Nonlocality - fact or fiction?

[Fra]

What I have never understood is how people rather cling to locality than realism?
WTF does locality matter if the worlds not real anyway?

I'm no realist, but to me locality means sense as an emergent concept.

Compare to a game theoretic setting. Each player makes a (rational) decision and this decision is based on the information available to the player. This is a sort of locality, in the sense that the players action depends only on local information. I find this is highly plausible also from a philosophical point of view. The extension to this to a more continuous model would be to say that the player bases his actions (decisions) on information available to him, rated according to it's confidence. This then gives a probabilistic interpretation of locality in that his actions is "unlikely" to be much influenced by any piece of information that he is not confident it. Anything else, doesn't seem rational.

One may ask, what if the player make irrational decisions, and what does this have to do with physics? I like to see this associated with some darwinist ideas. Where there is a selection for rational actions. Irrational actions are simply not preserved.

In this perspective it's not too hard to appreciate that this "game" is driven by expectations, not what is real. I would expect that all other players would act based upon what they think they know about what I know, not what I really know or is.

This doesn't bother me. I think it's philosophically satisfactory and beautiful.

/Fredrik

 

[Doc Al]

Bohm

Read also the papers on the experimental violation of the Leggett inequality that has an even stringent criteria and have written off a large class of nonlocal realistic model.

This guy heard of bohm?

I haven't read Leggett's paper or studied his definition of "realism", but at least one paper on the experimental violation of Leggett's inequality (S. Groeblacher, et. al., Nature 446, 871-875 (2007)) explicitly mentions Bohm's theory as being outside the class of theories considered by Leggett.

 

[akhmeteli]

So you accept every single word Zeilinger said, but ignore completely his phrase "however unlikely"? Read what I've written and see if this is familiar with what I've been trying to argue..

I did not say I accept everything Zeilinger said. I did not say I accept everything Shimony said. I said I don't see any difference between positions of Zeilinger and Shimony, whom you discarded so lightly as off-mainstream. I do believe that words of both Zeilinger and Shimony confirm my statement: there is no experimental evidence of violation of the genuine Bell inequalities. I certainly did not ignore Zeilinger's, Shimony's, and your opinion that future experiments will (most likely) provide such evidence. I respect your and other experts' opinion, but I have my reasons to strongly doubt it until experiment proves me wrong. Why are you trying to be a stricter mentor than Zeilinger (and it was not me who mentioned him as an expert), who at least recognizes that the loopholes are essential and allows his reader to have his/her own opinion? Again, Shimony is not quite happy about the detection loophole, Zeilinger is not quite happy, you are not quite happy, and all of a sudden I should be absolutely happy when people try to prove that something is greater than two, the experimental value they obtain is 0.15, then they multiply this value by twenty, as the detector efficiency is just 5%, and jubilantly declare that the resulting three is greater than two (which it is:-) ), so the Bell inequalities have been successfully violated.

Read all the papers by Zeilinger related to the GHZ inequality.

With what purpose?

I can double check all the published papers that I've printed on this in my office on Monday and will give you all the quotes that you'd want.
Zz.

Again, quotes confirming what exactly? That there is experimental evidence of violation of genuine Bell inequalities? I am not looking forward to seeing such a quote, but I would certainly appreciate it, as I would appreciate a bitter, but efficient medicine. However, both Shimony and Zeilinger seem to be either unaware of such quote or distrustful.

 

[ZapperZ]

I did not say I accept everything Zeilinger said. I did not say I accept everything Shimony said. I said I don't see any difference between positions of Zeilinger and Shimony, whom you discarded so lightly as off-mainstream. I do believe that words of both Zeilinger and Shimony confirm my statement: there is no experimental evidence of violation of the genuine Bell inequalities. I certainly did not ignore Zeilinger's, Shimony's, and your opinion that future experiments will (most likely) provide such evidence. I respect your and other experts' opinion, but I have my reasons to strongly doubt it until experiment proves me wrong. Why are you trying to be a stricter mentor than Zeilinger (and it was not me who mentioned him as an expert), who at least recognizes that the loopholes are essential and allows his reader to have his/her own opinion? Again, Shimony is not quite happy about the detection loophole, Zeilinger is not quite happy, you are not quite happy, and all of a sudden I should be absolutely happy when people try to prove that something is greater than two, the experimental value they obtain is 0.15, then they multiply this value by twenty, as the detector efficiency is just 5%, and jubilantly declare that the resulting three is greater than two (which it is:-) ), so the Bell inequalities have been successfully violated.

While there is a detection loophole, the LIKELYHOOD that it is influencing the violation of Bell inequality is "highly unlikely", in the words of Zeilinger himself. If you have looked at the experiment involving multipartite systems (as in the GHZ theorem), the coincidence of such occurrence would be unbelievably small! It is why I kept asking you if you think that different experiments that are influenced by different "loopholes" that have nothing to do with each other, can somehow conspire, in turn, to create the same conclusion.

I can also say that a vase that has been broken into a million pieces, can assemble itself back into the original vase when I throw it onto the floor. The probability of it is very small, but the phase space for that to occur isn't zero! Yet, we design our working world with the idea that it cannot happen. You, on the other hand, want "proof" that it can never happen.

Again, quotes confirming what exactly? That there is experimental evidence of violation of genuine Bell inequalities? I am not looking forward to seeing such a quote, but I would certainly appreciate it, as I would appreciate a bitter, but efficient medicine. However, both Shimony and Zeilinger seem to be either unaware of such quote or distrustful.

Quote confirming that for many of these experimenters, there's sufficient grounds to claim with a high degree of confidence of the violation of local realism. Don't look at me, you were the one who were playing the quotation game. In fact, the two abstracts from the tests of the Leggett inequality experiment clearly indicate such a thing.

Zz.

 

[akhmeteli]

You still haven't addressed the two facts that I mentioned earlier. The FACTS were : a set of experiments that closed the detection loophole (but not the locality loophole) claimed to violate the Bell inequality, and the set of experiments that closed the locality loophole (but not the detection loophole) violates the Bell inequality. I asked you if, knowing how these experiments work and how such things are detected, that you think it is simply mere coincidence that they both arrive at the identical conclusion even when they not only use different entanglement/objects to detect, but also different loopholes that were possibly left open. Remember, the "detection" loophole has a different set of statistics that has nothing whatsoever to do with the "locality" loophole. Unless you've never done any experiment in your life, changing two different, independent conditions should not give the same type of results!

