I Anti-realist Interpretations of QM

[DrChinese]

We can construct algebras that reference spin before measurement has occurred that will still produce the same correct predictions.

Unless I don't understand your comment, Bell precludes that.

There are no data sets or statistical averages for quantum spins independent of the measurement setting(s). Keeping in mind that there are a multitude of statistical requirements due to the multitude of possible settings (thinking of typical Bell tests here).

 

[Lynch101]

Answer 2) is mostly the standard view of physicists. That QM is complete as is.

That is the understanding I had gotten, although I wasn't exactly sure what the breakdown of proponents was.

I just think there is a serious issue with the idea that there is nothing at all "inside the box", because if there were something "inside the box" then to my mind there is something to be described. If there is nothing at all inside the box, then it raises the question of how nothing can interact with a measurement device to produce something i.e. a measurement outcome.

Although Bohmians might argue that a more complete specification of the system is possible. No quibble as interpretations each address this.

The Bohmian picture seems to be the most intuitive to me but I think there is a middle ground between the idea that a more complete specification of the system is possible and the idea that there is nothing in need of description. There might be something "inside the box" to be described, but it might not be possible to probe it in such a way that we can meaningfully describe it. We could still make certain limited deductions however.

The unquantified properties of an ENTANGLED system can be discussed. They follow conservation rules. A+B=zero/constant/initial value.

Is this more a statement about rules that they follow as opposed a description of the properties?

 

[Lynch101]

If we were to distinguish anti-realism from instrumentalism, we could say an anti-realist is agnostic towards the nature of the reality of quantum systems, and rejects physical properties in our models as real, while an instrumentalist is agnostic towards both the nature of reality of quantum systems and also the ontic status of the physical properties present in our models.

Ah thank you Morbert, I think I see the distinction you're making, now. Is the following accurate?

The anti-realist in QM says that the (for want of a better term) mathematical elements of QM don't have a 1-to-1 correspondence with the quantum system itself, or with reality we might say. It says that the model only enables us to make the probabilistic predictions we see in QM. It says that there might be something "inside the box" or there might not, either way the mathematical formalism doesn't describe what is "inside the box"?

On the other hand, instrumentalism says the model might have a direct correspondence to reality or it might not, who cares, just SUAC?

Beables are a feature of a particular category of physical models. If it is the case that there is an objective reality, but it cannot be modeled with beables or hidden variables, then beables would not be a good description of this objective reality. It may be the case, for example, that reality cannot be thoroughly accounted for with physical theories.

Ah, I see. Thanks for the clarification on that too.

 

[Lynch101]

I've re-ordered your post to reply to a specific point first. Hopefully this doesn't distort it in any way.

So your classical biases are showing through. You clearly want to paint a nice neat real number on each property ignoring the fact it's been shown by experiment that this isn't possible. It's simply not the way the world is observed to work, ever. Classical macroscopic physics is an approximation superseded by QM, a better one. It's now the case that one must provide a theory of measurement justifying classical mechanics in terms of quantum measurements, not the reverse. Your philosophical machinations really aught to be inverted.

Classical bias would be to say that the baseball follows a simple trajectory through the building with a definite location and momentum at every point en route to the window. Experiment shows that this isn't the case when we have say two slits, inside the building, through which the baseball can travel and both are open. If we open one slit at a time then it would appear as though we could infer our classical notions of trajectory. Of course, this wouldn't account for what happens when both slits are open, so we can't simply infer our classical notions of trajectory.

To account for what happens when both slits are open we might try to infer a different classical bias. We might say that the baseball spreads out like a wave and goes through both slits, interferes with itself and then strikes the one of the windows. We might say that the mathematical formalism is a description of what is happening inside the building and the process it describes is that of a baseball riding on top of a pilot wave and that it is the pilot wave that interferes with itself, carrying the baseball to one of the windows to smash it. All of these offer an explanation as to how the baseball gets from the machine to the window to smash it.

If, however, we reject all of these and say that our mathematical formalism only tells us the probability of which window will get broken, and nothing more, we are then left with the question of what is actually happening inside the building? How does the baseball get from the machine to the window to break it?

