Ballentine's Ensemble Interpretation Of QM

[atyy]

I don't understand. Why should it have "teeth" against something which it doesn't oppose?

If we try an interpretation in which the wave function is everything, yet applies only to ensembles, we obtain a contradiction because we still need classical apparatus to perform measurements and cause state vector reduction. The existence of classical apparatus as fundamental in the ensemble interpretation prevents the wave function from being everything.

 

[vanhees71]

If dBB stands for de Broglie-Bohm, I disagree with the statement that it is a flavor of the ensemble interpretation, because it adds "trajectories" to the quantum-mechanical particle description in a fancy non-local way. However, this doesn't add anything to observable predictions compared to quantum theory in the other interpretations that just take the probabilistic view (particularly of course the minimal statistical interpretation).

On top, as far as I know, there is no proper de Broglie-Bohm interpretation for relativistic quantum-field theory. So I don't see any merit of the de Broglie-Bohm interpretation compared to the minimally interpreted QT but a lot of additional trouble introduced.

I've also seen that there are statements about the incompatibility of the minimal statistical interpretation with the (in my opinion clearly observed) quantum-Zeno effect. In interpretations with a collapse, the effect is explained that whenever an observable is measured, the system right after the measurement necessarily "collapses" to an eigenstate of the corresponding self-adjoint operator (which one in the case of degeneracy is determined by the state immediately before the measurement by the projection postulate of the collapse interpretation).

I don't think that this is a valid contradiction to the ensemble interpretation, because the collapse description is just an effective hand-waving way to describe the dynamics between the measurement apparatus and the measured system. There are papers on this that show that you can explain the quantum Zeno effect without taking recurse to the collapse assumption. It's explained by the standard quantum dynamics with time-dependent interaction Hamiltonians between the measured system and the measurement apparatus, e.g.,

Dynamical quantum Zeno effect
S Pascazio, M Namiki
PRA 50, 4582 (1994)
http://pra.aps.org/abstract/PRA/v50/i6/p4582_1

 

[atyy]

I've also seen that there are statements about the incompatibility of the minimal statistical interpretation with the (in my opinion clearly observed) quantum-Zeno effect.

I don't think so either. The question is not whether a correct ensemble interpretation exists with quantum Zeno effect, but whether Ballentine's 1998 exposition of the quantum Zeno effect with regards to the ensemble and Copenhagen interpretations is correct.

I don't think that this is a valid contradiction to the ensemble interpretation, because the collapse description is just an effective hand-waving way to describe the dynamics between the measurement apparatus and the measured system. There are papers on this that show that you can explain the quantum Zeno effect without taking recurse to the collapse assumption. It's explained by the standard quantum dynamics with time-dependent interaction Hamiltonians between the measured system and the measurement apparatus, e.g.,

Dynamical quantum Zeno effect
S Pascazio, M Namiki
PRA 50, 4582 (1994)
http://pra.aps.org/abstract/PRA/v50/i6/p4582_1

Yes, this is available also in Copenhagen, it just depends on how much of the universe one explicitly includes in the Hamiltonian. But in Copenhagen both explanations are correct. Does the ensemble interpretation really not allow wave packet reduction (defined within the ensemble interpretation) as the explanation? As I understand, the ensemble interpretation still has state vector reduction, and if everything (Hamiltonian, state, state vector reduction) applies to ensembles, shouldn't what is acceptable in Copenhagen just carry over to the ensemble interpretation?

 

[bohm2]

Actually, isn't the wave function real in dBB? For example, http://arxiv.org/abs/0706.2661 classifies the wave function as real but incomplete in dBB.

From my understanding there are at least 4-5 different varieties of BM with respect to the ontology of the wave function.

1. Durr/Goldstein/Zhingo/Maudlin: wave function is kind of "real" as it is nomological (a law of nature).
2. Valentini: wave function is a non-local field
3. Bohm/Hiley: wave function is an informational field that guides the particle?
4. David Albert: there is just a single 3N-dimensional wavefunction, and the division of reality into separate three-dimensional objects, including organisms, is just the product of our internal representation. Thus, for Albert objects exist as single points, evolving one way or another in this very high-dimensional space.

 

[kith]

If we try an interpretation in which the wave function is everything, yet applies only to ensembles, we obtain a contradiction because we still need classical apparatus to perform measurements and cause state vector reduction.

Why do we need state vector reduction if our description isn't about single runs of the experiment?

 

[stevendaryl]

If dBB stands for de Broglie-Bohm, I disagree with the statement that it is a flavor of the ensemble interpretation, because it adds "trajectories" to the quantum-mechanical particle description in a fancy non-local way.

I don't think that means it can't be a variety of the ensemble interpretation. The point of an ensemble approach (as I understand it) is to describe the statistics of an ensemble of systems that have the same macroscopic description (in terms of preparation). It doesn't rule out the possibility that there might be a more fine-grained description of what's going on for a single system, it's just agnostic about it.

 

[atyy]

An interesting treatment of the quantum Zeno effect may be that in Berthold-Georg Englert's http://books.google.com/books?id=OnSiIpIxorgC&source=gbs_navlinks_s (p32). Englert seems to hold a version of the ensemble interpretation in that book, as well as http://arxiv.org/abs/1308.5290 , yet describes the quantum Zeno effect as being due to control measurements.

