Statistical ensemble interpretation done right

[PeterDonis]

how do you justify this probabilistic reasoning, in an empirical and setting (that at least in principle, is doable for the class of "obsevers" we entertain, in a real interaction), without beeing able to repeating the process

You can repeat the process. That is the whole point of having a preparation procedure that you can run the same way many times.

 

[Fra]

You can repeat the process. That is the whole point of having a preparation procedure that you can run the same way many times.

Yes agreed. But I have a feeling we have some misunderstanding here.

I read martinb to suggest that, when do to repeat, it's no longer the SAME system. Ie. it's not the SAME electron beeing fired etc. And at the same time, he wants to attribute say the the density matrix to the system, and not the "ensemble" produced by a given preparation procedure given infinite number of samples?

I did I miss something?

/Fredrik

 

[PeterDonis]

I read martinb to suggest that, when do to repeat, it's no longer the SAME system.

It's not the same system, but that doesn't mean it's not the same preparation process. The same preparation process can prepare multiple systems.

at the same time, he wants to attribute say the the density matrix to the system, and not the "ensemble" produced by a given preparation procedure given infinite number of samples?

There are interpretations that do this. However, I'm not sure @martinbn is using one. Is there something specific he said that makes you think so?

 

[Fra]

It's not the same system, but that doesn't mean it's not the same preparation process. The same preparation process can prepare multiple systems.

Agreed.

There are interpretations that do this. However, I'm not sure @martinbn is using one. Is there something specific he said that makes you think so?

I might have misinterpreted his post #81 as I read it it again.

What I meant in post #84 is that I agree that strictly speaking the ensemble as well as the p-distribution itself are fictions or abstractions. My point was based on that i thought it was questioned, without this empirical side, how do we justify the abstractions?

Does real observations or information processing approximate our theories, or is it the other way around? We interpret theories, but do we interpret information processing?

/Fredrik

 

[PeterDonis]

without this empirical side, how do we justify the abstractions?

We can't. We justify the abstractions ultimately by the fact that they make accurate predictions (if they do) about what we observe and measure empirically.

Does real observations or information processing approximate our theories, or is it the other way around? We interpret theories, but do we interpret information processing?

I'm not sure what role "information processing" plays here. We use our theories to construct models, and we compare the models with reality through their predictions about what we should observe and measure, compared with what we actually observe and measure. I'm not sure how this fits in to whatever picture you have. But that is how I would describe what is going on in as plain and simple language as I can.

 

[Fra]

We can't. We justify the abstractions ultimately by the fact that they make accurate predictions (if they do) about what we observe and measure empirically.

I don't think we disagree here, perhaps what martinb tried to say was unclear to me.

I'm not sure what role "information processing" plays here. We use our theories to construct models, and we compare the models with reality through their predictions about what we should observe and measure, compared with what we actually observe and measure.

Yes, thats the de facto information processing we do and what i meant in this case. Trying to stick to basics. In the more general picture but "information process" I would probably count every physical process in the macropscopic environment, that implicitl encodes information about subsystems. But the principle is the same.

Anyway, I can't see I disagree with you anywhere here.

/Fredrik

 

[martinbn]

Yes agreed. But I have a feeling we have some misunderstanding here.

I read martinb to suggest that, when do to repeat, it's no longer the SAME system. Ie. it's not the SAME electron beeing fired etc. And at the same time, he wants to attribute say the the density matrix to the system, and not the "ensemble" produced by a given preparation procedure given infinite number of samples?

I did I miss something?

/Fredrik

That is not what I meant. It is the same system, say the same electron, but it is not a member of the same ensemble any more. For example if it was prepared so that it is a member of the ensemble with state spin |up>, and you measure spin in a horizontal direction and you get "left", now this same electron is a member of an ensemble in the sate |left>. So any following measurement will be on the original system, but not as originally prepared.

And if you prepare another electron in the spin up, then it is not the same system, but it is still the same ensemble.

 

[PeterDonis]

perhaps what martinb tried to say was unclear to me

In post #81 he was just responding to the statement he quoted by @vanhees71. There is a difference between saying that the quantum state describes the results of a preparation procedure on a single system (which is what @vanhees71 said) and saying that the quantum state describes an ensemble of systems all prepared by the same preparation procedure (which is the type of interpretation that the title and OP of this thread refer to).

 

[vanhees71]

I don't understand, how you can build an ensemble to be in a given state, if you are not able to relate it to the preparation procedure on a single system. Otherwise I think @martinbn and I agree on the interpretation of the state, which as any probabilistic description refers to the properties of an ensemble, because you can experimentally test the probabilistic predictions only on an ensemble of equally prepared systems.

On the one hand the state thus is the description of a preparation procedure on a single system, but on the other the physical meaning of the state refers only to ensembles.

