Assumptions of the Bell theorem

[PeterDonis]

To find it around $\vec{a}$ or around $\vec{b}$, or somewhere else far away,
It must be:
- either located at $\vec{a}$ or around $\vec{b}$, or somewhere else far away
- located at all $\vec{a}$ and around $\vec{b}$, and somewhere else far away

Why are these the only possibilities? So far, you have given no basis for any such claim.

 

[Lynch101]

That QT appears to violate realism doesn't necessarily mean that it's incomplete. It could be that your notion of physical reality could be wrong.

When you say 'violate realism' do you mean it in the ontological sense that it says the system does not exist at all prior to measurement, or in the operational sense of the mathematical formalism not being a description of physical reality?

 

[EPR]

When you say 'violate realism' do you mean it in the ontological sense that it says the system does not exist at all prior to measurement, or in the operational sense of the mathematical formalism not being a description of physical reality?

In the physics sense. That quantum systems have definite properties before measurement.
What is this lengthy argument about?

 

[vanhees71]

To find it around $\vec{a}$ or around $\vec{b}$, or somewhere else far away,
It must be:
- either located at $\vec{a}$ or around $\vec{b}$, or somewhere else far away
- located at all $\vec{a}$ and around $\vec{b}$, and somewhere else far away

If it is not located at any of these, how could it possibly interact with a measurement device that is located there?

As I said, all you can know within QT is this probability distribution, given the preparation of the particle in this state.

Of course the interaction with the measurement device is local (in the sense of relativistic QFT). If there is some non-zero probability for the particle to be at the location of the device (and this is always a region of a finite volume, never a single point in space, i.e., there's always a finite resolution of the position measurement) there is some probability that the particle is measured at the location of the apparatus. An ideal apparatus can only confirm (or refute) the predicted probabilities when you repeat the very same experiment with many such prepared particles.

 

[Lynch101]

In terms of QM, this would mean that it has a quantum state, or at least is included in the quantum state of the universe, correct?

I would presume so.

If so, @vanhees71 has correctly pointed out in post #657 that this statement, while true, is useless, since it just tells us something we already know anyway.

Unless the quantum system under consideration is the entire universe, then the mathematical formalism would need to tell us where in the universe the system is located. It doesn't need to be a a single pre-determined value, but it would have to be more than just the predictions of location after interaction with a measurement device.

If "located somewhere in the universe" means "is part of the quantum state of the universe", as above, then your claim here is simply false.

Not necessarily. If the quantum system is a subset of the quantum state of the universe, then we can ask about its location prior to measurement. We can ask, where in the universe it is.

If the probability distribution is telling us something about the location of the quantum system prior to measurement, then we can ask, what is it telling us?

If the answer is, it only tells us about the location after measurement, then it can't possibly be telling us anything about the location prior to measurement - as a matter of definition.

If "must be located somewhere" means "is part of the quantum state of the universe" as above, the all the probability distribution tells us is what any probability distribution tells us. Namely, the probabilities of possible measurement results.

We don't prepare the 'quantum state of the universe' in QM experiments, we prepare a subset of it, namely the system under consideration. We can therefore ask, where in the universe the system under consideration is located. This doesn't require a sinlge location as an answer, it could be spread out across a broader region, it could be riding along a pilot wave, or myriad other explanations as to why we get probabilistic predictions as to its location.

But, if the answer is, the predictions only give us the probability for measurement outcomes, then they don't describe the system prior to measurement, they describe the system upon measurement.

We are not talking about what "some" claim. We are talking about what you claim. You are making very strong claims that, so far, you have failed to back up with a definition of "located somewhere in the universe" that supports them. The only definition you have come up with so far does not tell us anything useful, as I have shown above. So you either need to come up with a different definition or drop this line of argument since you cannot support it.

In effect, I'm saying there is nothing in the mathematics which describes the location of the system prior to measurement. That is, there is nothing in the mathematics corresponding to the systems location 'somewhere in the universe' prior to measurement.