 

[TrickyDicky]

Already the interpretation of the Heisenberg uncertainty relation is, as discussed in this forum, at least questionable.

Is there really a standard interpretation of the hup as discussed in this forum? (I assume you mean this PF quantum physics forum)

 

[atyy]

Why do we need state vector reduction if our description isn't about single runs of the experiment?

Take an ensemble and make a measurement. Then let it evolve and make another measurement.

Don't you need state vector reduction to handle this case?

 

[kith]

Take an ensemble and make a measurement. Then let it evolve and make another measurement. Don't you need state vector reduction to handle this case?

No, you would get wrong predictions. The ensemble is not in an eigenstate after the first experiment because you have measured different values in different runs. In order to get an eigenstate you have to filter the ensemble which means you have to implement a projective (unitary) time evolution.

 

[atyy]

No, you would get wrong predictions. The ensemble is not in an eigenstate after the first experiment because you have measured different values in different runs. In order to get an eigenstate you have to filter the ensemble which means you have to implement a projective (unitary) time evolution.

So is it the case that state vector reduction in the ensemble interpretation is not merely wave function collapse of Copenhagen, just renamed and reinterpreted? At least from a naive view of the wave function as one's subjective information, it would seem that something like state vector reduction should occur as an analogy to Bayesian updating.

 

[bhobba]

dBB could be viewed as underlying the ensemble interpretation.

That's true - but only if you want to hold to the much more natural view that what you observe is there prior to observation and the ensemble is independent of the actual observation. You need something like DBB, Nelson Stochastics or Primary State Diffusion to underlie it for that. The advantage over those interpretations is you can leave it up in the air exactly how its done - its just done - somehow.

That's why I hold to the ignorance ensemble interpretation with decoherence. It APPEARS to be like that - it isn't really like that - but you can hold to the fiction it is, and if anyone 'calls your bluff' so to speak you can say - observationaly its exactly the same - but really it isn't.

As the link I am won't to give on decoherence and the measurement problem states, decoherence does not touch the central issue (generally called the problem of outcomes) so does not solve the measurement problem. That's true - but what I would add is that's not really the claim of decpherence enthusiasts like myself - its that it APPEARS to solve the issue.

Thanks
Bill

 

[kith]

So is it the case that state vector reduction in the ensemble interpretation is not merely wave function collapse of Copenhagen, just renamed and reinterpreted?

State vector reduction and collapse are two names for the same thing. They refer to the "reduction" of a superposition to an eigenstate in a single run of the experiment. They are not part of the ensemble interpretation because individual outcomes are not associated with states there.

 

[atyy]

And is wave function collapse really not needed in the Ensemble interpretation? Isn't there also state vector reduction?

Yes, you have state vector reduction. However, if you do not consider the wave function as real, you also do not need to interpret state vector reduction as collapse.

State vector reduction and collapse are two names for the same thing. They refer to the "reduction" of a superposition to an eigenstate in a single run of the experiment. They are not part of the ensemble interpretation because individual outcomes are not associated with states there.

I see your point, but I think Cthugha said the opposite when he replied to me above.

 

[kith]

I see your point, but I think Cthugha said the opposite when he replied to me above.

Cthugha seems to use "state vector reduction" if we consider the wave function to be only a calculation tool and "collapse" if we are realistic about it. I agree that this distinction could be made but I don't agree that any of these notions is used in the ensemble interpretation.

 

[atyy]

Cthugha seems to use "state vector reduction" if we consider the wave function to be only a calculation tool and "collapse" if we are realistic about it. I agree that this distinction could be made but I don't agree that any of these notions is used in the ensemble interpretation.

That's interesting. I wonder whose version of the ensemble interpretation Cthugha is using. I looked briefly at Ballentine, and he really doesn't seems to have it.

But if there is no collapse, how is filtering possible as a method of state preparation?

 

[Cthugha]

Sorry, if I was misleading. There are two ways of how state vector reduction can enter.

One way is found when you consider the wave function as real and perform some measurement. Here state vector reduction is another name for collapse.

The second way is found, when one performs a conditional measurement, so you pick a subensemble out of a full ensemble. This can be referred to as state reduction, though I admit that there are people out there who find this terminology unacceptable and would insist that one should pick a different name and state reduction is reserved for changes due to the results of single measurements.

State reduction in the sense of collapse does not exist in the ensemble interpretation. Also, please note that I am personally not really adhering to the ensemble interpretation.

 

[strangerep]

But if there is no collapse, how is filtering possible as a method of state preparation?

Maybe take another look through Ballentine's chapters 8 and 9?

 

[atyy]

Maybe take another look through Ballentine's chapters 8 and 9?

OK, I will. But let me just make sure I understand you are disagreeing Cthugha's statement (ie. it's not just that I used the term "collapse" instead of "state reduction"):

The second way is found, when one performs a conditional measurement, so you pick a subensemble out of a full ensemble. This can be referred to as state reduction, though I admit that there are people out there who find this terminology unacceptable and would insist that one should pick a different name and state reduction is reserved for changes due to the results of single measurements.

