I Minimal vs Instrumental vs Ensemble

[gentzen]

you must associate a single system with a state

In the minimal statistical interpretation, no, you don't do this. States do not describe single systems in this interpretation. They either describe abstract ensembles, or they describe preparation procedures.

Wait, I just see that you quoted from a very long sentence of mine here:

If you look at SEI from an operational verification perspective, then yes, you must associate a single system with a state before you know the results of the non-preparation measurements.

OK, I see that my sentences seem to be much too long. I will try to work on it. For me, the meaning of the quoted part changed significantly by leaving out the "before you know" part. And stripping away an "if ... then" part in general also risks to change meaning. However, I would also have stripped it away in this case, because it didn't impact the meaning.

 

[vanhees71]

The preparation procedure prepares each single system, forming together the ensemble. You cannot prepare an ensemble if you cannot prepare individual system independently. The state preparation, however, does not determine all properties (i.e., the values of all observables) of the single system, and thus its meaning concerning the properties refers to the statistical properties for the outcome of measurements and thus refers to the ensemble. The important point is this distinction between preparation (referring to prerparation procedures for single systems) and observation (referring to statistical properties of the corresponding ensembles of equally prepared systems).

 

[gentzen]

observation (referring to statistical properties of the corresponding ensembles of equally prepared systems)

maybe not important, but this parenthetical clarification is not helpful for me

 

[vanhees71]

What is not helpful? I tried to explain what I mean when I say a state represents a preparation procedure for a single system and at the same time describes the statistical properties for the outcomes of measurements on an ensemble of equally so prepared systems.

 

[gentzen]

What is not helpful? I tried to explain what I mean when I say a state represents a preparation procedure for a single system and at the same time describes the statistical properties for the outcomes of measurements on an ensemble of equally so prepared systems.

The description of a state and a preparation procedure was helpful. But the text in the parenthesis behind the word "observation" doesn't make sense to me.

 

[PeterDonis]

Sigh. Do I really have to copy the parts from the texts I quoted.

No, you just have to read what they actually say instead of what you would like them to say.

 

[PeterDonis]

The preparation procedure prepares each single system, forming together the ensemble.

That's not what Ballentine says. Ballentine says the ensemble is not the actual group of actual systems that are prepared by some preparation procedure. It is the abstract set of an infinite number of abstract systems that could be prepared by that preparation procedure.

 

[vanhees71]

Yes, that's the theoretical formulation, but in practice you must work with finite samples and do a corresponding statistical analysis to ensure that the predicted probabilities agree with the measured "frequencies". Practice shows that in the here discussed experiments, which probe the foundations of QT concerning entanglement, violation of Bell's inequalities, etc. this can be done with FAPP arbitrarily high accuracy. That together with the fact that also all other considered loopholes are closed (sometimes even in one and the same experiment) makes me believe that the distinction between finite samples and the infinite theoretical ensembles are not at the heart of the interpretational problems.

 

[martinbn]

Yes, that's the theoretical formulation, but in practice you must work with finite samples and do a corresponding statistical analysis to ensure that the predicted probabilities agree with the measured "frequencies". Practice shows that in the here discussed experiments, which probe the foundations of QT concerning entanglement, violation of Bell's inequalities, etc. this can be done with FAPP arbitrarily high accuracy. That together with the fact that also all other considered loopholes are closed (sometimes even in one and the same experiment) makes me believe that the distinction between finite samples and the infinite theoretical ensembles are not at the heart of the interpretational problems.

This is unrelated. You were making claims about Ballentine's interpretation, which were wrong.

 

[vanhees71]

I quoted Ballentine verbatim. Where can this be wrong? Here it is again from the RMP by Ballentine:

It's an ensemble of single electrons being prepared by a procedure (to be specified for each state). So why do you claim it's wrong?

 

[martinbn]

I quoted Ballentine verbatim. Where can this be wrong? Here it is again from the RMP by Ballentine:

View attachment 339207

It's an ensemble of single electrons being prepared by a procedure (to be specified for each state). So why do you claim it's wrong?

The quote is not wrong. Your statements are. You write "for a single elctron the state represents". Ballentine clearly says that the state represents the infinite abstract ensemble. You are wrong when you claim that Ballentine says what you say. He does not. Thr two of you use different interpretations. Yours is a Copenhagen interpretation in the way Bohr uses it.

 

[gentzen]

Yours is a Copenhagen interpretation in the way Bohr uses it.

No, vanhees71's interpretation is not a Copenhagen interpretation, independent of whether he adheres exactly to Ballentine or not.

 

[vanhees71]

But he says that the preparation procedure refers to a single electron. A bit later he even emphasizes that the so defined ensembles are different from preparing a bunch of electrons at once. I think it's pretty clear that the preparation procedure must relate to single electrons, if you want to strictly define an ensemble of "equally prepared single electrons", and as far as I understand him Ballentine precisely states this. The statistical interpretation is anyway very close to Copenhagen a la Bohr. Here's the precise quote from Ballentine:

Again in I the preparation procedure refers to single systems. Concerning the properties of the system described by the so prepared state it provides only the statistical properties and thus only refers to ensembles of such prepared single systems.

