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DarMM said:A value on the card I assume. Let's just focus on the nonlocality. In your table how does it manifest?
The probability for each result for one particle depends on the setting for the measurement of the other particle.
DarMM said:A value on the card I assume. Let's just focus on the nonlocality. In your table how does it manifest?
DarMM said:A value on the card I assume.
stevendaryl said:We have 16 possibilities, which we can characterize by 4 numbers: ##A_j##, ##a_j##, ##B_j##, ##b_j## where ##A_j## is the ##j^{th}## measurement on the first particle, ##a_j## is the ##j^{th}## result of that measurement (either "up" or "down"), ##B_j## is the ##j^{th}## measurement on the second particle, and ##b_j## is the ##j^{th}## result of that measurement.
DarMM said:take the observable ##B_2##.
DarMM said:There is only a subset on which ##B_{\frac{3\pi}{4}}## is defined as a random variable.
How is that enough to establish nonlocality rather than just correlation, i.e. isn't that just ##P(R_1|R_2) \neq P(R_1)##stevendaryl said:The probability for each result for one particle depends on the setting for the measurement of the other particle.
Josh0768 said:Hey, could you tell me what book/paper that quote is from?
A. Neumaier said:But he forgets the collapse, which is not part of the minimal statistical interpretation ...
DarMM said:How is that enough to establish nonlocality rather than just correlation, i.e. isn't that just ##P(R_1|R_2) \neq P(R_1)##
(##R## being the results)
Faye identifies the Copenhagen interpretation with Bohr's views alone, whereas it is usually considered to be the whole spectrum of views in Bohr's and Heisenberg's writings. Note that Faye acknowledges that Heisenberg endorsed collapse:Lord Jestocost said:As Jan Faye puts it (https://plato.stanford.edu/entries/qm-copenhagen/):
Jan Faye said:it was Heisenberg's exposition of complementarity, and not Bohr's, with its emphasis on a privileged role for the observer and observer-induced wave packet collapse that became identical with that interpretation.
This is in direct opposition with the quote from Heisenberg given in post #21, where he denies causality.Jan Faye said:Heisenberg, in contrast to Bohr, believed that the wave equation gave a causal, albeit probabilistic description of the free electron in configuration space.
James Henderson said:There are, however, several strains of Copenhagenism extant, each largely accepting Born’s assessment of the wave function as the most complete possible specification of a system and the notion of collapse as a completely random event.
DarMM said:Here it no longer is, but rather is the outcome of another random variable: "Device Setting". So perhaps we can agree that you can have a single sample space, but at the "price" of forgoing ##S_{\theta}##, with ##\theta## any angle, being a physical quantity. The only physical quantity is "device setting", thus rendering the account non-representational.
PeterDonis said:I think this is misstated. You are only making one measurement on each particle, so there is no need for an index ##j## saying which measurement. For ##A## and ##B##, you have two possible orientations you can choose for the one measurement.
I think that's fine and we've already agreed that essentially only one spin (let's say) observable gets to become a macroscopic observable in each round.stevendaryl said:This has probably gone on long enough, but the point of this "toy" model is to realize the idea that the only thing that's "real" is macroscopic observables. Microscopic observables are calculational tools, merely. It's a toy model, not to be taken seriously. BUT I claim that it is empirically equivalent to standard quantum mechanics. I really think that the minimal interpretation basically amounts to this.
One must be a bit careful, because in the early writings particularly by Heisenberg there hasn't been made the very important difference between causality and determinism.A. Neumaier said:Faye identifies the Copenhagen interpretation with Bohr's views alone, whereas it is usually considered to be the whole spectrum of views in Bohr's and Heisenberg's writings. Note that Faye acknowledges that Heisenberg endorsed collapse:Moreover, I doubt that Faye is a completely reliable source. For example, in the same article he also claims that
This is in direct opposition with the quote from Heisenberg given in post #21, where he denies causality.
Finally, to show that Faye's position is not the consensus on the issue of collapse in the Copenhagen interpretation, note that
writes in the abstract:
- Henderson, J. R. (2010), Classes of Copenhagen interpretations: Mechanisms of collapse as a typologically determinative, Studies in History and Philosophy of Modern Physics, 41: 1-8.
Well, the notion of state also changed with time.vanhees71 said:One must be a bit careful, because in the early writings particularly by Heisenberg there hasn't been made the very important difference between causality and determinism.
The modern view is, e.g., according to Schwinger, Quantum Mechanics, Springer Verlag (see the very concise Prologue of this book about a very detailed exposition of a physical heuristics for QM) as follows:
(a) Causality (time-local form): If the state of a system is precisely known at time ##t_0## and the dynamics of the system is precisely known, then the state of the system is precisely und uniquely known at any later time ##t>t_0##.
