Is wave function a real physical thing?

[vanhees71]

I don't think QBism makes sense, but many aspects of it seem very standard and nice to me. For example, how can we understand wave function collapse? An analogy in classical probability is that it is like throwing a die, where before the throw the outcome is uncertain, but after the throw the probability collapses to a definite result. Classically, this is very coherently described by the subjective Bayesian interpretation of probability, from which the frequentist algorithms can be derived. It is fine to argue that the state preparation in QM is objective. However, the quantum formalism links measurement and preparation via collapse. If collapse is subjective by the die analogy, then because collapse is a preparation procedure, the preparation procedure is also at least partly subjective.

Hm, I don't think that collapse is needed in probabilistic theories. What's the point of it? I throw the die, ignoring the details of the initial conditions and get some (pseudo-)random result which I read off. Why then should there be another physical process called "collapse"? The probabilities for some outcome is simply the description of my expectation how often a certain outcome of a random experiment will occur when I perform it under the given conditions. The standard assumption $P(j)=1/6$ is due to the maximum-entropy principle: If I don't know anything about the die, I just take the probability distribution of maximum entropy (i.e., the least prejudice) in the sense of the Shannon entropy. This hypothesis I can test with statistical means in an objective way throwing the die very often. Then you get some new probaility distribution according to the maximum entropy principle due to the gained statistical knowledge, which may be more realistic, because it turns out that it's not a fair die. Has then anything in the physical world "collapsed", because I change my probabilities (expectations about the frequency of outcomes of a random experiment) according to more (statistical) information about the die? I think not, because I don't know, what should that physical process called "collapse" should be. Also my die remains unchanged etc.

Also for me there is no difference between the quantum mechanical probabilities and the above example of probabilities applied in a situation where the underlying dynamics is assumed to be deterministic in the sense of Newtonian mechanics. The only difference is that the probabilistic nature of our knowledge is in the quantum case not just because of the ignorance of the observer (in the die example about the precise initial conditions of the die as a rigid body, whose knowledge would enable us in principle to predict with certainty the outcome of the individual toss, because it's a deterministic process) but it's principally not possible to have determined values for all observables of the quantum object. In quantum theory on those observables have a determined value (or a value with very high probability) which have been prepared but then necessarily other observables that are not compatible with those which have been prepared to be (pretty) determined are (pretty) undetermined. Then I do a measurement on an indivdual so prepared system of such an undetermined observable and get some accurate value. Why should there be any collapse, only because I found a value? For sure there's an interaction of the object with the measurement apparatus, but that's not a "collapse of the state" but just an interaction. So also in the quantum case there's no necessity at all to have a strange happening called "collapse of the quantum state".

 

[atyy]

Hm, I don't think that collapse is needed in probabilistic theories. What's the point of it? I throw the die, ignoring the details of the initial conditions and get some (pseudo-)random result which I read off. Why then should there be another physical process called "collapse"? The probabilities for some outcome is simply the description of my expectation how often a certain outcome of a random experiment will occur when I perform it under the given conditions. The standard assumption $P(j)=1/6$ is due to the maximum-entropy principle: If I don't know anything about the die, I just take the probability distribution of maximum entropy (i.e., the least prejudice) in the sense of the Shannon entropy. This hypothesis I can test with statistical means in an objective way throwing the die very often. Then you get some new probaility distribution according to the maximum entropy principle due to the gained statistical knowledge, which may be more realistic, because it turns out that it's not a fair die. Has then anything in the physical world "collapsed", because I change my probabilities (expectations about the frequency of outcomes of a random experiment) according to more (statistical) information about the die? I think not, because I don't know, what should that physical process called "collapse" should be. Also my die remains unchanged etc.

Also for me there is no difference between the quantum mechanical probabilities and the above example of probabilities applied in a situation where the underlying dynamics is assumed to be deterministic in the sense of Newtonian mechanics. The only difference is that the probabilistic nature of our knowledge is in the quantum case not just because of the ignorance of the observer (in the die example about the precise initial conditions of the die as a rigid body, whose knowledge would enable us in principle to predict with certainty the outcome of the individual toss, because it's a deterministic process) but it's principally not possible to have determined values for all observables of the quantum object. In quantum theory on those observables have a determined value (or a value with very high probability) which have been prepared but then necessarily other observables that are not compatible with those which have been prepared to be (pretty) determined are (pretty) undetermined. Then I do a measurement on an indivdual so prepared system of such an undetermined observable and get some accurate value. Why should there be any collapse, only because I found a value? For sure there's an interaction of the object with the measurement apparatus, but that's not a "collapse of the state" but just an interaction. So also in the quantum case there's no necessity at all to have a strange happening called "collapse of the quantum state".

