# Measurement problem in the Ensemble interpretation

• A
Gold Member
The ensemble interpretation asserts that QM is only applicable to an ensemble of similarly prepared systems and has nothing to say about an individual system and in this way, it seems, it can prevent the need for introducing the concept of wave-function collapse and so it may seem that there is nothing called measurement problem in this interpretation. But is it really correct to say that ensemble interpretation prevents the measurement problem? If not, how would you describe the measurement problem in ensemble interpretation?
I think there is still a measurement problem in ensemble interpretation because I can't even see how can I start to think about quantum to classical transition in ensemble interpretation. It seems that ensemble interpretations just obscures the measurement problem.
Thanks

AlexCaledin, Truecrimson and Demystifier

bhobba
Mentor
The ensemble interpretation asserts that QM is only applicable to an ensemble of similarly prepared systems and has nothing to say about an individual system and in this way, it seems, it can prevent the need for introducing the concept of wave-function collapse and so it may seem that there is nothing called measurement problem in this interpretation. But is it really correct to say that ensemble interpretation prevents the measurement problem? If not, how would you describe the measurement problem in ensemble interpretation?

There is no collapse - in the usual sense anyway, being replaced with the concept of preparation. All a filtering type observation does is prepare the system differently and states are the equivalence class of preparation procedures leading to the same state.

The measurement problem however has a number of parts as explained by Schlosshauer:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

1. Why we generally do not observe interference.
2. The preferred basis problem ie why we get particular stable eigenstates in certain observations.
3. Why do we get any outcomes at all. Technically its how a improper mixed state becomes a proper one.

The formalism of QM (ie in any interpretation including ensemble), with some what I consider minor caveats no need to go into here, explains 1 and 2 via decoherence. However it stands powerless before 3. Some interpretations like BM and MW explain 3 with ease, but minimalist interpretations like Ensemble and most versions of Copenhagen do not - they simply assume it. There are some modern interpretations like Decoherent Histories that skirt it entirely - in that interpretation QM is the stochastic theory of histories.

So Ensemble does not solve the measurement problem, but with our modern understanding of decoherence has morphed it somewhat. There is also the issue of if its a problem at all - nature may simply be like that ie improper mixed states are the same as proper ones. That's the view of my interpretation ignorance ensemble - you simply accept its the same.

Thanks
Bill

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Physics Footnotes, eloheim, vanhees71 and 2 others
Gold Member
Thanks Bill. One more question:
An example of a filtering type observation that comes to my mind, is the Stern-Gerlach experiment. You can do this experiment with very dim beams, so you can't think of the beam as an ensemble of particles. What does ensemble interpretation has to say about such experiment?
What concerns me here, is the quantum to classical transition. Because ensemble interpretation surely is good in usual measurements on ensembles where you want to check whether you've calculated the correct wave-function by comparing the theoretical and experimental probability distributions for different measured quantities. But when talking about the quantum to classical transition, we usually think about how just one system behaves quantum mechanically on some level and then behaves classically on another. It seems to me if ensemble interpretation only cares about ensembles, then its simply unable to address such issues, not that it hasn't yet, but that its impossible for it to do!

vanhees71
Gold Member
2021 Award
In the case of the SG experiment you can have 1 particle in the apparatus at any time you do the experiment. You just have to repeat the experiment with this one particle, always prepared in the same way, in the apparatus many times, and you get an ensemble.

With the appropriate setup the motion of the particle in the SG experiment is very close to the classical approximation. For a fully quantum theoretical treatment, see

Potel, G., Barranco, F., Cruz-Barrios, S., Gómez-Camacho, J.: Quantum mechanical description of Stern-Gerlach experiments, Phys. Rev. A 71, 2005

bhobba
Demystifier
Gold Member
The ensemble interpretation asserts that QM is only applicable to an ensemble of similarly prepared systems and has nothing to say about an individual system and in this way, it seems, it can prevent the need for introducing the concept of wave-function collapse and so it may seem that there is nothing called measurement problem in this interpretation. But is it really correct to say that ensemble interpretation prevents the measurement problem? If not, how would you describe the measurement problem in ensemble interpretation?
I think there is still a measurement problem in ensemble interpretation because I can't even see how can I start to think about quantum to classical transition in ensemble interpretation. It seems that ensemble interpretations just obscures the measurement problem.
I absolutely agree with every word you say above.

