability of finding the cat dead, and 50% of finding it alive. Yet the two states are orthogonal, meaning they are mutually exclusive. In a sense, one is the negation of the other. So they can hardly be equivalent to each other. In fact, if we wish to state that the cat is in a state in which it makes no sense to ask about relative phase (which presumably corresponds to reality) we should use density matrices, which describe such a situation.

If the cat were in fact in a coherent superposition, we could measure in which of the two above states it is, instead of measuring whether it is alive or dead. This, among other possibilities, does make it possible to resuscitate a cat: first perform that measurement on a dead cat. As a result, the cat will be either in the first or second state. But both have probability 50% of the cat's being alive. So if I follow that first measurement by a (simpler) measurement of whether a cat is dead or alive, I have 50% chances of resuscitating the cat.

Strictly speaking there are no problems when the "cat states" refer to e.g. quantum effects in the cooling of atoms down to temperatures of the order of 10-9 K and the creation of split atom states. The "problem" appears when scaling up the situation to macroscopic order including the scenario of life forms like cats etc. As I have already commented:

To account for dead and alive cats as well as Wigner's friend one would also need a theory of consciousness that also involves the brain of the cat. If the cat could communicate with Wigner's friend he/she would convey if he/she is still alive – at any rate the cat would be more intelligent than the AI as far as surviving dangers and catching mouse involving the evolution of the species denoted as cats.

Re Charles: At the end of the day, one cannot rely on what one is taught. It is necessary to get to the bottom of mathematical structure and to see what is consistent and what can be deduced

Your frequent and usual claim, but I maintain that mapping the assumptions to reality is a far more frequent source of error. In a way, I see you coming around to this position in your comments about all parts of a model not necessarily corresponding to reality, something you've explored in detail on the black hole formation thread. See response below also.

Re Erkki: The "problem" appears when scaling up the situation to macroscopic order including the scenario of life forms like cats etc. ... To account for dead and alive cats as well as Wigner's friend one would also need a theory of consciousness

Why not just stop at "scaling up to macroscopic order"? The intent of my question was to show that consciousness has nothing to do with it, as the AI may not necessarily be conscious. There are simpler properties of macroscopic order. The most obviously relevant is mass.

@all We are obviously missing a useful math model of measurement. The ideas we have are too simple and wind up with a dichotomy, which tempts us to define measurement in terms of perception. But a mass-uncertainty based model would give the best of both worlds. Massive objects would still permit superpositions, but only over states separated by tiny amounts of uncertainty. We don't need a subtle poison to kill the cat. The way I first heard the story, it was a bomb. The dx dp difference between the live cat and a dead one dismembered and plastered on the walls of the box is too large to persist as a superposition in this model. We don't need a theory of consciousness to apply it. What do you think about that approach?

@Soumitra, not sure what you are getting at.

https://www.youtube.com/watch?v=IOYyCHGWJq4

Robert,

I am not sure what you are after. Removing consciousness, we also remove dead and alive cats. Applying pioneering QM to the manipulation of atoms with photons in the micro- or even nanokelvin domain is already a well researched and established area with several Nobel Laureates and still with a promising and exciting future. 

If you are simply referring to the measurement problem, one must of course come to grips with the idealization of isolated systems, which undoubtedly lead to conceptual difficulties like the collapse of the wave function etc.. However, as mentioned earlier, the Mandelstam's indirect measurement process provides a more realistic alternative to the measurement problem, see e.g. the book on Quantum Measurement by Braginski and Kahlili.

In general, however, such a hypothesis must be followed up by a rigorous formulation that incorporates appropriate (quantum-thermal) correlations between the system and the apparatus. The latter is of course easier said than done, nevertheless the latter can be incorporated in a rigorous context that does not impart the usual contradictions.

@ Charles:

You talk about two states being ``orthogonal, but empirically equivalent''. In a sense, of course, I agree: it is practically impossible to measure phases.

But then I believe that, in such a circumstance, it is misleading to say that the cat is in any superposition at all. Rather, it is in a density matrix. Which is OK with me. But, in my book, the wave function of the cat has then been reduced by decoherence already. The problem, if problem there is, of measurement, lies precisely in this transition from pure to mixed states, which cannot be performed without some unpleasant admixture of subjectivism. The Schroedinger equation as such will not give it, and Lindblad equations or their analogues are approximations.

@ Charles: We may agree to disagree, then. To my mind, two orthogonal projectors correspond to a proposition and its negation. So the + and - states I gave above are a logical alternative, in the sense that a proposition and its negative are. If such a measurement as that of the relative phase of two cats were ever to be performed, it could only give one of two exclusive results and would project our feline lriend in one of these two states.

But to say that a proposition and its negation are ``for all practical purposes'' equivalent, is beyond what I am willing to accept, just as a matter of language and logic.

Further, we may point out that such issues are not as black and white as they are sometimes made to sound. Quantum optics provides us with a large number of cats, of variable size, so that in many cases the issue of measurability of the phase will not be so clear cut.

Of course they belong to the same Hilbert space! If you add two vectors, you can only do so if they belong to the same Hilbert space, and then you get a result in the same Hilbert space. The same, of course, holds for subtraction.

As for quantum optics, it does yield states in which light is, say, in a coherent superposition of very different coherent states. Similarly, diffraction experiments using molecules of atomic weight > 1000 have been performed. There we are measuring the phase of objects which are often thought of as macroscopic. I insist the line between the macro and the micro world is not sharp. There are two such realities, but the separation is blurred and largely depends on experimental abilities, and intentions.