Collapse is an essential part of the quantum formalism. The only debate should be whether it is a physical process or not. What you seem to be saying is that collapse is epistemic.

 

[vanhees71]

I guess, it's what's called epistemic. But again, why do you consider the "collapse" as essential? Where do you need it?

 

[atyy]

I guess, it's what's called epistemic. But again, why do you consider the "collapse" as essential? Where do you need it?

Hmmm, are we still disagreeing on this? Collapse is in Landau and Lifshitz, Cohen-Tannoudji, Diu and Laloe, Sakurai and Weinberg (and every other major text except Ballentine, whom I'm sure is wrong), so it really is quantum mechanics. To see that it is essential, take an EPR experiment in which Alice and Bob measure simultaneously. What is simultaneous in one frame will be sequential in another frame. As long as one has sequential measurements in which sub-ensembles are selected based on the measurement outcome, one needs collapse or an equivalent postulate.

 

[bhobba]

Hmmm, are we still disagreeing on this?

As he should.

Its a logical consequence of the assumption of continuity - but has anyone every measured a state again an infinitesimal moment later to check if the assumption holds?

Its not really needed - one simply assumes the filtering type measurement it applies to is another state preparation. Of course a systems state changes if you prepare it differently - instantaneously - well that's another matter - observations don't happen instantaneously.

Thanks
Bill

 

[atyy]

Its a logical consequence of the assumption of continuity - but has anyone every measured a state again an infinitesimal moment later to check if the assumption holds?

Yes! The measurement has been performed in the Bell tests. If there is a frame in which the measurements are simultaneous, then there will be another frame in which Bob measures an infinitesimal moment after Alice. So far, all predictions are consistent with quantum mechanics (including collapse) and relativity.

Its not really needed - one simply assumes the filtering type measurement it applies to is simply another state preparation. Of course a systems state changes if you prepare it differently - instantaneously - well that's another matter.

It is needed, because in a filtering experiment, the preparation procedure involves choosing the sub-ensemble based on the outcome of the immediately preceding measurement. So preparation and measurement are linked.

 

[bhobba]

the preparation procedure involves choosing the sub-ensemble based on the outcome of the immediately preceding measurement. So preparation and measurement are linked.

Exactly how long does that prior measurement take to prepare the system differently? And what's the consequence for instantaneous collapse? Think of the double slit. The, say electron, interacts with the screen and decoheres pretty quickly - but not instantaneously. We do not know how the resultant improper state becomes a proper one - but I doubt however that's done its instantaneous - although of course one never knows. Either way, until we know for sure, saying it's instantaneous isn't warranted.

Thanks
Bill

 

[atyy]

Exactly how long does that prior measurement take to prepare the system differently? And what's the consequence for instantaneous collapse? Think of the double slit. The, say electron, interacts with the screen and decoheres pretty quickly - but not instantaneously. We do not know how the resultant improper state becomes a proper one - but I doubt however that's done its not instantaneous - although of course one never knows.

You can take the instantaneous part as just a convenient model that has not been falsified yet. What is clear is that unitary evolution alone is insufficient, and there has to be some other postulate for sequential measurements, which in standard quantum mechanics is the non-unitary evolution of wave function collapse (suitably generalized).

 

[bhobba]

non-unitary evolution of wave function collapse (suitably generalized).

Sure - but in modern times I think the problem of outcomes is a better way of stating the issue than collapse which has connotations I don't think the formalism implies.

Thanks
Bill

 

[atyy]

Sure - but in modern times I think the problem of outcomes is a better way of stating the issue thamn collapse wjich has connotations I don't think the formalism implies.

That's fine if it is just a matter of terminology. I do prefer the old fashioned terminology, since I do use Copenhagen as a default interpretation, where the wave function is not necessarily real, and consequently the wave function evolution including collapse is also not necessarily real. So "collapse" is just the updating of the wave function after a measurement without committing to whether it is ontic or epistemic.