 

[Ken G]

well, nonlinear quantum mechanics make different predictions than standard quantum mechanics (a linear one), then is another model.

Yes, one important service that the various interpretations could provide is guidance toward the next theory. Here we would have to let nature adjudicate what works, so there would be no purpose in "preferring" one interpretation over another, except for personal guidance in our own efforts to find the next theory if we were ambitious enough to try. A key role of theory is not just to explain what we've already seen, but also to help us know what we might want to look for next. I think that's the place where the interpretations have the most value, and who knows which one will be the most helpful there. Thus we see both the advantages and disadvantages of a "minimal" interpretation like the ensemble approach-- it keeps us from going too far out on a limb, but it also provides minimal opportunity to jump to the next branch.

 

[Demystifier]

On top, as far as I know, there is no proper de Broglie-Bohm interpretation for relativistic quantum-field theory.

http://lanl.arxiv.org/abs/0904.2287 [Int. J. Mod. Phys. A25:1477-1505, 2010]

 

[vanhees71]

Yes, this is available also in Copenhagen, it just depends on how much of the universe one explicitly includes in the Hamiltonian. But in Copenhagen both explanations are correct. Does the ensemble interpretation really not allow wave packet reduction (defined within the ensemble interpretation) as the explanation? As I understand, the ensemble interpretation still has state vector reduction, and if everything (Hamiltonian, state, state vector reduction) applies to ensembles, shouldn't what is acceptable in Copenhagen just carry over to the ensemble interpretation?

The problem is that there is no clear definition of what's "the" Copenhagen interpretation. For me the difference to the ensemble interpretation is pretty small. The only difference is that within the Copenhagen interpretation the state (represented by a statistical operator) is taken as a real object, i.e., it is assiciated to, e.g., a single particle. Then, however the collapse assumption is nearly unavoidable, because if you find a certain value for an observable and you assume that then the single system has to take this value with certainty when measuared again immediately after the first measurement, you must assume that the state has changed to a pure state represented by a (normalized) eigenvector of this observable to the measured eigenvalue. More concretely, the standard Copenhagen interpretation determines this vector by the projection postulate
|\psi \rangle=N \sum_{\beta} |a,\beta \rangle \langle a,\beta|\hat{\rho}|a,\beta \rangle,
where the parameter(s) \beta in the orthonormal basis of eigenvectors |a,\beta \rangle to the measured eigenvalue a of the observable A.
That's so, because an observable has only a determined value if the system is in an eigenstate of the measured observable.

In the ensemble interpretation you don't need this collapse as the result of the measurement, because the state does not represent the single particle (or more general system) but an ensemble of equally prepared particles (or systems). Thus the state does not need to collapse necessarily to an eigenstate in the way of a non-unitary time evolution describing a single system.

Within the ensemble interpretation, If you decide to filter out a subensemble according to the measurement of the observable (provided your measurement process admits such a filtering), then you simply get a new (in general smaller) ensemble of particles (or systems) described by the corresponding eigenstate as in the Copenhagen interpretation.

E.g., in a properly built Stern-Gerlach apparatus, out of an ensemble of arbitrarily prepared particles, you get clearly separated particle beams which almost certainly sort the different spin states. If you simply dump all particles in all these beams except one, you have prepared an ensemble with particles with a certain spin state. Up to the "dumping" of the particles you can describe the Stern-Gerlach apparatus by solving the Schrödinger equations for particles with spin in an inhomogeneous magnetic field, i.e., by the usual unitary time evolution.

In this sense there is only very little formal difference between the Copenhagen and the no-collapse interpretation. The difference is more philosophical, whether you interpret the state as a real physical object associated with a single system (Copenhagen a la Heisenberg) or as a mathematical description of an ensemble of particles (Ensemble Interpretation).

 

[bohm2]

Yes, one important service that the various interpretations could provide is guidance toward the next theory. I think that's the place where the interpretations have the most value, and who knows which one will be the most helpful there. Thus we see both the advantages and disadvantages of a "minimal" interpretation like the ensemble approach-- it keeps us from going too far out on a limb, but it also provides minimal opportunity to jump to the next branch.

Good point. Previously, I thought that no-go theorems may help us in this direction by eliminating certain interpretations but I've become more sceptical lately because it seems that one can always question some of the assumptions of most, if not all these no-go theorems. Perhaps, the only way out of this stagnation will be to test models that make different predictions than QM. There are a few such models but experiments aren't yet feasible.

 

[atyy]

Within the ensemble interpretation, If you decide to filter out a subensemble according to the measurement of the observable (provided your measurement process admits such a filtering), then you simply get a new (in general smaller) ensemble of particles (or systems) described by the corresponding eigenstate as in the Copenhagen interpretation.

E.g., in a properly built Stern-Gerlach apparatus, out of an ensemble of arbitrarily prepared particles, you get clearly separated particle beams which almost certainly sort the different spin states. If you simply dump all particles in all these beams except one, you have prepared an ensemble with particles with a certain spin state. Up to the "dumping" of the particles you can describe the Stern-Gerlach apparatus by solving the Schrödinger equations for particles with spin in an inhomogeneous magnetic field, i.e., by the usual unitary time evolution.