To me, it seems that there is a realistic solution: if you assume that some parts of the system are simply beyond your ability to measure or control, and if such parts of the system do interact with the system you are interested in, then unitary evolution will provide transitions from pure states to mixed states, for the system of interest, of course. In an experiment involving diffraction of large molecules, you must control very accurately such interactions with the outside world. As soon as you do not, these phenomena do become unobservable. All in good agreement with the usual formalism.

Charles,

Do let us be serious: if I construct a Hilbert space containing |L> and |D>, then, very much by the definition of what a Hilbert space is, it will contain both their sum and difference. If |L> and |D> are orthogonal, then so will the sum and the difference be.

I know that difficulties arise in field theory, but these are very much linked to the infinite number of degrees of freedom involved. Of course, for cats, you might try and do something along these lines, say involving some kind of superselection rule, but as long as you consider cats as not being *rigorously* infinite (and I gather from some of your work that you are no great fan of the ``actual infinite'') then you can in principle add and subtract states in the same Hilbert space.

Besides, whereas such superselection rules might conceivably work for huge objects, such as actual cats, it would hardly shed any light on the shadowy transition zone I have been mentioning.

I understand that the cat has been beaten to death many years ago in arguments like these so I likely have noting of real substance to add. I happen to favor the most spartan of views on QM where there seems to be no mystery that I can see. As soon as one adopts the Born Rule the wave function stops being a property of an individual system and becomes a statement being made about the limiting behavior of an infinite number of measurements on an infinite number of systems. This would seem to be required by the definition of probability. Now even in the limit of identically prepared cats and the assumption that the states "live" and "dead" are eigenstates (which they really aren't) in any individual system will see (measure) the cat as alive or dead state. This is no different than seeing if an individual atom has decayed or not. One never observes a half decayed atom anymore than one sees an alive or dying cat.  

``One never observes a half decayed atom’’. This, to the best of my knowledge, is simply incorrect. If you have a two-level atom, it is absolutely routie to put it into a coherent superposition of the ground state and the excited state. Such combinations can last quite long (at least on the order of seconds, I think).

As to QM being a science of repeated measurements, I see no objection to this point of view. But then, how should we explain the fact that QM works just fine in several experiments involving single particles (single atoms in traps, for example)?

"If you have a two-level atom, it is absolutely routine to put it into a coherent superposition of the ground state and the excited state." This is the kind of language that leads to most of the debate. It's a very common usage of terms and phrases that while accepted as "correct", misses that actual situation in QM. As soon as probability is introduced via the Born Rule there is an implied ensemble of identical systems and measurements. The wave function only has meaning relative to an essentially infinite series of repeated measurements, never a single one. This remains true even for a single system like atom traps etc with repeated measurements.  

"``One never observes a half decayed atom’’. This, to the best of my knowledge, is simply incorrect." 

How exactly is a half decayed atom observed? Do you really mean to assert this?

This is actually a poster child of my point. In a single observation a two level atom is observed either in the lower OR the upper state. QM gives you no other choices. I think what you are thinking in the quoted statement above is that one can make observations on an ensemble of atoms (yes, or multiple measurements on the same atom) prepared in a superposition of excited or de-excited states. The fact remains that a single given measurement yield one of the two states and not a half-excited one. 

@ Paul Colby: By no means: one can perfectly well prepare an atom in such a superposed state. If need be, one can then verify, by an appropriate observation, that it still is in that state. You are right, of course, that this observation would not be an ordinary observation of energy, nor an observation of whether the atom is in the excited state or not.  The point is, that at least in the microscopic domain, the richness of possible observations goes very far. Essentially any self-adjoint operator in Hilbert space can be measured, hence observed.

It is in the macroscopic domain that more or less basic practical considerations make it impossible to observe any possible observable. But the transition from microscopic to macroscopic is blurred. One should therefore be careful in interpreting quantum superposition in classical terms.

@ F. Leyvraz  "the transition from microscopic to macroscopic is blurred" You're very much in the majority on this one. I don't think this is the case. If asked what do I mean by observation, the answer is clear and unambiguous. I would provide a detailed description of the experimental setup. The Geiger tube clicks at a random rate, these clicks are observations. One either registers a count in a given interval or not. There is no half count, no half alive / dead superposition for the individual event. When the theory is said and done one obtains a transition rates which are compared with experiment statistically. This is always the case.

Many seem to insist that a "complete" theory nature must apply uniformly to individual observations / events as it does to collections of such. What I see as true is that QM is fundamentally a theory of the ensemble and can't be further reduced. To do so would require a new theory. I see no guaranty that such a refined theory need exists, no matter what philosophical arguments we feel are compelling.   

I guess I was unclear: I do not mean that, in the measurement process, the transition is blurred. Indeed, we always amplify the measurement result until it is unambiguously macroscopic. What I do mean is that, you can measure an observable relating to an atom being in a superposition of an excited and the ground state. In such a measurement, of course, the final instruments telling you what the measurement's results are, are fully macroscopic, and they are not, of course, in any superposition.

The argument I am making is that, whereas you can make this kind of observations on atoms, you clearly cannot on macroscopic objects. But this transition, from atoms, for which arbitrary measurements can be performed, to cats, for which they clearly cannot,  is not sharp.

As for the issue of individual observations: the ensemble interpretation of QM could be something very satisfactory as long as observations of isolated quantum systems was unrealisable. But that has long since ceased to be the case. We have observations of photons in a cavity entangled with atoms, for example, atoms in traps, and we even have mechanical levels, the vibrations of which are quantum mechanical. In such systems, it does not appear natural to insist that only ensemble averages make sense, when we actually observe individual events.