OK, but in fact, collapse is one of the reasons that it seems reasonable to try to think of the wave function as epistemic. Indeed, if I understand vanhees71 correctly, he would like to think of collapse as epistemic. All I'm pointing out is that earlier he argued that the wave function is ontic, and that it isn't obviously consistent to say that the wave function is ontic, but that collapse is epistemic, since collapse is a state preparation procedure, so if collapse is epistemic, then the wave function prepared by collapse is presumably at least partly epistemic.

 

[stevendaryl]

Ok, then what's in your view the difference between Bayesian and frequentist interpretations of probabilities, particularly the statement probabilities make sense for a single event?

You can go one better: Bayesian statistics allows us to have a probability for something with zero events. Of course, in that case, it's just a guess (although you can have a principled way of making such guesses). A single event provides a correction to your guess. More events provide better correction.

E.g., when they say in the weather forecast, there's a 99% probability to have snow tomorrow, and tomorrow it doesn't snow. Does that tell you anything about the validity of the probability given by the forecast? I don't think so.

It doesn't tell you a lot, but it tells you something. If the forecast is for 99% chance of snow, and it doesn't snow, then (for a Bayesian), the confidence that the forecast is accurate will decline slightly. If for 100 days in a row, the weather service predicts 99% chance of snow, and it doesn't snow any of those days, then for the Bayesian, the confidence that the reports are accurate will decline smoothly each time. It would never decline to zero, because there's always a nonzero chance that that an accurate probabilistic prediction is wrong 100 times in a row, just like there is a nonzero chance that a fair coin will yield heads 100 times in a row.

The frequentist would (presumably) have some cutoff value for significance. The first few times that the weather report proves wrong, they would say that no conclusion can be drawn, since the sample size was so small. Then at some point, he would conclude that he had a large enough sample to make a decision, and would decide that the reports are wrong.

Note that both the Bayesian and the frequentist makes use of arbitrary parameters--the Bayesian has an arbitrary a priori notion of probability of events. The frequentist has an arbitrary cutoff for determining significance. The difference is that the Bayesian smoothly takes into account new data, while the frequentist withholds any judgement until some threshold amount of data, then makes a discontinuous decision.

It's just a probability based on experience (i.e., the collection of many weather data over a long period) and weather models based on very fancy hydrodynamics on big computers. The probabilistic statement can only be checked by evaluating a lot of data based on weather observations.

Of course, there's Bayes's theorem on conditional probabilities, which has nothing to do with interpretations or statistics but is a theorem that can be proven within the standard axiom system by Kolmogorov:
$$P(A|B) P(B) = P(B|A) P(A),$$
which is of course not the matter of any debate.

Bayes' formula is of course valid whether you are a Bayesian or a frequentist, but the difference is that the Bayesian associates probabilities with events that have never happened before, and so can make sense of any amount of data. So for the example we're discussing, there would be an a priori probability of snow, and an a priori probability of the weather forecaster being correct. With each day that the forecaster makes a prediction, and each day that it does or does not snow, those two probabilities are adjusted based on the data, according to Bayes' formula.

So Bayes' formula, together with a priori values for probabilities, allows the bayesian to make probabilistic statements based on whatever data is available.

I'm really unable to understand why there is such a hype about Qbism,

Well, I'm not defending Qbism. I was just talking about bayesian versus frequentist views of probability. As I said previous, I don't think that Qbism gives any new insight into the meaning of quantum mechanics, whether or not you believe in bayesian probability.

 

[JPBenowitz]

This is a contradiction in itself: If you assume a relativistic QFT to describe nature, by construction all measurable (physical) predictions are Poincare covariant, i.e., there's no way to distinguish one inertial frame from another by doing experiments within quantum theory. As Gaasbeek writes already in the abstract: The delayed-choice experiments can be described by standard quantum optics. Quantum optics is just an effective theory describing the behavior of the quantized electromagnetic field in interaction with macroscopic optical apparati in accordance with QED, the paradigmatic example of a relativistic QFT, and as such is Poincare covariant in the prediction about the observable outcomes, and quantum optics indeed is among the most precisely understood fields of relativistic quantum theory: All predictions are confirmed by high-accuracy experiments. So quantum theory cannot reintroduce an "aether" or however you like to call a "preferred reference frame" into physics! By construction QED and thus also quantum optics fulfills relativistic causality constraints too!