There are essentially two broad answers to this question:
1) There is something happening inside the building. For a complete model of nature we would need to describe the process occurring inside the building.
2) There is absolutely nothing happening inside the building and therefore nothing to describe.

Yes and yes.
By the time development of the system state vector.

Hopefully I'm phrasing this correctly but, do you attribute ontic status to these?

In my own terminology I would ask if you believe that these parts of the model correspond directly to reality?

Well, yes just not at all in the manner you describe. One can show experimentally for fields in $\alpha$-states that the photons in fact have no trajectory (in fact the entire question isn't meaningful). Closest one can get is the wave nature of the field. Again, asking a classically motivated question about quantum systems isn't at all meaningful. Similar arguments hold for electrons and nuclei. If this is the picture you hold in mind, it's counter-factual.

My apologies, I think my wording is a little to imprecise at times, or perhaps carries with it certain connotations that I don't intend. I try not to have any specific picture in mind.

Apologies again for coming back to this basic point, but it helps me to frame the issue in my mind; the question of the description of the system prior to measurement. If we say it is meaningless to talk about it or that the formalism only gives us predictions, then I interpret that to mean that it doesn't describe what happens "inside the building".

I may be misinterpreting what you are saying but in one sense you appear to be saying that the formalism does describe the system prior to measurement i.e. saying that it describes how the "particle" makes its way through the experimental set-up, prior to measurement.

 

[PeterDonis]

Experiment shows that this isn't the case when we have say two slits, inside the building, through which the baseball can travel and both are open.

Experiment shows no such thing. Nobody has done a double slit experiment showing interference with baseballs. Buckyballs, yes, but not baseballs. Buckyballs are many, many, many orders of magnitude smaller.

 

[Lynch101]

Even if a quantum entity “exists” prior to a measurement, what would it mean that there is something to be described. At first, one has to state, how the quantum entity exists, i.e., what is the character of its “existence” (realism).^** That’s a requirement for a “pictorial representation” in relation to the quantum formalism.

I guess its partly a question of what our physical models are supposed to represent. If they are meant to model reality then we might think of them as descriptions of what exists in nature or, more pointedely, a description of what nature comprises. If nature comprises quantum systems, then a complete model of nature would have to describe a quantum system. If nature comprises quantum systems prior to measurement then a complete model of nature would require a description of the quantum system prior to measurement.

If physical models aren't meant as descriptions of nature, rather computational tools to make predictions about nature, which may or may not represent reality, then that would carry a different set of requirements and consequences.

A pictorial representation is a formalism that has an isomorphic relation to the objects it represents such that the visualized structure of the representation corresponds to a similar structure in nature. Conversely, a symbolic representation does not stand for anything visualizable. It is an abstract tool whose function it is to calculate a result whenever this representation is applied to an experimental situation.”

The anti-realist position represents the symbolic representation and as such, appears to calculate the result of an experiment i.e. it gives us the probabilistic predictions of which measurement will occur. Measurements themselves are classical [level] phenomena, so if QM is only a tool to calcualte macro-level phenomena, to what extent does it describe the quantum world at all? As a computational tool does it just represent the amount of information that we can put into the calculation?

This still leaves us asking the question about the quantum system prior to measurement. Even if there is no quantum system, if it is classical all the way down and it is our lack of information that gives us probabilistic predictions, we still have the question of the system prior to measurement. What happens in the intervening time between switching on our device (which prepares the system) and seeing the exposure event on the Stern-Gerlach plate?

^** Regarding claims concerning the character of the “existence” of a quantum entity, the problems were clearly expressed by J. Robert Oppenheimer in “Atom and Void: Essays on Science and Community”:

If we ask, for instance, whether the position of the electron remains the same, we must say "no"; if we ask whether the electron's position changes with time, we must say "no"; if we ask whether the electron is at rest, we must say "no"; if we ask whether it is in motion, we must say "no."

