The Probability Distribution and 'Elements of Reality'

[Lynch101]

TL;DR Summary

The purpose of the thread is to investigate how the probability distribution of a system corresponds to 'elements of reality'.

The below comment by @vanhees71 is an interesting one and I would be interested in exploring its implications. I am inclined to think that we can draw certain inferences about nature based on how we interpret the probability function and what it tells us about the elements of reality of the quantum system.

The probability distribution obviously corresponds to elements of reality, because it can be tested by observations on ensembles of equally prepared systems.

What elements of reality does the probability distribution correspond to?
Which elements of reality does it correspond to for each run of an experiment?

It's described by the position-probability distribution, which tells you for any region in space what the probability is to find it there when looking.

If the position-probability distribution tells us the probability for finding the system in the given region of space, does this mean that there is an element of reality of the system in each region of space with a non-zero probability value?

 

[vanhees71]

For me an element of reality is an objectively observable phenomenon of Nature. One phenomenon is, e.g., in a double-slit experiment with single particles, that the position, where a particle going through the double slit hits the screen is random. Quantum theory predicts the probability distribution of these observable positions. To test this prediction you need to repeat the experiment often enough to be able to collect enough statistics to confirm or disprove the connection with a given level of significance.

 

[Demystifier]

For me an element of reality is an objectively observable phenomenon of Nature.

It's irrelevant what is element of reality for you. (Likewise, a new age guru might say that for him energy is the force that governs the universe.) What matters is what is meant by element of reality in the quantum foundations community.

 

[vanhees71]

Ok, is there a single clear definition of "element of reality" in the quantum foundations community? I doubt it!

 

[Demystifier]

Ok, is there a single clear definition of "element of reality" in the quantum foundations community? I doubt it!

There isn't, but just because the concept is not entirely clear in the community does not mean that any idea that comes outside of the community is relevant in the community.

Likewise, the concept of global energy may not be entirely clear in the general relativity community, but it doesn't mean that the insight of guru in my previous post is relevant.

 

[vanhees71]

Well, then we cannot discuss about these issues anyway. It's then really a subject for a closed "quantum foundations community". Well, I better stick with the physicists who have clear definitions and perform well-described real-lab experiments a la Zeilinger et al and no-nonsense theorists a la Weinberg.

 

[Demystifier]

Well, I better stick with the physicists who have clear definitions and perform well-described real-lab experiments a la Zeilinger et al and no-nonsense theorists a la Weinberg.

If you didn't often make claims that go far beyond Zeilinger and Weinberg, nobody would make objections.

 

[Lynch101]

For me an element of reality is an objectively observable phenomenon of Nature. One phenomenon is, e.g., in a double-slit experiment with single particles, that the position, where a particle going through the double slit hits the screen is random. Quantum theory predicts the probability distribution of these observable positions. To test this prediction you need to repeat the experiment often enough to be able to collect enough statistics to confirm or disprove the connection with a given level of significance.

In the first run of an experiment, however, we have a probability distribution. What 'elements of reality' (according to your definition) does it correspond to?

 

[vanhees71]

I don't understand the question.

 

[Lynch101]

I don't understand the question.

You mentioned that the probability distribution 'corresponds to elements of reality'. I'm asking to which 'elements of reality*' the probability distribution corresponds for the first run of an experiment and each subsequent run?

*According to your own definition of 'elements of reality'

 

[vanhees71]

You mean in a single experiment?

The meaning of the state is twofold: (a) it describes the result of a preparation procedure of a single system and (b) it provides the probabilities for the outcome of measurements of observables given this preparation procedure/state.

Elements of reality are the equipment used to prepare the system and to measure the observables. Quantum theory provides a description thereof.

 

[Fra]

What elements of reality does the probability distribution correspond to?
Which elements of reality does it correspond to for each run of an experiment?