 

[martinbn]

No, vanhees71's interpretation is not a Copenhagen interpretation, independent of whether he adheres exactly to Ballentine or not.

Why not? Where does he differ?

 

[martinbn]

But he says that the preparation procedure refers to a single electron. A bit later he even emphasizes that the so defined ensembles are different from preparing a bunch of electrons at once. I think it's pretty clear that the preparation procedure must relate to single electrons, if you want to strictly define an ensemble of "equally prepared single electrons", and as far as I understand him Ballentine precisely states this. The statistical interpretation is anyway very close to Copenhagen a la Bohr. Here's the precise quote from Ballentine:

View attachment 339219
Again in I the preparation procedure refers to single systems. Concerning the properties of the system described by the so prepared state it provides only the statistical properties and thus only refers to ensembles of such prepared single systems.

The statistical interpretation falls in group (I) from the quote, and yours in group (II).

 

[gentzen]

Why not? Where does he differ?

At many points. He accepts neither the role of classical concepts in Bohr's thinking, nor the collapse of the wavefunction as an update of knowledge in Heisenberg's thinking. And your claim

The statistical interpretation falls in group (I) from the quote, and yours in group (II).

feels strange to me. When has vanhees71 ever asserted that "a pure state provides a complete and exhaustive description of an individual system (e.g., an electron)"?

 

[vanhees71]

The statistical interpretation falls in group (I) from the quote, and yours in group (II).

My interpretation falls in group I, because for me all the state describes concerning the properties of the systems prepared in a state are the statistical properties, which of course refer to an ensemble of equally prepared systems. I just say the same as what Ballentine says with different words.

 

[PeterDonis]

he says that the preparation procedure refers to a single electron

What you actually mean here is that the phrase "single electron" occurs in the passage in question from Ballentine's book. But it occurs in the context of describing an ensemble, which, as Ballentine makes clear, is not the same thing as the real collection of real electrons that get prepared and measured in real experiements. So you are taking Ballentine out of context when you claim that his use of the phrase "single electron" means that he takes the quantum state or the preparation procedure to apply to real single electrons in real experiments. Read in context, that is not what he is saying.

 

[PeterDonis]

I just say the same as what Ballentine says with different words.

Perhaps you think you do, but nobody else here appears to agree.

 

[vanhees71]

But then you couldn't use the formalism to describe real-world experiments. That's for sure not what Ballentine implies.

 

[vanhees71]

Perhaps you think you do, but nobody else here appears to agree.

@gentzen obviously understands it as I mean it.

 

[PeterDonis]

But then you couldn't use the formalism to describe real-world experiments.

Sure you can. Ballentine describes how: you treat the real world statistical sample as just that, a statistical sample from the abstract ensemble that the formalism describes. Then you use standard statistical techniques to see how well the statistical sample matches what you would expect from the abstract ensemble.

 

[vanhees71]

That's what I also say the whole time, and you get this statistical sample by preparing single electrons (using Ballentine's example for the argument) repeatedly in the same way, i.e., with a preparation procedure referring to a quantum state. This is even emphsized by Ballentine himself in distinguishing it from preparing once a many-electron system, which of course, if repeated. forms another statistical sample, which is not the same as preparing many times a single electron:

 

[PeterDonis]

you get this statistical sample by preparing single electrons

Yes.

distinguishing it from preparing once a many-electron system, which of course, if repeated. forms another statistical sample, which is not the same as preparing many times a single electron

Yes.

with a preparation procedure referring to a quantum state

The state can be taken to refer to the preparation procedure, but if you take the state this way, it refers to the preparation procedure as it applies to the ensemble, not as it applies to an actual single electron in an experiment. The state is part of the mathematical model, not part of what you compare the model's predictions to. The actual preparation you do in the experiment, and the actual electron you do the preparation on, are part of what you compare the model's predictions to.

In other words, the term "preparation procedure", without any context, is ambiguous. There is the actual preparation you do in the actual experiment, that prepares single electrons, repeatedly, and there is the abstract "preparation procedure" in the model, that prepares an abstract ensemble. These are two different things, and the state, which is also in the model, if it is taken to refer to a preparation procedure, refers to the second thing just described, not the first.

 

[vanhees71]

Yes, of course the math is the math the real world is the real world, but the math accurately describes the real world according to the observations. So the samples you prepare with a preparation procedure are described by the formalism correctly, i.e., they are proxies of the ensembles described by the used preparation procedure. In high-precision experiments you can make the samples to come as close as you wish to the ensembles by just "collecting enough statistics", i.e., by repeating the experiment sufficiently often.