In this sense there is only very little formal difference between the Copenhagen and the no-collapse interpretation. The difference is more philosophical, whether you interpret the state as a real physical object associated with a single system (Copenhagen a la Heisenberg) or as a mathematical description of an ensemble of particles (Ensemble Interpretation).

Would you agree with Cthugha that in the ensemble interpretation this filtering can be called "state reduction"?

The second way is found, when one performs a conditional measurement, so you pick a subensemble out of a full ensemble. This can be referred to as state reduction, though I admit that there are people out there who find this terminology unacceptable and would insist that one should pick a different name and state reduction is reserved for changes due to the results of single measurements.

(Excerpted from Cthugha's post #267)

 

[Ken G]

Perhaps, the only way out of this stagnation will be to test models that make different predictions than QM. There are a few such models but experiments aren't yet feasible.

Yes, and by suggesting such experiments, we find the greatest value of the interpretations, if only we could find one that can actually be done! As we've seen on this thread, sometimes there is an experiment interpreted as being contrary to an interpretation, but it usually just means the interpretation itself is being misrepresented. The experiment is not a winner until it obtains a result that the current formalism of quantum mechanics would not have predicted.

 

[Cthugha]

Would you agree with Cthugha that in the ensemble interpretation this filtering can be called "state reduction"?

Let me clarify a bit what I was intending to say. In chapter 9.5 (page 243 in my edition) Ballentine discusses a neutron spectrometer subject to fluctuations. Here he agrees that the "reduced" state has physical significance under some circumstances, but should be considered as a phenomenological description of the environment on a system, where the environment has been left out of the definition of the system for convenience. He then argues that one may also include the environment in the definition of the system directly, thereby avoiding this apparent reduction.

This is of course correct. It isalso not really different from simplistic collapse interpretations. In those (at least in most), the collapse also describes some external impact on some system, usually via some external detector outside of the system. However, one may also choose to describe a larger system including the detector. This whole system now is in a superposition state and you need another external detector to collapse the new system. You can continue this chain until you reach the wave function of the universe which cannot be collapsed as there is nothing outside of the system.

This is somewhat in line with information-theory-like interpretations where state reduction is an update about our subjective knowledge of the system.

 

[atyy]

Let me clarify a bit what I was intending to say. In chapter 9.5 (page 243 in my edition) Ballentine discusses a neutron spectrometer subject to fluctuations. Here he agrees that the "reduced" state has physical significance under some circumstances, but should be considered as a phenomenological description of the environment on a system, where the environment has been left out of the definition of the system for convenience. He then argues that one may also include the environment in the definition of the system directly, thereby avoiding this apparent reduction.

This is of course correct. It isalso not really different from simplistic collapse interpretations. In those (at least in most), the collapse also describes some external impact on some system, usually via some external detector outside of the system. However, one may also choose to describe a larger system including the detector. This whole system now is in a superposition state and you need another external detector to collapse the new system. You can continue this chain until you reach the wave function of the universe which cannot be collapsed as there is nothing outside of the system.

This is somewhat in line with information-theory-like interpretations where state reduction is an update about our subjective knowledge of the system.

Is Ballentine's description of the neutron interferometer correct? I don't have access to Summhammer (1982), but a couple of other things which seem pretty close describe the first element as something like a beam splitter, in contrast to Ballentine's description of the first element as something that according to Copenhagen would do a measurement, ie. is his claim that Copenhagen would use Eq 9.18 a strawman?
http://www.users.csbsju.edu/~frioux/q-intro/NeutronInterferometry.pdf
http://www.ncnr.nist.gov/summerschool/ss09/pdf/Wietfeldt_FP09.pdf
https://www.univie.ac.at/physikwiki/images/0/06/Neutron_Interferometry.pdf

 

[Sugdub]

... For me the difference to the ensemble interpretation is pretty small. The only difference is that within the Copenhagen interpretation the state (represented by a statistical operator) is taken as a real object, i.e., it is assiciated to, e.g., a single particle. Then, however the collapse assumption is nearly unavoidable, because if you find a certain value for an observable and you assume that then the single system has to take this value with certainty when measuared again immediately after the first measurement, you must assume that the state has changed to a pure state represented by a (normalized) eigenvector of this observable to the measured eigenvalue. ...
...The difference is more philosophical, whether you interpret the state as a real physical object associated with a single system (Copenhagen a la Heisenberg) or as a mathematical description of an ensemble of particles (Ensemble Interpretation).

I think this “nearly unavoidable” conclusion is essentially triggered by a different hypothesis than the association of the state vector to one single particle. In particular one must assume that in the experiment B involving two consecutive filters, the state vector has a definite value at the entrance of the first filter, namely the value that was measured in the experimental context A involving only the first filter (before the “dump” of all beams except one), and another value at the entrance of the second filter. There is of course no empirical evidence for the state vector taking two values (would they be equal) at different places inside the same experimental device B.