I don't think it's a coincidence. This is a reflection of the fact that both types of experiments do not satisfy the assumptions of the Bell theorem. I think you'll agree that it is not difficult to find situations where the Bell inequalities are satisfied, but they are of no interest for experimental physicists, so they are looking for violations, and they can certainly find what they look for if they cut themselves some slack, just enough to circumvent the Bell inequalities. There is more than one way to skin a cat. The locality loophole is one way, the detection loophole is another. I think that the genuine Bell inequalities can only be violated and are indeed violated when this is compatible with unitary evolution of quantum mechanics, i.e. when the spatial separation is not enough. If we have a spin singlet pair of electrons, and a spin projection on axis z for one of them is measured to be +1/2, the projection postulate states that the spin projection for the other electron immediately becomes equal to -1/2, no matter what spatial separation. And this is the real source of the nonlocality and of violation of the Bell inequality. Mind you, there is nothing like that with unitary evolution of quantum mechanics, as no measurement is ever completely finished, because unitary evolution can provide no irreversibility. Earlier in this thread (post #20) I cited the article of Allahverdyan et al. For me it was an eye-opener. And I guess not only for me. When I listened to their presentation at a conference a few years ago, Scully (I bet I don't need to tell you who he is) said something like (I don't remember the exact words) "Good work. Why didn't I do it?" They consider spin measurement based on an exactly soluble model and demonstrate in detail how it occurs. What's important for me, they show how the contradiction between final measurement and never-final unitary evolution is resolved. It is resolved in the same way as the contradiction between irreversibility in thermodynamics and reversibility in mechanics (classic or quantum) is resolved: while there is no way the Poincare recurrence theorem can be circumvented, the recurrence time is mind-boggling. In their article the measurement occurs through interaction with a large paramagnetic system, and that ensures practical irreversibility (but there is no way around theoretical reversibility). What I am trying to say is the projection postulate might be a good approximation or a bad approximation, but it is just an approximation, and unitary evolution rules supreme,while the Bell inequalities hinge on the projection postulate. Mind you, I have said nothing about local realism or absence thereof. I very much doubt there will be any experimental evidence of violation of genuine Bell inequalities because I suspect such violation would contradict unitary evolution and because I believe that unitary evolution directly contradicts the projection postulate, at least on the theoretical level, so you have to choose between them anyway. As I said, you cannot have them both.
Nevertheless, one can attack the fair sampling assumption based on local realism, and this is indeed very instructive, no matter what you think of local realism. Let me give you an example: while there is nothing wrong with von Neumann's proof of impossibility of hidden variable theories (LHV) from the point of view of mathematics, this proof lost any significance when the Bohm interpretation (BI) was introduced. You may like BI or hate it, but its mere existence demonstrates that the assumptions of the von Neumann's proof are ridiculously strict. Of course, BI is not local, but Santos (Physics Letters A 327 (2004) 33–37; I guess there should be a version in arxiv as well) proposed LHV theories that do not satisfy the fair sampling assumption and emulate the results of the existing experiments on violations of the Bell inequalities. Again, you may like or hate such theories, but their mere existence demonstrates that existing experimental data just cannot bury local realism. I won't repeat other excellent nightlight's arguments here.

And I don't buy this argument that you have no need to the details of the experiment. In fact, I would say that your ignorance of the experiment IS the source of this disagreement. The knowledge of what a photodetector can and cannot do is vital in the degree of confidence in the result. I will put it to you that you have placed your life and the lives of your loved ones on knowledge with the SAME degree of confidence as what we get out of the photodetectors used in these experiments.

I don't think my ignorance of the experiment IS the source of this disagreement. nightlight is not ignorant of the experiment, but rejects the fair sampling assumption. The same can be said about other people. As for me, I readily agree that it would be just great if I knew more about photodetectors, but I don't. However, as I said, I cannot agree that if I don't know something really important, I have no right to have my own opinion on such extremely important things as the Bell inequalities. After all, we disagree about the results of the future experiments, not the existing ones. You believe that one result of the future experiments is likely, I expect another result.
Another thing. To reject some work on perpetuum mobile, I don't need to know the details of the specific implementation. In the same way, in our discussion, I am trying to apply some general principles (which, I guess, you fully accept, by the way), such as unitary evolution. Again, I do wish I knew more about photodetectors, but nobody can browbeat me into thinking that unitary evolution is not applicable to photodetectors.

It is a FACT that there are no Bell-type experiments being conducted has ever proclaim that these loopholes were responsible for the apparent Bell violation. As an experimentalist, when I look at the body of evidence, and the lack of even ONE experiment to cast a doubt on the conclusion, then there is an overwhelming evidence for the validity of that conclusion. You throw around the word "proofs" as if we have "proofs" in physics. Find me something in physics that has the "proof" that you accept. Again, you have picked on these experiments, while ignoring the fact that other parts of physics have the same "baggage".

You never did tell me whether you accepted all the various phenomena that I listed. Are you experts in those areas as well so much so that you know the intricate details to know that they are valid? If not, then how come you don't complain about, say, the validity of the experiments in superconductivity? why are you sitting back and accepting the conclusions from the experts on this, but not for the Bell-type experiments?

It is a FACT that there is no experimental evidence of violations of the genuine Bell inequalities. As a theoretical physicist, when I look at the body of evidence, and the lack of even ONE experiment to demonstrate such violation, then there is an overwhelming evidence for the impossibility of such violations.

Actually, you demand that I cut you some slack and accept something without proper proof. I would like to oblige, but in this case I just can't. Sorry. I cannot accept the projection postulate and its corollary, violation of the genuine Bell inequalities, for the simple reason that they are in contradiction with unitary evolution. Unitary evolution is thoroughly proven experimentally, and I cannot reject it. Neither can you, I guess. This is the answer to your question, why I accept various phenomena that you mentioned (I do accept them), sometimes relying just on experts' opinion, but cannot be equally gullible in this case. I just cannot swallow two things that are in glaring contradiction with each other. I have to choose.

As for my being/not being an expert in the areas that you mentioned, I don't want to start a pissing contest here, but if you would really like to know more about my background, let me know, and I 'd be happy to send you a PM.

 

[JesseM]

Sorry. I cannot accept the projection postulate and its corollary, violation of the genuine Bell inequalities, for the simple reason that they are in contradiction with unitary evolution. Unitary evolution is thoroughly proven experimentally, and I cannot reject it.