The measurement problem is a problem about outcomes of single measurements. What exactly happens when we perform one measurement? That is the measurement problem. As long as ensemble interpretation refuses to talk about single measurements, it cannot say anything about the measurement problem. An inability to say anything about the problem is a problem itself.

AlexCaledin, eloheim, Truecrimson and 1 other person
kith
If you take the ensemble view in QM serious, it carries over to classical mechanics.

For example in a single particle interpretation, you may have a particle with a narrow probability distribution of both position and momentum where you can approximate the dynamics with Newton's laws. In the ensemble view, you end up with a (conceptual) ensemble of particles which behave classically. The single particle ontology seems to be natural in classical mechanics but it is an assumption nevertheless. You cannot check predictions with single particles.

So if the ensemble interpretation "solves" the measurement problem, it does so by weakening the explanatory power of physics in general.

eloheim
A. Neumaier
The measurement problem is a problem about outcomes of single measurements. What exactly happens when we perform one measurement?
The real problem here is to clarify what it means to perform a measurement. This is a very complex task in general, and has even classically no clear definition. Thus it is no surprise that interpretations that assume that there is a unique, perfect meaning to it have problems.

bhobba
Demystifier
Gold Member
The real problem here is to clarify what it means to perform a measurement. This is a very complex task in general, and has even classically no clear definition. Thus it is no surprise that interpretations that assume that there is a unique, perfect meaning to it have problems.
True, but it is even less surprising that interpretations that do not assume anything specific about measurements have problems too, simply by being unable to say anything specific about that important and interesting issue.

A. Neumaier
True, but it is even less surprising that interpretations that do not assume anything specific about measurements have problems too, simply by being unable to say anything specific about that important and interesting issue.
They don't have problems since they exclude the question from their domain of discourse.

Not making statements about single particles is practically equivalent with treating the latter as nonexistent and assigning properties (hence existence) only to the beams containing them. Though the ensemble interpretation replaces the term ''beams'' by ''preparation procedure'', there is little difference in practice.

The beam is obviously existent and has clear and objective properties while the particles are unobservable entities (thought of being inside them) with mysterious properties that reveal a glimpse of their existence only through their macroscopic traces or impacts.

dextercioby and vanhees71
Demystifier
Gold Member
They don't have problems since they exclude the question from their domain of discourse.
This is like saying that non-relativistic mechanics applied to low velocities has no problems because high velocities are excluded from its domain of discourse. OK, you may say that it is not a problem, but it is definitely a deficiency.

atyy, eloheim and vanhees71
Gold Member
So if the ensemble interpretation "solves" the measurement problem, it does so by weakening the explanatory power of physics in general.

They don't have problems since they exclude the question from their domain of discourse.

Just to clarify what I meant (which I think is also what Demystifier means):
The measurement problem is usually stated as "what is wave-function collapse?". So its no surprise that when people encounter with an interpretation of QM that discards wave-function collapse entirely, they may think "amazing, problem vanished!". This seems to be true about the de Broglie-Bohm and the Many worlds interpretations but its not true about the ensemble interpretation. Because actually there are two problems here, the nature of wave-function collapse and the quantum to classical transition. In the interpretations that embrace collapse, these two problems are the same and if you explain collapse, you've explained quantum to classical transition. But this shouldn't lead one to think that if you prevent the question of the nature of wave-function collapse, you've also prevented the problem of quantum to classical transition, it just means that you've decoupled the questions and eliminated one of them, still retaining the other. So the situation is you either have two synonymous questions (collapse interpretations) or only one question (no-collapse interpretations).

