A Assumptions of the Bell theorem

[PeterDonis]

To try and outline the reasoning a bit more clearly

You're not doing that in the rest of your post. You're just restating your personal opinion. You are still not giving any argument for why anyone else should care about your personal opinion or adopt the personal definition of "elements of reality" or "complete description of reality" that you have adopted.

 

[WernerQH]

What's measured in the quoted article are approximate photon momenta. I've to read the details to understand, how they can claim that what they calculate out of these measurements were Bohmian trajectories of photons though photons don't even have a position observable to begin with.

I only read the abstract and was puzzled. Theorists are unable even to define the trajectories, but smart experimentalists can observe them anyway. ;-)

 

[PeterDonis]

Having a non-zero value for the wave function in a given spatial region is not sufficient for interaction with a measurement device, since we can put measurement devices in all of those regions with a non-zero probability and not observe interactions with all of the measurement devices.

You are shifting your ground. Before, you wanted the theory to tell you whether the system was capable of interacting with a given measurement device. Now, you want the theory to tell you which specific measurement device, out of multiple measurement devices that the system is capable of interacting with, the system will actually interact with. In other words, now you want to require the theory to be deterministic; just having the necessary "elements of reality" isn't enough.

 

[Lynch101]

You're not doing that in the rest of your post. You're just restating your personal opinion. You are still not giving any argument for why anyone else should care about your personal opinion or adopt the personal definition of "elements of reality" or "complete description of reality" that you have adopted.

It's not my personal definition.

From the EPR paper

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.

Some interpretations of QM simply define themselves as incomplete according to this criterion. Namely instrumentalist/'anti-realist'/minimal statistical interpretations*.

Am I correct in saying that psi-epistemic is the umbrella term?

What I have described is anti-realism as it is used in literature: The claim that the properties in QM do not refer to real properties of the system.

When EPR talk about a complete description of physical reality, they are talking about describing every element of the system under consideration. What they refer to as 'elements of [physical] reality'.

As I have been saying, any interpretation that only gives us the probability of measurement outcomes e.g. the aforementioned interpretations is, by the EPR definitions, an incomplete description of physical reality.

We can further establish this by asking the simple question, do those interpretations describe the system prior to measurement. IF they only predict the outcome of interactions with measurement devices then, again by definition, they do not describe the system prior to measurement.

The question then becomes, is there a system prior to measurement? If the answer is yes, then we ask do the above interpretations fully describe it? The answer to that is no, because they don't describe it prior to measurement. Therefore, they are incomplete according to the criterion set out by EPR.I think, perhaps, the baby is getting thrown out with the bathwater. Violations of Bell inequalities demonstrate that quantum systems do not have a single, pre-defined value for location prior to measurement. This, however, does not mean that the system has no location whatsoever.

I am contending that location is 'an element of reality' of the system. Not that it has a single, pre-defined value, simply that location is a property of the system that must be described - whatever form that takes. My contention is that any interpretation that fails to describe the location of the system prior to measurement cannot be considered complete, according to the EPR criterion.

It has been suggested that the probability distribution does describe the location of the system prior to measurement. We can explore what exactly this description does and does not tell us and make certain inferences about the 'complete description of physical reality'.

The alternative is to claim that there is no location to be described whatsoever i.e. it is not located in the universe. This too has consequences which we can explore.

 

[EPR]

It has been suggested that the probability distribution does describe the location of the system prior to measurement. We can explore what exactly this description does and does not tell us and make certain inferences about the 'complete description of physical reality'.

The alternative is to claim that there is no location to be described whatsoever i.e. it is not located in the universe. This too has consequences which we can explore.

In the MWI, which is a very sensible interpretation btw, every particle has a location before being measured. The MWI is pure QM as it is.
QM without the need for an interpretation and with no human baggage.

 

[PeterDonis]

It's not my personal definition.

From the EPR paper

This paper gives a general definition of "completeness" that involves elements of reality, but it does not claim that "location" is an element of reality. Only you are claiming that.

 

[Lynch101]

This paper gives a general definition of "completeness" that involves elements of reality, but it does not claim that "location" is an element of reality. Only you are claiming that.

And those interpretations that 'claim the properties in QM do not refer to real properties of the system' i.e. instrumentalist/'anti-realist'/minimal statistical are, according to that general definition, incomplete. Would you agree with that?