The assumption above derives in turn from another assumption whereby the experimental device can be split in two parts which respectively “prepare” a physical state and “measure” that physical state, in other words whereby the state is “available” for observation at a specific location inside the device, at the entrance of the measurement apparatus. It is then a property of a subset only of the overall device (the preparation). Again there is no empirical evidence for this.

Indeed the ensemble interpretation assigns the state vector to the ensemble of particles better than to each of them, this state being “available” for observation at the entrance of the measurement device. But in the Copenhagen view the measurement process of the state is equally fractioned over a series of discrete observations, none of which can be considered as a “measurement”: all discrete observations contribute to the statistical measurement process (actually the measurement apparatus, a set of “counters”, would it be human or material, is external to the device as described by physicists). The difference between the Ensemble- and the Copenhagen- interpretations does not seem significant since in both cases the outcome of the measurement process holds at a certain location inside the experimental device. So ultimately I don't understand how the Ensemble-interpretation can claim avoiding the "measurement problem".
Overall, I think the real trigger for the emergence of the state vector collapse (between the entrances of the first and the second filters) is the assumption that the state vector is assigned to a certain location inside the experimental device, therefore it can take different values at different locations. It is not specifically due to the assignment of the state vector to one single iteration, to “something” uniquely produced by each iteration.
Thanks.

 

[Ken G]

To preserve the ensemble interpretation, I'm not sure you want to break your measuring apparatus into multiple separate pieces. Instead, just think of it as a single apparatus that is capable of testing correlations on the ensemble. In other words, if you have two Stern-Gerlach apparatus lined up the same way, you expect the beam that emerges from the top of the first to all go the same way through the second, and similarly for the beam that emerges from the bottom. But rather than thinking of this as measuring or preparing the spins in two separate sub-encounters within the apparatus, simply think of it as a mechanism for generating outcomes like "up-up", "down-down", "up-down", and "down-up", and note that quantum mechanics predicts the ensemble expectation values of "up-down" and "down-up" are both zero.

So it's still an ensemble expectation value, and it still corresponds to a single apparatus, it just affords a higher level of information because it includes ensemble correlations. We still treat the entire apparatus as a single measurement, and we never have to ask if the spin was "collapsed" in any individual instance in the middle of the apparatus, because all we are trying to get is the likelihood of the 4 possible outcomes, over the conceptual ensemble that represents whatever was the preparation incident to the apparatus. The analog of the CI collapse is simply that up-down and down-up results never happen. The CI interprets collapse because it holds that each particle has a spin in the middle (and end) of the experiment, but that is not actually tested by that apparatus, only the expectation values of the instrumental outcomes.

Still, I see this as very CI-like, because to me the defining feature of CI is not collapse, it is the commitment to the idea that physics is represented by outcomes of classical devices. This is why I do see an essential role for the observer, because when Bohr says "there is no quantum world," what I believe he means is that physics is done by the physicist, and the physicist does not inhabit any quantum world. Given this, it would be unnatural to hold that collapse, as an assertion of the state of a quantum system, is the key aspect of the CI, if the CI is held to be Bohr's distrust in any such thing as a quantum system!

 

[TrickyDicky]

From the link I referenced:


"A fact beyond doubt, confirmed by numerous experiments and accepted by supporters of all interpretations, is that the predictions of QT are probabilities.
...The fact that probabilities are predictions concerning statistical ensembles and cannot be used to make predictions on single events is not a consequence of the specific structure of QT. Rather it is true on very general grounds - by definition of the term probability.
Thus, starting from a simple analysis of the physical structure of QT we arrive immediately at a very important conclusion concerning the range of validity of the theory, namely that QT is not a theory about single particles.
If, on the other hand, we postulate - as in the CI - for metaphysical reasons that QT is a theory about single particles, we are faced with the difficult task to understand how a probabilistic theory can be a ’complete’ theory for single particles . This ’problem’ has been called ’the measurement problem’ and had to be invented eighty years ago, simultaneously with the completeness postulate of the CI . It is, not unexpectedly for many physicists, still unsolved and will remain unsolved forever because it represents a contradiction to the formalism of the QT."
Agree about this distinction of ensemble vs CI?

 

[audioloop]

http://lanl.arxiv.org/abs/0904.2287 [Int. J. Mod. Phys. A25:1477-1505, 2010]

and

http://arxiv.org/pdf/1307.1714v1.pdf

Yes, one important service that the various interpretations could provide is guidance toward the next theory. Here we would have to let nature adjudicate what works, so there would be no purpose in "preferring" one interpretation over another, except for personal guidance in our own efforts to find the next theory if we were ambitious enough to try. A key role of theory is not just to explain what we've already seen, but also to help us know what we might want to look for next. I think that's the place where the interpretations have the most value, and who knows which one will be the most helpful there. Thus we see both the advantages and disadvantages of a "minimal" interpretation like the ensemble approach-- it keeps us from going too far out on a limb, but it also provides minimal opportunity to jump to the next branch.

indeed. soon i think.

 

[bhobba]

Guys - yes this discussion of CI is interesting.