"In such systems, it does not appear natural to insist that only ensemble averages make sense, when we actually observe individual events." Okay, what does this sentence mean? The phrase "appear natural" is an appeal to ones sense of what is "natural" about which I need give no weight. What's natural to you is not what is natural to me and is not what the observed phenomena implies. In a two state system, one observes individual events with values A or B. You can't weasel out of it, A or B that's it. So an individual event is not a superposition even at the microscopic level. Where a superposition is required and meaningful is in the prepared state for the ensemble. Looking at things this way has no blurred anything as far as I can tell. A careful reading of your reply does nothing to change this for me. I find much of the confusion is alleviated by simply recognizing that wave functions apply only to ensembles and not individual events. In your (I think more common) view some magic must occur between the microscopic and macroscopic worlds for a observation. This path appears to lead to nonsense like discussions of cat superpositions. For me it's time to let the thing die.     

"What I do mean is that, you can measure an observable relating to an atom being in a superposition of an excited and the ground state." Okay, thus changing the system being measured. A spin 1/2 system in an eigenstate 1/2 along z is in a superposition along any other direction. Along this new direction individual events are seen as +1/2 or -1/2 and I'm right back to where I started. As far as I can see the same ensemble arguments apply and in the very same way.

Paul,

The ensemble interpretation is limited to representations where the density matrix exhibits statistical weights due to random phase approximations. Note that identifying the basic concepts like Hamiltonian, state function and the basic postulates such as the Schrödinger equation and its eigenvalue equations result in an axiomatic formulation totally free from subjective elements and heuristic devices.

Note also that the whole domain of quantum chemistry is rooted in delocalized states providing the best description of atomic and molecular properties.

For instance the benzene molecule is not a resonance between classical structures, but contains delocalized 𝜋-electron orbitals that give it the characteristic aromatic property.

Other examples of macroscopic quantum states are given by the alternating structures of the recent discovered cuprate and iron-based high Tc superconductors. 

Erkki,

"The ensemble interpretation is limited to representations where the density matrix exhibits statistical weights due to random phase approximations."

If we take the Born Rule as a basic postulate (which I do) then the quoted statement is false. From my perspective the ensemble "interpretation" isn't an added interpretational bit but rather cooked into the QM rules from the very beginning. One may try to replace or treat the Born Rule as a derived result and I think this is what the decoherence crowd tries to do. And so the endless cat discussions.

I have no desire to convince anyone of this viewpoint and I don't expect to win anyone over. However, if there is a clean experimental way of showing me the error of my ways, I'm always open to learn. My problem is, as an experimentalist, I always ask what is the underlying experimental setup and how is the data collected and reduced. When asking these questions the ensemble view of QM always seems to work without flaw or mystery and the other "interpretations" appear as poor representations of the facts.

You may not win anyone over, Paul, but at least I can offer that I need no persuading. I agree this is what QM is about. Moreover, the lack of any further theory looks to me like what we should expect. The current situation is metaphysically very coherent and indeed elegant, even if it offends naive realism.

@ Paul: My two difficulties:

1) I do not see how this alleviates the problem of the transition to classical systems: will you say that, if I toss a coin, the coin's wave function only states what will happen in a large number of coin tosses? The question, once more, is not as idle as it sounds. We have, for example, mechanical resonators, the vibrational states of which have quantum features.

2) There are experiments where one does not simply perform a series of measurements. Consider, for example, a typical Zeno effect experiment: you have an isolated atom in a trap, it is in an excited state B, which can decay to the ground state A, but it is in the presence of a strong EM field which excites the transition from the ground state A to a state C unconnected to B. Under those circumstances, the decay from B to A is found to be suppressed. The interpretation of this can be done in various ways, some of which involve the idea that this EM field performs a continuous measurement, which stops the state from changing. No matter what one thinks of this, it is hard to see where the ensemble is. We have one atom only, and what this atom does is not really probabiliistic: it simply fails to decay (OK, we may well grant that in fact it will decay, but with a different rate. But should we really say that we are only measuring the ensemble of atoms necessary to determine the precise distribution of the modified decay rates? Are we not witnessing a property of one single atom?).

I am not aiming to convert anyone. My argument is merely that quantum mechanics is not altogether straightforward, and that claims according to which all mystery in QM disappears if... should be viewed with misgivings.

@F. Leyvraz

On difficulty 1) (Fact) In QM the wave function yields statistical predictions. Verification of any QM prediction requires measurements on either an ensemble of similarly prepared systems or repeated measurements of an isolated system. (Fact) One can not do statistics with only a single measurement. (Fact) Single events in QM yield only eigenvalues of the observable. 

"We have, for example, mechanical resonators, the vibrational states of which have quantum features."

Okay, so? In what sense are the rules of QM violated or affirmed. Betcha a nickel when the experimental setup and data collections methods are made clear, so will the ensembles and averaging I've been talking about.

2) As far as ion trap measurements go must confess I know very little. However, having admitted that, I also wager that measurements are made on these isolated atoms with light sources like lasers, which involves photon counting, which very much involves statistics, background subtraction and a whole host of things involving statistical arguments at their root. If not then help me understand how. I'd be very interested.  

I am not a physicists by training but the issue under discussion has become critical for me in understanding perception. I think Paul has the correct analysis and I have found Leibniz very helpful in teasing this out because Leibniz points out that the distinction between an analysis of individual indivisibles (quanta or monadic units) and an analysis of aggregates must necessarily take a different logical form. The difference between quantum and classical logic is fully explainable simply by the difference in type of account. Leibniz could not find the Schrodinger equation but he would have known why it was like that if he had found it.

