Undergrad The Probability Distribution and 'Elements of Reality'

[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.

 

[vanhees71]

Ad 1) The randomness is an "element of reality". The EPR criterion is experimentally disproven by all the Bell tests demonstrating the violation of the Bell inequality.

Ad 2) QT precisely describes how Nature behaves randomly. Of course the very observable is measured the apparatus used to measure it is constructed for. The outcome of a measurement is unique, if this apparatus is properly constructed. The observables don't have determined values if the system is not prepared in a state, in which they have determined values. Thus the outcome of a measurement is usually random, and QT predicts the probabilities and only the probabilities for the outcome of measurements. A system interacts with the measurement device as described by the Standard Model of particle physics. At least we don't know of any other interactions yet. It's likely that our knowledge is incomplete, i.e., it's pretty sure that there should be more particles than yet discovered and described by the Standard Model.

QT is incomplete with respect to the gravitational interaction.

 

[Lynch101]

The EPR criterion is experimentally disproven by all the Bell tests demonstrating the violation of the Bell inequality.

Bell tests do not disprove the general criterion, that 'every element of the physical reality must have a counterpart in the physical theory'.

What they do disprove is the 'local hidden variable' criterion which EPR chose to focus on. But, as EPR stated, that was just one possible way of determining an 'element of reality'. It did not exhaust all possible ways.

Ad 1) The randomness is an "element of reality".

The randomness of the system may well be an 'element of reality'. But, it is not the only element of reality of the system. If the detection event is indeed 'element of reality'* of the system and if it only becomes 'an element of reality' at the moment of observation, then it doesn't correspond to anything in the SI, since it always occurs with certainty. In this case, the SI would be incomplete according to the general EPR criterion and also by your own criterion of accounting for all observable facts.

Ad 2) QT precisely describes how Nature behaves randomly. Of course the very observable is measured the apparatus used to measure it is constructed for. The outcome of a measurement is unique, if this apparatus is properly constructed. The observables don't have determined values if the system is not prepared in a state, in which they have determined values. Thus the outcome of a measurement is usually random, and QT predicts the probabilities and only the probabilities for the outcome of measurements. A system interacts with the measurement device as described by the Standard Model of particle physics. At least we don't know of any other interactions yet. It's likely that our knowledge is incomplete, i.e., it's pretty sure that there should be more particles than yet discovered and described by the Standard Model.

QT is incomplete with respect to the gravitational interaction.

QT doesn't describe precisely how the system behaves randomly, it simply predicts that it will behave randomly. The question is, how does the system randomly appear in a single unique position? Some interpretations say that the system is in multiple locations simultaneously and spontaneously collapses into a single well defined positon. What does the SI say?

When we say that randomness is 'an element of reality' what we mean is that the system randomly appears in a single well-defined position. This idea has implications that we can explore.

Again, we can pose the question as to what this 'randomness' tells us about the system. Does it tell us:
1) In truth, there is 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.

Ruling out #1, we are left with #2. We can explore the implications of this.

From there we can pose the question:
A) Contrasting with scenario #1 above, what does it mean, or how can it be the case, that there are several
genuinely possible outcomes?
B) How does the system go from several genuinely possible outcomes to a single observed outcome?

 

[PeterDonis]

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?

You phrased that claim specifically in terms of the EPR definition of "complete". I was agreeing that, in terms of that definition, the statistical interpretation is incomplete, because the statistical interpretation does not, by the EPR definition, include any "elements of reality" at all, and the EPR definition (at least as I understand it) assumes that there are at least some elements of reality that any complete theory must include (although the EPR definition itself makes no specific assertions about what those elements of reality are).

 

[Fra]

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.

I agree some of these questions are reasonable to ask, but I think different interpretations provide context where these questions are interpreted differently, some questions are perhaps denied. For people that have different abstractions, it may be hard to even agree what the questions means, or what counts as an "answer", or have explanatory value.