I say this because this is what proponents of certain interpretations of QM have stated i.e. the mathematics only gives us probabilistic predictions for measurement outcomes. On that basis, given that QM does not describe the location of the system prior to measurement, it cannot be a complete description of physical reality.

 

[Lynch101]

Unless and until you can give this statement a definite meaning in the math of QM, it is meaningless noise. I have asked you once already to do that. Can you?

I'm saying there is nothing in the mathematics corresponding to that, which is the reason it is not a complete description of physical reality.

 

[Lynch101]

In the physics sense. That quantum systems have definite properties before measurement.
What is this lengthy argument about?

That isn't a denial of realism, it's a denial of the idea of systems having definite properties prior to measurement.

The system still has properties, which a full description of physical reality should describe. A theory which only describes the 'definite properties' of the system after interactions with a measurement devices , doesn't, by definition, describe the properties of the system prior to that interaction and so, cannot be considered a complete description of physical reality.

In other words, QM is incomplete* just not for the reasons that EPR expected.

*is not a complete description of physical reality.

 

[Lynch101]

Why are these the only possibilities? So far, you have given no basis for any such claim.

Are there other possibilities?

The basis for such a claim is that a system cannot interact with a measurement device if it is not co-located. To suggest otherwise would be to invoke 'spooky action'.

 

[Lynch101]

As I said, all you can know within QT is this probability distribution, given the preparation of the particle in this state.

Of course the interaction with the measurement device is local (in the sense of relativistic QFT). If there is some non-zero probability for the particle to be at the location of the device (and this is always a region of a finite volume, never a single point in space, i.e., there's always a finite resolution of the position measurement) there is some probability that the particle is measured at the location of the apparatus. An ideal apparatus can only confirm (or refute) the predicted probabilities when you repeat the very same experiment with many such prepared particles.

Would you agree that a particle must be 'at the location of the device' in order to interact with it?

If so, then if there is a non-zero probability for the particle to be at the location of the device and the particle does indeed interact with the device, does this mean that the particle was located in that region of finite volume prior to measurement, or at least a region of finite volume adjacent to it?

 

[EPR]

That isn't a denial of realism, it's a denial of the idea of systems having definite properties prior to measurement.

The system still has properties, which a full description of physical reality should describe.

It is a denial of realism in the physics sense. Your intuition is completely irrelevant to how reality works. It is also no basis to label a theory incomplete.
You make strong claims without providing arguments or evidence.

 

[PeterDonis]

Unless the quantum system under consideration is the entire universe, then the mathematical formalism would need to tell us where in the universe the system is located.

Why?

I understand that this is your opinion. However, so far I have not seen anything from you which would explain to me why I need to share your opinion. And you cannot base an argument on something that's just your opinion.

This applies to basically everything you're saying.

 

[PeterDonis]

Are there other possibilities?

I don't know. But since you are making the strong claim that they are the only possibilities, the burden of proof is on you to support that claim. So far you have given no support whatever; you're just making bare assertions of your opinion. (Again, this applies to basically everything you are saying.)

The basis for such a claim is that a system cannot interact with a measurement device if it is not co-located.

What does "co-located" mean?

The usual QM meaning would be, heuristically, that there is overlap of the wave functions of the two systems in the spatial region in question. But that meaning does not support the claims you are making.

 

[Lynch101]

It is a denial of realism in the physics sense. Your intuition is completely irrelevant to how reality works. It is no basis to label a theory incomplete

It's not my intuition, it's on the basis of the EPR criterion for a theory to be considered a complete description of physical reality.

EPR chose to focus on position and momentum but as they said,

It seems to us that this criterion, while far from exhausting all possible ways of recognizing a reality, at least provides us with one.

Their criterion for a complete theory:

Whatever the meaning assigned to the term complete, the following requirement for a complete theory appears to be a necessary one: every element of the physical reality must have a counterpart in the physical theory. We shall call this the condition of completeness.

EPR paper

 

[Lynch101]

Why?

To be considered a complete, in the broader EPR sense.

 

[PeterDonis]

To be considered a complete, in the broader EPR sense.

Why is "location of the particle" an element of physical reality? Measurements have spatial locations, but that is not the same as the stronger claim you are making.