I would be inclined to think that this points to an inability on our part to describe the quantum system as opposed to its lack of "existence", or to put it another way, it's absence from what nature comprises.

 

[Lynch101]

Experiment shows no such thing. Nobody has done a double slit experiment showing interference with baseballs. Buckyballs, yes, but not baseballs. Buckyballs are many, many, many orders of magnitude smaller.

Apologies, the baseball and the windows is meant to be an analogy highlighting where I perceive the gap in explanation. I mightn't have referenced it clearly to the previous post where I started the analogy.

 

[PeterDonis]

There are essentially two broad answers to this question:
1) There is something happening inside the building. For a complete model of nature we would need to describe the process occurring inside the building.
2) There is absolutely nothing happening inside the building and therefore nothing to describe.

You're leaving out a third possibility:

3) The "something" in between the source and the measurement results cannot be described in terms of "processes" or "something happening", or in terms of "nothing is happening" or "nothing to describe". None of those combinations of words are a good description of that something.

One should always beware of false dichotomies, but interpretations of QM are an area where one has to be particularly careful in this respect.

 

[Paul Colby]

1) There is something happening inside the building.

In classical physics without the tacit assumption of measurement you can't say what's happening inside the building either. You may construct a model but without ever looking it, it may or may not happen to follow your model. You simply don't know.

In regard to the ability to measure both classical and quantum both make sweeping tacit assumptions that certain types of measurements can be made.

If one looks at the Bohr Einstein debates one sees a series of thought experiments proposed challenging the quantum view. One by one Bohr provided the supplemental measurement device interactions showing that the quantum result would prevailed. Einstein was the clear loser in this debate. It's not an accident that Bohr used the physics of the measurements to make his argument.

Now, quantum mechanics says, go ahead and look in the building but by doing so you must introduce additional measurement devices which will effect what you find. That's just the way the world is structured. I suggest you get used to it.

 

[DrChinese]

I guess its partly a question of what our physical models are supposed to represent. If they are meant to model reality then we might think of them as descriptions of what exists in nature or, more pointedely, a description of what nature comprises. If nature comprises quantum systems, then a complete model of nature would have to describe a quantum system. If nature comprises quantum systems prior to measurement then a complete model of nature would require a description of the quantum system prior to measurement.

...

Again, this is a very old position. Goes back to pre-1935 days. So you really must follow the EPR argument (which argued a more complete specification of the system was possible) and the Bell argument (that no such specification is possible if the quantum mechanical predictions are correct) and the Aspect argument (that the quantum mechanical predictions are correct). Conclusion: there is no more complete specification of the system.

If you fail to include Bell in the discussion, we will simply go 'round and 'round. You can say all day long that you believe there are things happening for which there is no evidence, and for which evidence exists that it cannot be. Even the Bohmian position is contextual (i.e. there is no well-defined value independent of the act of observation). That's because there are no data sets that match the quantum expectation values.

Quantum mechanics does not provide a "physical model" in the manner you describe. It is best considered a mathematical model. The interpretations attempt to supply some outline of a physical model, but all have issues of one sort or another.

 

[Paul Colby]

I may be misinterpreting what you are saying but in one sense you appear to be saying that the formalism does describe the system prior to measurement i.e. saying that it describes how the "particle" makes its way through the experimental set-up, prior to measurement.

Before measurement the isolated quantum system is described by a system state vector evolving in time. At measurement the quantum system interacts by exchanging some finite amount of energy with the macroscopic measuring device which then records the result. You just don't like this answer but it's what measurements actually are. Does this answer have ontic status? Don't know. Ontic Sounds like a fairly mushy meaningless term but I'm no expert.

 

[Lynch101]

You're leaving out a third possibility:

3) The "something" in between the source and the measurement results cannot be described in terms of "processes" or "something happening", or in terms of "nothing is happening" or "nothing to describe". None of those combinations of words are a good description of that something.

One should always beware of false dichotomies, but interpretations of QM are an area where one has to be particularly careful in this respect.