Saying there is evidence for unitary evolution but not the projection postulate makes little sense to me--can you give an example of evidence for unitary evolution that does not depend on the assumption that the wave function's amplitudes should be interpreted as giving probabilities for getting different outcomes? And if you'd agree that amplitudes should be interpreted as giving probabilities, do you agree that all the evidence suggests that if you want to make predictions about the outcome of a later measurement #2 after a prior measurement #1, you have to use the Schroedinger equation to calculate the evolution of the eigenstate corresponding to the result of measurement #1 (in other words, assuming that at the moment of measurement #1 the system's quantum state was 'collapsed', onto that eigenstate, which then evolved forward according to the Schroedinger equation) up until the moment of measurement #2, and that if you instead used the Schroedinger equation to calculate the evolution of the quantum state the system was in prior to measurement #1, without any discontinuous non-unitary change in the quantum state at the moment of measurement #1, that would give the wrong answer for the probabilities for different outcomes at the moment of measurement #2? Without the projection postulate, how do you explain the fact that if we measure the system in a time-independent eigenstate of some variable A (say, spin in the x-direction), then if our subsequent measurements are of the same variable we'll get the same result each time, but if we then make a measurement of a variable B that doesn't commute with A (like spin in the y-direction), then a subsequent measurement of A could give a different result?

 

[akhmeteli]

While there is a detection loophole, the LIKELYHOOD that it is influencing the violation of Bell inequality is "highly unlikely", in the words of Zeilinger himself. If you have looked at the experiment involving multipartite systems (as in the GHZ theorem), the coincidence of such occurrence would be unbelievably small!

I respectfully disagree with you and Zeilinger that it is "highly unlikely". According to my estimate, it is "highly likely". I am saying this because I believe that unitary evolution is thoroughly proven. As a friend of mine, an experimental physicist, likes to say : "There is no such thing as miracles. There is such thing as poor soldering, though."

It is why I kept asking you if you think that different experiments that are influenced by different "loopholes" that have nothing to do with each other, can somehow conspire, in turn, to create the same conclusion.

I tried to answer this question in post #75 in this thread. I think it's no coincidence: experimentalists specifically looked for evidence of violations of Bell inequalities, and they immediately succeeded as soon as some assumption of the Bell theorem was discarded: either spatial separation was not sufficient, or the correlations prescribed by the theorem were replaced with some ersatz based on the fair sampling assumption.

I can also say that a vase that has been broken into a million pieces, can assemble itself back into the original vase when I throw it onto the floor. The probability of it is very small, but the phase space for that to occur isn't zero! Yet, we design our working world with the idea that it cannot happen. You, on the other hand, want "proof" that it can never happen.

This is an excellent example, but I am afraid it just proves my point, not yours. I don't "want" proof that it can never happen: I know that there can be no such proof because of unitary evolution, which is reversible. You could give me hundreds of such examples and "prove" that there is no unitary evolution because there is apparent irreversibility. However, you know better than this and, I suspect, also swear by unitary evolution, as I do. In the same time, you don't have any problems defending ideas that actually contradict unitary evolution, whereas I do have problems with such ideas.

 

[akhmeteli]

Saying there is evidence for unitary evolution but not the projection postulate makes little sense to me--can you give an example of evidence for unitary evolution that does not depend on the assumption that the wave function's amplitudes should be interpreted as giving probabilities for getting different outcomes?

I would say that unitary evolution was thoroughly proven using the Born rule as an operational principle. That may be close to what you said (though maybe not as close as you would like), but I prefer to avoid using your specific wording.

And if you'd agree that amplitudes should be interpreted as giving probabilities, do you agree that all the evidence suggests that if you want to make predictions about the outcome of a later measurement #2 after a prior measurement #1, you have to use the Schroedinger equation to calculate the evolution of the eigenstate corresponding to the result of measurement #1 (in other words, assuming that at the moment of measurement #1 the system's quantum state was 'collapsed', onto that eigenstate, which then evolved forward according to the Schroedinger equation) up until the moment of measurement #2, and that if you instead used the Schroedinger equation to calculate the evolution of the quantum state the system was in prior to measurement #1, without any discontinuous non-unitary change in the quantum state at the moment of measurement #1, that would give the wrong answer for the probabilities for different outcomes at the moment of measurement #2? Without the projection postulate, how do you explain the fact that if we measure the system in a time-independent eigenstate of some variable A (say, spin in the x-direction), then if our subsequent measurements are of the same variable we'll get the same result each time, but if we then make a measurement of a variable B that doesn't commute with A (like spin in the y-direction), then a subsequent measurement of A could give a different result?

As I said, the projection postulate may be a good approximation or a bad approximation, but it's an approximation anyway, so it cannot have the same status as unitary evolution. Indeed, for a rigorous description of a measurement we need to consider unitary evolution of a system including the particle and the instrument, therefore, a measurement is never final, as unitary evolution is reversible. And if a measurement is never final, how can we state that repeated measurements will give the same result for variable A? That's what I mean: the projection postulate directly contradicts unitary evolution. One can speculate whether the difference between predictions for unitary evolution and for the projection postulate is significant or not, but I think there can be no doubt that in principle such difference does exist. And I think unitary evolution is more fundamental than the projection postulate. You may disagree and favor the projection postulate instead, but I think you'll agree that one cannot have both as precise laws.

 

[ZapperZ]

I respectfully disagree with you and Zeilinger that it is "highly unlikely". According to my estimate, it is "highly likely". I am saying this because I believe that unitary evolution is thoroughly proven. As a friend of mine, an experimental physicist, likes to say : "There is no such thing as miracles. There is such thing as poor soldering, though."

I tried to answer this question in post #75 in this thread. I think it's no coincidence: experimentalists specifically looked for evidence of violations of Bell inequalities, and they immediately succeeded as soon as some assumption of the Bell theorem was discarded: either spatial separation was not sufficient, or the correlations prescribed by the theorem were replaced with some ersatz based on the fair sampling assumption.

But what you just said here exactly leads to my question on why there isn't an experiment done that look at the raw data and draw the conclusion that the loopholes were the ones responsible for the apparent violation! I have mentioned this repeatedly that there have been ZERO experimental report that contradict such conclusion based simply on the data! So remove those "ersatz" on fair sampling and show me results to the contradictory. How come no one has done this yet? How come no experimentalist have removed this "coincidence" by not looking vor evidence of such violations? Did ALL experimentalists so far conspired to "specifically looked" for such evidence? Not even ONE is not biased? What is the likelihood of THAT happening?

In the current search for dark matter, the Italian group at Gran Sasso has now twice tried to claim that http://physicsworld.com/cws/article/news/33870" as the dark matter source. This has been disputed, but look at how it is being disputed. They don't just say "Oh, there's something wrong with their data" or "They didn't take into account such-and-such". Nope. They also showed that there are other experiments with detectors within the same energy range that showed no such effects. This is what is throwing doubts into the claim! No such thing has been done for the Bell inequality violation. For all the talk that such-and-such loophole is the reason for the apparent violation, no one has really put their money where their mouths are and actually do the experiment and claim otherwise. This is what is glaringly missing, and in science, such absence of contradictory result is significant, especially in light of the numerous experiments that have been done!