So, as I understand it, there is no mystery to the quantum/classical divide. It is not about size. It is about whether the account is of individuals or aggregates. And until individuals are actual they have to be described as ensembles of potential individuals - they are causal connections and until they have completed their connection they have no individuality. There is no such thing as a photon until it has been absorbed at the timeplace that, together with the point of emission, makes it THAT photon. 

An atom can be considered as aggregate or individual but whether one considers the excited mode (presumably based on potential electron orbitals) as the whole or a  subcomponent, until that mode has 'connected' it consists of a range of potential dynamic connections - an ensemble. It has no identity. Energy content does not confer identity. There is no 'this electron and that electron'. Dollops of energy are indiscernible so have no identity, unless they connect, in which case there is a measurement of something. The logical underpinning of this tends to take about six pages to run through. Simon Saunders does quite a good job in his paper on Leibniz and the Principle of identity of Indiscernibles. But one can work it out for oneself from simple logic as long as one is prepared to stop intuitions about individuality getting in the way.

So I think the bottom line is that the traditional QM idea that there is 'an individual in superposition' was always wrong. It is a pretty meaningless concept anyway. It is trying to force the use of naive realist models where they should not apply. I think someone said that superposition meant that something was neither in this place nor that place nor both places nor neither place - pointing out that the word does not actually mean what it says. Leibniz explains why, I think, but a lot of people find the austerity of his arguments tough.

I now see Charles's point about the term ensemble. I think I agree that it may not be the best term and may itself confuse the issue of real individuals, but I think it works as a description of a class of possible connections rather than an actual connection.

Paul,

The ensemble interpretation could be further ground for confusion and miscommunications. For instance it is not clear what one means with "all the members being in the same state". For a system, given to be in a particular quantum mechanical state one can define its density matrix – a mapping of the Hilbert space on itself. This matrix is subject to a Liouville equation, which incorporates both pure quantum states as well as statistical ensembles, the latter introducing some kind of ignorance.

Of course no one is right or wrong in this interpretative battle, except that my statement concerning the axiomatic structure of QM "that identifying the basic concepts like Hamiltonian, state function and the basic postulates such as the Schrödinger equation and its eigenvalue equations result in an axiomatic formulation totally free from subjective elements and heuristic devices" becomes minimalistic.

The ensemble representation based on density matrices + appropriate postulates would, to me, be the best starting point for a formulation to open-dissipative systems. However, within this framework, QM interpretations takes on a different clothing.

Erkki,

"For instance it is not clear what one means with "all the members being in the same state""

Actually, in any given example the above has a clear and well defined operational definition. 

The word ensemble likely has a meaning that is narrower than I intend. My usage of it is merely to drive home the role of probability in QM. I'm always assuming that flipping the same coin 1000 times is the same as flipping 1000 coins at the same time and so on. The point is a coin flipped yields a head or tail and the result is random. Flipping a coin once doesn't verify it's a fair coin. No amount of Bayesian window dressing will alter this basic fact though it might well help in writing some papers or give a more clear understanding of probability.

Density matrices are fun and useful. Weinberg has written a paper in which the density matrix is taken as more fundamental than a state vector approach to QM. I would have no problems with this if only for the reason that the absolute state vector phase drops out nicely in the DM formalism. 

Also, what is it you mean by a "subjective element" in QM? Is this like an "if a Geiger counter clicks in the woods and there's no one there to write a paper does it still work" kind of question? The answer is yes, it all works even if we don't look.

@ Charles: Yes, we do need the assumption that every self-adjoint operator can be measured. In fact, if the assumption fails (and the assumption of such a failure is at the root of decoherence) then it will generally happen that a pure state is indistinguishable from a mixed state using the available observables. The whole formalism of quantum mechanics rests on the assumption that pure states are elements of a Hilbert space and that they can be distinguished from each other and from mixed states. For this to hold, one needs the assumption that all self-adjoint operators are observable.

Of course, in practice, in the macroscopic limit, the assumption does fail, and this is where decoherence enters the picture: to the extent that a pure state becomes operationally identical with a mixed one we have (in effect) realised a transition from a pure state to a mixed one, and thereby presumably achieved the first stage of the ``collapse of the wave function’’. 

@ Paul: You want to drive home the importance of probability in QM. Well and good. I do not think there is anyone in this thread who doubts it. But the issue remains: there are very real differences between QM and classical mechanics, even within the probabilistic framework. So what is your take on the transition between classical and quantum objects and their probabilistic properties?

Paul,

You say: "Actually, in any given example the above has a clear and well defined operational definition".

This is also the problem. The outcome of a measurement depends not only on the measured property, but also on the type of apparatus. Hence there is neither a general theory of measurement of a given property nor a universal theory of measurement of any property. It must therefore be specific concerning what is measured and how it is measured.

The coin-flip analogy is misleading since QM probabilities are not "Beyesian"!

"So what is your take on the transition between classical and quantum objects and their probabilistic properties?"

In my opinion there is never a discrete transition to classical objects. Classical physics is the limit of a complex QM world. For the atomic-decay cat death problems, atoms decay at a given rate, cats die at this same rate independent of any external AI or observer. Why is this so hard for people to accept?   

Erkki,

"This is also the problem...."

I think the problem is I don't see this as a problem. It's simply the way the world is. Too often people try to bend the facts into a shape they think is "reasonable" or acceptable to their intuition. Hence all the collapsing wave functions and cat questions.