I'm inclined to agree with this and I think it demonstrates a fundamental limit on our ability to try and apply conceptual labels to reality, which is itself non-conceptual. There is a buddhist saying which says that "the finger pointing to the moon is not the moon" which can be interpreted as meaning that our conceptual descriptions of something are not the thing in itself and indeed, the thing in itself cannot be conceptualised.

So while we cannot capture the essence of the thing we wish to describe we can point to "something" that is there i.e. inside the box. If it is not possible to model whatever is there then it means that we can not have a complete model of nature. I think there are still certain conclusions that we can draw however.

I'm inclined to think that it points to the fact that there is information which we cannot acquire about a system, and this might explain why we end up with probabilistic predictions.

 

[Lynch101]

In classical physics without the tacit assumption of measurement you can't say what's happening inside the building either. You may construct a model but without ever looking it, it may or may not happen to follow your model. You simply don't know.

I think we are in agreement on this point. The point I am trying to get at however is that, to my mind, there must be, for want of a much better phrase, something happening inside the box. If we cannot model what is happening inside the box then our model does not represent a complete model of nature. There is information missing, which we may never be able to acquire. I'm inclined to think this lack of information is the reason for probabilistic interpretations but ultimately a realist explanation must be the case. That would be my reasoning.

If one looks at the Bohr Einstein debates one sees a series of thought experiments proposed challenging the quantum view. One by one Bohr provided the supplemental measurement device interactions showing that the quantum result would prevailed. Einstein was the clear loser in this debate. It's not an accident that Bohr used the physics of the measurements to make his argument.

Have you read the book What is real? by Adam Becker? I may be misremembering, but I think he paints a different picture of the Bohr-Einstein debates. IIRC he suggests that Bohr published a number of papers purporting to address Einstein's objections but didn't actually address them.

Was it Bell's work that ultimately demonstrated that the EPR argument was incorrect?

Now, quantum mechanics says, go ahead and look in the building but by doing so you must introduce additional measurement devices which will effect what you find. That's just the way the world is structured. I suggest you get used to it.

I completely accept that, but our inability to model what is inside the building doesn't mean that there is absolutely nothing inside the building. I think it is reasonable to say that there absolutely must be something inside the building and to have a complete model of nature we would need to model what is inside. If we cannot model it, then I don't think we can have a complete model of nature.

I believe the alternative is that there is absolutely nothing inside the building. This position however doesn't seem reasonable and has, what I believe are insurmountable issues, more so than even FTL [non-signalling[ communication.

@PeterDonis suggests that there is a third option but my reading of it is that it just demonstrates our inability to model what is happening inside the building. There is still either something or nothing in there we just could not model it either way. That is just my reading of it though, and there might be some nuance that I am not yet getting.

 

[Lynch101]

Again, this is a very old position. Goes back to pre-1935 days. So you really must follow the EPR argument (which argued a more complete specification of the system was possible) and the Bell argument (that no such specification is possible if the quantum mechanical predictions are correct) and the Aspect argument (that the quantum mechanical predictions are correct). Conclusion: there is no more complete specification of the system.

If you fail to include Bell in the discussion, we will simply go 'round and 'round. You can say all day long that you believe there are things happening for which there is no evidence, and for which evidence exists that it cannot be. Even the Bohmian position is contextual (i.e. there is no well-defined value independent of the act of observation). That's because there are no data sets that match the quantum expectation values.

To my mind, it sounds as though the baby gets thrown out with the bath water with Bell's theorem. I know that the EPR paper argued that particles do have definite postion and momentum even if we don't measure them. The idea was to measure the position of one pair of entangled particles and the momentum of another and by doing so we would know the position and momentum of the other (is that due to the conservation of momentum?)

I might be butchering this but did Bell show that, with the assumptions of local realism and statistical independence (and others?), if the particles did have these predefined values then they would obey an inequality pertaining to the measurement results? The experimental results violate the inequality however demonstrating that the system cannot have these predefined values*.

This is where it looks to me as though the baby is getting thrown out with the bath water. The system might not have predefined values for these specific properties but that doesn't mean that the system has no properties whatsoever, prior to measurement.