/Fredrik

 

[Lynch101]

You phrased that claim specifically in terms of the EPR definition of "complete". I was agreeing that, in terms of that definition, the statistical interpretation is incomplete, because the statistical interpretation does not, by the EPR definition, include any "elements of reality" at all,

Would you say then, that the statistical interpretation does give a complete description of the quantum system?

the statistical interpretation does not, by the EPR definition, include any "elements of reality" at all, and the EPR definition (at least as I understand it) assumes that there are at least some elements of reality that any complete theory must include (although the EPR definition itself makes no specific assertions about what those elements of reality are).

Not to state the obvious, but EPR are talking about describing the quantum system so, 'every element of the physical reality' simply refers to every piece of information about the quantum system, observable and/or unobservable.

So, if the statistical definition does not include any 'elements of reality' at all, then it means it doesn't contain any information about the quantum system at all, which would make it incomplete by any definition.

 

[Lynch101]

I agree some of these questions are reasonable to ask, but I think different interpretations provide context where these questions are interpreted differently, some questions are perhaps denied. For people that have different abstractions, it may be hard to even agree what the questions means, or what counts as an "answer", or have explanatory value.

/Fredrik

I would agree with you on this, different interpretations provide context for the questions and, in some cases, the questions may even be denied. Even the denial of the questions, however, have implications about how nature is.

The questions themselves represent pretty basic ideas about nature and to deny them would be to state that such concepts do not apply at the quantum level. This then would necessitate further clarification or description to explain how the quantum world gives rise to observations at the classical level, where such concepts do apply.

 

[PeterDonis]

Would you say then, that the statistical interpretation does give a complete description of the quantum system?

I don't think that question is a physics question to begin with. I think it's a philosophy question which does not have a well-defined answer.

EPR are talking about describing the quantum system so, 'every element of the physical reality' simply refers to every piece of information about the quantum system, observable and/or unobservable.

The EPR definition gives a very precise definition of "elements of reality", and this is not it.

if the statistical definition does not include any 'elements of reality' at all, then it means it doesn't contain any information about the quantum system at all

This is false, even according to the EPR definition. See above.

 

[Lynch101]

I don't think that question is a physics question to begin with. I think it's a philosophy question which does not have a well-defined answer.

Is it not the purview of physics to [attempt to] give a complete description of the quantum system? Your answer would seem to suggest that only philosophy can then [attempt to] determine the completeness of any given interpretation.

The EPR definition gives a very precise definition of "elements of reality", and this is not it.This is false, even according to the EPR definition. See above.

Are you referring to the 'predict without disturbing criterion'?

 

[PeterDonis]

Is it not the purview of physics to [attempt to] give a complete description of the quantum system?

No. It's the purview of physics to construct models that make accurate predictions. Physics cannot prejudge what such models will require.

 

[PeterDonis]

Are you referring to the 'predict without disturbing criterion'?

Yes.

 

[Lynch101]

No. It's the purview of physics to construct models that make accurate predictions. Physics cannot prejudge what such models will require.

EPR seem to be calling for a complete description or complete model of the quantum system.

If the raison d'etre of a model was simply to make accurate predictions then an infinite number of models could be created, with lots of superfluous and unobservable attachments which, nonetheless, make accurate predictions. There certainly seems to be an inclination in the field of physics towards finding the 'correct' model.

If making accurate predictions were the sole purview of physics, there would be no need for QM interpretations, would there?

 

[Lynch101]

Yes.

As per EPR, that represents just one way of identifying an 'element of reality' and is 'far from exhausting all possible ways'.

 

[PeterDonis]

EPR seem to be calling for a complete description or complete model of the quantum system.

That does not mean that physics must require that. It just means it was their opinion that physics should require that. Their opinion might be wrong. We will only find out by continuing the process of constructing models that make predictions and comparing those predictions with experiments. And it is that process that will tell us what is "required" for a theory of physics, not a priori statements or people's opinions.

 

[PeterDonis]

If making accurate predictions were the sole purview of physics, there would be no need for QM interpretations, would there?

