A Assumptions of the Bell theorem

[Lynch101]

Okay, so what does "located somewhere in the universe" mean? What does it correspond to in the math of QM?

I strongly suspect that you will be unable to give a valid answer to this question that supports the claims you are making--i.e., that is inconsistent with the things other people are saying that you have been objecting to.

'Located somewhere in the universe' simply means it is in the universe, such that it will be included in any full description of the universe aka 'physical reality'.

That is, however, the crux of the issue. It's that, by definition, interpretations which say that the mathematics only give us probabilistic predictions for the outcomes of experiments do not have anything in the mathematics which correspond to "located somewhere in the universe".

Since the quantum system must be located somewhere in the universe, at all times, a theory which only gives probabilistic predictions for when the system interacts with a measurement device does not, by definition, describe the system prior to measurement.

If "has a definite location" means "is located at some single point", then the answer to this is obviously no, since, as I have already stated, states with definite positions--where a particle is located at a single point--are not normalizable and hence cannot be realized physically.

If "has a definite location" means something else, then you need to explain what you are using that term to mean.

If the system is not "located at some single point" then the probability distribution isn't telling us that the system is always located at some single point and it's just a lack of information on our part that gives us the probabilistic predictions.

Given that the system must be located somewhere, what does the probability distribution tell us? Does it tell us the system is distributed across a broader area than a single location, with 'more' of it (or a greater density of it) in one location than another?

If the probability distribution only tells us the probability of the system interacting with a measurement device at a given location, then it doesn't describe the system prior to that interaction - as a matter of definition.

 

[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?

The issue is that some claim that the math of QM does not have such a thing, when, in order to be considered a complete description of physical reality, it should.

 

[EPR]

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.

 

[PeterDonis]

'Located somewhere in the universe' simply means it is in the universe, such that it will be included in any full description of the universe aka 'physical reality'.

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?

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.

by definition, interpretations which say that the mathematics only give us probabilistic predictions for the outcomes of experiments do not have anything in the mathematics which correspond to "located somewhere in the universe".

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.

Given that the system must be located somewhere, what does the probability distribution tell us?

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.

The issue is that some claim that the math of QM does not have such a thing,

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.

 

[Lynch101]

Yes indeed, for a single realization of this experiment you cannot know before the measurement in which spot (around $\vec{a}$ or around $\vec{b}$) you will find the particle. It could even by found (with correspondingly smaller probability of course) somewhere else far away from both $\vec{a}$ and $\vec{b}$. All you know and (as far as quantum theory is complete) all you can know are the probabilities given by the probability distribution $|\psi(\vec{x})|^2$. That it is "somewhere" is clear, because by definition
$$\int_{\mathbb{R}^3} \mathrm{d}^3 x |\psi(\vec{r})|^2=1.$$

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?

 

[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.