 

[facenian]

This paper gives a general definition of "completeness" that involves elements of reality, but it does not claim that "location" is an element of reality. Only you are claiming that.

Pardon me for stepping in. I think that according to the paper "position" is an element of physical reality(at least in special cases). However, I also think that it is an unnecessary metaphysical concept that Einstein himself immediately rejected. As it is well known, he preferred to argue against completeness using his separation principle. In my opinion, the infamous metaphysical concept of "elements of physical reality" has produced much confusion in the literature, and experts in quantum foundations do not even mention it. They only use Einstein's "separation principle".

 

[PeterDonis]

I think that according to the paper "position" is an element of physical reality(at least in special cases).

There was one particular thought experiment proposed (not, IIRC, in the paper, but in the general discussion around that time that the paper was part of--I think this particular proposal was during one of the Solvay conferences) in which it would have been, yes: basically, you prepare an entangled pair of particles in an eigenstate of total momentum and separation (i.e., difference in position), such that measuring the position of one enables you to know the position of the other without measuring it. However, IIRC it was never clear that the states assumed in this thought experiment were actually valid states (because of possible lack of normalizability, which would make them not physically realizable).

In any case, the qualifier you give, "at least in special cases", is already sufficient, IMO, to cast doubt on the whole concept of "elements of reality" (which you appear to be dubious about as well). Intuitively, one would not expect what things count as "elements of reality" to depend on what states we prepare or what particular experiment we are doing.

 

[PeterDonis]

And those interpretations that 'claim the properties in QM do not refer to real properties of the system' i.e. instrumentalist/'anti-realist'/minimal statistical are, according to that general definition, incomplete. Would you agree with that?

With that very weak claim, yes, I agree. But you have been making much stronger claims than just that.

 

[Demystifier]

I thought a photon does not have a position operator.

It does, but it does not have a Lorentz covariant position operator. A photon detector detects a photon at a certain position, so photon position certainly has an operational meaning.

How do you compute the trajectory of a photon in Bohmian mechanics?

In this case, by postulating a preferred Lorentz frame with respect to which the position operator is defined. As you might know, a preferred Lorentz frame is needed in Bohmian mechanics for other reasons as well.

 

[Demystifier]

Of course, because the Born rule is about probabilities for the outcome of measurements.

Please answer with yes or no to the following questions:
1. Can measurement be defined in a closed (not open) system?
2. If not, does it mean that the Born rule only makes sense for open systems?
3. If so, does it mean that the Universe as a whole is deterministic?
4. Or would you prefer to say that the whole Universe cannot be measured, so it's a meaningless concept?

I think that your answers are this:
1. no
2. yes
3. no
4. yes
but please confirm or correct!

 

[Lynch101]

With that very weak claim, yes, I agree. But you have been making much stronger claims than just that.

I'm not sure how you view that as the weaker claim since it is effectively establishes the overarching claim of EPR, that the QM description of physical reality is incomplete. Those interpretations essentially define themselves as incomplete descriptions of physical reality.

Weaker Claim
The subsequent claim I am making is much weaker than you might think. It simply amounts to the question, 'where is the system prior to measurement?'. Usually, answers to 'where' questions will take the form of a 'location'. We might, however, prefer to talk about 'position' instead.

So, I'm saying that the system must be 'somewhere' prior to measurement - a very weak claim. Therefore, to provide us with a complete description of the system we need a description of where it is 'located' prior to measurement. Or, if we prefer, we need a description of its position prior to measurement.

This is where the baby appears to get thrown out with the bathwater, since the description of the position of the system [prior to measurement] does not require a single, pre-defined value. There are myriad possible descriptions. To give two (of possibly very many) examples:
- it might have multiple pre-defined values for position
- it might be spread out across a broader spatial region such that a single pre-defined value doesn't fully describe its 'location' or 'position'.

Whatever form the description of the system's location/position takes is immaterial. What is required for the purpose of completeness, however, is some description of location/position prior to measurement; any description. By their own definition, interpretations which only give us probabilistic predictions about measurement outcomes do not give us any description of the systems location/position prior to measurement whatsoever. Therefore, by definition, those cannot be said to be complete descriptions of the system or, in the words of EPR, physical reality.