This is an excellent example, but I am afraid it just proves my point, not yours. I don't "want" proof that it can never happen: I know that there can be no such proof because of unitary evolution, which is reversible. You could give me hundreds of such examples and "prove" that there is no unitary evolution because there is apparent irreversibility. However, you know better than this and, I suspect, also swear by unitary evolution, as I do. In the same time, you don't have any problems defending ideas that actually contradict unitary evolution, whereas I do have problems with such ideas.

In high energy physics experiments, there is such a thing as quoting a result and including the "sigma" of the event. This indicates the degree of confidence that the event is real, rather than due to background or due to other sources. Why? Because other events can mimic the same event that one is looking for. In fact, there's a whole study on just simulating the background events. This means that just detecting one event isn't sufficient to claim that the event exist. The statistics, which is something I had mentioned earlier, must be strong enough that the event should at least have a 5-sigma confidence for it to be seriously considered to be valid.

How come I don't see you arguing that the top quark also doesn't exist, for example? After all, it has an even smaller sigma than many results coming out of the Bell experiments? They may not have been able to close all the loophole, but what is the degree of confidence that the result that got were NOT due to the loopholes? That is why I stressed the importance of understanding the nature of the experiment and the nature of the detection. The degree of violation be quoted clearly indicates the confidence level of these experiments. It isn't just based on a single measurement, simply because of the reason that they require a strong statistical result to claim any violation. It is why Zeilinger found it "highly unlikely" that such violation is due to the loophole.

It all boils down to the FACT that no experiment has claimed otherwise. No experiment has claimed that the loophole is affecting the data that somehow show the violation of Bell inequality. So such conclusion hasn't been falsified.

Zz.

 

[akhmeteli]

But what you just said here exactly leads to my question on why there isn't an experiment done that look at the raw data and draw the conclusion that the loopholes were the ones responsible for the apparent violation! I have mentioned this repeatedly that there have been ZERO experimental report that contradict such conclusion based simply on the data! So remove those "ersatz" on fair sampling and show me results to the contradictory. How come no one has done this yet? How come no experimentalist have removed this "coincidence" by not looking vor evidence of such violations? Did ALL experimentalists so far conspired to "specifically looked" for such evidence? Not even ONE is not biased? What is the likelihood of THAT happening?

As I said, I don't know how to experimentally prove that the detection loophole is the cause of apparent violations, other than to conduct an experiment without loopholes (which seems impossible with current technology) and demonstrate absence of violations. If you know how to do it, please advise. What I do know, is that the detection loophole was present big way in all experiments with sufficient spatial separation, therefore, the assumptions of the Bell theorem were not satisfied, therefore, no violations of the genuine Bell inequalities were demonstrated.

When I said that experimentalists were specifically looking for violations, I did not mean to insult them or imply that they were biased. All I meant was if experimentalists found no violations, that meant no news, no publications, no interest. So naturally they were looking for something unusual and interesting, such as violations, rather than for something banal and boring, such as compliance with BI. Naturally, they explored all possible avenues for that, but only succeeded where the assumptions of the theorem were not fulfilled, as I suspect there can be no violations if all the assumptions are satisfied. Such successes were widely publicized, but their true meaning is not clear. You say that these are violations, I say that the genuine Bell inequalities are not violated in those experiments.

In the current search for dark matter, the Italian group at Gran Sasso has now twice tried to claim that http://physicsworld.com/cws/article/news/33870" as the dark matter source. This has been disputed, but look at how it is being disputed. They don't just say "Oh, there's something wrong with their data" or "They didn't take into account such-and-such". Nope. They also showed that there are other experiments with detectors within the same energy range that showed no such effects. This is what is throwing doubts into the claim! No such thing has been done for the Bell inequality violation. For all the talk that such-and-such loophole is the reason for the apparent violation, no one has really put their money where their mouths are and actually do the experiment and claim otherwise. This is what is glaringly missing, and in science, such absence of contradictory result is significant, especially in light of the numerous experiments that have been done!

Of course, it's better to be rich and healthy, rather than poor and sick. If you have alternative experimental results, your life is much easier. But you don't always have them. You may remember that many years ago a Russian group announced the results of an experiment demonstrating nonvanishing neutrino mass. There was no other data of this kind, but some objections were raised. Eventually the results were proven wrong. So we fight with what weapons we have.

Another thing. Let me repeat that just one reproducible experiment confirming violations of the genuine BI would solve the issue once and for all. As you know, there has been nothing of the kind so far.

In high energy physics experiments, there is such a thing as quoting a result and including the "sigma" of the event. This indicates the degree of confidence that the event is real, rather than due to background or due to other sources. Why? Because other events can mimic the same event that one is looking for. In fact, there's a whole study on just simulating the background events. This means that just detecting one event isn't sufficient to claim that the event exist. The statistics, which is something I had mentioned earlier, must be strong enough that the event should at least have a 5-sigma confidence for it to be seriously considered to be valid.

How come I don't see you arguing that the top quark also doesn't exist, for example? After all, it has an even smaller sigma than many results coming out of the Bell experiments? They may not have been able to close all the loophole, but what is the degree of confidence that the result that got were NOT due to the loopholes? That is why I stressed the importance of understanding the nature of the experiment and the nature of the detection. The degree of violation be quoted clearly indicates the confidence level of these experiments. It isn't just based on a single measurement, simply because of the reason that they require a strong statistical result to claim any violation. It is why Zeilinger found it "highly unlikely" that such violation is due to the loophole.

It all boils down to the FACT that no experiment has claimed otherwise. No experiment has claimed that the loophole is affecting the data that somehow show the violation of Bell inequality. So such conclusion hasn't been falsified.

As soon as you accept the fair sampling assumption, it's no sweat to get as many sigmas as you wish. I like this one about a Russian who came from London with a lot of money and explained: "We were playing poker, one of the players declared that he had a flush. I asked him to show his hand, but was told that gentlemen trust each other on their word. Immediately after that I had a mind-boggling streak of luck."

Again, I don't know what experiment can demonstrate that the loophole is responsible for violations, unless you conduct an experiment without loopholes, which currently cannot be done.

 

[ZapperZ]

So I fully expect you to start another thread complaining that the top quarks (and in fact, most of the other quarks beyond u and d) to really have not been observed and verified, the W's and Z's are still not there, and the neutrinos have not been found, much less, having any mass.

Zz.

 

[JesseM]

As I said, the projection postulate may be a good approximation or a bad approximation, but it's an approximation anyway, so it cannot have the same status as unitary evolution. Indeed, for a rigorous description of a measurement we need to consider unitary evolution of a system including the particle and the instrument, therefore, a measurement is never final, as unitary evolution is reversible. And if a measurement is never final, how can we state that repeated measurements will give the same result for variable A? That's what I mean: the projection postulate directly contradicts unitary evolution. One can speculate whether the difference between predictions for unitary evolution and for the projection postulate is significant or not, but I think there can be no doubt that in principle such difference does exist. And I think unitary evolution is more fundamental than the projection postulate. You may disagree and favor the projection postulate instead, but I think you'll agree that one cannot have both as precise laws.