What if we use a scale-free network to describe a discrete quantum space time? Inertial frames would be indistinguishable by the scale-invariance imposed by a particular renormalization group. Of course I have no idea how you would experimentally verify this but it has been proposed.

 

[JPBenowitz]

If the wave function is a physical object, then is Hilbert Space a physical space? In other words if the wave function is a physical object then would this necessitate that quantum spacetime is an infinite dimensional complex vector space?

 

[atyy]

If the wave function is a physical object, then is Hilbert Space a physical space?

Yes.

 

[bhobba]

If the wave function is a physical object, then is Hilbert Space a physical space? In other words if the wave function is a physical object then would this necessitate that quantum spacetime is an infinite dimensional complex vector space?

Its easy to get caught in semantic 'nonsense' if you are not careful in how you use terms. Mathematical spaces like Hilbert space are not physical - they are a modelling tool of physical situations. When one uses QFT to give a quantum theory of gravity, space-time is then in a sense modeled by a Fock space - but since quantum gravity breaks down beyond a cut-off its quite likekly another model is a better choice - string theory maybe.

Thanks
Bill

 

[TrickyDicky]

You can go one better: Bayesian statistics allows us to have a probability for something with zero events. Of course, in that case, it's just a guess (although you can have a principled way of making such guesses). A single event provides a correction to your guess. More events provide better correction.
It doesn't tell you a lot, but it tells you something. If the forecast is for 99% chance of snow, and it doesn't snow, then (for a Bayesian), the confidence that the forecast is accurate will decline slightly. If for 100 days in a row, the weather service predicts 99% chance of snow, and it doesn't snow any of those days, then for the Bayesian, the confidence that the reports are accurate will decline smoothly each time. It would never decline to zero, because there's always a nonzero chance that that an accurate probabilistic prediction is wrong 100 times in a row, just like there is a nonzero chance that a fair coin will yield heads 100 times in a row.

The frequentist would (presumably) have some cutoff value for significance. The first few times that the weather report proves wrong, they would say that no conclusion can be drawn, since the sample size was so small. Then at some point, he would conclude that he had a large enough sample to make a decision, and would decide that the reports are wrong.

Note that both the Bayesian and the frequentist makes use of arbitrary parameters--the Bayesian has an arbitrary a priori notion of probability of events. The frequentist has an arbitrary cutoff for determining significance. The difference is that the Bayesian smoothly takes into account new data, while the frequentist withholds any judgement until some threshold amount of data, then makes a discontinuous decision.
Bayes' formula is of course valid whether you are a Bayesian or a frequentist, but the difference is that the Bayesian associates probabilities with events that have never happened before, and so can make sense of any amount of data. So for the example we're discussing, there would be an a priori probability of snow, and an a priori probability of the weather forecaster being correct. With each day that the forecaster makes a prediction, and each day that it does or does not snow, those two probabilities are adjusted based on the data, according to Bayes' formula.

So Bayes' formula, together with a priori values for probabilities, allows the bayesian to make probabilistic statements based on whatever data is available.
Well, I'm not defending Qbism. I was just talking about bayesian versus frequentist views of probability. As I said previous, I don't think that Qbism gives any new insight into the meaning of quantum mechanics, whether or not you believe in bayesian probability.

Maybe this discussion about frequentism versus Bayesianism can shed some light on the parallel discussion about collapse. Following the quoted post logic we could make compatible both absence and presence of collapse as two ways of introducing irreversibility(i.e. entropy thru probability and preparation or thru measurement-collapse) in the quantum theory, two ways of contemplating how probabilities are updated by measurements. Probably collapse is a rougher way of viewing it but it is a matter of taste. It all amounts to the same QM.

 

[vanhees71]

Hmmm, are we still disagreeing on this? Collapse is in Landau and Lifshitz, Cohen-Tannoudji, Diu and Laloe, Sakurai and Weinberg (and every other major text except Ballentine, whom I'm sure is wrong), so it really is quantum mechanics. To see that it is essential, take an EPR experiment in which Alice and Bob measure simultaneously. What is simultaneous in one frame will be sequential in another frame. As long as one has sequential measurements in which sub-ensembles are selected based on the measurement outcome, one needs collapse or an equivalent postulate.