Alternatives
Of course, we are free to reject this reasoning. However, doing so leaves us with a very clear alternative. That alternative* is simply that the system is 'nowhere' prior to measurement. If this is the position we wish to adopt, then we can explore the implications of it.What might appear as the middle-ground, could be the position that the probability distribution does tells us something about the location/position of the system prior to measurement. However, it is less of a middle ground since it either tells us that the system is 'somewhere' prior to measurement or that it is 'nowhere'.

What we can do is probe what the probability distribution tells us about the location/position of the system prior to measurement. This might not give us the complete description of reality we are looking for, but it can certainly narrow the domain of possible descriptions. It might point, inexorably, to certain unavoidable features.*A further alternative might be that notions such as 'somewhere' and 'nowhere' do not apply at the quantum level. This too would have potential consequences for observations at the classical level. We could probe whether or not this idea could lead to observational results which appear to be superluminal at the classical level.

 

[Lynch101]

In the MWI, which is a very sensible interpretation btw, every particle has a location before being measured. The MWI is pure QM as it is.
QM without the need for an interpretation and with no human baggage.

The MWI, as far as I can tell, would fall under the category of 'potentially complete descriptions of physical reality' - as long as it describes all possible worlds. It would, at least, fall under the category of 'potentially complete descriptions of this world'.

The point I am making is that those 'interpretations' which remain agnostic would not, by their own definition, fall under the category 'potentially complete descriptions of physical reality'. They rule themselves out by declaring that the mathematical formalism does not correspond to 'physical reality'.

 

[Lynch101]

It does, but it does not have a Lorentz covariant position operator. A photon detector detects a photon at a certain position, so photon position certainly has an operational meaning.In this case, by postulating a preferred Lorentz frame with respect to which the position operator is defined. As you might know, a preferred Lorentz frame is needed in Bohmian mechanics for other reasons as well.

Is a preferred Lorentz frame necessary, or is it more that absolute simultaneity is required?

 

[Demystifier]

Is a preferred Lorentz frame necessary, or is it more that absolute simultaneity is required?

Absolute simultaneity is what is actually required.

 

[PeterDonis]

I'm saying that the system must be 'somewhere' prior to measurement - a very weak claim.

No, it isn't, it's a strong claim. It includes the claim that "location" (or "position" or whatever you want to call it) is an element of reality for all quantum systems at all times. That is a much stronger claim than just claiming that statistical-type interpretations of QM are incomplete by the EPR criterion. The latter claim says nothing whatever about what, specifically, is missing from statistical-type interpretations; it just says that something is.

 

[Lynch101]

No, it isn't, it's a strong claim. It includes the claim that "location" (or "position" or whatever you want to call it) is an element of reality for all quantum systems at all times. That is a much stronger claim than just claiming that statistical-type interpretations of QM are incomplete by the EPR criterion.

I really don't think the claim is as strong as it appears, particularly when we consider the question that is being asked.

The question is simply, where is the system prior to measurement? Would you agree that, very broadly speaking, there are two possible answers:
1) The system is somewhere.
2) The system is nowhere.

The latter claim says nothing whatever about what, specifically, is missing from statistical-type interpretations; it just says that something is.

The latter claim says that everything is missing. It says that nothing in the mathematics corresponds to the 'elements of reality' of the system. Instead, it says the mathematics tells us what we will observe on measurement devices at the classical level.

 

[PeterDonis]

I really don't think the claim is as strong as it appears, particularly when we consider the question that is being asked.

The question you are asking is itself part of the strong claim--since you must already have established that "location" is an element of reality, for all quantum systems, all the time, in order for the question to make sense.

Would you agree that, very broadly speaking, there are two possible answers:
1) The system is somewhere.
2) The system is nowhere.

Only if your strong claim has already been established. Otherwise the question itself is not well-defined.

The latter claim says that everything is missing.

This rewording does not change any of the points I am making.

 

[Lynch101]

The question you are asking is itself part of the strong claim--since you must already have established that "location" is an element of reality, for all quantum systems, all the time, in order for the question to make sense.

Only if your strong claim has already been established. Otherwise the question itself is not well-defined.

OK, let's take it back a step.

Do you agree that one of the two following propositions must be true:
1) Location is an element of reality of the system, prior to measurement.
2) Location is not an element of reality of the system, prior to measurement.

Do the following make sense:
A) If someone tells you that they have hidden something valuable and if you find it, you can keep it. You ask, where should I look and they tell you, in that field over there. Would that make sense to you?
EDIT: i.e. they tell you that 'it's somewhere in the the field'.