"The coin-flip analogy is misleading since QM probabilities are not "Bayesian"!"

I'd need help on this one. Probability is probability in my view. And yes, I'm well aware that probabilities don't add in QM like they do in classical physics. I'm referring here to the transition rates and probabilities one gets from QM calculations that are then used in the analysis of actual experiments.

Charles,

Time is a parameter in pioneering QM and the theorem, referred to, relates "time evolution" to a one parameter group, represented by unitary operators. However, frequentist and Bayesian probabilities do not strictly hold in QM.

Note that there is a QBism interpretation of Quantum Mechanics. This, to me, is not really an alternative. It is a sneaky way, however interesting, to involve the mind of an observer into the discussion. Although cleverly designed it does not serve as an option to replace conventional quantum mechanics (or the existing 10-15 different interpretations).

To involve the environment to a quantum system necessitates a rigorous extension of quantum mechanics, as I have proposed many times before on RG.

``Pure states are vectors in Hilbert space. Mixed states are not.''. Of course. But physically, how can you tell the two apart? It is an operational issue, not an ontological one. You are only guaranteed to be able to do so if you can measure sufficiently many (essentially all) self-adjoint operators.

I believe decoherence, which amounts to saying that, for all intents and purposes, a pure state can be replaced by a mixed one, because the operators that distinguish the two are not practically observable, is an essential part of resolving the various paradoxes, such as Schroedinger's cat, arising from the macroscopic limit.

@ Paul:

``On difficulty 1) (Fact) In QM the wave function yields statistical predictions. Verification of any QM prediction requires measurements on either an ensemble of similarly prepared systems or repeated measurements of an isolated system. (Fact) One can not do statistics with only a single measurement. (Fact) Single events in QM yield only eigenvalues of the observable.''

No difficulty with your facts. But they are all identical in QM and Classical Probabilistic mechanics. So these facts cannot really help with the problem of explaining the transition from a world in which amplitudes add up, to one where probabilities do.

Finally, I would, as a minor point, slightly take issue with your statement that ``One cannot do statistics with a single measurement''. Take the Zenon effect I mentioned. There, the effect to be measured is a lengthening of the decay time. Assume the decay time is predicted to become 20 times longer. Surely, a single measurement of decay lasting twenty times longer (or 15 or 25), is already sufficient to be considered strong evidence for the effect.

``cats die at this same rate independent of any external AI or observer'' Indeed. But that is not the issue. If QM were unrestrictedly valid, as you seem to claim, then it would be straightforward, instead of measuring whether whether the cat was alive, and obtaining a yes answer answer with 50% probability, to measure whether it is

live + dead

as opposed to

live - dead.

And if the cat was indeed prepared in a live + dead state, the probability of getting that answer is, in fact, one and not 1/2.

That is the sort of thing that worries me. Of course, you are free to keep on saying that no issue arises.

``As scientists we must accept the universe we live in, not one dictated by prejudice.''

I surely agree with that. But I also think scientists ought candidly to recognise the fact that they do not fully understand something. In my case, I fail to grasp how giving up on spacetime solves either the locality issues brought up by Bell, or the problems involved in the transition to classical mechanics. On the other hand, if you say the word paradox was ill chosen, I can agree with that: there are no mathematical contradictions in QM, though there may be things hard for me to grasp.

@F. Layvraz

I'm starting to just repeat myself so it's likely a good time to let my argument rest. Since I went and typed the following I might as well hit "Add your answer".

"And if the cat was indeed prepared in a live + dead state,..."

Consider that the above is incorrect beyond being merely unachievable. The dimension of your average cat state space is well in excess of 10^23. I can't help but feel that making arguments as if the state space of a cat were 2 dimensional leads to most your concerns. In reality the above equation should really read

live - dead = live + dead = nonsense.

You appear to consistently ignore the fact that in QM supper positions aren't observed in isolated events, eigenvalues are, makes for mildly frustrating discussion.

That said, I certainly agree that the celebrated correspondence principle isn't a universal white wash to be applied liberally. Thinking in terms of your mechanical resonators with QM like properties I expect will be more fruitful since the discussion could have a concrete observational component.  

@ Paul:

Schroedinger's point was precisely that preparing a cat in a live + dead state is quite achievable: start with a spin in an s_x state, measure the z component, kill the cat if the answer is down, let him live if it is up. The cat will then, by linearity of the Schroedinger equation, be iin a live + dead state.

``In QM superpositions are not observed in isolated event''. What do you mean? For a spin system, an s_x + eigenstate is a superposition of an s_z plus and an s_z minus. And of course, I can both measure s_x and s_z, but, of course, not both at the same time.

In fact, in QM, it does not really make sense to say that a state is in a superposition: with respect to what? If you are going to measure a given observable, then you can indeed say: the state is in a superposition of the eigenstates of the observable I intend to measure. So ``being in a superposition'' is not an objective property of the state you consider, it is a property of the pair ``state you observe and observable you measure''.

In macroscopic systems, some observables, in which the state is localised in space, are in essence, as you point out, the only sensible ones. In that case, limiting oneself to such observables is wise and gives meaningful results. But this procedure does not follows imply, or unambiguously, from the quantum mechanical formalism.

Of course, as you correctly state, and as I have also repeatedly argued, the issue of mechanical resonators is much more intereting than actual cats, for which the problem is a caricature (we should not forget that Schroedinger's point in describing his cat, was to show the insufficiency of quantum mechanics).