From my perspective (interpretation from agent/qbist view), the element of reality the expectation corresponds to is the physical state of the agent itself. Thus, I assign the reality to the observer side of things, not to the black box. This sort of element of reality, is however fundamentally subjective, and often hidden to other agents, just like the black box is to the original agent.

Works for me. In a minimal interpretation I supposed it makes sense to assign "reality" to the actual evidence; ie. the data that makes up the ensemble, or statistics collected. This "data" and the expectations that's implicit in it, is as "real" as it gets for me.

/Fredrik

 

[Lynch101]

@vanhees71 If you agree with the following, then the subsequent points might be redundant.

The Statistical Interpretation, according to which a pure state (and hence also a general state) provides a description of certain statistical properties of an ensemble of similarily prepared systems, but need not provide a complete description of an individual system.

The Statistical Interpretation of Quantum Mechanics

Elements of reality are the equipment used to prepare the system and to measure the observables. Quantum theory provides a description thereof.

Am I correct in presuming that the element of reality of the quantum system would be the 'detection event' or the 'flash' made on the detector, as opposed, simply, to a measurement device that hasn't made a measurement?

For any given run of an experiment then, we have a probability distribution prior to making a measurement. So, to which elements of reality of the QM system do these non-zero probabilities correspond?

If the the flash on the detector screen is indeed the element of reality of the QM system, then in what sense does the probability distribution correspond to that element of reality, since detection events always occur with certainty?
EDIT: Only one measurement event occurs for the given system, with a probability of 1.

You mean in a single experiment?

The meaning of the state is twofold: (a) it describes the result of a preparation procedure of a single system and (b) it provides the probabilities for the outcome of measurements of observables given this preparation procedure/state.

I'm probably missing something here, but this sounds like we have a beginning and an ill-defined end, but no middle.

 

[Lynch101]

From my perspective (interpretation from agent/qbist view), the element of reality the expectation corresponds to is the physical state of the agent itself. Thus, I assign the reality to the observer side of things, not to the black box. This sort of element of reality, is however fundamentally subjective, and often hidden to other agents, just like the black box is to the original agent.

Works for me. In a minimal interpretation I supposed it makes sense to assign "reality" to the actual evidence; ie. the data that makes up the ensemble, or statistics collected. This "data" and the expectations that's implicit in it, is as "real" as it gets for me.

/Fredrik

Apologies Fredrik, I'm not overly familiar with the qbist interpretation. I was intending this more as a discussion of the statistical interpretation. I'll have to brush up on the qbist interpretation as I only have a very crude notion that the probability distribution applies to the knowledge of the 'agent', as you put it.

 

[Lynch101]

There isn't, but just because the concept is not entirely clear in the community does not mean that any idea that comes outside of the community is relevant in the community.

Sometimes it's easy to over-complicate these things. I think it's pretty clear what EPR were trying to get at when they were talking about a 'complete description of physical reality' and representing the 'elements of reality' of the system in the mathematics of the theory.

They were basically saying, describe everything about the quantum system i.e. provide all the information about the quantum system. They used the term 'elements of reality' to refer to the pieces of information or the 'features'/'characteristics'/'elements'/'parts'/[insert other descriptor here].

While they focused on one possible 'element of reality', they stated that it was far from 'exhausting all possible ways of recognizing physical reality'.

Likewise, the concept of global energy may not be entirely clear in the general relativity community, but it doesn't mean that the insight of guru in my previous post is relevant.

A wise guru once advised against blindly following the insights of gurus

Do not believe in anything simply because you have heard it. Do not believe in anything simply because it is spoken and rumored by many. Do not believe in anything simply because it is found written in your religious books. Do not believe in anything merely on the authority of your teachers and elders. Do not believe in traditions because they have been handed down for many generations. But after observation and analysis, when you find that anything agrees with reason and is conducive to the good and benefit of one and all, then accept it and live up to it.

​

 

[vanhees71]

@vanhees71 If you agree with the following, then the subsequent points might be redundant.
For any given run of an experiment then, we have a probability distribution prior to making a measurement. So, to which elements of reality of the QM system do these non-zero probabilities correspond?