B) If we have two laboratories, one in Paris the other in Rome. Does it make sense to say that, as part of our experiment to test quantum theory, a system was prepared in the lab in Paris?

C) If the system is prepared in the lab in Paris, does it make sense to say that the system is located in the lab in Paris and not in the lab in Rome?

This rewording does not change any of the points I am making.

It does. The claim that every element [of reality of the system] is missing is a stronger claim than a single element of reality is missing. Not only does it say that every element of reality is missing, it says, no matter what element of reality we can think of, it is missing from the theory.

Either way, it establishes the primary claim of EPR, that the QM description of physical reality is incomplete.

 

[PeterDonis]

The claim that every element [of reality of the system] is missing is a stronger claim than a single element of reality is missing.

I didn't say "a single" element of reality. I just said "something" was missing, with the "something" being "elements of reality", which makes no claim whatever about what specifically the missing elements are, or how many elements there are that are missing, or anything else. Saying "every" element of reality is missing is saying the same thing, just in different words.

 

[PeterDonis]

let's take it back a step.

We already have. I've already agreed with the claim that "statistical" interpretations of QM (ones that say the quantum state just gives probabilities for measurement results and doesn't say anything about the actual state of individual systems) are incomplete by the EPR criterion. I don't see the point of belaboring that any further.

Your argument for location being an element of reality for all quantum systems, all the time, seems to boil down to the observation that classical, macroscopic systems (which includes measurement devices) have well-defined locations. This is by no means a new argument in this area, and probably deserves a thread of its own, based on some of the (voluminous) literature on it, if you really want to discuss it further. It is well off of the topic of this thread, since Bell's theorem does not say anything specifically about location as a possible element of reality or hidden variable.

 

[PeterDonis]

Either way, it establishes the primary claim of EPR, that the QM description of physical reality is incomplete.

Only for "statistical" interpretations (as I defined that term in post #742). I've already agreed to that, as I have pointed out.

 

[vanhees71]

And it's not incomplete even for "statistical interpretations" (i.e., the standard or "orthodox" interpretation of QT) if nature "really" is random at the most fundamental level, and I think all the Bell tests quantum theory passed with bravour indicate that this is pretty likely.

It's also pretty clear that, given the atomistic structure of matter, the EPR criterion cannot be right, because you cannot observe something without disturbing it, when it comes to probing the elementary atomistic building blocks. E.g., to the best of our knowledge electric charge of the observable (i.e., asymptotic free) particles come in integer multiples of $e$ (the elementary charge). If you want to measure the electric field of, e.g., an electron (charge $-e$) you have to use another charged particle. To do this "without disturbing" the electron you'd need a particle with a much smaller charge with $|q| \ll e$, but that doesn't exist. So it's the EPR "reality" criterion which is quite "unrealistic" given the fact that matter is atomistic and not QT, which describes all phenomena in accordance with all observations.

 

[Lynch101]

Only for "statistical" interpretations (as I defined that term in post #742). I've already agreed to that, as I have pointed out.

Yes, my apologies, I should have been clearer in my wording.

I didn't say "a single" element of reality. I just said "something" was missing, with the "something" being "elements of reality", which makes no claim whatever about what specifically the missing elements are, or how many elements there are that are missing, or anything else. Saying "every" element of reality is missing is saying the same thing, just in different words.

We already have. I've already agreed with the claim that "statistical" interpretations of QM (ones that say the quantum state just gives probabilities for measurement results and doesn't say anything about the actual state of individual systems) are incomplete by the EPR criterion. I don't see the point of belaboring that any further.

Your argument for location being an element of reality for all quantum systems, all the time, seems to boil down to the observation that classical, macroscopic systems (which includes measurement devices) have well-defined locations. This is by no means a new argument in this area, and probably deserves a thread of its own, based on some of the (voluminous) literature on it, if you really want to discuss it further. It is well off of the topic of this thread, since Bell's theorem does not say anything specifically about location as a possible element of reality or hidden variable.

Good call. I'll start a separate thread, thank you.

Just for the purpose to try and link this back to the topic of this thread, is it correct to say that one of the assumptions of Bell's theorem is that systems have well defined [single] values for position, prior to measurement. With the violation of Bell's inequality having implications for this assumption?

 

[Lynch101]

And it's not incomplete even for "statistical interpretations" (i.e., the standard or "orthodox" interpretation of QT) if nature "really" is random at the most fundamental level, and I think all the Bell tests quantum theory passed with bravour indicate that this is pretty likely.