However in most versions of Copenhagen, as far as I can tell anyway, while the state can be applied to a single system, it only represents a state of knowledge, simply a theoretical construct indicating a theorists 'confidence' in a particular observation outcome (when combined with an observable via the Born rule of course). Copenhagen also believes it gives a full and exhaustive description of that single system. It is of zero concern if such discontinuously changes, collapses or whatever terminology you want to use. Ballentine's arguments in Chapter 9 only apply if you think its in some sense real - and indeed interpretations where it is has issues with it. But if you don't think it real then there is no problem.

Thanks
Bill

 

[atyy]

Maybe take another look through Ballentine's chapters 8 and 9?

Does he introduce state reduction in Eq 9.28? Or is 9.28 derived, even in the case where R and S don't commute?

 

[Ken G]

Copenhagen also believes it gives a full and exhaustive description of that single system.

It is certainly true that there are "flavors" of CI, but I tend to let Bohr be its primary spokesperson, as opposed to, say, Heisenberg, and if we do that, then CI would probably rather say that the wave function gives an exhaustive description of the meeting of a single system and a macro instrument. In other words, "collapse" is not so much an effect on the quantum system carried out by the macro instrument (the quantum system has only a kind of inscrutable existence in CI in the first place), it is more like an effect on the macro instrument mediated by the quantum system. Collapse in CI is the only glimpse of the quantum world you ever get, and since it is seen through a glass darkly, we don't claim to have "really seen" the quantum world at all. Indeed, Bohr doesn't think we can even claim existence for that quantum world, we see it so dimly. So I don't think we can say that CI treats collapse as a real effect on the quantum world-- more like a real effect on a classically understood apparatus. You might even say collapse is a side effect of the means we choose to do science.

 

[kye]

Contemplating on all this, you guys didn't put emphasis on interference between the ensembles. Even though you view them as statistics, they have perfect interference.. in the one at a time electron or photon double slit experiment, each electron doesn't just appear in the screen randomly.. but they avoided the destructive interference zones.. so this gets us back to the position that particles are also wave. And force us back into the single experiment setup. The ensemble interpretation is easier to take if there is no interference, mathematically if what we see are all mixed states... but in pure states, there is interference, it's like throwing coins randomly at the floor and the ensembles form interference... so how does the individual coin knows where to avoid. This force us to see the coin as behaving as wave too. So is a coin particle or wave. In Heisenberg potentia. He conjectured that before measurement, the quantum state is literally a vector in Hilbert Space. I guess this is the essence of strong Copenhagen because if you still think superposition is due to the state b and c existing at the same time meaning the particle stays as particles during superposition, then it's really Many worlds in disguised. I got this arguments from Fredrik and it makes sense.

 

[strangerep]

Does [Ballentine] introduce state reduction in Eq 9.28?

Not sure what you're asking here. It's state preparation by filtering. I can't really say any more than what Ballentine has already said there.

IMHO, filtering is not measurement. Rather, a filter is an operator: you give it a state and it produces another state. That's what (9.28) represents. (The denominator is just a normalization factor.)

But imagine removing the final screen from a Stern-Gerlach setup, so the beams just continue on to infinity (or more likely the walls of a pipe, or whatever). Then nothing has been measured, except perhaps how many Watt-hours of electricity were wasted in operating the experiment.

Reinsert the detector screen, and you cannot do anything useful with the particles after they've been "detected" by interacting with the screen. See also Ballentine's commentary after eqn (9.29).

Or is 9.28 derived, even in the case where R and S don't commute?

There is no "S" in (9.28) in my copy of Ballentine.

The case of noncommuting R,S is discussed a little further on, over on p248. His equation (9.26) is only for commuting R,S.

BTW, the subtleties in all this are why he defers discussion of Cox's probability axiom #4 (see p30) until much later, here in ch 9.

 

[Demystifier]

and

http://arxiv.org/pdf/1307.1714v1.pdf

This is about relativity in BM, but not about quantum field theory. About relativity, see also
http://lanl.arxiv.org/abs/1309.0400

 

[kith]

Would you agree with Cthugha that in the ensemble interpretation this filtering can be called "state reduction"?

I would say this is mostly a question about semantics which doesn't address the main issue. Cthugha is of course right that you could call it so but I think this would be misleading. The filtering is not problematic. It simply means you split an ensemble in subensembles and pick out a certain one. The motivation to speak of state reduction comes from the macroscopic superposition state which occurs after a measurement without filtering. The CI says such superpositions are not possible and introduces state reduction to avoid them. But the ensemble interpretation has no problem with them.

Still, I see this as very CI-like, because to me the defining feature of CI is not collapse, it is the commitment to the idea that physics is represented by outcomes of classical devices.

There is no need for classical devices if the macroscopic superposition refers to an ensemble of systems and devices like it does in the ensemble interpretation. These interpretations may be not so different from an empiricist point of view but I think the conceptual differences are big enough to distinguish between them.

 

[vanhees71]

This is about relativity in BM, but not about quantum field theory. About relativity, see also
http://lanl.arxiv.org/abs/1309.0400

Thanks for pointing this references out. I'll have a closer look at it over the weekend. The most challenging task of a Bohmian in my opinion is twofold: (a) how to formulate a Einstein-causal non-local pilot wave theory that is at the same time Lorentz covariant and (b) how to implement the fact that relativistic interacting particles can be destroyed and created, i.e., how to describe the many-body aspects of relativistic QT, which is the very reason why modern formulations of relativistic QT (almost?) exclusively use the QFT formulation.