An experiment consists of a preparation procedure followed by a measurement. E.g. in the SG experiment you put silver vapor into an oven at a given temperature and let out the silver atoms through a little hole. That's the "preparation". The so prepared "ensemble of silver atoms" is described by a quantum state (it's of course a mixed state, but that doesn't matter too much for the discussion of principles). Then you let this stream of Ag atoms go through a nicely tailored inhomogeneous magnetic field. By evaluating the time evolution of the system you can show that then the momentum and the spin component determined by the direction of the (homogeneous large part of the) magnetic field are entangled (you can make the entanglement almost perfect). What's predicted by this procedure is the probability distribution for finding each Ag atom on a plate. The measurement is of course simply done by putting a real plate somewhere, which you can then use to compare the distribution of hits on the plate with the predicted probablity distribution. You'll find two spots.

That the momenta/positions of the Ag atoms are really entangled with the value of the prepared spin component you need to perform other experiments, e.g., using another SG magnet on one of the two partial beams to demonstrate that the spin component is determined in this partial beam etc.

If the the flash on the detector screen is indeed the element of reality of the QM system, then in what sense does the probability distribution correspond to that element of reality, since detection events always occur with certainty?
EDIT: Only one measurement event occurs for the given system, with a probability of 1.

If the system wasn't prepared in a state, where the observable takes a determined value the probability for any outcome is not 1. The observable fact that the outcome is random is an element of reality described quantitatively by the quantum state and the corresponding probabilities.

I'm probably missing something here, but this sounds like we have a beginning and an ill-defined end, but no middle.

 

[Lynch101]

An experiment consists of a preparation procedure followed by a measurement. E.g. in the SG experiment you put silver vapor into an oven at a given temperature and let out the silver atoms through a little hole.

Presumably we know the position of this little hole, so can we conclude that, at some time, the particle must have been located within that region i.e. it must have had a definite position to within a certain margin of error.

If the system wasn't prepared in a state, where the observable takes a determined value the probability for any outcome is not 1. The observable fact that the outcome is random is an element of reality described quantitatively by the quantum state and the corresponding probabilities.

The question of completeness comes down to the correspondence of the mathematical formalism to 'elements of reality of the system'. If the element of reality of the system is the 'flash' on the detector screen then it cannot correspond to the probability distribution since 'the element of reality' is a single, definite event.

As per the L.E. Ballentine quote above

The Statistical Interpretation, according to which a pure state (and hence also a general state) provides a description of certain statistical properties of an ensemble of similarly prepared systems, but need not provide a complete description of an individual system.

It predicts the probability of measurement outcomes for an ensemble of similarly prepared systems, it doesn't provide a complete description of an individual system and so it is incomplete.

 

[vanhees71]

One element of reality is that outcomes of measurements of an observable are random except the system is prepared in a state, where it is not random. That's why the probability distribution for me is an "element of reality". Of course, Ballentine is right: To verify the predicted probability distribution you have to use a sufficiently large ensemble of equally prepared systems.

I don't know, what you consider as a complete description. For me QT is complete as long as nobody has found another theory compatible with all empirical facts that proves that in fact observables always take determined values. Within QT the randomness of the outcome of measurements is objective, i.e., it is not due to our lack of knowledge, as in classical statistical physics, but because the values of observables are really random variables.

 

[Lynch101]

I don't know, what you consider as a complete description. For me QT is complete as long as nobody has found another theory compatible with all empirical facts that proves that in fact observables always take determined values. Within QT the randomness of the outcome of measurements is objective, i.e., it is not due to our lack of knowledge, as in classical statistical physics, but because the values of observables are really random variables.

For me a complete description is one that describes the system fully and completely. It is not necessarily limited to what is observable since it might be the case that there are limits to what we can observe. It might be possible that a complete description is not even possible in principle. I don't think that prevents us from drawing further conclusions however. If we start with certain principles, then we can deduce what must be the case according to those principles. To borrow the aphorism, 'the finger pointing to the moon is not the moon'. While we might not be able to fully describe the system, I think we can point in the direction of a more complete description.