 

[Lynch101]

I don't know. But since you are making the strong claim that they are the only possibilities, the burden of proof is on you to support that claim. So far you have given no support whatever; you're just making bare assertions of your opinion. (Again, this applies to basically everything you are saying.)

My apologies, there is another possibility, that spatially separated systems can interact instantaneously.

Logically, I can think of no other possibilities, but I am open to correction.

What does "co-located" mean?

The usual QM meaning would be, heuristically, that there is overlap of the wave functions of the two systems in the spatial region in question. But that meaning does not support the claims you are making.

We're talking about interaction with a macroscopic measurement device. In this sense 'co-located' would mean not spatially separated.

It would be the criterion by which objects can interact without the need for superluminal communication i.e. they have to be adjacent to each other.

 

[EPR]

It's not my intuition, it's on the basis of the EPR criterion for a theory to be considered a complete description of physical reality.

EPR chose to focus on position and momentum but as they said,
Their criterion for a complete theory:

EPR paper

This criterion made sense in 1935, when QT was several years old and debates were raging whether this theory had a future(mainly Einstein doubted it). It's almost 100 years since then. These "issues" about realism are not relevant today. They are the mainstream.

 

[PeterDonis]

Logically, I can think of no other possibilities

Which does not establish that there are none, only that you can think of none. That's not a valid argument.

We're talking about interaction with a macroscopic measurement device. In this sense 'co-located' would mean not spatially separated.

You're missing the point. I have already stated how QM represents this: overlap of wave functions in the spatial region in question. So if "capability to interact with a measurement device" is an element of reality, then QM does represent it and the EPR criterion is satisfied. So what's the problem?

 

[Lynch101]

Why is "location of the particle" an element of physical reality? Measurements have spatial locations, but that is not the same as the stronger claim you are making.

If by 'location' you mean a definite pre-determined value, that isn't necessarily the case.

'The Universe' is generally what we use to refer to 'all the elements of physical reality'. If there was only one 'element of reality' then it would be the universe as a whole then the location of that element of reality would be 'everywhere'.

If there is more than one 'element of reality' i.e. subsystems, then those subsystems cannot be located 'everywhere'. They must still be located within the universe however, since the universe is the totality of all 'elements of reality'.

If we are describing the subsystems and we only describe their location after interaction with a measurement device then, by definition, we don't describe their location prior to measurement. Since non-existent systems cannot interact with measurement devices, the system must exist prior to measurement. It is therefore and element of reality, prior to measurement. As such an element of reality, it must have a location within the universe, unless it is the entire universe itself. Failure to describe its location prior to measurement is therefore to give an incomplete description of physical reality.

 

[PeterDonis]

If by 'location' you mean a definite pre-determined value

By "location" of a measurement, I mean whatever spatial region the measurement takes place in. For measurements this would be part of the data of the measurement. Since measurement data is stated classically, this is not an issue.

If we are describing the subsystems and we only describe their location after interaction with a measurement device then, by definition, we don't describe their location prior to measurement.

I have not said either of these things. I have said that measurements are associated with spatial regions as I described above. That is not the same as either describing or not describing the location of the measured system after measurement. Nor is it the same as either describing or not describing the location of the measured system before measurement.

Since non-existent systems cannot interact with measurement devices, the system must exist prior to measurement.

What does "exist" mean? If it means "has a wave function", then of course the system exists prior to measurement. If it means something else, what?

As such an element of reality, it must have a location within the universe

I have already explained how QM represents this: by the wave function in the position representation. You have given no argument whatever for why that is not sufficient.

 

[Lynch101]

Which does not establish that there are none, only that you can think of none. That's not a valid argument.

I'm not saying there are none, I'm saying that I can't think of any other logical possibilities. The burden of proof therefore lies on anyone claiming there are more to demonstrate there are more.

You're missing the point. I have already stated how QM represents this: overlap of wave functions in the spatial region in question. So if "capability to interact with a measurement device" is an element of reality, then QM does represent it and the EPR criterion is satisfied. So what's the problem?