 

[martinbn]

I don't understand, how you can build an ensemble to be in a given state, if you are not able to relate it to the preparation procedure on a single system. Otherwise I think @martinbn and I agree on the interpretation of the state, which as any probabilistic description refers to the properties of an ensemble, because you can experimentally test the probabilistic predictions only on an ensemble of equally prepared systems.

On the one hand the state thus is the description of a preparation procedure on a single system, but on the other the physical meaning of the state refers only to ensembles.

You misunderstood me. I am not saying how things are, but how things are according to one interpretation (which is not even my proffered one). You on the other hand are saying how things are according to a different interpretation. But in addition you claim that this is the only possibility and you think that your statements are interpretation independent. That is where we disagree.

 

[Morbert]

I don't understand, how you can build an ensemble to be in a given state, if you are not able to relate it to the preparation procedure on a single system. Otherwise I think @martinbn and I agree on the interpretation of the state, which as any probabilistic description refers to the properties of an ensemble, because you can experimentally test the probabilistic predictions only on an ensemble of equally prepared systems.

On the one hand the state thus is the description of a preparation procedure on a single system, but on the other the physical meaning of the state refers only to ensembles.

A minimal statistical ensemble (MSE) proponent can certainly associate a state with a preparation procedure, but what motivates the MSE interpretation of a state as an infinite ensemble is the avoidance of pitfalls in thought processes. E.g. Both MSE and Copenhagen proponents can associate a state with a preparation procedure, but a Copenhagen proponent would happily proceed to think about measurement propensities in a single experimental run while an MSE proponent would not. They would only concern themselves with relative frequencies in several experimental runs and how they compare with rates in the infinite ensemble, as they are obliged to interpret the state as representing an infinite ensemble. They would hope to avoid ambiguities a Copenhagen proponent might be more vulnerable to.

 

[PeterDonis]

I don't understand, how you can build an ensemble to be in a given state, if you are not able to relate it to the preparation procedure on a single system.

The ensemble is not something that gets "built". It's an abstraction. Please read the passages from Ballentine that I referenced.

 

[vanhees71]

It's not an abstraction. At colliders you prepare particles at pretty well determined momenta and let them collide (in fact it's bunches of many particles, but that are details not too relevant for the general argument). This you repeat zillion of times to "collect enough statistics". Particularly for "rare probes" (as my beloved "dileptons and photons" in heavy-ion collisions) you need a lot of statitics. One point of the recent upgrade of the LHC was to get higher luminosities to get "the statistics" in a shorter time. Another great challenge was to also adapt the detectors to cope with these higher rates!

 

[martinbn]

It's not an abstraction.

You do understand that it can be an abstraction in one interpretation and not in another, don't you?

 

[PeterDonis]

It's not an abstraction.

Again, please read the passages from Ballentine that I referenced. As far as I know Ballentine's definition of "ensemble" is the usual one in ensemble interpretations of QM. And it is inconsistent with what you are saying.

 

[vanhees71]

Of course, from a mathemtical point of view you need infinite abstract ensembles to define probabilities. QT is, however a physical theory and it is successfully applied to real-world experiments, where you deal with real-world finite ensembles, including the corresponding systematical and statistical errors, which you have to carefully estimate as an experimentalist. Of course, Ballentine is right with his formal cautions about the meaning of probabilities, but there's no contradiction to apply probability theory to statistics of real-world experiments/observations. If this were the case, QT (or any other probabilistic theory, as classical statistical physics!) wouldn't have any connection to real-world experiments, and nobody would consider it as a physical theory.

 

[PeterDonis]

Of course, from a mathemtical point of view you need infinite abstract ensembles to define probabilities.

So now you agree that an ensemble is an abstract infinite set?

QT is, however a physical theory and it is successfully applied to real-world experiments, where you deal with real-world finite ensembles

No, you deal with real-world finite sets of actual experiments, which are not, as Ballentine says, correctly described as "ensembles".

 

[Fra]

Both MSE and Copenhagen proponents can associate a state with a preparation procedure, but a Copenhagen proponent would happily proceed to think about measurement propensities in a single experimental run while an MSE proponent would not.

Except for the wordings, to me the "propensitites" in a single experiment, follwing a preparation still only has a the same operational statisitical meaning.

Or would you suggest that the MSE propoent would refuse to even use the term prospensities, they call it instead probability? How does that make a difference? or are we talking I think about interpretation of "probability" and not just interpretation of QM?

/Fredrik

 

[Fra]

No, you deal with real-world finite sets of actual experiments, which are not, as Ballentine says, correctly described as "ensembles".

I think all would agree with this. The limit is a mathematical object only. But I didnt think this was the topic, it seemed too obvious.