One element of reality is that outcomes of measurements of an observable are random except the system is prepared in a state, where it is not random. That's why the probability distribution for me is an "element of reality". Of course, Ballentine is right: To verify the predicted probability distribution you have to use a sufficiently large ensemble of equally prepared systems.

For me, there seems to be a gap in the description here, which makes me think it's incomplete. It might be a gap in my understanding but if you're willing to explore it we might be bale to plug one of the gaps (the smart money is on the gap in my understanding!)

I'm trying to understand how the outcomes of measurements can be random. We have the position-probability distribution which tells us the probability of measuring the system in a given spatial region. How is it then that the system only registers in one location on the measurement device?

If the probability distribution were simply a reflection of our ignorance, it would mean that the system has a pre-defined value for position of which we are unaware. It means that, in truth, there is only ever one possible measurement outcome, we just don't know what it is - hence the probability distribution.

But, if it doesn't simply reflect our ignorance and there is a genuine possibility that the system could be measured in anyone of the regions with a non-zero probability, does that not mean that the system must, in some sense, be located at each of those but then spontaneously 'collapses' into a single location?

 

[vanhees71]

For me a complete description is one that describes the system fully and completely. It is not necessarily limited to what is observable since it might be the case that there are limits to what we can observe. It might be possible that a complete description is not even possible in principle. I don't think that prevents us from drawing further conclusions however. If we start with certain principles, then we can deduce what must be the case according to those principles. To borrow the aphorism, 'the finger pointing to the moon is not the moon'. While we might not be able to fully describe the system, I think we can point in the direction of a more complete description.

For me QT is describing the system completely, because the randomness of the outcome of measurements of observables is an observed fact of Nature.

For me, there seems to be a gap in the description here, which makes me think it's incomplete. It might be a gap in my understanding but if you're willing to explore it we might be bale to plug one of the gaps (the smart money is on the gap in my understanding!)

I'm trying to understand how the outcomes of measurements can be random. We have the position-probability distribution which tells us the probability of measuring the system in a given spatial region. How is it then that the system only registers in one location on the measurement device?

If you consider, e.g., a single electron, you can either detect it as a one single electron or you don't detect it at the place where you put the detector. You cannot detect the same electron at several places, because you cannot split an electron in some "smeared" pieces. That's why Schrödinger's original idea that the wave function of a single electron could be interpreted as a classical field describing an electron, was substituted by Born's probability interpretation. In other words: Schrödinger's "smeared-electron interpretation" contradicts the observable facts.

If the probability distribution were simply a reflection of our ignorance, it would mean that the system has a pre-defined value for position of which we are unaware. It means that, in truth, there is only ever one possible measurement outcome, we just don't know what it is - hence the probability distribution.

Yes, but if this were true, you'd need a new theory with hidden variables or something like it. None has been found (yet).

But, if it doesn't simply reflect our ignorance and there is a genuine possibility that the system could be measured in anyone of the regions with a non-zero probability, does that not mean that the system must, in some sense, be located at each of those but then spontaneously 'collapses' into a single location?

I don't know, why one would need a collapse because of that, but that's not accepted by everybody. If for some reason, there'd be an observation which makes a collapse necessary, then you need a new theory extendeing QT. There are indeed such extensions of quantum theory incorporating a collapse, e.g., the GRW theory, which is an extension of QT, i.e., goes beyond a reinterpretation of the meaning of QT:

https://en.wikipedia.org/wiki/Ghirardi–Rimini–Weber_theory

 

[PeterDonis]

For me a complete description is one that describes the system fully and completely.

So a complete description is...a complete description. This is an empty definition.

Basically, your only criterion for a complete description is that you think it's complete. Which is subjective and therefore not a workable definition for physics.

 

[Lynch101]

So a complete description is...a complete description. This is an empty definition.