@F. Layvraz

On the cat thing, if the cat by linearity of the SE is in a live+dead, what exactly is your operational definition of what this means? In QM it has a very definite and apparent operational meaning with respect to individual observations and the implied ensemble. The QM answer is exactly what one intuitively expects to see in such an experiment.  So, what is your answer? 

"``In QM superpositions are not observed in isolated event''. What do you mean? "

It boils down to what is meant by "observed." This has a technical meaning in these discussions and appear in the fundamental statement of the rules of QM. For the spin 1/2 case it means; if a single atom passes a z-oriented SG in the +1/2 state, then I say that I have "observed" the spin projection along z and it's +1/2 for said atom. The QM rules state that for a z-oriented SG +1/2 and -1/2 will be the only allowed results of each observation. 

"In fact, in QM, it does not really make sense to say that a state is in a superposition: with respect to what?" 

Of course it does. I would drop the "in" from the quoted sentence. The "what?" is relative to ones apparatus or relative to ones chosen basis set.

Charles Francis,

Born's quantum law concerns the interpretation of the absolute square of the wave function as a probability density.To prove that this is identical to frequentist probability you must a) prove that the quantum coin is the same before and after the toss and b) overcome the no-cloning theorem.  

``The "what?" is relative to ones apparatus or relative to ones chosen basis set.'': exactly. But the aparatus, the observable you choose to observe, in quantum mechanics is altogether arbitrary. So a state which could be ``a superposition'' from one point of view, namely if you measure one observable, ceases to be such for another observable. That is the whole issue of the cat: if you decide to observe whether it is alive or dead, the result are of one kind. If, on the other hand, you decide to measure whether it is

live + dead

or

live - dead

you get something distinct. No one denies that the latter is largely absurd, but the issue is what QM and its formalism has to say about it.

Indeed, if all you know about the cat is that it is allive or dead, with 50% probability, then QM most emphatically states that it is in a density matrix. The phase is absolutely required to be able to talk of a pure state.

Just an example in which you may actually have indirect knowledge of a cat's phase: consider a Bell pair of photons, and assume you measure the z polarisation at one end and at the other have a device killing a cat if the x polarisation is down and doing nothing if it is up. Once you measure the z polarisation, do you not then know, by inference, the relative phase of the live and dead cat?

Once more, these issues are not important in experimental terms (they may well become so for the mechanical resonators and other intermediate systems). They are important because they show results which the QM formalism predicts, and which are somehow at odds either with experience or with common sense.

F. Leyvraz

In the bell photon case if a +z-polarization photon is detected the cat dies. Measuring the other of the bell photons tells you if the phase of the deceased cat. In the setup of the experiment the eigenstates are |+z>x|dead> and |-z>|live> for the cat side of the system. Why is this confusing? One sees what is both intuitive and predicted by QM.

One common misconception is that one is somehow "free" to chose to measure the x-photon and not the z-photon. However, once the box is constructed, the z-polarization cat death-actuator installed and the cat placed in the box, this freedom is removed. Every x-photon measurement implies a z-polarization one and an outcome for the cat.   

The cat is always connected to the microscopic system through a Hamiltonian. The "choice" of this interaction operator is not an unconstrained choice. So constructing an experiment that has the live+dead and the live - dead eigenstates may not be physically possible. This is why I ask for operational definitions. 

Hello all ... my, 6 pages of discussion while I was traveling for a week.  I probably have not absorbed every bit of it, but noticed some things going astray in posts on pages 3-4.

Erkki and Charles seem to compound a misunderstanding that the consciousness of the cat is at issue.  I neither know nor care if cats are conscious.  I was (I thought obviously) referring to consciousness of an observer, and Erkki does consider that I may be talking about "the measurement problem."  Obviously, this question thread is about the measurement problem.  

in a separate post Charles says "we have very good math models of measurement."  I did a bit of research on this, and Charles, if I did not find what you were talking about, please illuminate us...

First, I learned that the von Neumann idea of collapse of the wave function is "dated."  See https://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics .  "note, however, that von Neumann's description dates back to the 1930s and is ...  not applicable to most present-day measurements."  A (possibly incomplete) summary of views is found at https://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics :

• The model of decoherence through interaction (with measuring device or environment) requires nothing beyond Schrodinger's equation, no separate collapse postulate
• This method leaves unanswered questions about whether measurement is deterministic or random, locality, etc.

Specifically what we have in my question, which as the other Robert pointed out is essentially Wigner's friend, is a thought experiment in which a measurement experiment is placed inside an outer (or meta) measurement experiment.  The question then is whether the inner measurement experiment collapses the wavefunction (or decoheres it in the modern view) for the outer experiment as well?

Previously I was using the old von Neumann collapse model, and it seems others have used this approach also, which allows at least the possibility that the inner measurement may NOT collapse the outer one.  The interesting thing to me, in that possible scenario, was that this partitions the data from the inner experiment, so that Wigner's friend (or my AI) which is selected by the collapse in the outer measurement is always paired with consistent data, so that it perceives only the outcomes consistent with its memory history even though other outcomes are still superposed.  Obviously this has some relation to, or may be an alternate interpretation of, the many worlds theory.

The objection to this scenario (in my mind) is that applying it on the time and size scale of the universe is implausible.  The universe does not physically evolve in that case.  All alternative outcomes are still available, we only have to find some way of communing with the outer meta-observer to select a different one.

Since I have not long studied the decoherence model, I cannot say that the same dilemma persists.  Would someone care to explain the Wigner's friend / AI puzzle in terms of the decoherence measurement model, and comment on how it affects the dilemma?  Perhaps the interaction of the inner measurement decoheres the wavefunction so that the outer observer does not see a superposition of all possible outcomes, but instead merely probabilities of the possible outcomes?