It seems to me that if you want unitary evolution to continue at the moment of measurement, then the measuring apparatus and the system being measured will just become entangled in a giant superposition of macroscopic states, so you'll have to adopt the many-worlds interpretation. And many advocates of the many-worlds interpretation believe it does allow you to retain locality, at the expense of a certain form of "realism" (you have to get rid of the idea that measurements yield unique outcomes). For example, this paper says:

In the Everett interpretation the nonlocal notion of reduction of the wavefunction is eliminated, suggesting that questions of the locality of quantum mechanics might indeed be more easily addressed. On the other hand, while wavefunctions do not suffer reduction in the Everett interpretation, nonlocality nevertheless remains present in many accounts of this formulation. In DeWitt’s (1970) often-quoted description, for example, “every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on Earth into myriads of copies of itself.” Contrary to this viewpoint, others argue (Page, 1982; Tipler, 1986, 2000; Albert and Loewer, 1988; Albert, 1992; Vaidman, 1994, 1998, 1999; Price, 1995; Lockwood, 1996; Deutsch, 1996; Deutsch and Hayden, 2000) that the Everett interpretation can in fact resolve the apparent contradiction between locality and quantum mechanics. In particular, Deutsch and Hayden (2000) apply the Everett interpretation to quantum mechanics in the Heisenberg picture, and show that in EPRB experiments,1 information regarding the correlations between systems is encoded in the Heisenberg-picture operators corresponding to the observables of the systems, and is carried from system to system and from place to place in a local manner. The picture which emerges is not one of measurement-type interactions “splitting the universe” but, rather, producing copies of the observers and observed physical systems which have interacted during the (local) measurement process (Tipler, 1986).

Also, in this subsequent paper by the same author, I think he's arguing that the Everett/many-worlds interpretation of quantum field theory can also be understood in terms of information encoded in purely local operators.

Still, the MWI predictions about what each version of the observer in the superposition will experience are identical to the usual predictions of the Copenhagen interpretation, including the prediction that when different observers compare their results they'll find violations of the Bell inequalities (as I understand it, the reason this is compatible with locality is essentially that each observer locally splits into multiple copies when they measure their particle, but there is no need for the universe to decide which copy of observer #1 is mapped to which copy of observer#2 until a signal actually passes between them moving at the speed of light). So, it still doesn't make any sense for you to say that the evidence in favor of unitary evolution somehow constitutes evidence against violations of the Bell inequalities.

 

[confusedashell]

MWI is a joke, give me one proof of other universes or this magical splitting?
If your to view wavefunction as the whole universe, we'd be in superpositions all the time, we ain't so. No. sorry.

Bohm is by far the best choice if your not willing to give up everything you percieve and experience in life.
+ nonlocality is at it's heart, so the more evidence for nonlocality the more Bohm wins the race towards "truth".

 

[JesseM]

MWI is a joke, give me one proof of other universes or this magical splitting?
If your to view wavefunction as the whole universe, we'd be in superpositions all the time, we ain't so. No. sorry.

Yes, the idea of the MWI is that we are in superpositions all the time, but that different macroscopic elements of the superposition are unaware of one another, which I think is related to decoherence. And it's odd that you would say "give me one proof" when you go on to advocate the Bohm interpretation--there can be no experimental evidence for any of the unique aspects of the Bohm interpretation either, like the nonlocal pilot wave or the hidden position variable associated with particles at all times. That's why they are all called "interpretations" rather than "theories", because they are all experimentally indistinguishable from one another.

In any case, I was not really attempting to advocate for the MWI in that post, I was just pointing out that it's the natural conclusion of akhmeteli's idea that the same unitary evolution which guides the behavior of the wavefunction of a small quantum system between measurements is still operating when measurements are made, with the wavefunction of both the small system and the larger measuring apparatus still evolving in the usual unitary way.

 

[akhmeteli]

So I fully expect you to start another thread complaining that the top quarks (and in fact, most of the other quarks beyond u and d) to really have not been observed and verified, the W's and Z's are still not there, and the neutrinos have not been found, much less, having any mass.
Zz.

I regret that I sound so obstinate :-( , but, however important the top quark and other quarks are, they do not turn philosophy upside down, whereas possible violations of the Bell inequalities can do just that. There is a general rule: the more radical the result is, the higher is the burden of proof. As for the neutrino mass, the fact that neutrino oscillations seem to have been pretty reliably proven by now does not make the old Russian results correct.

 

[akhmeteli]

It seems to me that if you want unitary evolution to continue at the moment of measurement, then the measuring apparatus and the system being measured will just become entangled in a giant superposition of macroscopic states,

I agree.

so you'll have to adopt the many-worlds interpretation.

I'm afraid now you're moving too fast for me. I don't understand why MWI is necessary to describe a system of many particles. I guess the standard quantum theory is quite enough for that. As far as I know, I owe nothing to MWI, except for maybe cold respect, so I don't know how the quotes on MWI are relevant.

So, it still doesn't make any sense for you to say that the evidence in favor of unitary evolution somehow constitutes evidence against violations of the Bell inequalities.

Again, that may be close to what I said, but I still prefer a somewhat different wording: one of the assumptions that the Bell theorem uses is the projection postulate. As this postulate is in contradiction with unitary evolution, this specific assumption of the Bell theorem may be less than correct, so violations of the Bell inequalities may be less inevitable than they seem. I appreciate that what I say does not necessarily make sense for you, and it would certainly help if you could advise which part of my reasoning in post #78 in this thread seems dubitable.

 

[JesseM]

I'm afraid now you're moving too fast for me. I don't understand why MWI is necessary to describe a system of many particles. I guess the standard quantum theory is quite enough for that. As far as I know, I owe nothing to MWI, except for maybe cold respect, so I don't know how the quotes on MWI are relevant.

The MWI is essentially just "standard quantum theory" without the projection postulate. Take the Schroedinger's cat thought-experiment--do you agree that if we only allow the wavefunction to evolve via unitary evolution, we'll end up with a state that's a superposition which assigns nonzero amplitude to different position eigenstates corresponding to both "dead cat" and "live cat"? Without anything but unitary evolution, do you agree the wavefunction is not going to settle on one macroscopic possibility or the other? Apply the same reasoning to the wavefunction of the universe and you have the MWI.

Again, that may be close to what I said, but I still prefer a somewhat different wording: one of the assumptions that the Bell theorem uses is the projection postulate.