Basically, your only criterion for a complete description is that you think it's complete. Which is subjective and therefore not a workable definition for physics.

'Complete description' is pretty self-explanatory but in the context of this discussion it is juxtaposed with a description which only describes the measurement outcomes.

EDIT: Where we can deduce that there is more to be described than just the measurement outcomes, we can deduce that such interpretations are incomplete. A complete description would, therefore, also describe those elements left out by the other interpretation, fully and completely.

 

[PeterDonis]

'Complete description' is pretty self-explanatory

Self-explanatory in the sense of being subjective, yes. But that is not at all helpful if we are trying to do physics, instead of philosophy. "What Lynch101 thinks is complete" is not a workable physics definition.

Where we can deduce that there is more to be described than just the measurement outcomes, we can deduce that such interpretations are incomplete.

We can never deduce any such thing, since we don't have a complete set of premises that is known to cover all possible cases.

We can infer that there is more to be described in some particular scenario, but such inferences are, like the term "complete" itself, subjective: different people disagree about when such inferences are justified. So this is not a workable physics definition either.

 

[Lynch101]

Self-explanatory in the sense of being subjective, yes. But that is not at all helpful if we are trying to do physics, instead of philosophy. "What Lynch101 thinks is complete" is not a workable physics definition.We can never deduce any such thing, since we don't have a complete set of premises that is known to cover all possible cases.

We can infer that there is more to be described in some particular scenario, but such inferences are, like the term "complete" itself, subjective: different people disagree about when such inferences are justified. So this is not a workable physics definition either.

I am content to work with other people's definitions and explore the implications of those to see what we can either deduce or infer, as I have been doing with Vanhees.

 

[Lynch101]

For me QT is describing the system completely, because the randomness of the outcome of measurements of observables is an observed fact of Nature.

It is an observed fact, the implications of which we can explore. I am very much open to correction on what follows.

What we observe are single detection events. These are what you have labelled 'elements of reality'. When the 'element of reality' is measured, it is measured with certainty. So, by my reasoning, the probability distribution cannot correspond to that 'element of reality', nor the subsequent 'elements of reality' since they too are observed with certainty - that is, if they only become 'elements of reality' at the moment of detection.

The randomness which the probability distribution describes appears to be the pattern of the ensemble. While the pattern itself may indeed be 'an element of reality' it is distinct from the individual 'elements of reality' i.e. detection events. There doesn't appear to be anything in the SI which corresponds to those, which would render it incomplete by your own definition.

It is as L.E. Ballentine said,

The Statistical Interpretation, according to which a pure state (and hence also a general state) provides a description of certain statistical properties of an ensemble of similarly prepared systems, but need not provide a complete description of an individual system.

Where the statistical properties of the ensemble is the pattern, but that doesn't give us a complete description of the individual systems.One Possible Alternative*
Unless the randomness refers to the process by which a single, well-defined value for position is observed, from all genuinely possible positions with non-zero probabilities. In which case, by my reasoning, a description of this process would be required for the purpose of completeness.

If you consider, e.g., a single electron, you can either detect it as a one single electron or you don't detect it at the place where you put the detector. You cannot detect the same electron at several places, because you cannot split an electron in some "smeared" pieces. That's why Schrödinger's original idea that the wave function of a single electron could be interpreted as a classical field describing an electron, was substituted by Born's probability interpretation. In other words: Schrödinger's "smeared-electron interpretation" contradicts the observable facts.

Yes, but if [our ignorance is the reason for the probability distribution] were true, you'd need a new theory with hidden variables or something like it. None has been found (yet).

Indeed, we do not measure the system in several places but, according to the Statistical Interpretation (SI), the probability distribution tells us that there is a genuine possibility that the particle could be measured in any region with a non-zero probability. If the probability distribution does not merely describe the pattern of the ensemble then, by my reasoning, the randomness must refer to the process by which the 'element of reality' [that is the detection event] appears in a single, well-defined position.