There isn't any "need" for QM interpretations as a matter of physics; they are not physical theories, they are stories people like to tell about a physical theory. As a matter of physics, a QM interpretation would only be "needed" if it turned out to lead to a different theory, one that made different predictions from standard QM, and had those predictions confirmed by experiments.

 

[Morbert]

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.

What I am doing is trying to unpack the various senses of complete.

E.g. Yes QM suggests that nature behaves objectively randomly. What occurs follows probabilisticially from what was prepared. But it is still the case that reality exhibits only one history. This history is "ontologically privileged", but a quantum theory does not mark out any history as privileged or distinct. QM cannot therefore report a complete ontological account.

This is a very precise sense of incomplete that is not normally what physicists talk about when they use the word, but it is what a lot of lay people seem to be asking about.

 

[Lynch101]

That does not mean that physics must require that. It just means it was their opinion that physics should require that. Their opinion might be wrong. We will only find out by continuing the process of constructing models that make predictions and comparing those predictions with experiments. And it is that process that will tell us what is "required" for a theory of physics, not a priori statements or people's opinions.

There isn't any "need" for QM interpretations as a matter of physics; they are not physical theories, they are stories people like to tell about a physical theory. As a matter of physics, a QM interpretation would only be "needed" if it turned out to lead to a different theory, one that made different predictions from standard QM, and had those predictions confirmed by experiments.

There certainly seems to be a rich history of physicists seeking interpretations for the mathematical models they develop. It seems to go beyond simply shutting up and calculating. Making predictions is certainly the means by which the accuracy of the models is verified, where accuracy is the correspondence of the model to the universe we live in.

Would you say that interpreting the mathematical models is then the purview of philosophy and not physics?

 

[Lynch101]

What I am doing is trying to unpack the various senses of complete.

E.g. Yes QM suggests that nature behaves objectively randomly. What occurs follows probabilisticially from what was prepared. But it is still the case that reality exhibits only one history. This history is "ontologically privileged", but a quantum theory does not mark out any history as privileged or distinct. QM cannot therefore report a complete ontological account.

This is a very precise sense of incomplete that is not normally what physicists talk about when they use the word, but it is what a lot of lay people seem to be asking about.

Is it not the sense of completeness that EPR were seeking i.e. a complete description of physical reality?

 

[PeterDonis]

There certainly seems to be a rich history of physicists seeking interpretations for the mathematical models they develop.

For QM, yes. But not for other theories of physics. There is not a rich history of physicists seeking interpretations for Newtonian mechanics or relativity.

Would you say that interpreting the mathematical models is then the purview of philosophy and not physics?

In the sense you mean "interpreting", yes, since it has nothing to do with the predictions the model makes. Models are not reality. Perhaps you have heard the saying, "All models are false but some are useful." I suggest that you spend some time reflecting on that.

 

[Fra]

We will only find out by continuing the process of constructing models that make predictions and comparing those predictions with experiments. And it is that process that will tell us what is "required" for a theory of physics, not a priori statements or people's opinions.

This reminds my of the thinking around Poppers falsification, where one tries to put most emphasis on corroboration and falsification, and not so much on the creative process of finding new hypothesis in a way that does not flood us with more hypothesis that our corroboration capacity can handle. Paradoxally this create part is essential to the progress in science, but it's also the most murky and fuzzy part, which can be annoying, and one can be tempted to deny it's importance due to it's subjective nature.

Although subjective, and beloning to the murky waters, the "interpretation" is to me at least part of the deeper understanding of things, that is important to the process of extrapolating or extending it in a rational way, rather than trying random modifications in a hypothesis space which would gurantee a random walker to get lost. In this sense one might sense that the choice of interpretation reflects the way we think we "understand" things. But of course only the future will tell if it's right or wrong.

/Fredrik

 

[PeterDonis]

the "interpretation" is to me at least part of the deeper understanding of things, that is important to the process of extrapolating or extending it in a rational way

That is what advocates of various QM interpretations are basically claiming: that their preferred interpretation will lead to a deeper understanding by being extrapolated or extended to a different theory that can be experimentally tested. But so far that hasn't happened.