The issue in question is the location of the system prior to measurement. Does the wave function describe the location of the system prior to measurement?

The contention by proponents of certain interpretations/theories, here, is that not it doesn't, it only describes the probability of the measurement outcome. If that is the case, then that particular interpretation cannot be considered a complete description of physical reality - that is simply a matter of definition.

There is some contention that the probability distribution does actually describe the location prior to measurement. If this is the case, then we can explore what it tells us about the location of the system prior to measurement.

We know that when we measure the system, the probability of its location 'collapses' to 1 i.e. we find it in a single location (within the given error bars). With this in mind, what does the probability distribution tell us about the location of the system prior to measurement?

It either tells us that the system has a definite location (within the given error bars) and we calculated probabilistic outcomes due to a lack of information on our part. Or, it tells us that the system doesn't have a definite location prior to measurement.

But, we know that it must have some location if it is indeed part of the universe. So, how can it have a location that doesn't have a pre-defined value?

 

[Lynch101]

What does "exist" mean? If it means "has a wave function", then of course the system exists prior to measurement. If it means something else, what?I have already explained how QM represents this: by the wave function in the position representation. You have given no argument whatever for why that is not sufficient.

What does the wave function tell us? Does it contain a description of the system prior to interacting with the measurement device or does it only tell us the probability of the measurement outcome?

 

[PeterDonis]

Does it contain a description of the system prior to interacting with the measurement device or does it only tell us the probability of the measurement outcome?

False dichotomy. The wave function always tells you the probabilities of measurement outcomes; but depending on which interpretation of QM you adopt, it can also be a description of the system prior to interacting with the measurement device. So those two things are not mutually exclusive.

 

[PeterDonis]

The burden of proof therefore lies on anyone claiming there are more to demonstrate there are more.

No, the burden of proof lies on you to support your positive claim that there are no other possibilities, since your argument rests on that claim. Just saying that you can't think of any other possibilities is not enough.

I am not making a positive claim so there is nothing for me to have to prove. I am simply pointing out that you have not given sufficient support for your claim.

Does the wave function describe the location of the system prior to measurement?

If "location" means "the spatial region in which the system is capable of interacting with a measurement device", then yes, as I have already explained.

If "location" means something else, then what does it mean, and why should I care about that meaning?

The contention by proponents of certain interpretations/theories here is that it doesn't, it only describes the probability of the measurement outcome.

No, the contention by others in this thread has been that the wave function does not describe the system being in a definite location, by which they meant "a single point at which the system is known to be located". You attempted to gerrymander the definition by replacing "point" with "finite region", but that still doesn't work, because you are conflating two different claims. The claim that the system can interact with a measuring device in any spatial region in which its wave function is nonzero--which is the only claim that your arguments about measurements being "elements of reality" actually justify--is a much weaker claim than the claim you are trying to argue about, which is the claim that the system must be "definitely located" in the spatial region occupied by the measurement device. That claim, at least according to QM, is false: QM in no way requires that a system's wave function be nonzero only in some particular finite spatial region, presumably the one occupied by the measurement device (which is what "definitely located" means), in order to interact with that device.

There is some contention that the probability distribution does actually describe the location prior to measurement.

Where? Who has contended this?

We know that when we measure the system, the probability of its location 'collapses' to 1 i.e. we find it in a single location (within the given error bars).

No, we do not know this. We know that we have to apply the collapse postulate in order to make accurate predictions about future measurements, but what, if anything, that says about the "actual" location of the system depends on which QM interpretation you adopt.

In summary: you are reasoning from premises that no one else but you accepts, and you have given no reason why anyone else should accept them. That is why no one else is accepting your arguments.

 

[Lynch101]

False dichotomy. The wave function always tells you the probabilities of measurement outcomes; but depending on which interpretation of QM you adopt, it can also be a description of the system prior to interacting with the measurement device. So those two things are not mutually exclusive.

But the proponents of some interpretations say that the wave function only tells us the probabilities of measurement outcomes and is not a description of the system prior to interacting with the measurement device.