We can contrast this with the hidden variables (HV) interpretation(s) which say that there is not a genuine possibility of measuring the system at all regions with a non-zero probability. The HV interpretation(s) say that the system has a single pre-defined value at all times and that the probability distribution is reflective of our ignorance. It is this single, pre-defined value which explains why we observe the detection event in the spatial region that we do.

As you say, if this were truly the case then we would need a new theory. But, we're not saying that it is true simply that we need a comparable explanation as to how we go from several, genuinely possible positions to observing only one single, well-defined position.

What is the random process at play?

I don't know, why one would need a collapse because of that, but that's not accepted by everybody. If for some reason, there'd be an observation which makes a collapse necessary, then you need a new theory extendeing QT. There are indeed such extensions of quantum theory incorporating a collapse, e.g., the GRW theory, which is an extension of QT, i.e., goes beyond a reinterpretation of the meaning of QT:

https://en.wikipedia.org/wiki/Ghirardi–Rimini–Weber_theory

If the probability distribution doesn't simply correspond to the observed pattern of the ensemble then, by my reasoning, it must correspond to the random process by which gives rise to a single, certain observation. Random collapse is just one possible explanation. There may indeed be others, but some description of the process would be required for completeness, by my reasoning.*of which there may be many.

 

[Morbert]

A quantum theory of a system (in the sense of a quantum state + dynamics) will assign probabilities to mutually exclusive alternatives, but treats all alternatives with nonzero probability on equal footing. The theory does not contain a notion of the one possibility that actually happens, distinct from other alternatives, but unknown to the observer.

If we assume that only one possibility among a set of alternatives ever occurs in the real world, as opposed to e.g. an Everettian multiverse where all possibilities occur, then we could say a quantum theory of a system does not completely describe the reality of that system, since a quantum theory only ever tenders probabilities for the different possibilities, and does not select the one that occurs. This is the case even if on a fundamental level facts emerge probabilistically from antecedents.

However, most physicists believe quantum theories are complete in the following sense: There is no deeper physical conceptualisation waiting to be discovered that will pierce this probabilistic nature of quantum theories, rendering the probabilities from a pure state as statements of ignorance to be resolved by the deeper physical conceptualisation. Better theories might come along in the sense that state spaces or specified dynamics might be improved, but the probabilistic language and equal treatment of possibilities is fundamental.

 

[PeterDonis]

I am content to work with other people's definitions

Well, "what vanhees71 thinks is complete" isn't a workable physics definition either.

and explore the implications of those to see what we can either deduce or infer, as I have been doing with Vanhees.

As far as I can tell, @vanhees71 does not agree with what you are deducing or inferring from his stated definitions. So we are just back again to the subjectivity of the term "complete": even when you adopt @vanhees71's definitions, you don't agree with him about what they imply.

 

[Fra]

But, if it doesn't simply reflect our ignorance and there is a genuine possibility that the system could be measured in anyone of the regions with a non-zero probability, does that not mean that the system must, in some sense, be located at each of those but then spontaneously 'collapses' into a single location?

I frequently entertain another possibility. Bell theorem only rules out the naive form of HV, where the uncertainty is effectively the physicists ignorance; and the physicists is not interacting, just observing - passively. This is why the physicstis ignorances takes on a trivial form.

If you picture and agent, that is interacting, then the agents ignorance has additional implications, that will not follow the naive form of ignorance of Bells ansatz. In this case the mutual ignorance of the parts in the interaction itself may even help explain the interactions in a deeper way. Such thinking my I think related to several interpretations. Demystifiers solipsist HV, or and interacting agent picture. Where the agents internal states are simply hidden to other agents - in a way that is non-trivial and can not be described in a form that looks like ignorance with respect to an extenal agent. But such thinks, if you think about it, suggests a reconstruction of QM and interaction terms, so it's entangled with open questions, that are speculative. But I think they are nevertheless logically sound possibilities.