This would mean the outer observer cannot, for example, resurrect the cat or otherwise recover possible outcomes via the conjugate measurement technique.

@ Paul: I am totally confused by your take on my cat example. I am assuming you only measure the distant photon, far from the cat, leaving the cat as is. The cat's fate depends on the x polarisation of the photon measured in the device. The measured photon is measured in its z polarisation. So finding it to be, say, in a + state, means that the photon that triggered the cat's death or otherwise,was in a state having well determined phase between the two x components. Since it is these two x polarisation components that determine whether the cat dies, the cat is in a well defined superposition of alive and dead with a well determined phase.

Robert, 

There is no misunderstanding or controversy, whether you talk about the measurement problem or the “conscious cat”. In general the wave function decohere when it cannot be “protected” from the environment.

This “protection” has been studied in detail by e.g modern interferometry, see e.g. recent work, quoted by Stefano in another thread, by the Wineland Group. In vernacular language one speaks of “Schrödinger cats” – how big they are – how many legs etc.

I enclose a summary of a Nobel Symposium that concerned modern concepts in Quantum Phenomena pertaining to the comment above, containing contributions from preNobel Laureates.

Charles Francis,

I do not agree. QM-, Bayesian- as well as frequentist probabilities are not the same. For instance classical- and QM logic are fundamentally different! As Jaynes says in his book” if the Bayesian probability were correct in QM one should be able to write joint probability distributions for position and momentum, which violates the uncertainty principle”.

Charles,

It is rooted in quantum logic and therfore fundamental.

In fact, quantum mechanics is nonlinear (see, for example, Melkikh, A.V., 2015. Nonlinearity of quantum mechanics and the solution of the problem of wave function collapse. Communications in Theoretical Physics. V.64, issue 1, 47-53).

That is, the problem of wave function collapse can be sovled without additional assumptions (including AI).

@F. Leyvraz

You seem to suffer from an ever more common misconception that "not measured" is the same in QM as "Well, I'm just not going to look at the result and assume that nothing has happened." If the x-photon is detected then the z-photon of the bell pair has entered the z-polarizer and was detected in some definite polarization z-eigenstate. This is a basic property of the experimental setup. "Not measured" in this context would mean removing the z-polarizer from the experiment and it's corresponding coupling to the cat. 

(edited, I reread your example and I have interchanged x and z directions. Other than this the reply is valid.)

@F. Leyvraz 

I can see the confusion abounds. I find your experimental setup is not well enough defined for me to follow. This still doesn't change the basic facts in anyway that I think is important. Let me spell out what I think your example is. If I'm wrong about it please fill in enough details so I can make a meaningful reply. 

First we have an entangled pair of photons. We have two polarizing beam splitters each with two photodetectors. Let's label the splitters 1 and 2. Splitter 1 has two detectors, A1 and B1 while splitter 2 has A2 and B2. The experiment is designed so that if A1 or B1 registers a count, so will A2 or B2. What we're saying here is the propagation directions of the photons are known and correlated. Now we tie our poor cat to the first splitter such that if B1 registers a count it dies and if A1 clicks it's safe. If we observe a count in A2 or B2 we are assured that a corresponding count happened in A1 or B1. We arranged out splitters so that a click in A2 implies that spitter 1 will be subjected to a A1+B1 photon while if the B2 detector clicks the 1 photon will be A1-B1.

What quantum mechanics and common sense says will happen is that the photon in splitter 1 will be detected in either the A1 branch OR the B1 branch. The results from splitter 2 allow you to "distinguish" what the phase of the 1 splitter photon had going into the splitter. Okay, so? In any event one or the other outcome happen. By the basic rules of QM the cat is now in one of the eigenstate A1 or B1 of splitter 1 and we may use the results of splitter 2 to assign a phase. Why should we care?

@Melkikh, can you send me a copy of your paper?

@Colby, exactly my point, thank you for reinforcing it.  And further, expectation or expected value is not the same as QM measurement.  

@Charles and @Erkki, your back and forth illustrate two points of view that are at odds.  It is interesting that (Charles) the decoherence model is at odds with certain other models.  Therefore as far as I can tell, there is not a consensus view, so there might be models, but not agreement, and some of the models are just "magic" (from one state to another) without resolving fundamental questions about what happens with the cat.

Regarding the consciousness of the cat and returning to von Neumann's suppositions about consciousness - while some of you have already concluded consciousness has nothing to do with it, as I have, not all of you have, and I just discovered this is again a restatement of Wigner's friend.

That is ... IF the CAT is CONSCIOUS, then the experiment is already "Wigner's friend" without adding a friend, an AI, or another experimenter, because the cat could make a measurement of the bomb or poison or whatever and collapse its own wavefunction.

But forget consciousness again and consider this particular question - Can the cat, or a friend, or an AI, or a large lump of matter, or any number of experimenters, collapse (all or part) the wave function, when viewed by an outer or meta experimenter?

• Yes or no?
• Answer for each particular model of measurement
• State, if you can, what experiments have or can be done to validate one model over another, and your prediction for whether it allows collapse of wave functions for meta experimenters.

My impression is, and I may have misread the discussion, the decoherence model really does partly collapse the wave function even for an outer experimenter, and is at odds with the multiple worlds theory.  

Any model that produces only a probability, or expected value, and not a superposition, collapses the wave function for the outer experimenter and is at odds with multiple worlds.