It is this position which cannot be considered a complete description of physical reality because the system it does not describe the system prior to measurement.

 

[Fra]

While it might be a classical bias to expect a definite value for position, prior to measurement, the system in question must be somewhere as it cannot be nowhere. If the mathematics doesn't describe this 'somewhere' it cannot give a complete description of physical reality.

Some interpretations ascribe an ontology to the wave function which attempts to describe this 'somewhere', which make them [an attempt at] a complete description of physical reality. Any interpretation that only gives probabilistic predictions for the outcomes of measurements cannot be said to describe the location of the system prior to measurement. Since the system must be somewhere - even if that doesn't imply a definite location - such an interpretation/theory cannot be said to be a complete description of physical reality.

This is of course interpretation dependent, but there is also the possibility that the nature of inference - what an observer can state about the system - is limted in a much deeper way than thinking that it's an "incomplete description" in the sense of the observers ignorance. The apparent incompleteness may come from the nature of asking many non-commutative questions, and trying to bring the answers together into one "state space". And it may very well be that the physical interaction between two subsystems are determined, merely by their mutual expectations.

This is why I think that the best way to understand QM interactions is not in terms of physical objects bouncing around, but as two "expectations" interacting via information exchange. That seems the natural way to make sense of things, at least for me. Though I know some will frown upon introducin the notion of "information" as a new ontology.

/Fredrik

 

[Lynch101]

No, the burden of proof lies on you to support your positive claim that there are no other possibilities, since your argument rests on that claim. Just saying that you can't think of any other possibilities is not enough.

I am not making a positive claim so there is nothing for me to have to prove. I am simply pointing out that you have not given sufficient support for your claim.

I am not saying that no other possibilities exist, I am saying the emboldened part.

If other possibilities exist, then the burden of proof is on anyone (not necessarily you) to demonstrate these possibilities. It is possible to reject the possibilities I have suggested and not proffer any alternatives but to not do so leaves us with an incomplete description of physical reality.

If "location" means "the spatial region in which the system is capable of interacting with a measurement device", then yes, as I have already explained.

OK, so then you are not contending that the wave function only gives probabilistic predictions for measurement outcomes, but also describes the location of the system prior to measurement.

Does the wave function tell us the probability of measuring the system in "the spatial region in which the system is capable of interacting with a measurement device"?

No, the contention by others in this thread has been that the wave function does not describe the system being in a definite location, by which they meant "a single point at which the system is known to be located".

Vanhees has taken the aforementioned position

My conclusion from this simply is that we just have to take the quantum state as what it tells us: The probabilities for the outcomes of measurements.

and you have stated as much yourself (emphasis added by me)

The wave function always tells you the probabilities of measurement outcomes; but depending on which interpretation of QM you adopt, it can also be a description of the system prior to interacting with the measurement device.

From that we can have the position that wave function tells you the probabilities of measurement outcomes or we can have the position that wave function tells you the probabilities of measurement outcomes and be a description of the system prior to interacting with the measurement device.

It is the former that is the incomplete description of physical reality.

You attempted to gerrymander the definition by replacing "point" with "finite region", but that still doesn't work, because you are conflating two different claims. The claim that the system can interact with a measuring device in any spatial region in which its wave function is nonzero--which is the only claim that your arguments about measurements being "elements of reality" actually justify--is a much weaker claim than the claim you are trying to argue about, which is the claim that the system must be "definitely located" in the spatial region occupied by the measurement device. That claim, at least according to QM, is false: QM in no way requires that a system's wave function be nonzero only in some particular finite spatial region, presumably the one occupied by the measurement device (which is what "definitely located" means), in order to interact with that device.

I'm simply stating that there are two options, as per your statement above:
1) The wave function tells us the probabilities of measurement outcomes only
2) The wave function tells us the probabilities of measurement outcomes and be a description of the system prior to interacting with the measurement device.

I am saying #1 cannot be a complete description of reality because it does not describe the system prior to measurment.

If we adopt position #2, we can ask what the wave function tells us about the location of the system prior to measurement.