/Fredrik

 

[Lynch101]

A quantum theory of a system (in the sense of a quantum state + dynamics) will assign probabilities to mutually exclusive alternatives, but treats all alternatives with nonzero probability on equal footing. The theory does not contain a notion of the one possibility that actually happens, distinct from other alternatives, but unknown to the observer.

If we assume that only one possibility among a set of alternatives ever occurs in the real world, as opposed to e.g. an Everettian multiverse where all possibilities occur, then we could say a quantum theory of a system does not completely describe the reality of that system, since a quantum theory only ever tenders probabilities for the different possibilities, and does not select the one that occurs. This is the case even if on a fundamental level facts emerge probabilistically from antecedents.

However, most physicists believe quantum theories are complete in the following sense: There is no deeper physical conceptualisation waiting to be discovered that will pierce this probabilistic nature of quantum theories, rendering the probabilities from a pure state as statements of ignorance to be resolved by the deeper physical conceptualisation. Better theories might come along in the sense that state spaces or specified dynamics might be improved, but the probabilistic language and equal treatment of possibilities is fundamental.

Am I interpreting this correctly as saying, QT 'does not does not completely describe the reality of [the] system' but most physicists believe that a more complete description is not possible?

 

[Lynch101]

Well, "what vanhees71 thinks is complete" isn't a workable physics definition either. As far as I can tell, @vanhees71 does not agree with what you are deducing or inferring from his stated definitions. So we are just back again to the subjectivity of the term "complete": even when you adopt @vanhees71's definitions, you don't agree with him about what they imply.

I take your points.

For me, I'm just looking to 'probe and prod' to see what conclusions can be drawn about the universe we live in - 'shake the tree to see what falls out', so to speak.

You mentioned in the 'Assumptions of Bell's Theorem' thread that you agree with the 'weak' claim that the Statistical Interpretation is incomplete. In what sense would you say that it is incomplete? Do you think we can infer or deduce anything from the probability distribution beyond it's incompleteness?

 

[vanhees71]

If we assume that only one possibility among a set of alternatives ever occurs in the real world, as opposed to e.g. an Everettian multiverse where all possibilities occur, then we could say a quantum theory of a system does not completely describe the reality of that system, since a quantum theory only ever tenders probabilities for the different possibilities, and does not select the one that occurs. This is the case even if on a fundamental level facts emerge probabilistically from antecedents.

Of course, a probability distribution doesn't select which outcome you'll get when performing the random experiment. It just tells you the probability for that outcome. QT can be considered complete if you accept that Nature behaves objectively random as described by it. If you don't accept this, you consider QT as incomplete. Of course, you can neither prove that QT is complete nor that it is incomplete. One can only say that with the hitherto observed facts there is no need for an alternative theory, because QT describes all the observed facts very well.

 

[Lynch101]

Of course, a probability distribution doesn't select which outcome you'll get when performing the random experiment. It just tells you the probability for that outcome.

And we can explore what this probability distribution is telling us about nature. Is it telling us:

1) There is, in truth, only one possible outcome but we calculate a probability due to a lack of information.
2) In truth, every position with a non-zero probability, has a genuine possibility of being measured.

#1 tells us precisely why we only ever measure the system in a single, well-defined position. #2 doesn't tell us this.

If the answer is 2), then we can explore how it is a genuine possibility that any position could be measured but ultimately we only ever measure the system in a single, well-defined position. What random process is at play here?

QT can be considered complete if you accept that Nature behaves objectively random as described by it. If you don't accept this, you consider QT as incomplete.

We can accept that Nature behaves objectively random but still request an explanation of the random process.

We start by preparing the system in a lab and then we randomly detect it on a screen in another lab, but what happens in between?

Of course, you can neither prove that QT is complete nor that it is incomplete. One can only say that with the hitherto observed facts there is no need for an alternative theory, because QT describes all the observed facts very well.

Again, I think it's important to come back to the title of the EPR paper, 'Can quantum-mechanical description of physical reality be considered complete?' (emphasis mine). They set out their general criterion for completeness, that 'every element of physical reality must have a counterpart in the physical theory'.