 

[Demystifier]

Thanks for pointing this references out. I'll have a closer look at it over the weekend. The most challenging task of a Bohmian in my opinion is twofold: (a) how to formulate a Einstein-causal non-local pilot wave theory that is at the same time Lorentz covariant and (b) how to implement the fact that relativistic interacting particles can be destroyed and created, i.e., how to describe the many-body aspects of relativistic QT, which is the very reason why modern formulations of relativistic QT (almost?) exclusively use the QFT formulation.

I definitely agree that these are the most challenging tasks for Bohmian mechanics. In addition to the suggested references above, see also
https://www.physicsforums.com/blog.php?b=2240

 

[atyy]

Not sure what you're asking here. It's state preparation by filtering. I can't really say any more than what Ballentine has already said there.

IMHO, filtering is not measurement. Rather, a filter is an operator: you give it a state and it produces another state. That's what (9.28) represents. (The denominator is just a normalization factor.)

But imagine removing the final screen from a Stern-Gerlach setup, so the beams just continue on to infinity (or more likely the walls of a pipe, or whatever). Then nothing has been measured, except perhaps how many Watt-hours of electricity were wasted in operating the experiment.

Reinsert the detector screen, and you cannot do anything useful with the particles after they've been "detected" by interacting with the screen. See also Ballentine's commentary after eqn (9.29).

My question is whether the filtering method of state preparation follows from the axioms in Chapters 2 (and 3), or whether it is an additional axiom.

There is no "S" in (9.28) in my copy of Ballentine.

The case of noncommuting R,S is discussed a little further on, over on p248. His equation (9.26) is only for commuting R,S.

BTW, the subtleties in all this are why he defers discussion of Cox's probability axiom #4 (see p30) until much later, here in ch 9.

I meant that 9.28 and 9.29 apply (I think) even in the case of non-commuting R, S which are discussed later, even though they were derived via 9.26 which only applies for commuting R,S. For commuting R,S it does look like he can derive 9.28 and 9,29. But for non-commuting R,S, are 9.28 and 9.29 then new axioms?

 

[Ken G]

There is no need for classical devices if the macroscopic superposition refers to an ensemble of systems and devices like it does in the ensemble interpretation. These interpretations may be not so different from an empiricist point of view but I think the conceptual differences are big enough to distinguish between them.

I'm just saying that the interpretations seem to fall into three general classes based on their top priority. For CI and ensemble, the top priority is to hold firm to the idea that physics is a tool for predicting outcomes that we the physicists can perceive as outcomes, and theories organize the information we use to do that, but theories can mislead us if we take them too seriously. For BM, the top priority is that the classical models we use to understand our instruments are themselves fundamentally the reality, not just the way our minds work, and theories should always be interpreted so as to maintain that consistency. For MWI, the top priority is that the abstract elegance of the theory should be regarded as the fundamental truth, and observations test truth but can trap us in illusions of perception if we interpret them too literally. Against those basic schisms, I have a hard time seeing any other distinctions as being of equal importance, but certainly everyone can navigate the remaining nuances to tailor the details of their own picture.

Added: So what I'm saying is, if you want to see all the interpretations as similar, insofar as they are all quantum mechanics, a good approach is to start with the ensemble interpretation, and then make relatively minor tweaks to achieve results that function a lot like each of the other interpretations. But if you want to see the interpretations as very different, perhaps to use one to inspire some new theory, then it might be useful to expand on those three basic different priorities. As some of the other interpretations have already begun that process, the ensemble interpretation could be viewed as minimalist.

 

[bohm2]

So what I'm saying is, if you want to see all the interpretations as similar, insofar as they are all quantum mechanics, a good approach is to start with the ensemble interpretation, and then make relatively minor tweaks to achieve results that function a lot like each of the other interpretations. But if you want to see the interpretations as very different, perhaps to use one to inspire some new theory, then it might be useful to expand on those three basic different priorities. As some of the other interpretations have already begun that process, the ensemble interpretation could be viewed as minimalist.

That makes sense and I don't see how progress can occur without commitment to some form of scientific realism. Sure, all of our evidence will come to us in the form of macroscopically observable phenomena, but we need not restrict ourselves to these concepts when constructing scientific theories. That's where interpretation comes in. I mean, hasn't this always been the norm of science? I just find operationalism a dead end.

 

[Ken G]

What's more, I have never actually met anyone who "shuts up and calculates." Some claim they hold to that view, but they end up, just like the rest of us, wanting more from the equations than just testable outcomes. Let's face it, we do science because we want to understand.

 

[atyy]

What's more, I have never actually met anyone who "shuts up and calculates." Some claim they hold to that view, but they end up, just like the rest of us, wanting more from the equations than just testable outcomes. Let's face it, we do science because we want to understand.