It's also pretty clear that, given the atomistic structure of matter, the EPR criterion cannot be right, because you cannot observe something without disturbing it, when it comes to probing the elementary atomistic building blocks. E.g., to the best of our knowledge electric charge of the observable (i.e., asymptotic free) particles come in integer multiples of $e$ (the elementary charge). If you want to measure the electric field of, e.g., an electron (charge $-e$) you have to use another charged particle. To do this "without disturbing" the electron you'd need a particle with a much smaller charge with $|q| \ll e$, but that doesn't exist. So it's the EPR "reality" criterion which is quite "unrealistic" given the fact that matter is atomistic and not QT, which describes all phenomena in accordance with all observations.

The EPR criterion of 'not disturbing the system', in their words, 'far from exhausting all possible ways of recognizing a physical reality'.

The more general claim was that all elements of reality must have a counterpart in the physical theory. Therefore, 'statistical interpretations' would have to say that the wave function or probability distribution corresponds to elements of physical reality.

 

[AndreiB]

...if nature "really" is random at the most fundamental level, and I think all the Bell tests quantum theory passed with bravour indicate that this is pretty likely.

Bell's theorem is designed for local deterministic theories for the simple fact that the local non-deterministic ones were already ruled out by EPR. So, if you accept all Bell's assumptions you need to conclude that physics is non-local. If this is the case, both random and deterministic theories are possible. So, EPR + Bell do not increase the probability that nature is random. On the contrary, determinism is more likely, since it is still possible in its local form if Bell's statistical assumption is denied. Local non-deterministic theories are completely ruled-out since EPR does not use any other assumption besides locality.

It's also pretty clear that, given the atomistic structure of matter, the EPR criterion cannot be right, because you cannot observe something without disturbing it, when it comes to probing the elementary atomistic building blocks. E.g., to the best of our knowledge electric charge of the observable (i.e., asymptotic free) particles come in integer multiples of $e$ (the elementary charge). If you want to measure the electric field of, e.g., an electron (charge $-e$) you have to use another charged particle.

This is not true. In the EPR setup you measure particle A and deduce the state of particle B. B could be arbitrarily far away, hence your measurement of A does not disturb B (at least for the case the measurements are space-like).

 

[vanhees71]

The EPR criterion of 'not disturbing the system', in their words, 'far from exhausting all possible ways of recognizing a physical reality'.

The more general claim was that all elements of reality must have a counterpart in the physical theory. Therefore, 'statistical interpretations' would have to say that the wave function or probability distribution corresponds to elements of physical reality.

No! EPR say all elements of reality must have a counterpart in the physical theory. That doesn't mean that any mathematical element of the theory must have a counterpart in reality. The wave function indeed is not observable and thus has not a counterpart in reality. The probability distribution obviously corresponds to elements of reality, because it can be tested by observations on ensembles of equally prepared systems.

 

[vanhees71]

Bell's theorem is designed for local deterministic theories for the simple fact that the local non-deterministic ones were already ruled out by EPR. So, if you accept all Bell's assumptions you need to conclude that physics is non-local. If this is the case, both random and deterministic theories are possible. So, EPR + Bell do not increase the probability that nature is random. On the contrary, determinism is more likely, since it is still possible in its local form if Bell's statistical assumption is denied. Local non-deterministic theories are completely ruled-out since EPR does not use any other assumption besides locality.
This is not true. In the EPR setup you measure particle A and deduce the state of particle B. B could be arbitrarily far away, hence your measurement of A does not disturb B (at least for the case the measurements are space-like).

QFT is local (microcausal) by construction and still predicts correctly the violation of Bell's inequality. So what I have to give up is determinism, not locality, because giving up locality would mean to give up a (if not the) deciding cornerstone of relativistic QFT.

If I measure particle A and I know that it is entangled with particle B I know what an observer at particle B must get when measuring the corresponding observable which is 100% correlated with the variable that I measured. That doesn't imply a spooky action of a distance, but just refers to the correlations described by the entangled state being prepared in the very beginning. My local measurement indeed doesn't do anything to particle B.

 

[Demystifier]

On the contrary, determinism is more likely, since it is still possible in its local form if Bell's statistical assumption is denied.

By determinism + denial of Bell's statistical assumption, do you mean superdeterminism?