Now the measurement problem in collapse interpretations is the nature of collapse(which is synonymous to quantum to classical transition) which with the help of decoherence(as Bill mentioned), is partly solved. In non-collapse interpretations, the measurement problem is only the quantum to classical transition which the dBB and the MW interpretations seem to completely solve but it seems they have other theoretical problems.

But the situation about the ensemble interpretation is different from other non-collapse interpretations. It discards collapse and makes it impossible to state the problem of quantum to classical transition at least clearly. So ensemble interpretation, although prefect for physicists who only care to use QM efficiently(which is of course fine), is inadequate for addressing foundational questions about QM. It seems to me an advocate of the ensemble interpretation who also cares about the foundational questions, is inevitably an advocate of hidden variables.

eloheim, Truecrimson and Demystifier
A. Neumaier
you may say that it is not a problem, but it is definitely a deficiency.
I agree. But every theory except a Theory Of Everything has such a deficiency. And the latter also has one since it can never be detailed enough to predict everything.

Demystifier
Gold Member
I agree. But every theory except a Theory Of Everything has such a deficiency. And the latter also has one since it can never be detailed enough to predict everything.
I agree. But you cannot blame me for preferring theories with less deficiencies. So if one theory can say something about single measurements and the other can't, I think it's a good reason for having more interest in the former theory.

Demystifier
Gold Member
It seems to me an advocate of the ensemble interpretation who also cares about the foundational questions, is inevitably an advocate of hidden variables.
Exactly!

Denis
A. Neumaier
So the ensemble interpretation, although perfect for physicists who only care to use QM efficiently (which is of course fine), is inadequate for addressing foundational questions about QM.
The ensemble interpretation is there precisely to avoid the foundational problems; so this deficiency is its virtue, as it makes the success of quantum mechanics understandable without any need to resolve these problems.

I understand both merits and limits of the Copenhagen interpretation and the ensemble interpretation although I adhere to neither. My own thermal interpretation is a golden way in-between that solves the foundational questions, at least to my own satisfaction. It makes meaningful statements about the individual case that become more and more crisp as the observables studied become more and more macroscopic. Thus it displays the quantum to classical transition in an easily comprehensible way.

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bhobba, Truecrimson, Mentz114 and 1 other person
Demystifier
Gold Member
The ensemble interpretation is there precisely to avoid the foundational problems; so this deficiency is its virtue, as it makes the success of quantum mechanics understandable without any need to resolve these problems.
The best defend of ensemble interpretation I have ever seen!

bhobba
Mentor
The best defend of ensemble interpretation I have ever seen!

I think adherents (and I am one) would rather use the word minimalist than avoid

But discussions of interpretations leads to long threads that don't really resolve anything and can get rather heated. Still understanding them can be quite illuminating.

Thanks
Bill

bhobba
Mentor
Exactly!

That's what Ballentine pretty much did in his original 1970 article. But since then has changed his conception a bit to skirt the issue.

There is zero doubt the ensemble interpretation leaves a number of questions unanswered, the most fundamental being exactly how does a improper state become a proper one. Its purely a matter of scientific tact, taste etc etc if that is a problem or a virtue. Its even debatable if its a problem at all. Being philosophy its not likely to have an answer without some way to decide it experimentally.

My view as you might have guessed is its not a problem, nature is just like that. But as I often stress, and an ex boss of mine stressed this to me when I was working as a programmer, opinions are like bums, everyone has one - it doesn't make it right - but its important to have one.

Thanks
Bill

Demystifier
Gold Member
opinions are like bums, everyone has one - it doesn't make it right - but its important to have one.
Why is it important to have bums?

eloheim and bhobba
Gold Member
Why is it important to have bums?
To avoid a naked singularity!

atyy, Demystifier and bhobba
Demystifier
Gold Member
To avoid a naked singularity!
I guess my problem is that I don't know what the word "bum" really means.