(b) Determinism: In any state any observable of a system takes a definite value.
Obviously in this sense QT is causal but not deterministic
No. DarMM is correct. You can't combine outcomes from two different experiments into the one sample space if the experiments are incompatible. The sample space corresponds to all possible outcomes from a single experiment. ##d1## is a different experiment from ##d2## and since you can't do both at the same time, you can't combine the their outcomes into one sample space.Demystifier said:But I refuse to think of it as formalism, with or without ##\lambda##. I insist on thinking about it as possible events in the laboratory, which is quite Copenhagenish in spirit. In the case of spin measurement by SG apparatus, the possible outcomes are macroscopic dark spots on the screen at 4 possible positions (corresponding to 2 possible spins in direction ##d1## plus 2 possible spins in direction ##d2##). Those 4 possible positions of macroscopic dark spots on the screen can certainly be placed in a single sample space.
Nature lacks counterfactuals because that is what it means to be counterfactual. It is an epistemological concept that can never exist in actually measured experimental data.DarMM said:As for why nature lacks counterfactuals, that goes unexplained.
In post #76 I gave reference to an experiment where photon polarizations are measured in different bases as part of a single experiment.lodbrok said:No. DarMM is correct. You can't combine outcomes from two different experiments into the one sample space if the experiments are incompatible. The sample space corresponds to all possible outcomes from a single experiment. ##d1## is a different experiment from ##d2## and since you can't do both at the same time, you can't combine the their outcomes into one sample space.
This of course is true, but when we discuss general properties of nature (rather than results of particular experiment) we are using models. And counterfactuals is the essence of models. Basically it is meaningless to use counterfactuals when we speak about facts (nature itself) and it is meaningless not to use counterfactuals when we speak about models (properties of nature).lodbrok said:Nature lacks counterfactuals because that is what it means to be counterfactual. It is an epistemological concept that can never exist in actually measured experimental data.
What if the experiment is enriched with an additional piece of equipment that randomly decides whether the measurement will be performed in ##d1## or ##d2## direction? In this case all 4 outcomes are possible results of the measurement, so all 4 belong to the same sample space.lodbrok said:No. DarMM is correct. You can't combine outcomes from two different experiments into the one sample space if the experiments are incompatible. The sample space corresponds to all possible outcomes from a single experiment. ##d1## is a different experiment from ##d2## and since you can't do both at the same time, you can't combine the their outcomes into one sample space.
It depends on what one means by "satisfactorily". I am quite satisfied with the idea proposed in my signature below.vanhees71 said:an exception is Bohmian mechanics which is a deterministic interpretation, but so far not satisfactorily generalized to relativistic Q(F)T
A state cannot preserve energy and momentum or not. Energy and momentum are conserved if the Hamiltonian is not explicitly time-dependent and momentum if the Hamiltonian doesn't depend on position. In the formalism an observable ##A## (maybe explicitly time dependent) is conserved iff the operator for its time, derivative,A. Neumaier said:Well, the notion of state also changed with time.
In 1927, Born, Bohr and Heisenberg always equated ''state'' with ''stationary state'', and not with a general wave function. See the quotes given in post #21. These states preserve energy and momentum exactly (as all three authors emphasize) but don't respect causality in the form (a), which was also the notion used by Born, Bohr and Heisenberg.
In contrast, the modern notion of state respects causality in the form (a), but preserves in the statistical interpretation energy and momentum only on the average.
In my thermal interpretation, the q-expectation of total energy and total momentum are exactly conserved beables, and the collection of all q-expectations is causal and deterministic in your sense (a) and (b), since the observables are not the operators but their q-expectations.
This is the case for every closed system, in particular for the universe as a whole. Of course I don't claim conservation in open systems.vanhees71 said:Energy and momentum are conserved if the Hamiltonian is not explicitly time-dependent and momentum if the Hamiltonian doesn't depend on position.
Only the quantum state as interpreted today, which is what I had already asserted. But in 1927, the notion of state was different!vanhees71 said:Of course, the quantum state obeys (a).
Well said! There is no theoretical physics without counterfactuals.zonde said:This of course is true, but when we discuss general properties of nature (rather than results of particular experiment) we are using models. And counterfactuals is the essence of models. Basically it is meaningless to use counterfactuals when we speak about facts (nature itself) and it is meaningless not to use counterfactuals when we speak about models (properties of nature).
