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martinbn
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I must say that I am confused. Either I don't understand something (most likely) or what he calls ensemble interpretation is more that an ensemble interpretation, it is ensemble++.
C++ is C plus object programming. Ensemble++ is ensemble plus object-ive existence.martinbn said:I must say that I am confused. Either I don't understand something (most likely) or what he calls ensemble interpretation is more that an ensemble interpretation, it is ensemble++.
So how is then in this example ##\lambda## defined and how do you then conclude that the quantum state is "ontic"? The quantum-mechanical calculation is of course simple and clear, and I still don't see how this example or any other can "disprove" the ensemble interpretation.Demystifier said:Yes, ##\lambda## is something like that in the Bell theorem. But it is not assumed that it is deterministic and local. It is only assumed that it is ontic, in the sense defined mathematically (but quite abstractly) in the paper.
No it's very well defined by quantum theory, what's objective: It's the probabilities for the outcome of measurements of any observable, given the state/preparation of the system. "Minimal" means that there's no other objective "reality" than these probabilities described by the quantum state. "Ensemble" means that you can empirically check these probabilities only on an ensemble by statistical evaluation of the measurement outcomes.Demystifier said:Because the Ballentine interpretation assumes that objective microscopic properties exist, but does not specify what they are. PBR also assume that they exist (they call them ##\lambda##) and also don't specify what they are.
It is not defined explicitly, the proof is not constructive. The theorem proves that ##\lambda## with certain property does not exist in the mathematical sense, by assuming that it does and proving a contradiction. It's quite abstract, so it's not so easy to understand it with a typical physicist way of thinking.vanhees71 said:So how is then in this example ##\lambda## defined and how do you then conclude that the quantum state is "ontic"?
So how do you interpret the Ballentine's claim of incompleteness (post #14)?vanhees71 said:Whether or not this is a complete description of nature the minimal interpretation is agnostic about.
vanhees71 said:... "Minimal" means that there's no other objective "reality" than these probabilities described by the quantum state. ...
In contrast, the Statistical Interpretation considers a particle to always be at some position in space, each position being realized with relative frequency ##|\psi(r)|^2## an ensemble of similarily prepared experiments.
martinbn said:It is from Ballentine's paper on the statistical interpretation.
May be I havn't ready carefully and have taken it out of context. May be in that paragraph he is making the point that it is not like that. May be.Morbert said:This stood out to me as well. I always thought of the "statistics" in the statistical interpretation as statistics regarding measurement outcomes as opposed to statistics regarding Bell-like beables.
Ok, I try to understand it again. There must be some meaning in what's contradicted by the quantum formalism to what's described by probability distributions for ##\lambda## which is not defined ;-)). I'm always a bit lost with such presumably "mathematical" proofs with only vaguely defined quantities, which then are supposed to have some philosophical meaning like the contradistinction between ontic and epistemic ;-)). It's strange to have vague definitions in mathematics and proving something about these vague definitions ;-)).Demystifier said:It is not defined explicitly, the proof is not constructive. The theorem proves that ##\lambda## with certain property does not exist in the mathematical sense, by assuming that it does and proving a contradiction. It's quite abstract, so it's not so easy to understand it with a typical physicist way of thinking.
I don't know, I'm not able to read Ballentine's mind ;-)).Demystifier said:Maybe for Ballentine "to be" means "to be measured"?
I don't think so, but maybe @vanhees71 could use such an argument.
I agree, except that I would not call it vague but abstract. The famous Godel theorems, as well as the Banach-Tarski paradox, are also of this sort.vanhees71 said:Ok, I try to understand it again. There must be some meaning in what's contradicted by the quantum formalism to what's described by probability distributions for ##\lambda## which is not defined ;-)). I'm always a bit lost with such presumably "mathematical" proofs with only vaguely defined quantities, which then are supposed to have some philosophical meaning like the contradistinction between ontic and epistemic ;-)). It's strange to have vague definitions in mathematics and proving something about these vague definitions ;-)).
This quote I would not sign. In QT an observable has either a determined value (due to preparation) or it has no determined value, because the system is prepared in a state, where the probability for finding some value is non-zero for at least one possible outcome of the measurement.martinbn said:What about this
"In contrast, the Statistical Interpretation considers a particle to always be at some position in space, each position being realized with relative frequency an ensemble of similarily prepared experiments."
It is from Ballentine's paper on the statistical interpretation.
Except Bohm, of course.vanhees71 said:Then you'd need an extension of QT to some (according to Bell and the empirical findings about Bell's inequality necessarily non-local) deterministic theory, which however nobody ever has been able to formulate.
So you disagree with Ballentine?vanhees71 said:This quote I would not sign.
Demystifier said:Except Bohm, of course.
