- 14,564
- 7,158
So you disagree with Ballentine?vanhees71 said:This quote I would not sign.


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.
atyy said:[...]Incidentally, the paper also has another wrong criticism of the standard interpretation. The paper claims that position and momentum can be simultaneously measured, but in the counterexample he gives, the position and momentum are not canonically conjugate. [...]
dextercioby said:Do you have /know of a proof of that?
It doesn't determine the momentum in the orthodox sense. It only determines momentum if one assumes a semi-classical picture in which the particle is a point-like object with straight (not Bohmian) trajectory. As Einstein would say, it is theory that determines what is measurable.atyy said:Using the position at the screen to measure the momentum gives the momentum at the slit.
Demystifier said:It doesn't determine the momentum in the orthodox sense. It only determines momentum if one assumes a semi-classical picture in which the particle is a point-like object with straight (not Bohmian) trajectory. As Einstein would say, it is theory that determines what is measurable.
The point is the uniqueness. For each point inside a simplex, there is a decomposition into ## \sum_i p_i n^i## where ##n^i## are the vertices of the simplex. In 3D those vertices would be maximal four points. If you start with more vertices in 3D, the convex hull is in general no longer a simplex, and the decomposition is no longer unique.atyy said:I'm not sure off the top of my head, but in corresponds to a classical uncertainty being a unique mix of "pure states" (the complete state that can be assigned to a single system), whereas quantum density matrices don't have a unique decomposition into pure states (ie. preferred basis must be picked out by measurement or decoherence or whatever).
Holevo has some discussion at the start of his book (I'm don't have it with me at the moment).
vanhees71 said:In this way the states are referring on the one hand to single objects (preparation procedure for single objects). On the other hand they don't have much of a meaning for the single object and measurements [...]
vanhees71 said:Well, to talk about preparation and measurement you must give a meaning to preparing of and measuring observables on the single objects making up the ensemble.
vanhees71 said:What are "events" if not "clicks of a detector"?
...
It's also not true that we only measure quantum-mechanical expectation values.
vanhees71 said:What are "events" if not "clicks of a detector"? Measurements always mean the interaction of the measured object with a macroscopic measurement device which enables an irreversibly stored measurement result. That such devices exist is (a) empirically clear, because quantum physicists in all labs successfully measure quantum objects (single photons, elementary particles, etc.) and (b) also follows from quantum statistics, according to which the macroscopic ("coarse grained") observables indeed follow classical laws.
vanhees71 said:It's also not true that we only measure quantum-mechanical expectation values. E.g., in the usual Stern-Gerlach experiment with unpolarized Ag atoms we don't measure 0 spin components but ##\pm \hbar/2## components for each individual silver atom. Of course, on the average over a large example we get 0.
vanhees71 said:Landau and Lifshitz is some decades old. There's much progress in the understanding of the classical behavior of macroscopic systems from the point of view of quantum theory. Nevertheless note that Landau and Lifshitz vol. X is the only general textbook containing a derivation of the transport equation (classical) from the Kadanoff-Baym equation (though it's not named so, as is understandable, because it's a Russian textbook ;-)).
vanhees71 said:Sure if you know all cumulants you know the complete probabilities/probability distribution, but that's far more than just the expectation values. You need an ensemble to measure all (relevant) cumulants to reconstruct the probability function, i.e., you have to measure on single systems of an ensemble with a sufficient accuracy. The resolution of the detector must be the better and the ensemble must be the larger (and the more accurately prepared) the more cumulants you want to resolve.