Gold Member
I guess my problem is that I don't know what the word "bum" really means.
I had to check it too!
It means buttock. But I think its slang.

Demystifier
bhobba
Mentor
I guess my problem is that I don't know what the word "bum" really means.
I had to check it too! It means buttock. But I think its slang.

Its actually a real word - but described as informal, although in Australia its probably categorized correctly as slang:
http://www.collinsdictionary.com/dictionary/english-thesaurus/bum

One thing I have found posting here is words in common use here in Australia that you would not think twice about using because everyone understands it is not true elsewhere. Its really interesting actually

A very common saying here is opinions are like bums - everyone has one.

Thanks
Bill

Among the physicists participating on this thread. Only one holds to the ensemble interpretation. May I know how many percentage approximately of the physicists worldwide hold to the ensemble interpretations? is it only 10% or 90% Any polls or studies?

And I'd like to understand specifically how they view single systems like atoms. Perhaps they think the de Broglie waves are really physical there in single systems and the probability only comes in when you view the particle part.. that is..

one system = de Broglie waves
ensemble = particle appears probabilistically?

If this is not correct. Then how do people who holds to the ensemble interpretation think of one atom and their electrons? Since they don't believe the electrons wavefunctions can collapse when measured.. then do they think it's literally de Broglie standing waves in one atom system. I kept googling about this and reading the archive and can't find the atom thing so I'd like to ask it here so I'd understand the mindset of these people.

Thanks.

bhobba
Mentor
And I'd like to understand specifically how they view single systems like atoms.

No idea of percentages that hold to it etc. The modern version is called ignorance ensemble because it takes into account decoherence. The central issue then is why do we get any outcomes at all or technically how does a improper mixed state become a proper one. But that is a whole new thread - start one if you like.

But as far as single systems go its exactly the same way single outcomes are handled in the frequentest interpretation of probability.

Much of QM interpretations is actually an argument about probability:
http://math.ucr.edu/home/baez/bayes.html

Thanks
Bill

As long as ensemble interpretation refuses to talk about single measurements

The ensemble interpretation deals with single measurements just fine, because the ensemble is conceptual, not necessarily realized. You imagine a large number of copies of the experiment and then the Rules of Quantum Mechanics reflect statistical properties of this ensemble; yet it need not exist anywhere other than the experimenter's head.

The ensemble interpretation is really just a more frequentist way of thinking of some "minimal" interpretation of quantum mechanics where quantum states are mathematical devices rather than something wholly physical.

Demystifier
Gold Member
The ensemble interpretation deals with single measurements just fine, because the ensemble is conceptual, not necessarily realized. You imagine a large number of copies of the experiment and then the Rules of Quantum Mechanics reflect statistical properties of this ensemble; yet it need not exist anywhere other than the experimenter's head.

The ensemble interpretation is really just a more frequentist way of thinking of some "minimal" interpretation of quantum mechanics where quantum states are mathematical devices rather than something wholly physical.
So what can ensemble interpretation say about the measurement problem of single measurements?

stevendaryl
Staff Emeritus
I am gradually coming around to the point of view that the weirdness of quantum mechanics in its minimal interpretation is not (directly) about collapse, and is not (directly) about nonlocality. I think the weirdness is about the preferred basis problem, or maybe about the problem of splitting the world up into System of interest + Environment (everything else). I don't think that the ensemble interpretation does anything to help in that regard.