Beables are not observables. The concept of beables was introduced by John Bell precisely to emphasize that they are different from observables. See e.g. the paper in my signature for more details.vanhees71 said:"beables" (in normal language "observables")
Well certainly it lacks counterfactuals in the sense that if I put jam on my toast, then I didn't put marmalade on my toast, i.e. the event that didn't occur simply didn't occur. Only Many-Worlds lacks this factual definiteness as it is called in Quantum Foundations, since there all events occur.lodbrok said:Nature lacks counterfactuals because that is what it means to be counterfactual. It is an epistemological concept that can never exist in actually measured experimental data.
Yes, but the point is that there isn't an outcome of the form ##(S_x, S_y, S_z)## that's what is meant when it is said there isn't a single sample space. For example in your case the outcomes are:Demystifier said:What if the experiment is enriched with an additional piece of equipment that randomly decides whether the measurement will be performed in ##d1## or ##d2## direction? In this case all 4 outcomes are possible results of the measurement, so all 4 belong to the same sample space.
Perhaps the example in the post above helps. So you can think of such an experiment as having a single sample space, but the point is that unlike classical mechanics ##(S_x, S_y, S_z)## don't all occur on each line. For instance if Spin were classical (even if it was stochastic) then for @Demystifier 's experiment we'd have something like (ignoring ##S_y##):zonde said:Any Bell inequality test that aims to close communication loophole has to combine all four experiments into one single experiment. Experiments like that have been performed number of times. Here is one https://arxiv.org/abs/quant-ph/9810080
So you are not making much sense to me.
Demystifier said:What if the experiment is enriched with an additional piece of equipment that randomly decides whether the measurement will be performed in ##d1## or ##d2## direction? In this case all 4 outcomes are possible results of the measurement, so all 4 belong to the same sample space.
And by the way, in the consistent histories interpretation, which perhaps is the most ontological version of "Copenhagen" interpretation, those 4 outcomes correspond to 4 histories that belong to the same consistency class.
Demystifier said:Beables are not observables. The concept of beables was introduced by John Bell precisely to emphasize that they are different from observables. See e.g. the paper in my signature for more details.
stevendaryl said:Yes, for Bell, a "beable" is some property that has a value whether it is observed, or not. Some physicists deny that there is such a thing, that nothing has a value unless it's measured. But that seems to me either to give a special role to consciousness or to lead to infinite regress: The particle doesn't have a position until it is detected, by (say), making the Geiger counter click. The Geiger counter doesn't click unless there is a microphone to record it. The microphone doesn't record it unless there is someone to play back the recording and hear it...
stevendaryl said:I just don't understand what is meant when people talk about things not being from the same sample space.
Basically what is meant is that the quantum observables alone can't be put in a single sample space together. To have a single sample space you have to also include the actual device settings. This is directly related to or simply another variant of contextuality/lack of counterfactual definiteness and is the difference between QM and a classical stochastic theory.stevendaryl said:But it seems to me that if we include the choice and the result, we can certainly put them all into the same probability space
I think there is problem with your choice of terminology. If you replace "single sample space" with "single set of initial conditions" it makes more sense. But it works only up to the point because then it would become quite clear that you are talking about superdeterminism, retrocausality or acausal constrain (there is correlation between initial conditions and measurement settings).DarMM said:However in the quantum case in #178 you can't do this. There isn't a single sample space for the quantum observables and your experimental setting is sort of intrinsically embedded in the outcomes preventing you from isolating "facts" about the microscopic system.
You do have a single sample space, but it's not one for the properties of the subatomic system alone of the form you are able to construct in classical mechanics. It's a macroscopic setting and subatomic variable product space. So contextuality is still manifest and in fact this is a consequence of contextuality.
Does that make more sense?
Perhaps, but I don't get to choose it. It's the standard terminology.zonde said:I think there is problem with your choice of terminology.
"Single sample space for the quantum observables alone" is perhaps cleanest.zonde said:If you replace "single sample space" with "single set of initial conditions" it makes more sense
Or as you said it's:
"If I measure the spin in the x-direction, there is a 50% chance of getting 'up', and if I measure the spin in the y-direction, there is a 50% chance of getting 'up'"
i.e. "chance if I measure...that I get" rather than "chance that it is". That's the difference between QM and a classical stochastic theory and is a direct consequence of contextuality/lack of counterfactual definiteness/lack of a single sample space for the observables themselves alone.
As far as I can trust wikipedia it is not standard terminology.DarMM said:Perhaps, but I don't get to choose it. It's the standard terminology.
Well yes of course a nonlocal classical theory can do it, but this is the whole point of this thread.stevendaryl said:You can certainly concoct a classical model with the same probabilities as, say, the EPR experiment. Bell's theorem just tells us that you can't do it using local interactions.