We disagree in the one point that you say collapse is a necessary part of the quantum-theoretical formalism. I think it's superfluous and contradicts very fundamental physical principles, as pointed out by EPR. As far as I remember, Weinberg is undecided about the interpretation at the end of his very nice chapter on the issue. I think that the minimal statistical interpretation is everything we need to apply quantum theory to observable phenomena. Another question is whether you consider QT as a "complete theory". This was the main question, particularly Heisenberg was concerned about, and this gave rise to the Copenhagen doctrine, but as we see in our debates here on the forum, there's not even a clear definition, what the Copenhagen interpretation might be. That's why I prefer to label the interpretation I follow as the "minimal statistical interpretation". I think it's very close to the flavor of Copenhagen due to Bohr, although I'm not sure about what Bohr thinks with regard to the collapse. I don't agree with his hypothesis that there must be a "cut" between quantum and classical dynamics, because it cannot be defined. Classical behavior occurs due to decoherence and the necessity of coarse graining in defining relevant "macroscopic" observables but not from a cut at which quantum theory becomes invalid and classical dynamics takes over.

The "collapse" to my understanding is just the trivial thing that after I take notice of the result of a random experiment that then for this instance the before undetermined or unknown feature is decided. There's nothing happening in a physical sense. Nowadays most experiments take data, store them in a big computer file and then evaluate these outcomes much later. Would you say there's a collapse acting on things that are long gone, only because somebody makes some manipulation of data on a storage medium? Or has the collapse occurred when the readout electronics have provided the signal to be written on that medium? Again, I don't think that the collapse is necessary to use quantum theory as a probabilistic statement about the outcome of measurements with a given preparation (state) of the system.

 

[atyy]

We disagree in the one point that you say collapse is a necessary part of the quantum-theoretical formalism. I think it's superfluous and contradicts very fundamental physical principles, as pointed out by EPR. As far as I remember, Weinberg is undecided about the interpretation at the end of his very nice chapter on the issue. I think that the minimal statistical interpretation is everything we need to apply quantum theory to observable phenomena. Another question is whether you consider QT as a "complete theory". This was the main question, particularly Heisenberg was concerned about, and this gave rise to the Copenhagen doctrine, but as we see in our debates here on the forum, there's not even a clear definition, what the Copenhagen interpretation might be. That's why I prefer to label the interpretation I follow as the "minimal statistical interpretation". I think it's very close to the flavor of Copenhagen due to Bohr, although I'm not sure about what Bohr thinks with regard to the collapse. I don't agree with his hypothesis that there must be a "cut" between quantum and classical dynamics, because it cannot be defined. Classical behavior occurs due to decoherence and the necessity of coarse graining in defining relevant "macroscopic" observables but not from a cut at which quantum theory becomes invalid and classical dynamics takes over.

Weinberg is undecided about interpretation, and it is true that one can do without collapse provided one does not use Copenhagen or a correct version of the minimal statistical interpretation. For example, one can use the Bohmian interpretation, or try to use a Many-Worlds interpretation, both of which have no collapse. But it is not possible to use Copenhagen or a correct version of the minimal statistical interpretation without collapse (or equivalent assumption such as the equivalence of proper and improper mixtures). This is why most major texts (except Ballentine's erroneous chapter 9) include collapse, because the default interpretation is Copenhagen or the minimal statistical interpretation.

Peres argues that one can remove the cut and use coarse graining, but Peres is wrong because the coarse-grained theory in which the classical/quantum cut appears to be emergent yields predictions, but the fine grained theory does not make any predictions. So the coarse graining that Peres mentions introduces the classical/quantum cut in disguise. It is important that the cut does not say that we cannot enlarge the quantum domain and treat the classical apparatus in a quantum way. What the cut says is that if we do that, we need yet another classical apparatus in order for quantum theory to yield predictions.

Another way to see that the minimal statistical interpretation must have a classical/quantum cut and collaspe (or equivalent postulates) is that a minimal interpretation without these elements would solve the measurement problem, contrary to consensus that a minimal interpretation does not solve it.

The "collapse" to my understanding is just the trivial thing that after I take notice of the result of a random experiment that then for this instance the before undetermined or unknown feature is decided. There's nothing happening in a physical sense. Nowadays most experiments take data, store them in a big computer file and then evaluate these outcomes much later. Would you say there's a collapse acting on things that are long gone, only because somebody makes some manipulation of data on a storage medium? Or has the collapse occurred when the readout electronics have provided the signal to be written on that medium? Again, I don't think that the collapse is necessary to use quantum theory as a probabilistic statement about the outcome of measurements with a given preparation (state) of the system.