They then set out an argument which aimed to demonstrate that there are facts about the system which are unobserved (and possible unobservable). Bell tests demonstrate that their assumptions [about physical reality] cannot account for the observations of experiments. EPR, however, state that their approach is just one possible way of identifying 'elements of reality' and that it does not exhaust all the possible ways of identifying 'elements of reality'.

EPR opens us to the possibility that there are unobserved/unobservable facts about the system but that those facts do not necessarily take single, pre-defined values. That doesn't mean, however, that there are no unobserv-ed (-able) facts about the system.

EPR Completeness & Observables
But, even if we talk strictly about the observable facts of the system, and we classify these observable facts as 'elements of reality' - the alternative is to deny them as 'elements of reality' - these individual elements of reality do not correspond to anything in the mathematical formalism. The reason being, the individual detection events i.e. the elements of reality occur with certainty, so they cannot correspond to the probability distribution. So, in this sense the statistical interpretation fails the general EPR criterion for completeness.

Where the probability distribution does correspond to something is the pattern of detection events of an ensemble of 'elements of reality'. Is this pattern an 'element of reality'? Does the probability distribution correspond exactly to the pattern? Even if we answer yes to both these questions, the fact remains that the individual 'elements of reality' i.e. detection events do not correspond to anything in the mathematical formalism.

Again, it comes back to what Ballentine said.

 

[Lynch101]

Of course, a probability distribution doesn't select which outcome you'll get when performing the random experiment. It just tells you the probability for that outcome. QT can be considered complete if you accept that Nature behaves objectively random as described by it. If you don't accept this, you consider QT as incomplete. Of course, you can neither prove that QT is complete nor that it is incomplete. One can only say that with the hitherto observed facts there is no need for an alternative theory, because QT describes all the observed facts very well.

Just an additional note on this. If the probability distribution doesn't select which outcome you'll get when performing the random experiment then it doesn't account for all observed facts.

 

[vanhees71]

I don't know how I should rephrase my utmost simple (or maybe all too naive?) opinion to make clear what I mean: For me what's implied by all these Bell tests is that Nature is behaving in a genuinely random way. There is nothing about the observables than the probabilities for the outcome of measurements as given by the prepared state. A single outcome is always unique, provided you have an ideal measurement device. You get this unique outcome with a probability predicted by the quantum state. The randomness, quantified by the quantum probabilities, is an element of reality as well as the definiteness of the outcome of a measurement.

 

[Lynch101]

I don't know how I should rephrase my utmost simple (or maybe all too naive?) opinion to make clear what I mean: For me what's implied by all these Bell tests is that Nature is behaving in a genuinely random way. There is nothing about the observables than the probabilities for the outcome of measurements as given by the prepared state. A single outcome is always unique, provided you have an ideal measurement device. You get this unique outcome with a probability predicted by the quantum state. The randomness, quantified by the quantum probabilities, is an element of reality as well as the definiteness of the outcome of a measurement.

I'm taking your point, but we can separate the discussion into two strands:

Strand 1): EPR completeness - where all 'elements of reality' should have a counterpart in the theory. At the very minimum, I think most people would agree that the detection event represents an 'element of reality' of the system. The statistical interpretation does not have anything in the theory which corresponds to the individual detection events and so it is EPR-incomplete.

Strand 2): Implications of the SI - We can take the position that the statistical interpretation is complete and explore what it tells us about nature.

Simply saying that nature is behaving in a random way is not necessarily the end of the road in terms of what we can infer about nature. We want to know:
- how is nature behaving randomly?
- What is the process whereby several, genuinely possible outcomes is reduced to a single observable?
- In what sense can there be several, genuinely possible outcomes (as opposed to the alternative, where
only one outcome is possible)?
- If the system is not located in the spatial region adjacent to the measurement device, how does it interact
with it?

The answers to these and other questions have implications for how nature behaves.