The Bohmian interpretation is shut-up-and-calculate. Once we have Bohm we know all's well in principle (or at least not worse than classical statistical mechanics), so we can just shut-up-and-calculate

 

[Ken G]

That's really not what is meant by shut up and calculate though, as you can see if I ask you "why do I need a pilot wave". Does anyone really use the pilot wave to do the calculations, and if so, why doesn't everyone?

 

[atyy]

That's really not what is meant by shut up and calculate though, as you can see if I ask you "why do I need a pilot wave". Does anyone really use the pilot wave to do the calculations, and if so, why doesn't everyone?

Yes, I was joking. But there is a book "Applied Bohmian mechanics" http://arxiv.org/abs/1206.1084. Also, it doesn't mean that we have to use the full Bohmian apparatus everytime, even if one likes Bohmian ideas. It'd be like never using Newtonian mechanics, just because one had the standard model of particle physics.

 

[Ken G]

Sorry I missed the joke, but it's hard to tell, because people do have very different ideas-- some feel MWI is the simplest interpretation, a la Max Tegmark's "many worlds or many words", but I have a hard time imagining that 10⁵⁰⁰ or so other worlds is simple, just because you can write it in a simpler equation!

 

[Len M]

That makes sense and I don't see how progress can occur without commitment to some form of scientific realism. Sure, all of our evidence will come to us in the form of macroscopically observable phenomena, but we need not restrict ourselves to these concepts when constructing scientific theories. That's where interpretation comes in. I mean, hasn't this always been the norm of science? I just find operationalism a dead end.

Well I’m not sure about this. I know you have read some of d’Espagnat’s works, you may find this extract to be of interest - this is what he says about this particular criticism of operationalism that you seem to make.

On the ground that operationalism limits the aims of science to synthesizing communicable human experience its opponents often claim that taking it up often prevents invention and speculation from playing their parts in research. This view has only a small amount of truth in it. True, the theorist working in a field governed by – say – the quantum laws will not strive to invent naïve mechanistic theories since he or she knows beforehand that such constructs, grounded on concepts of “near realism” would automatically be doomed to failure. But the said theorist – operationalist, might we say, of necessity - still has many opportunities to imagine and speculate. Two possibilities along these lines are available and were indeed made use of -often simultaneously - by the most creative twentieth century physicists. One of them consists in letting oneself be guided – or better to say, inspired - by naive notions and pictures whilst being fully aware they are naive. One example is the astounding notion Dirac put forward of a “sea” of negative energy electrons; and another that electrons may pop out from it, leaving “holes” that “are” positrons. Let us remember that the two basic notions of antimatter and pair creation just come from this.

On the other hand, it must be realized that the fruitful concept of “sea” and “holes” were inspired by a most precise but also - until the relevant experimental checks were made - quite conjectural mathematical formalism. This brings to light the other manner the theorist has of putting his or her imaginative powers into action. It consists of in reflecting on the mathematical formulas, in wondering how they might be made more general and/or more beautiful (the two often go hand in hand), in discovering possible symmetries hidden in their bosom, and in striving to extend them. All this being, of course, subject to a posteriori experimental monitoring. In short, we recognise here the Pythagorean standpoint and observe once more that, after all, it is not conditioned by realism. Even though the theorists who make use of these methods incline in most cases (sometimes unconsciously) towards some kind of Einsteinian realism, such a realism hardly serves them in their work and is not therefore what guides them in practice.

I would suggest the scientific realism you refer to is intended by proponents as being more than naive pictures used by Dirac as described in the extract, rather I think it refers to a genuinely held (philosophical) view of what conceivably exists outside of phenomena. Operationalism would dismiss such notions of realism of course, but according to d’Espagnat, such realism is hardly necessary in which to invent new models.

I know that physicists could hardly work without pictures such as (for example) particles and trajectories, but there is quite a difference I would have thought between needing these kind of pictures as a means of creating new and imaginative predictive models and that of wishing to use them as realist interpretations. The former can certainly be an aid to understanding phenomena acting upon phenomena in terms of the verified mathematical model, the latter however offers little in the way of objective understanding of that which exists outside of phenomena.

So perhaps operationalism is not such a "dead end" area of physics, I tend to think it is exactly what physics proper is (in that I hold great store by the predictive mathematical model) whilst allowing free reign in using any form of enquiry in which to expand existing and create new mathematical predictive models - forms of enquiry that do not have to rely on realist models.

 

[Ken G]

Perhaps, by "operationalism", bohm2 simply meant the attitude that "if the formula works, I don't need to use it to inspire any naive pictures." So in that sense, Dirac's thinking about a sea of negative particles, with "holes" for positrons, would not be classified by bohm2 as operationalism, as Dirac is inspired by a picture rather than just the way the equations work. D'Espagnat seems to classify that as operationalism any time Dirac does not actually hold that the negative sea actually exists. So perhaps we can identify three levels of realism, not two: naive realism, where we take our pictures literally, inspirational realism, where we look for organizational pictures that may or may not be literally real (think, virtual particles as an example), and operationalism, where we just solve equations and "go through the motions." That doesn't seem to be the way D'Espagnat uses the terms, but it does seem like what bohm2 means, unless I'm mistaken.