Any model that preserves the wave function for an outer experimenter could support multiple worlds, and might be difficult to test, but theoretically it could be, using conjugate measurements to revive the dead cat.  

Such an experiment, in some cases or interpretations, might be tantamount to a randomized gateway to a different version of the multiple worlds.  Tantalizing as this is, I'm not sure I buy it.  

@ Paul: You are right about common sense, but I believe you are on less firm ground as far as QM goes. You say ``the results from splitter 2 allow you to distinguish what phase of the 1 splitter photon had going into the splitter.'' Yes. And now comes the crux: you mention ``the rules of QM'. Well and good. Your argument, and it is intrinsically correct, is that objectively the beam splitter 1 and the attached cat are large enough that we must apply von Neumann measurement. Well and good, and if you do that no problem arises.

But again, when are we forced to apply von Neumann? QM is unpleasantly silent on that issue. How large must the cat be, for this reasoning to be conclusive? If, for whatever reason, we do not, then we are led, by the rules of QM, to having a large system in a coherent superposition.

Of course, the interpretation issues of QM rarely have experimental consequences. That is, presumably, why they remain open. Nevertheless, I, for one, find the idea of diamond crystals in quantum superpositions of their vibrational states, or proteins being diffracted on a double slit, peculiar. But all of these things have been realised experimentally.

@Leyvraz, not only diamond crystals, but interference experiments have been done with C60!  That is probably large enough to answer some questions, if the right question is asked.  Not just whether a superposition remains, but the scope of it, and whether it contains all possibilities.

F. Leyvraz

That there are two polarizers in the experiment is not a subjective fact. Now, as far as I can tell the QM rules speak rather directly to the measurement of observables. It's a fact of life that any and every observable measurement will involve some form of lab equipment or measurement device. This is not something that will ever be circumventable. Is the mass, size or complexity of this piece of equipment somehow bounded? I don't think this is a burning issue because whatever this device is, it will measure eigenvalues of the observable it was designed for. 

Assuming you don't already, I would suggest spending more time in the lab and less at the blackboard. For me detecting alpha particles means I'm looking at the pulses from a charge sensitive amplifier connected to a silicon detector using an oscilloscope. All this discussion of "collapsing wave functions" and such is really drawn into perspective when you're hunting for a bad cable. 

@ Paul: I guess I have said what I had to say on the subject, and that any more would be repetitive. I am glad you have no problem with quantum mechanics.

I have a question about happens in your polarizer, vs. what happens in your detection equipment:

• The polarizer doesn't "just" reshape the wave function.  I know I'm going to hear screaming about this, but it partly collapses it.  It removes some percentage of the energy, without changing the beam dispersion.  This energy is absorbed in the polarizer.  The remaining energy is absorbed in the detector.  The polarizer could be monitored for absorption events.  In this case, would that knowledge have any material impact?  Could we set up an interference experiment in which the pattern would disappear if we "looked" at which photons were absorbed?
• One might be able to get around this problem by using a beam splitting polarizer, so that nothing is absorbed.

For the absorption case, if we place the polarizer in front of ONE of a PAIR of slits, I believe the relative intensity of the interference pattern will be reduced.  First, the total intensity is reduced by 1/4 assuming random polarization of input photons.  Second, for the photons that get through, only the ones that could pass through the polarizer contribute to the interference pattern.  The ones that couldn't will only impact the detector screen if they go through the other slit, in which case their history is known, even though we did not "look" and acquire the knowledge.  So this is an entirely physical process, without a detector at the slit per se, without experimenter knowledge of photon path, in which the wave function is "partly collapsed" as I suggested above.

If we use a beam splitting polarizer, and recombine the split off photons with the original beam over a sufficiently short distance, I suspect the interference is unaffected.  In a low intensity beam, too great a disparity in distance might have the same effect as the absorber above.  Any thoughts?

The point is, the detector is like peeking in the box to check on the cat.  The polarizer at the slit is sort of like the cat checking on whether the bomb or poison was triggered.  In the case of the bomb, the analogy is very good, as the cat's temperature rises in analogy to the polarizer absorbing a photon.

Hmmm..... is there a connection to entropy?  In the case of the poisoned cat, it is not obvious to me that the total energy need be changed, only the arrangement of it.  The only thing of a general nature I can think of is that there are probably many more arrangements of "dead cat" than "live cat," and so the entropy of dead cat is higher.  So the common factor may be entropy.  I had not previously thought of entropy in connection with quantum measurement.  Is there any existing work on this?

Whenever you have some irreversible phenomenon going on, like absorption, it plays the role of a ``measurement'' and destroys coherence. It does not matter whether anyone observes it or not. An example, due to Feynman, concerns scattering of atoms on a crystal: you have Bragg scattering, as an effect of quantum coherence, but if an atom undergoes a spin flip with one of the crystal atoms, then it can scatter in any direction. Now clearly, finding ``which atom in the crystal flipped its spin'' is a more than hopeless endeavour. Yet the very fact that the spin flip happened destroys the coherence, independently of any observation.

As for entropy, I am personally quite convinced that there is a rather deep connection. I believe von Neumann in his book commented on the fact that unitary evolution leaves the entropy of a density matrix invariant, whereas measurement, in his sense, increases it. I believe this would over all carry over to more general dynamics such as those defined by Lindblad equations, but am not sufficiently knowledgeable to say anything with great assurance.

Charles,

My remark on probability refers to kinematics not dynamics. Newton dynamics leads to time-reversible processes and certainty, while time-reversible quantum mechanical formulations do impart probability!

There is no way QM probability can be reduced to classical probability! Sorry.