I'm saying that when Quantum Probability and Quantum Foundations texts and papers say "there is no single sample space" their meaning is the one I'm giving and that that choice of phrase is not a personal invention of mine but comes from those communities.zonde said:As far as I can trust wikipedia it is not standard terminology.
Sample space: In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.
I would like to take a bit further this argument.stevendaryl said:Yes, for Bell, a "beable" is some property that has a value whether it is observed, or not. Some physicists deny that there is such a thing, that nothing has a value unless it's measured. But that seems to me either to give a special role to consciousness or to lead to infinite regress: The particle doesn't have a position until it is detected, by (say), making the Geiger counter click. The Geiger counter doesn't click unless there is a microphone to record it. The microphone doesn't record it unless there is someone to play back the recording and hear it...
If it's true I would say it is false confidence. Either you have to believe that microscopic systems have "beables" or you have to be able to explicitly demonstrate how apparent macroscopic "beables" can emerge from microscopic "beable-lessness" (and you should do that without any use of "bebles" obviously).stevendaryl said:I think that most physicists are fairly confident that measuring devices themselves are described by the same quantum mechanics as the systems being studied.
Yes. The problem, of course, is that there is no sharp border between macro and micro. Hence, if macroscopic properties are beables, then some microscopic properties must be beables too. Such a point of view naturally leads to Bohmian mechanics as explained in the paper in my signature.stevendaryl said:Copenhagen seems to put macroscopic properties in the role of "beables". They have definite values at all times.
DarMM said:Well yes of course a nonlocal classical theory can do it, but this is the whole point of this thread.
My point was to point out the difference between QM and Classical Stochastic theories.
rubi said:The situation is really simple: There is no state space ##\Lambda## such that ##A_\alpha: \Lambda\rightarrow\{-1,1\}## and ##B_\beta: \Lambda\rightarrow\{-1,1\}## are functions on this state space for every ##\alpha## and ##\beta## such that the correlations ##\left<A_\alpha B_\beta\right>## match the predictions of quantum mechanics. That's just a mathematical fact and there is just no way to circumvent it. It also has nothing to do with macroscopic or microscopic observables.
The only way to model the system on a single state space is to give up the idea that all ##A_\alpha## and ##B_\beta## are functions on the state space for all ##\alpha## and ##\beta##. One has to admit, that this is a truly novel situation, which never occurs in classical theories.
I think you and @rubi are using the word "classical" with different meanings.stevendaryl said:But as I have said a number of times, there is no problem getting the probabilities to work out the same as EPR using classical probabilities if we allow nonlocal interactions. So the correct conclusion, as Bell said, is that it's a situation which never occurs in LOCAL classical theories.
No, I was saying that the differences between QM and classical stochastic processes was in the contextuality/counterfactual indefiniteness.stevendaryl said:Okay, but every time the business about "different sample spaces" was brought up, it was said as if the probabilities themselves were incompatible with a stochastic process.
@Demystifier was basically asking about two things. Exactly what Copenhagen and similar views mean by "know" and exactly how they get around nonlocality or is their method for getting around nonlocality consistent. I answered the first part in my initial post and the rest has been about the second point.stevendaryl said:I would not say that this thread is about locality. It's about the meaning of the Copenhagen interpretation.
Well, then please provide a counterexample. It should look something like this:stevendaryl said:But that's not true. As I have said a number of times, there is no problem getting the probabilities to work out the same as EPR using classical probabilities if we allow nonlocal interactions.
A classical stochastic theory can replicate the statistics, but it doesn't need to either:stevendaryl said:But it doesn't seem to do that, since a classical stochastic theory can be contextual in the same way (which was what my example of implementing the EPR probabilities classically shows).
rubi said:Well, then please provide a counterexample. It should look something like this:
##\Lambda = \{x,y,z\}##
##A_0(x) = 1, A_0(y) = -1, A_0(z) = -1##
##A_1(x) = -1, A_1(y) = 1, A_1(z) = -1##
(and so on for ##B_\beta##).
Then provide a probability distribution on ##\Lambda##, e.g.
##P(x) = 0.5, P(y) = 0.5, P(z) = 0##
And then calculate the correlations ##\left<A_\alpha B_\beta\right>## and compare them to the QM result. You won't be able to do this (if you want them to match).
But your stochastic model will still not have the functions ##A_\alpha## and ##B_\beta##. One has to admit that this is a true novelty compared to classical mechanics.stevendaryl said:I'm not disputing Bell's theorem. I'm saying that the probabilities in the EPR model can be reproduced by a classical stochastic model, if you allow nonlocal interactions. So the EPR statistics don't say anything about classical versus nonclassical unless you impose locality.