It seems to me we should distinguish between two different aspects of the "projection postulate":

1. At the experimental level, if we want to connect the theoretical evolving wavefunction with actual experimental results, we must use the Born rule where the probability of a given outcome depends on the amplitude that the wavefunction assigns to the eigenstate associated with that outcome (the probability being the complex conjugate of the amplitude)

2. At a theoretical level, the projection postulate says that each measurement "collapses" the wavefunction, converting it at the moment of measurement into the eigenstate associated with whatever outcome was seen.

Obviously you reject #2, but your earlier comments in post #78 seemed to indicate that you'd accept #1:

Saying there is evidence for unitary evolution but not the projection postulate makes little sense to me--can you give an example of evidence for unitary evolution that does not depend on the assumption that the wave function's amplitudes should be interpreted as giving probabilities for getting different outcomes?

I would say that unitary evolution was thoroughly proven using the Born rule as an operational principle.

The MWI, too, is generally understood to accept that the Born rule must work out as an operational rule for the probabilities seen by any individual observer in the giant superposition that is the universal wavefunction, while rejecting the idea of #2 that anything special happens to the wavefunction during measurement. And as far as I can see, Bell's theorem depends only on accepting #1, not on #2...if you accept that probability can always be determined from the amplitudes using the Born rule, then if you calculate the relevant probabilities for an entangled state, you can find probabilities which violate Bell inequalities. Do you disagree?

 

[ZapperZ]

I regret that I sound so obstinate :-( , but, however important the top quark and other quarks are, they do not turn philosophy upside down, whereas possible violations of the Bell inequalities can do just that. There is a general rule: the more radical the result is, the higher is the burden of proof. As for the neutrino mass, the fact that neutrino oscillations seem to have been pretty reliably proven by now does not make the old Russian results correct.

You accepted "fair sampling" in neutrino detection but reject it in Bell-type experiments? What gives? How do you think they detect neutrinos in the first place?

Zz.

 

[jtbell]

MWI is a joke, give me one proof of other universes or this magical splitting?

Give me one proof of the Bohmian interpretation's particle trajectories.

(See for example http://plato.stanford.edu/entries/qm-bohm/ , about a third of the way down the page.)

 

[confusedashell]

I didnt say I got any proof of Bohm, I'm well aware of everything in that article I'm talking to Sheldon over email on regular basis.
All I said is that from what we experience in life, Bohm interpertation is by far the best.

Also trying to point out, there is SO many proponents of MWI without ANY reason for it, it's the next Copenhagen, "lets buy into that just because someone with authority advocates that".

ADD:

nonlocality is a very good indication of Bohm being right.
Mwi got nothing yet.
Bohms interpertation also lead to all of Bells work, that's pretty good for a interpretation.
Mwi hasn't lead to **** but $ in the money of those who write books on the subject

 

[Demystifier]

MWI are the only one who cling to locality, without it their theory falls apart, which it does in any rational mind I think either way, it rejects existence of particles...

Not the only. Most versions of the information interpretation (which can be viewed as modern versions of the Copenhagen interpretation) claim that QM is local. One of these versions even has a special name - the relational interpretation.

 

[confusedashell]

But then, why aren't these interpretations left? now that nonlocality seems more or less a fact?

 

[Demystifier]

But then, why aren't these interpretations left? now that nonlocality seems more or less a fact?

Because these interpretations claim that objective (i.e., existing even without observations) reality does not exist. Of course, these interpretations admit that there are nonlocal correlations (which is only what is truly experimentally proved), but they claim that reality itself is not nonlocal, simply because reality does not exist.

I am not saying that it makes sense to me, I am just saying what they say.

 

[confusedashell]

I understand they are crazy borderline solipsists and I don't take them serious, but that's not MWI's claim? thought it was meant to perserve realism

 

[Demystifier]

I understand they are crazy borderline solipsists and I don't take them serious, but that's not MWI's claim? thought it was meant to perserve realism

True, MWI preserves realism.
In fact, interpretations of QM can be classified according to the number of realities it contains:
0: Copenhagen, information theoretic, relational, ...
1: Bohm, objective collapse (GRW, Penrose), ...
infinite: MWI, ...

 

[Fra]

I suspect I am one of those crazy borderline "solipsists"

IMO, the notion of locality can't be discussed in isolation from a discusstion of the nature of spacetime. Because the notion of locality has meaning only in the context of a confidently established spacetime structure.

So what is the physical basis of locality implies questioning the physical basis of spacetime and various measures thereof.

Rather than saying that objective reality doesn't exist, I would prefer to simply say that I see no clean way by a finite and immediate procedure, to define an objective reality from the subjective information view - which btw, the real situation I am stuck with. Ie. reality whatever that is, is uncertain, and I have no other choice but to based my decisions on that uncertain information. Somehow that's life, and I figure also nature, because I think it's the same situation any system is facing.

The immediate question for me is, what do I do next? I need to make a choice. If there is some reality out there that I have no knowledge about, then that is no valid or existing basis for my decision making. That however doesn't mean that I will come to learn about this reality in the future. But that does not help my decision making process.

So for me objectivity serves the purposes of a reference, that is dynamical. To me the emergence of objectivity, is more or less closely related to, and the ultimate realisation of the the idea of background independent formulation.

The objectivity you don't want to let go off, is IMO a background. And how can I from the subjective view, know WHICH objectivity there is? And how come I don't already know? And meanwhile, business as usual forces me to act based on lack of this information :)

I may be close to a "borderline solipsist" but I'm proud to confess it.

/Fredrik

 

[Aeroflech]

Because these interpretations claim that objective (i.e., existing even without observations) reality does not exist. Of course, these interpretations admit that there are nonlocal correlations (which is only what is truly experimentally proved), but they claim that reality itself is not nonlocal, simply because reality does not exist.

I am not saying that it makes sense to me, I am just saying what they say.

I'd like you to show hard evidence that there is a reality outside our observations. Personally I don't think you can, as the only thing we have to define our reality by is our observations. Now, this does not mean that there can't be arguments for a observer independent reality. If a good theory that described the world well came along and implied as such, we would have no problem accepting that. In our world, however, the widely accepted theory that comes closest to affirming or denying that is QM. Many people have attempted to create an interpretation of QM that affirms observer independence. However, all such theories either disagree with the QM formalism on the observable effects of the theory or are required to hide them so that you can't observe the observer-independent parts in principle. These failures indicate to me that QM does not support observer independence.

 

[Demystifier]

you can't observe the observer-independent parts in principle.

It sounds almost like a tautology to me, that has nothing to do with quantum mechanics, but with general epistemology.
Can you observe the observer-independent parts of classical mechanics?