Let's take the very simplest quantum system, namely a two-component spinor. You have some state $\left( \begin{array}\\ \alpha \\ \beta \end{array}\right)$. The probabilistic meaning of this state is variously:
• The particle has a probability $|\alpha|^2$ of being measured to be spin-up in the z-direction, and $|\beta|^2$ of being measured to be spin-down in the z-direction.
• The particle has a probability $\frac{1}{2} |\alpha + \beta|^2$ of being measured to be spin-up in the x-direction, and $\frac{1}{2}|\alpha - \beta|^2$ of being measured to be spin-down in the x-direction.
• The particle has a probability $\frac{1}{2}|\alpha -i\beta|^2$ of being measured to be spin-up in the y-direction, and $\frac{1}{2}|\alpha + i \beta|^2$ of being measured to be spin-down in the y-direction
• etc
The problem (it seems to me) with these statements is this: What does it mean to say that you've measured spin-up? Well, it means that the spin state of the particle (spin up or spin down) has become correlated with the macroscopic state of a measurement device (measured spin up or measured spin down). It seems like an infinite regress: you can only give the meaning of the state of one system (the spin-1/2 particle) in terms of the state of a larger system (the particle + the spin measurement device). The way that the Copenhagen interpretation breaks the infinite regress is by declaring that for macroscopic systems, the state is given, not by a wave function, but by the classical notion of state, where macroscopic objects have more-or-less definite positions and velocities. To me, treating macroscopic systems as special has to be an ad hoc rule of thumb, and not a fundamental aspect of the theory.

I don't think that the ensemble interpretation does anything to change this.

MrRobotoToo and Demystifier
stevendaryl
Staff Emeritus
I don't think that the ensemble interpretation does anything to change this.

I suppose that in the limit of an infinitely large ensemble, the various expectation values for different quantities commute: If you have $N$ particles, and define

$S_x = \frac{1}{N} \sum_j S_{jx}$, where $S_{jx}$ is the x-component of the spin of the jth particle,

and similarly for $S_y$ and $S_z$, then you'll have:

$[S_x, S_y] = \frac{i}{N} S_z$

so in the limit as $N \rightarrow \infty$, the various averages commute. So they can be given simultaneous values.

On the other hand, it seems strange to say that the average value of some quantity exists and has a definite value if the quantity itself is undefined for the individual systems making up the ensemble.

atyy
Ballentine's ensemble interpretation is not even correct quantum mechanics. I wouldn't waste any time on it. The true ensemble interpretation is the Copenhagen interpretation, which of course has a measurement problem.

AlexCaledin
[]
To me, treating macroscopic systems as special has to be an ad hoc rule of thumb, and not a fundamental aspect of the theory.
[]
.
Interesting. But I don't think that 'classical' systems are being treated exceptionally. If we define the classical state as the large-number, no-ignorance limit of the quantum state, it becomes a sort of Platonic ideal because there is always some ignorance. This brings all dynamics under the same definition, differing only in the operational ignorance.

stevendaryl
Staff Emeritus
Interesting. But I don't think that 'classical' systems are being treated exceptionally. If we define the classical state as the large-number, no-ignorance limit of the quantum state, it becomes a sort of Platonic ideal because there is always some ignorance. This brings all dynamics under the same definition, differing only in the operational ignorance.

If the rules of quantum probabilities are formulated in terms of "If you measure such and such, you will get such and such, with such and such probability", then you're making measurement into a different type of interaction, so you are treating macroscopic objects such as measuring devices differently than you treat microscopic objects. Many-worlds in contrast does not assume a macroscopic/microscopic distinction, but on the other hand, it's very hard to understand how probabilities play out in Many-worlds.

entropy1 and MrRobotoToo
If the rules of quantum probabilities are formulated in terms of "If you measure such and such, you will get such and such, with such and such probability", then you're making measurement into a different type of interaction, so you are treating macroscopic objects such as measuring devices differently than you treat microscopic objects. Many-worlds in contrast does not assume a macroscopic/microscopic distinction, but on the other hand, it's very hard to understand how probabilities play out in Many-worlds.
The laws of physics are not written in terms of probabilities. Otherwise ##F=ma## has no meaning.

If you insist on that I cannot argue, obviously.

stevendaryl
Staff Emeritus