 

[PeterDonis]

the "interpretation" is to me at least part of the deeper understanding of things, that is important to the process of extrapolating or extending it in a rational way

Other than QM (for which, as I said in my previous post just now, no such extension has yet worked out), I am not aware of any physical theory that works that was arrived at by starting with an interpretation of a prior theory and then extrapolating or extending it. For example, relativity was not discovered by starting with some interpretation of Newtonian physics and then extrapolating or extending it. It was discovered by trying to construct a theory of mechanics that had the same transformation properties (Lorentz transformations) as Maxwell electrodynamics.

 

[Morbert]

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?

Is it not the sense of completeness that EPR were seeking i.e. a complete description of physical reality?

In the EPR discussion, they consider "every element of physical reality" as accounted for by a physical state that is not uniquely (and therefore not completely) characterised by a quantum wavefunction. A physicists can accept the probabilistic nature of QM, at odds with the singular nature of reality, but also reject the EPR argument by insisting that a wavefunction does uniquely characterise the physical state of a system.

 

[vanhees71]

Is it not the sense of completeness that EPR were seeking i.e. a complete description of physical reality?

For me EPR's description of physical reality is ruled out by all the very accurate Bell tests, including the most recent ones ruling out many if not all the loopholes. The difficulty seems to be still today that many philosophers (and also some physicists) seem not to accept what physics is telling us, i.e., that our all too classically formed intuition about how Nature behaves is flawed, and we have to adapt our intuitions to what quantum theory tells us about Nature's behavior. It's not the purpose of the natural sciences to confirm our prejudices but to learn how Nature "really" behaves, and obviously Nature's behavior is much closer to what's described by QT than by the (imho pretty vague) philosophical ideas by EPR. Particularly their conclusion about the predetermination of observables that are indetermined due to quantum mechanics is ruled out, at least for the class of local hidden-variable theories a la Bell.

The only example, which works as a theory is the Bohmian nonlocal reinterpretation of non-relativistic QT. The problem with this is that there's no satisfactory Bohmian reinterpretation of local relativistic QFT, which is the most comprehensive theory of matter yet found.

 

[Lynch101]

For QM, yes. But not for other theories of physics. There is not a rich history of physicists seeking interpretations for Newtonian mechanics or relativity.

With relativity we have the Lorentzian view based on absolute simultaneity and the Einsteinian based on relativity of simultaneity. From the Einsteinian view we have all manner of interpretations from the Block Universe, the growing block universe, the Relational Block Universe, Julian Barbour's 'Platonia', to the interpretation you've written about in your insight article.

In the sense you mean "interpreting", yes, since it has nothing to do with the predictions the model makes. Models are not reality. Perhaps you have heard the saying, "All models are false but some are useful." I suggest that you spend some time reflecting on that.

Yes, it is impossible to create a model of reality that matches it exactly but the models we create can reveal consequences not always obvious from the mathematical formalism - precisely because the mathematical formalism can be interpreted in different ways.

 

[Lynch101]

Was I interpreting your statement correctly when I interpreted it 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?

In the EPR discussion, they consider "every element of physical reality" as accounted for by a physical state that is not uniquely (and therefore not completely) characterised by a quantum wavefunction. A physicists can accept the probabilistic nature of QM, at odds with the singular nature of reality, but also reject the EPR argument by insisting that a wavefunction does uniquely characterise the physical state of a system.

I try to make the distinction between the EPR argument and the overall aim as suggested by the title of the paper. The argument that they put forward in the paper does not, they say, exhaust all possible ways of regocognising an element of physical reality.

Ultimately, what they are calling for is a complete description of the system and their general criterion is that all elements of physical reality i.e. everything about the system should correspond to something in the mathematics. You have stated previously that the statistical (or 'anti-realist') interpretation says that the wave function does not correspond to physical reality.