 

[Aeroflech]

It sounds almost like a tautology to me, that has nothing to do with quantum mechanics, but with general epistemology.
Can you observe the observer-independent parts of classical mechanics?

That assertion is incorrect. What I had in mind when I was writing that phrase down was the Kochen-Specker theorem.

 

[Demystifier]

That assertion is incorrect. What I had in mind when I was writing that phrase down was the Kochen-Specker theorem.

If this is what you had in mind, than it is your previous assertion that is incorrect.
The KS theorem does not say that you cannot observe the observer-independent things (which, as I already asserted, would be a trivial tautology), but that objective things, if exist, must necessarily be changed by the acts of experiments. Here it is essential to understand the subtle difference between the "objective" and the "observer-independent". For example, the velocity of a CLASSICAL particle is objective, but not observer independent. This is because the act of classical observation also involves an interaction (even if a tiny and negligible one) between the observer and the particle, which influences the particle velocity.

The difference between classical and quantum mechanics is that in the latter there is a lower bound on the strength of this influence. KS theorem essentially says that this influence cannot be made arbitrarily small.

A possible INTERPRETATION of the KS theorem is that then objective things do not exist. However, it is NOT a necessary logical consequence of that theorem.

 

[akhmeteli]

Take the Schroedinger's cat thought-experiment--do you agree that if we only allow the wavefunction to evolve via unitary evolution, we'll end up with a state that's a superposition which assigns nonzero amplitude to different position eigenstates corresponding to both "dead cat" and "live cat"?

I agree. Strictly speaking, this is correct.

Without anything but unitary evolution, do you agree the wavefunction is not going to settle on one macroscopic possibility or the other?

This is correct in the same sense as the Poincare recurrence theorem is correct. On the other hand, we'll have something very similar to a macroscopic outcome in the same sense in which we have irreversibility in thermodynamics. So I don't think this is a great problem. I think we should learn how to live with the idea of Schroedinger's cat, dead or alive. I think we should accept unitary evolution in all cases, not just when we like the results. Otherwise all kinds of problems arise.

Apply the same reasoning to the wavefunction of the universe and you have the MWI.

As you can see, I don't need MWI at all, because reversibility does not scare me (even if exemplified by a cat with a totally uncertain health status :-) ).

It seems to me we should distinguish between two different aspects of the "projection postulate":

1. At the experimental level, if we want to connect the theoretical evolving wavefunction with actual experimental results, we must use the Born rule where the probability of a given outcome depends on the amplitude that the wavefunction assigns to the eigenstate associated with that outcome (the probability being the complex conjugate of the amplitude)

I guess this is a typo, as probability should be real (should be "amplitude times its conjugate")

2. At a theoretical level, the projection postulate says that each measurement "collapses" the wavefunction, converting it at the moment of measurement into the eigenstate associated with whatever outcome was seen.

Obviously you reject #2, but your earlier comments in post #78 seemed to indicate that you'd accept #1:

As an operational principle, yes, I accept #1, although I suspect this is an approximation as well. I should emphasize though that there are different definitions of the projection postulate (#2).

The MWI, too, is generally understood to accept that the Born rule must work out as an operational rule for the probabilities seen by any individual observer in the giant superposition that is the universal wavefunction, while rejecting the idea of #2 that anything special happens to the wavefunction during measurement. And as far as I can see, Bell's theorem depends only on accepting #1, not on #2...if you accept that probability can always be determined from the amplitudes using the Born rule, then if you calculate the relevant probabilities for an entangled state, you can find probabilities which violate Bell inequalities. Do you disagree?

This is certainly a good question. I guess a lot depends on the exact definitions of the Born rule and the projection postulate. In your definition it is not clear what "outcome" means, whether it is an outcome of measurement of one observable or two. Other definitions mention just one observable. Actually, in the Bell theorem, correlations are calculated, so you should average a product of, say, spin projections for two particles. One may regard the relevant procedure as two measurements: one for the first particle, and the other for the second particle (the exact order is not important). Anyway, we must appreciate that any calculation procedure should correspond to the actual experimental situation, where indeed two measurements take place, or so I guess. So you have to apply the projection postulate to know how to describe the system after the first measurement. Maybe it is possible to generalize the definition of the Born's rule to include the projection postulate, but this would be a different story. For example, for what it's worth, the Wikipedia article (http://en.wikipedia.org/wiki/Bell's_Theorem ) uses the projection postulate. Thus, I believe the projection postulate (in some form) is used as an assumption of the Bell's theorem.

 

[Fra]

At least relative to my own thinking, the standard QM formalism as it stands, is not consistent with the lack of solid objectivity. It rather contains implicitly a kind of objectivity in the selection of a hilbert space, which also results in the determinism in the probability space.

IMH, in the general case, to truly implement the ideals of truly relational models, then even the relations are relative and dynamically so, and standard QM needs fundamental revision. But most of those who think along this lines, still pictures standard QM as beeing effectively emergent so as to be consistent with current experimental evidence.

In classical relational models like, GR. The observations the observers make differ, but their relations are somehow objective. In that sense there is a classical notion of objective relations between relative observations.

But I ask, who is establishing these objective relations? Here the notion of information and information capacity constraints really does hit me in the face. I don't even find rovelli's relational QM to solve this as far as I see. He takes an IMO excellent initiative, but I think "reinterpretations only" dosen't solve the main issue.

I agree that to a certain extent, it sure is possible in some sense, that there exists a universal objectivity at some level of abstraction. But the mere fact that it's "only" possible, and not a certainty, does influence at least my actions. This is why I do not think it's correct to say objectivity doesn't exists. Because I am uncertain about statement as well. It's possible that it exists, but to me the operational question is how to make progress. What strategy do I choose to make progress on this matter?

I don't think we all need to agree.

/Fredrik

 

[JesseM]

This is correct in the same sense as the Poincare recurrence theorem is correct. On the other hand, we'll have something very similar to a macroscopic outcome in the same sense in which we have irreversibility in thermodynamics.

What do you mean? In thermodynamics, it is overwhelmingly probable that entropy will increase, and you would have to wait a vast amount of time for entropy to decrease and the original state to recur. I don't see anything analogous to this with Schroedinger's cat if you believe only in unitary evolution. Unitary evolution will continually give you large amplitudes for both the live and dead state, it's not as if the amplitude will be concentrated almost entirely on one and the amplitude of the other will be overwhelmingly small.

As you can see, I don't need MWI at all, because reversibility does not scare me (even if exemplified by a cat with a totally uncertain health status :-) ).

You give no explanation of what reversibility has to do with the problem of significant amplitudes for completely different macroscopic states!

I guess this is a typo, as probability should be real (should be "amplitude times its conjugate")

Not exactly a typo, but writing too quickly...I was indeed thinking of multiplying the amplitude by its complex conjugate, but there was a malfunction somewhere between brain and keyboard.