I had another "fiction" in mind, namely wether there is a physical basis to the ensemble, set aside wether infinite or not. Here I see it physically encoded in the environment, as the tuned preparation setup and in that sense not fiction. I thought this was what vanhees tried to say?? to which i agree. The finite ensenble and the imperfect preparation procedure are not perfect, but not fiction?

/Fredrik

 

[gentzen]

Or would you suggest that the MSE propoent would refuse to even use the term prospensities, they call it instead probability? How does that make a difference? or are we talking I think about interpretation of "probability" and not just interpretation of QM?

I think all would agree with this. The limit is a mathematical object only. But I didnt think this was the topic, it seemed too obvious.

This and the previous discussion did not get off-track over physical disagreements, but over disagreements how the mathematical abstractions related to probabilities and ensembles are to be interpreted in concrete physical contexts.

 

[GarberMoisha]

QT is, however a physical theory and it is successfully applied to real-world experiments...

That would be a stretch. Remove the Born's rule and it becomes a non-physical theory altogether.

 

[PeterDonis]

wether there is a physical basis to the ensemble

The physical basis would be the preparation procedure, which involves actual physical equipment and processes. At least, that is how Ballentine explains it.

 

[PeterDonis]

The finite ensenble

There is no "finite ensemble". The term "ensemble" specifically means the abstract infinite set that has been described. It does not mean the actual finite set of actual systems we run the actual preparation procedure on.

 

[vanhees71]

The physical basis would be the preparation procedure, which involves actual physical equipment and processes. At least, that is how Ballentine explains it.

Exactly that's what I also say all the time. I don't see any contradiction between my view that real-world experiments use ensemles to test probabilistic predictions, including those of QT and what you quoted from Ballentine's intro chapter. It's well known that there's a difference between mathematical, idealized infinetely large ensembles and finite real-world empirical ensembles. Hypothesis testing thus is an entire subbranch of applied statistics.

 

[vanhees71]

There is no "finite ensemble". The term "ensemble" specifically means the abstract infinite set that has been described. It does not mean the actual finite set of actual systems we run the actual preparation procedure on.

Then just tell us which term you prefer for real-world collections of data, if we are not allowed to say "ensemble". It's really hard to discuss if one is not allowed to use standard terminology!

 

[vanhees71]

That would be a stretch. Remove the Born's rule and it becomes a non-physical theory altogether.

For me Born's rule is one of the fundamental postulates, and it's indeed crucial to make the theory to a physical theory.

 

[gentzen]

It's really hard to discuss if one is not allowed to use standard terminology!

I sort of agree, even so I don't want to voice an opinion on what is "standard". When I hint that "this and the previous discussion got off-track" in my opinion, it is because we started to disagree over so basic things (or talk past one another) that I don't even see which language we could use to reach a common understanding again.

 

[vanhees71]

Ballentine's book is very clear, as is Peres's. When I talk to experimentalists they all understand under "ensembles" their millions of repetitions of scattering experiments taken with real-world detectors (measurement) using particles from an accelerator (preparation).

 

[lodbrok]

The quantum state is the formal description of a preparation procedure on a single system. In this sense the quantum state refers to the single system. The meaning of the quantum state is, of course, entirely statistical

Focusing on the second part first -- statistics. You can generate statistics by (a) measuring a million different single systems once each or by (b) measuring the same single system a million different times (not always possible in practice, but in principle). Your measured statistics at CERN are of type (a), but by saying the system you are measuring is "an electron," you imply that it is of type (b).

The distinction you make in post #62 is not the appropriate one. It isn't between one million CERNS measuring one electron each vs one CERN measuring a million electrons. Rather, it's between one CERN measuring a single electron one million times vs one CERN measuring one million different similarly prepared electrons. Therefore, it is a fact that your measurements refer to an ensemble of similarly prepared elections or to the preparation procedure. To say the system being measured is "an electron" requires additional justification.

You are obviously free to interpret the QM state as referring to "an electron" rather than "an ensemble of similarly prepared electrons" (assuming you agree there's a difference between the two). That is not the issue. But then, how do you link the theory to the experiments? Only one of those "interpretations" is directly consistent with what you measure; you always measure an ensemble of similarly prepared electrons. Though each individual detector click refers to a particular electron, what justifies you putting all the results together, doing statistics on them, and then ascribing the resulting statistics to "an electron"? You will never ascribe the average height of people in a population to "an individual." Why do it here?

I guess I'm suggesting that you may have multiple ways of interpreting the math but only one way of interpreting the experiment.

 

[PeterDonis]

It's well known that there's a difference between mathematical, idealized infinetely large ensembles and finite real-world empirical ensembles.

My point is that Ballentine (who, I think, is a reasonable representative example of the literature) does not use the word "ensemble" at all to describe the latter (the "finite real-world" sets of systems). There might be some other standard term that is used for that, but it is not "ensemble". And we should be using terms the way they are used in the literature.