Collapse occurs immediately after the measurement. In a Bell test, the measurements are time stamped, so if you accept the time stamp, you accept that that is when the measurement happens, and not later after post-processing. It is ok not to accept the time stamp, because measurement is a subjective process. However, in such a case, there is no violation of the Bell inequalities at spacelike separation. If one accepts that quantum mechanics predicts a violation of the Bell inequalities at spacelike separation, then one does use the collapse postulate. It is important that at this stage we are not committing to collapse as a physical process, and leaving it open that it could be epistemic.

 

[bhobba]

We disagree in the one point that you say collapse is a necessary part of the quantum-theoretical formalism. I think it's superfluous and contradicts very fundamental physical principles, as pointed out by EPR.

So do I

Nowadays most experiments take data, store them in a big computer file and then evaluate these outcomes much later. Would you say there's a collapse acting on things that are long gone, only because somebody makes some manipulation of data on a storage medium? Or has the collapse occurred when the readout electronics have provided the signal to be written on that medium? Again, I don't think that the collapse is necessary to use quantum theory as a probabilistic statement about the outcome of measurements with a given preparation (state) of the system.

If you want collapse placing it just after decoherence would seem the logical choice. But I am with you - you don't need it.

Thanks
Bill

 

[vanhees71]

That's a good point: The state preparation in, e.g., a Stern-Gerlach experiments is through a von-Neumann filter measurement. You let run the particle through and inhomogeneous magnetic field, and this sorts the particles into regions of different $\sigma_z$ components (where $z$ is the direction of the homogeneous piece of the magnetic field). Then we block out all particles, not within the region of the desired value of $\sigma_z$.

Microscopically the shielding works simply as absorbers of the unwanted particles. One can see that there is no spontaneous collapse but simply local interactions of the particles with the shielding absorbing them and leaving the "wanted ones" through, because they are in a region, where there is no shielding. The absorption process is of course highly decoherent, it's described by local interactions and quantum dynamics. No extra "cut" or "collapse" needed.

 

[vanhees71]

Weinberg is undecided about interpretation, and it is true that one can do without collapse provided one does not use Copenhagen or a correct version of the minimal statistical interpretation. For example, one can use the Bohmian interpretation, or try to use a Many-Worlds interpretation, both of which have no collapse. But it is not possible to use Copenhagen or a correct version of the minimal statistical interpretation without collapse (or equivalent assumption such as the equivalence of proper and improper mixtures). This is why most major texts (except Ballentine's erroneous chapter 9) include collapse, because the default interpretation is Copenhagen or the minimal statistical interpretation.

Still there is no argument given, why you need the collapse. I don't understand, why one needs one within the minimal statistical interpretation. In no experiment, I'm aware of I need a collapse to use quantum theory to understand its outcome!

Peres argues that one can remove the cut and use coarse graining, but Peres is wrong because the coarse-grained theory in which the classical/quantum cut appears to be emergent yields predictions, but the fine grained theory does not make any predictions. So the coarse graining that Peres mentions introduces the classical/quantum cut in disguise. It is important that the cut does not say that we cannot enlarge the quantum domain and treat the classical apparatus in a quantum way. What the cut says is that if we do that, we need yet another classical apparatus in order for quantum theory to yield predictions.

Another way to see that the minimal statistical interpretation must have a classical/quantum cut and collaspe (or equivalent postulates) is that a minimal interpretation without these elements would solve the measurement problem, contrary to consensus that a minimal interpretation does not solve it.

Collapse occurs immediately after the measurement. In a Bell test, the measurements are time stamped, so if you accept the time stamp, you accept that that is when the measurement happens, and not later after post-processing. It is ok not to accept the time stamp, because measurement is a subjective process. However, in such a case, there is no violation of the Bell inequalities at spacelike separation. If one accepts that quantum mechanics predicts a violation of the Bell inequalities at spacelike separation, then one does use the collapse postulate. It is important that at this stage we are not committing to collapse as a physical process, and leaving it open that it could be epistemic.