This is certainly a good question. I guess a lot depends on the exact definitions of the Born rule and the projection postulate. In your definition it is not clear what "outcome" means, whether it is an outcome of measurement of one observable or two. Other definitions mention just one observable. Actually, in the Bell theorem, correlations are calculated, so you should average a product of, say, spin projections for two particles. One may regard the relevant procedure as two measurements: one for the first particle, and the other for the second particle (the exact order is not important). Anyway, we must appreciate that any calculation procedure should correspond to the actual experimental situation, where indeed two measurements take place, or so I guess. So you have to apply the projection postulate to know how to describe the system after the first measurement.

My memory of exactly how multiparticle systems are dealt with mathematically in QM is fuzzy, but I had the idea that one could assign a single amplitude to different possible combinations of measurement outcomes for two particles, in which case I'd think you'd be able to use the Born rule to get the probability of that combination in a pair of simultaneous measurements, without the need to have the first measurement "collapse" the system's wavefunction via the projection postulate in order to calculate probabilities for the second measurement. This page, for example, seems to confirm my memory, assigning single amplitudes to joint events like one photon being deflected by a half-silvered mirror while the other passes through. If you think I'm completely off here, though, maybe I should go back and reread my old college textbook...

 

[akhmeteli]

What do you mean? In thermodynamics, it is overwhelmingly probable that entropy will increase, and you would have to wait a vast amount of time for entropy to decrease and the original state to recur. I don't see anything analogous to this with Schroedinger's cat if you believe only in unitary evolution. Unitary evolution will continually give you large amplitudes for both the live and dead state, it's not as if the amplitude will be concentrated almost entirely on one and the amplitude of the other will be overwhelmingly small.

I am not sure what version of the Shroedinger's cat paradox you have in mind. The original version has a time limitation. For this discussion, let us imagine though that we consider the setup over an unlimited or extremely long time period. Eventually the atom will decay, triggering the killing mechanism, and the cat will die, either peacefully, or after prolonged suffering :-) If the box has finite dimensions, the system will apparently have discrete energy eigenvalues and thus satisfy the conditions of the quantum recurrence theorem (Phys. Rev. V.107 #2, pp.337-338, 1957), so after a hopelessly long period, the cat will rise from the dead, or, to be precise, will be as close to its initial state as you wish:-). On the other hand, this scary picture can perhaps coexist with practical irreversibility.

If this does not answer your question, please advise.

You give no explanation of what reversibility has to do with the problem of significant amplitudes for completely different macroscopic states!

Again, if the above explanation in this post does not seem satisfactory, please advise.

My memory of exactly how multiparticle systems are dealt with mathematically in QM is fuzzy, but I had the idea that one could assign a single amplitude to different possible combinations of measurement outcomes for two particles, in which case I'd think you'd be able to use the Born rule to get the probability of that combination in a pair of simultaneous measurements, without the need to have the first measurement "collapse" the system's wavefunction via the projection postulate in order to calculate probabilities for the second measurement. This page, for example, seems to confirm my memory, assigning single amplitudes to joint events like one photon being deflected by a half-silvered mirror while the other passes through. If you think I'm completely off here, though, maybe I should go back and reread my old college textbook...

First of all, after a cursory look at the link that you gave, I did not understand how it is relevant, as it seems to me that they describe some procedure (it does not matter whether the procedure is correct or not), but do not say whether they use the Born's rule or the projection postulate.

Technically, perhaps it might be possible from the point of quantum theory to measure the product of, say, spin projections of two different particles (I guess we can construct the relevant hermitian operator). However, in the tests of the Bell inequalities, measurements on the two particles are done pretty much independently, as far as I understand, and I am not sure it matters if these measurements are simultaneous or not quite, as the measurements are spatially separated anyway.

 

[JesseM]

I am not sure what version of the Shroedinger's cat paradox you have in mind. The original version has a time limitation. For this discussion, let us imagine though that we consider the setup over an unlimited or extremely long time period. Eventually the atom will decay, triggering the killing mechanism, and the cat will die, either peacefully, or after prolonged suffering :-) If the box has finite dimensions, the system will apparently have discrete energy eigenvalues and thus satisfy the conditions of the quantum recurrence theorem (Phys. Rev. V.107 #2, pp.337-338, 1957), so after a hopelessly long period, the cat will rise from the dead, or, to be precise, will be as close to its initial state as you wish:-). On the other hand, this scary picture can perhaps coexist with practical irreversibility.

If this does not answer your question, please advise.

No, it doesn't answer the question at all. My question has nothing to do with what happens a zillion years after the atom decays or doesn't decay (enough time for the system to have a significant likelihood of returning to its initial state), I don't understand why you think that would be relevant--I'm just asking what happens shortly afterwards, say after an hour. At this point, if you take unitary evolution seriously without the projection postulate, the cat should be in a superposition which assigns significant amplitudes to both the "atom decayed and cat is dead" states and the "atom didn't decay and cat is alive" states. So what do you think is the actual physical truth of the matter at this point in time? Do you think the cat is really one or the other, implying that unitary evolution can't be the whole story? Or do you think that since both outcomes are assigned a significant amplitude by the wavefunction, both must be on equal footing as far as 'physical truth' is concerned--and if so, how is this different from the many-worlds interpretation? Or do you suggest some third alternative, and if so what is it?

First of all, after a cursory look at the link that you gave, I did not understand how it is relevant, as it seems to me that they describe some procedure (it does not matter whether the procedure is correct or not), but do not say whether they use the Born's rule or the projection postulate.

I only brought up that link because it seemed to support my memory that in QM when you construct the wavefunction for a multiparticle system, you can use it to assign amplitudes to combinations of measurable outcomes. This is just a question about the mathematics of the theory of QM, you said you were a physicist yourself so I figured you'd know whether my memory on this is right or wrong; if not, then I can go dig up my old textbooks to see if I can find an example of such a multiparticle amplitude. But obviously if it's true that a single amplitude can be assigned to combinations of outcomes, then we can use the Born rule to calculate the probability of measuring such combinations, without the need to worry about the projection postulate discontinuously shifting the wavefunction between measurements.

Technically, perhaps it might be possible from the point of quantum theory to measure the product of, say, spin projections of two different particles (I guess we can construct the relevant hermitian operator). However, in the tests of the Bell inequalities, measurements on the two particles are done pretty much independently, as far as I understand, and I am not sure it matters if these measurements are simultaneous or not quite, as the measurements are spatially separated anyway.

For combinations of spin measurements it might be that there is no time-dependence in the amplitudes, in which case it wouldn't really matter whether the measurements were simultaneous or not.