- #106
martinbn
Science Advisor
- 3,674
- 1,874
You do understand that it can be an abstraction in one interpretation and not in another, don't you?vanhees71 said:It's not an abstraction.
You do understand that it can be an abstraction in one interpretation and not in another, don't you?vanhees71 said: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 said:It's not an abstraction.
So now you agree that an ensemble is an abstract infinite set?vanhees71 said:Of course, from a mathemtical point of view you need infinite abstract ensembles to define probabilities.
No, you deal with real-world finite sets of actual experiments, which are not, as Ballentine says, correctly described as "ensembles".vanhees71 said:QT is, however a physical theory and it is successfully applied to real-world experiments, where you deal with real-world finite ensembles
Except for the wordings, to me the "propensitites" in a single experiment, follwing a preparation still only has a the same operational statisitical meaning.Morbert said: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.
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.PeterDonis said:No, you deal with real-world finite sets of actual experiments, which are not, as Ballentine says, correctly described as "ensembles".
Fra said: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?
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.Fra said: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.
vanhees71 said:QT is, however a physical theory and it is successfully applied to real-world experiments...
The physical basis would be the preparation procedure, which involves actual physical equipment and processes. At least, that is how Ballentine explains it.Fra said:wether there is a physical basis to the ensemble
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.Fra said:The finite ensenble
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.PeterDonis said:The physical basis would be the preparation procedure, which involves actual physical equipment and processes. At least, that is how Ballentine explains it.
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!PeterDonis said: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.
For me Born's rule is one of the fundamental postulates, and it's indeed crucial to make the theory to a physical theory.GarberMoisha said:That would be a stretch. Remove the Born's rule and it becomes a non-physical theory altogether.
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 said:It's really hard to discuss if one is not allowed to use standard terminology!
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).vanhees71 said: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
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.vanhees71 said:It's well known that there's a difference between mathematical, idealized infinetely large ensembles and finite real-world empirical ensembles.
I am disputing whether "ensemble" is "standard terminology" for real-world collections of data, at least not in QM. That is why I gave Ballentine as a counter-example. I do not know another standard term for real-world collections of data. I just know that, at least according to Ballentine, "ensemble" is not that term.vanhees71 said: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!
Not if you are claiming he uses "ensemble" to mean finite real-world collections of data. I have already given specific quotes to show that he does not.vanhees71 said:Ballentine's book is very clear
Then perhaps there is a difference of terminology between different parts of the physics community in this regard. Is there a standard reference that experimentalists use for such terminology?vanhees71 said: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).
vanhees71 said: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).
I know that you are asking vanhees71 for a "reference of experimentalists terminology". I cannot help with that. But maybe I can help with terminology common among (applied) statisticians:PeterDonis said:Then perhaps there is a difference of terminology between different parts of the physics community in this regard. Is there a standard reference that experimentalists use for such terminology?
That is indeed a very good and readable book, and it contains a 24-page glossary and a 7-page index. Here are some examples from the glossary:haushofer said:I'm reading The art of statistics by Spiegelhalter now. Fun book which stresses conceptual aspects of statistics and data analysis.
I agree. Unfortunately Born's rule seems inextricably linked to the term "measurement" (and, in consequence, decoherence, macroscopic apparatus, etc.).vanhees71 said:For me Born's rule is one of the fundamental postulates, and it's indeed crucial to make the theory to a physical theory.
vanhees71 said:Measurements are nothing else than interactions between the system and a measurement device, which obey the same "quantum rules" as any other interaction.
Excellent. Your paper shows that (using the Schwinger-Keldysh formalism) one can write down expressions for observable quantities without the need to talk about measurements and (god forbid!) collapsing wavefunctions.vanhees71 said:In the paper we describe of course an open system, because we couple the particle to a heat bath, but the underlying equations are quantum time evolution
Sounds tautological. And beside the point. Obviously you disagree with John Bell ("Against Measurement").vanhees71 said:All of physics is about observation and thus measurement
vanhees71 said: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!
That's called a statistical sample.PeterDonis said:I do not know another standard term for real-world collections of data.
I understand that, but it is still a published reference. If there is indeed a difference of terminology in this area in different parts of the relevant scientific community, you should give published references for your preferred usage of the term "ensemble", as I have asked you.vanhees71 said:Ballentine's book is not the bible
Then I'm very confused about how you can be so confident about your usage, with no reference to back it up. I have given a reference to back up mine.vanhees71 said:I don't have specific references.
@A. Neumaier gave a term for it in post #132.vanhees71 said:Just tell me, how I'm allowed to call collected data of real-world experiments, that are taken from "equally prepared systems" in this forum
We can only discuss real issues if we agree on the terminology to describe them. If a particular term has multiple, incompatible usages, we don't have such agreement. That appears to be the case for the term "ensemble".vanhees71 said:so that we can discuss the real issues rather than pure semantics
vanhees71 said:I try to learn the special "Physics Forum's terminology" defined by @PeterDonis.
Yes I do! Just tell me, how you want me to phrase things, so that we can avoid this nonsensical debates about semantics!weirdoguy said:This is just ridiculous, @PeterDonis backed up his usage, and you are just quibbling all over the place. Do you even read what others are saying?