Where do you need a collapse here either? A+B use a polarization foil and photon detectors to figure out whether their respective photon run through the polarization foil or not, which practically ideally let's through only photons with a determined linear-polarization state; the other photons are absorbed, which is through local interactions of the respective photon with the foil and there is no long-distance interaction between A's foil with B's photon and vice versa. So there cannot be any collapse as in the Copenhagen interpretation (Heisenberg flavor I think?). So there cannot be a collapse at the level of the polarizers. The same argument holds for the photo detectors. Also note that the time stamps are accurate but always of finite resolution, i.e., the registration of a photon is a fast but not instantaneous process. On a macroscopic scale of resoulution, it's of course a "sharp time stamp". The photo detector is applicable for these experiments if the accuracy of the time-stamps is sufficient to unanimously ensure that you can relate the entangled photon pairs. For a long enough distance between the photon source and A's and B's detectors and low enough photon rates, that's no problem. Again, nowhere do I need a collapse.

Bohr was of course right in saying, that finally we deal with macroscopic preparation/measurement instruments, but in my opinion he was wrong that one needs a cut between quantum and classical dynamics anywhere, because the classical behavior of macroscopic objects are (at least FAPP :-)) an emergent phenomenon and clearly understandable via coarse graining.

I also must admit that I consider Asher Peres's book as one of the best, when it comes to the foundational questions of quantum theory. Alone his definition of quantum states as preparation procedures eliminate a lot of esoterics often invoked to solve the "measurement problem". FAPP there is no measurement problem as the successful description of even the "weirdest" quantum behavior of nature shows!

 

[atyy]

That's a good point: The state preparation in, e.g., a Stern-Gerlach experiments is through a von-Neumann filter measurement. You let run the particle through and inhomogeneous magnetic field, and this sorts the particles into regions of different $\sigma_z$ components (where $z$ is the direction of the homogeneous piece of the magnetic field). Then we block out all particles, not within the region of the desired value of $\sigma_z$.

Microscopically the shielding works simply as absorbers of the unwanted particles. One can see that there is no spontaneous collapse but simply local interactions of the particles with the shielding absorbing them and leaving the "wanted ones" through, because they are in a region, where there is no shielding. The absorption process is of course highly decoherent, it's described by local interactions and quantum dynamics. No extra "cut" or "collapse" needed.

It won't work. The state of the selected subsystem is a pure state. If you write the entire decoherent dynamics and take the reduced density matrix corresponding to the selected subsystem, you will get a mixed state.

 

[atyy]

Where do you need a collapse here either? A+B use a polarization foil and photon detectors to figure out whether their respective photon run through the polarization foil or not, which practically ideally let's through only photons with a determined linear-polarization state; the other photons are absorbed, which is through local interactions of the respective photon with the foil and there is no long-distance interaction between A's foil with B's photon and vice versa. So there cannot be any collapse as in the Copenhagen interpretation (Heisenberg flavor I think?). So there cannot be a collapse at the level of the polarizers. The same argument holds for the photo detectors. Also note that the time stamps are accurate but always of finite resolution, i.e., the registration of a photon is a fast but not instantaneous process. On a macroscopic scale of resoulution, it's of course a "sharp time stamp". The photo detector is applicable for these experiments if the accuracy of the time-stamps is sufficient to unanimously ensure that you can relate the entangled photon pairs. For a long enough distance between the photon source and A's and B's detectors and low enough photon rates, that's no problem. Again, nowhere do I need a collapse.

Let's start with particles in a Bell state. Do the particles remain entangled after A has made a measurement?

Bohr was of course right in saying, that finally we deal with macroscopic preparation/measurement instruments, but in my opinion he was wrong that one needs a cut between quantum and classical dynamics anywhere, because the classical behavior of macroscopic objects are (at least FAPP :) ) an emergent phenomenon and clearly understandable via coarse graining.

I also must admit that I consider Asher Peres's book as one of the best, when it comes to the foundational questions of quantum theory. Alone his definition of quantum states as preparation procedures eliminate a lot of esoterics often invoked to solve the "measurement problem". FAPP there is no measurement problem as the successful description of even the "weirdest" quantum behavior of nature shows!

If you use FAPP, then you do use a cut. The whole point of the cut and collapse is FAPP. Removing the cut and collapse are not FAPP, and would solve the measurement problem.

 

[bhobba]

Let's start with particles in a Bell state. Do the particles remain entangled after A has made a measurement?.

No - it's now entangled with the measurement apparatus. But I don't think that's what is meant by collapse.