This is where we have a range of possible explanations. I have listed some and, in general, this is where 'interpretations' of QM come into play. I am by no means saying that the options I listed is an exhaustive list, it is possible that there are more. At this juncture there are [at least] 3 options:

A) Suggest that the list is exhaustive
B) Suggest and addition to the list
C) Reject all options on the list and do not proffer any additional options.

To adopt position #C effectively puts us back to position #1 above, which leaves us with an incomplete description of reality.

Where? Who has contended this?

Vanhees has been attempting to reconcile positions #1 & #2 (emphasis added by me)

As I repeatedly said, the description of the system prior to measurement is given by the quantum state (statistical operator) at the initial time (after the "preparation" is finished). In classical mechanics it's given by the point in phase space at the initial time.

No, we do not know this. We know that we have to apply the collapse postulate in order to make accurate predictions about future measurements, but what, if anything, that says about the "actual" location of the system depends on which QM interpretation you adopt.

In summary: you are reasoning from premises that no one else but you accepts, and you have given no reason why anyone else should accept them. That is why no one else is accepting your arguments.

I'm not talking about future predictions, I'm talking about observations. When we measure the system we get a definite value for its location. The probability of the system being (or having been) where it registered on the measurement device is 1.

 

[PeterDonis]

It is this position which cannot be considered a complete description of physical reality because the system it does not describe the system prior to measurement.

To support this argument, you need to show that "the system prior to measurement" is an element of physical reality. You have not done so.

 

[PeterDonis]

If other possibilities exist, then the burden of proof is on anyone (not necessarily you) to demonstrate these possibilities.

Only if they are making a positive claim that depends on the existence of those other possibilities.

If you are making a positive claim that depends on the possibilities you listed being the only ones, then you need to demonstrate that that must be the case.

 

[Lynch101]

To support this argument, you need to show that "the system prior to measurement" is an element of physical reality. You have not done so.

The alternative is that it is not 'an element of reality'. If it is not an element of reality, then it could not possibly interact with the measurement device. Unless we contend that things which are not part of the universe can interact with things that are.

 

[PeterDonis]

then you are not contending that the wave function only gives probabilistic predictions for measurement outcomes, but also describes the location of the system prior to measurement.

I am saying that's a possible interpretation. That claim seems unproblematic since there are existing interpretations that say that.

Does the wave function tell us the probability of measuring the system in "the spatial region in which the system is capable of interacting with a measurement device"?

Since the wave function in the position representation tells you the probability of measuring the system in any spatial region, that would include the spatial region you describe.

 

[PeterDonis]

The alternative is that it is not 'an element of reality'. If it is not an element of reality, then it could not possibly interact with the measurement device.

Why? You are using a particular (implicit) definition of "element of reality", but you have given no argument for why I should care about this definition. You certainly have not argued, except by definition, that something must be an "element of reality" in order to interact with a measurement device. But if that is only true by definition, then I have already explained how QM meets this requirement (because it tells you whether or not the wave function is nonzero in the spatial region occupied by the measurement device)--in other words, on this interpretation, it is an element of reality, because it meets the definition (since it tells you whether or not the system can interact with a measurement device).

 

[Demystifier]

Then no physics is realistic or complete, because all of physics describes or predicts observations and thus, in quantified form, the outcome of measurements. How do you want to describe anything if not by referring to the phenomena we can observe about it?

Classical mechanics can consistently be formulated without referring to measurements. There are also such formulations of quantum mechanics (Bohmian mechanics is an example), but standard formulation of QM is not such a formulation.

 

[Demystifier]

If I never look, I can't check any predicted probabilities.

Sure, but if you take a look at a classical/analytical mechanics textbook, you will not see mentioning of measurements in the formulation of the theory. In quantum mechanics it's different. Why is that?

 

[Demystifier]

Can you specify more clearly, what you mean by the Born rule were not local? I have no clue, how the Born rule may be considered as local or non-local at all.

Read again what I said in the bracket! The Born rule by itself is neither local nor nonlocal. But when it is combined with other axioms, its consequences can be local or nonlocal, depending on definition of locality.