In contrast, the Statistical Interpretation considers a particle to always be at some position in space, each position being realized with relative frequency ##|\psi(r)|^2## an ensemble of similarily prepared experiments.
Can you phrase all that using statistical interpretation language? You talk about the system/particle, its state and the observables as if everything refers to a single object, but the state is the state of the ensemble, not of just one representative of it and so on.vanhees71 said:This quote I would not sign. In QT an observable has either a determined value (due to preparation) or it has no determined value, because the system is prepared in a state, where the probability for finding some value is non-zero for at least one possible outcome of the measurement.
For me the strength of the statistical interpretation was that it takes Born's rule seriously and states that the only meaning of the quantum state are the probabilities for the outcomes of measurements.
To assume that "a particle always is at some (definite) position in space" would somehow imply that the position vector has always a determined value, no matter in which state the particle is prepared, but this, at least for me, is not what the quantum formalism tells us. It then would immediately imply some HVs which determine this position and thus that the "quantum probabilities" would be only "subjective", i.e., due to incomplete knowledge about the state. Then you'd need an extension of QT to some (according to Bell and the empirical findings about Bell's inequality necessarily non-local) deterministic theory, which however nobody ever has been able to formulate.
The difference is that Ballentine is agnostic about determinism. Particle can have a position x at each time t, but x(t) can be stochastic (instead of deterministic). An explicit example is the Nelson interpretation.PeterDonis said:This quote from the 1970 paper...
...makes it seem to me like Ballentine himself is a Bohmian!
PeterDonis said:...makes it seem to me like Ballentine himself is a Bohmian!
vanhees71 said:Ok, I try to understand it again. There must be some meaning in what's contradicted by the quantum formalism to what's described by probability distributions for ##\lambda## which is not defined ;-)). I'm always a bit lost with such presumably "mathematical" proofs with only vaguely defined quantities, which then are supposed to have some philosophical meaning like the contradistinction between ontic and epistemic ;-)). It's strange to have vague definitions in mathematics and proving something about these vague definitions ;-)).
Perhaps it's time that you write down a paper on your own interpretation!vanhees71 said:I fear so ;-). I've to read the old RMP paper again. The more one thinks about the foundations the more you change your opinion yourself over the years!
What do you mean by "simplex"?atyy said:I think one way you can think of it is that the state space of quantum mechanics is not a simplex, However, the state space of classical probability is a simplex. The question is whether it is possible to construct a theory preserving all the predictions of QM (to some accuracy) that has an enlarged state space that is a simplex. [Though I guess this criterion is problematic for continuous variables, since I think the state space is not a simplex for classical continuous variables?]
Demystifier said:What do you mean by "simplex"?
Can you point to where the claim is, so that we can see the context.atyy said:...The paper claims that position and momentum can be simultaneously measured,...
So if I understood it correctly, classical probability space is simplex because the probabilities satisfy ##p_i\geq 0##, while the quantum state space is not simplex because the coefficients of superposition do not satisfy ##c_i\geq 0##, is that right?atyy said:A shape with sharp points. Like Fig 1.2 in https://www.researchgate.net/publication/258239605_Geometry_of_Quantum_States.
Demystifier said:So if I understood it correctly, classical probability space is simplex because the probabilities satisfy ##p_i\geq 0##, while the quantum state space is not simplex because the coefficients of superposition do not satisfy ##c_i\geq 0##, is that right?
Demystifier said:I think it would be very strange to deny that. Perhaps consistent-histories interpretation denies that (I'm not sure about that), but other interpretations don't.
Maybe, I've my own version of "minimal interpretation". So here I try to very quickly state my point of view:martinbn said:Can you phrase all that using statistical interpretation language? You talk about the system/particle, its state and the observables as if everything refers to a single object, but the state is the state of the ensemble, not of just one representative of it and so on.
Adding again one more interpretation? What should this be good for?Demystifier said:Perhaps it's time that you write down a paper on your own interpretation!
Don't you find it confusing?vanhees71 said:the states are referring on the one hand to single objects ... On the other hand they don't have much of a meaning for the single object
You would not need to respond to silly questions on this forum, you could just point to your paper. In that way you would have much more time for shut up and calculate.vanhees71 said:Adding again one more interpretation? What should this be good for?
There is no full inside agent theory yet but conceptually the ensemble picture of small subatomic physics seems to conceptually correspond to agents living in the the classical background environment, where they moreover can "communicate" classically and form consensus without "quantum weirdness" and without risk beeing "saturated" by information. Ie. the Agents can make inferences and non-lossy storage. These agents are making inferences and predictions from a "safe" distance, so that we can assume that they themselves are not affected by the backreaction ofthe system they interact with.Demystifier said:think the ensemble interpretation with non-objective properties would be more-or-less equivalent to QBism
martinbn said:Can you point to where the claim is, so that we can see the context.