I think the Wikipedia article on collapse is not too bad:
http://en.wikipedia.org/wiki/Wave_function_collapse
'Wave function collapse is not fundamental from the perspective of quantum decoherence. There are several equivalent approaches to deriving collapse, like the density matrix approach, but each has the same effect: decoherence irreversibly converts the "averaged" or "environmentally traced over" density matrix from a pure state to a reduced mixture, giving the appearance of wave function collapse.'

In the ensemble interpretation one assumes an observation selects an outcome from the conceptual ensemble associated with the mixed state after decoherence - no collapse required. There is the issue about exactly how that particular outcome is selected (the problem of outcomes) - but that doesn't mean the interpretation is invalidated or collapse occurred - it simply means that's a postulate.

Thanks
Bill

 

[atyy]

No - it's now entangled with the measurement apparatus. But I don't think that's what is meant by collapse.

Do you have a definite outcome yet?

At some point you will invoke that an improper mixture becomes a proper mixture. When you do that, you are using collapse.

 

[bhobba]

At some point you will invoke that an improper mixture becomes a proper mixture. When you do that, you are using collapse.

In the ensemble interpretation that is subsumed in the assumption an observation selects an outcome from a conceptual ensemble. Collapse is bypassed.

Thanks
Bill

 

[atyy]

In the ensemble interpretation that is subsumed in the assumption an observation selects an outcome from a conceptual ensemble. Collapse is bypassed.

If you have a conceptual ensemble, that is conceptual hidden variables.

 

[bhobba]

If you have a conceptual ensemble, that is conceptual hidden variables.

Its exactly the same ensemble used in probability. I think you would get a strange look from a probability professor if you claimed such a pictorial aid was a hidden variable.

Atty I think we need to be precise what is meant by collapse. Can you describe in your own words what you think collapse is?

My view is its the idea observation instantaneously changes a quantum state in opposition to unitary evolution. Certainly it changes in filtering type observations - but instantaneously - to me that's the rub. It changed because you have prepared the system differently but not by some mystical non local instantaneous 'collapse' - if you have states - you have different preparations - its that easy.

Added Later:
As the Wikipedia artice says:
On the other hand, the collapse is considered a redundant or optional approximation in:
the Consistent histories approach, self-dubbed "Copenhagen done right"
the Bohm interpretation
the Many-worlds interpretation
the Ensemble Interpretation

IMHO it's redundant in the above.

Thanks
Bill

 

[vanhees71]

Let's start with particles in a Bell state. Do the particles remain entangled after A has made a measurement?

No, they are disentangled due to the (local!) interaction of A's photon with the polarizer and photon detector. Usually it gets absorbed by the latter, and there's only B's photon left as long as his is not absorbed by his detector either.

If you use FAPP, then you do use a cut. The whole point of the cut and collapse is FAPP. Removing the cut and collapse are not FAPP, and would solve the measurement problem.

If you define this as cut, it's fine with me, but this doesn't say that there is a disinguished classical dynamics in addition to quantum dynamics.

 

[stevendaryl]

I go back and forth about whether I consider "collapse" an essential part of quantum mechanics or not. There is an operational sense in which "collapse" describes quantum mechanical practice: If you prepare a system in state |\psi\rangle, and then later perform a measurement corresponding to observable O and get value o, then afterward, you use the reduced state: |\psi'\rangle, which is the result of projecting |\psi\rangle (actually e^{-\frac{i}{\hbar} H t} |\psi\rangle) onto the space of eigenfunctions of O with eigenvalue o. That's part of the standard recipe for using quantum mechanics, and I don't think that there is any disagreement that this recipe "works" in the sense of allowing us to make predictions that agree with experiment.The disagreement is about what is the physical interpretation of this step of the quantum recipe.

If you view the state of a system as purely epistemic, it just reflects your knowledge about the system, then there is nothing physical going on with such a collapse, it's just an update to your knowledge.

The sense in which all you need is the minimal statistical interpretation is this: At the end, after you've done all your measurements and performed all your experiments with the system, you have a history of measurements. The minimal interpretation tells you the probability for each such history, given the initial state. The "collapse" that seemed to happen at each measurement can be understood, retroactively, as simply the application of ordinary conditional probabilities. So rather than having a "collapse" at every measurement event, one can get the same results by putting the collapse at the very end, after all the measurements were made.

But it still seems to me that you need at least one sort of "collapse" even in the minimal interpretation: The transition from probability amplitudes for many possible histories to a single history that is actually recorded. That's a kind of collapse.