Quantum mechanics does not provide a "physical model" in the manner you describe. It is best considered a mathematical model. The interpretations attempt to supply some outline of a physical model, but all have issues of one sort or another.

My thinking is that, if there is a system prior to measurement then a complete model of nature would have to include some description of the system prior to measruement. This might not be possible, but that would mean that our model is not a complete model of nature.

 

[Lynch101]

Before measurement the isolated quantum system is described by a system state vector evolving in time. At measurement the quantum system interacts by exchanging some finite amount of energy with the macroscopic measuring device which then records the result. You just don't like this answer but it's what measurements actually are. Does this answer have ontic status? Don't know. Ontic Sounds like a fairly mushy meaningless term but I'm no expert.

I'm obviously no expert myself, I'm just reasoning on the basis of the information that I have encountered. I hadn't really encountered the term "ontic" outside the context of interpretations of QM, although I presumed it has the same root as the term "ontology".

With respect to certain realist hidden variable theories that attempt to explain the predictions of quantum mechanics, the theorem rules that pure quantum states must be "ontic" in the sense that they correspond directly to states of reality, rather than "epistemic" in the sense that they represent probabilistic or incomplete states of knowledge about reality.

PBR Theorem - wiki

I've come across the terms "psi-ontic" and "psi-epistemic" and, if I'm understanding correctly, "psi-ontic" refers to interpretations which treat the wave function as a physically real element of reality, while "psi-epistemic" treat the wave function as a representation of an experimenters [incomplete] knowledge of the system.In your statement above, does the system state vector correspond to an element of reality in the sense that the wave function does in Bohmian mechanics?

 

[Paul Colby]

In your statement above, does the system state vector correspond to an element of reality in the sense that the wave function does in Bohmian mechanics?

Reality as understood by humans is comprised of macroscopic objects. I would need to first understand macroscopic objects in terms of QM to answer this question. A quantum measurement is itself a macroscopic object comprised of an initially isolated quantum system evolving via hamiltonian, $H_{S}$ , which at the time of measurement, $t$, interacts via an interaction hamiltonian, $H_I(t)$, with a macroscopic detector, $D$. The question is what is $H_D$ and what are its internal micro states? How do the micro state effect $H_I$? When there are an astronomical sized set of possible states all recognized as the very same macroscopic object what is done with $|D\rangle$? Clearly a two level system, $|\text{alive}\rangle$ and $|\text{dead}\rangle$ is a comical over simplification.

 

[PeterDonis]

did Bell show that, with the assumptions of local realism and statistical independence (and others?), if the particles did have these predefined values then they would obey an inequality pertaining to the measurement results?

What you are calling "predefined values" are an example of what Bell called "hidden variables". Bell's theorem shows that any hidden variable model that satisfies his assumptions (which include what you are calling "local realism" and "statistical independence") must obey the Bell inequalities and therefore cannot account for the actual experimental data that violates them.

 

[DrChinese]

I might be butchering this but did Bell show that, with the assumptions of local realism and statistical independence (and others?), if the particles did have these predefined values then they would obey an inequality pertaining to the measurement results? The experimental results violate the inequality however demonstrating that the system cannot have these predefined values*.

This is where it looks to me as though the baby is getting thrown out with the bath water. The system might not have predefined values for these specific properties but that doesn't mean that the system has no properties whatsoever, prior to measurement.

You use the words "no properties whatsoever" and those have no connection to what is being assumed by EPR or Bell.

a) EPR says that if any value can be predicted in advance, it must be pre-existing (and therefore QM is incomplete). Entangled particle pairs demonstrate this feature as EPR believed in 1935. It is sometimes called "perfect correlations" as there is 100% agreement when appropriate measurement settings are chosen.

b) The question Bell asked was: If there are values prior to measurement, then are the values INDEPENDENT of measurement? I.e. are they objectively real? I.e. are they observer independent? I.e. are values for all possible measurement settings predetermined? Bell showed that this extension to a) was NOT possible.

In the language of EPR: the question was whether the values (for each of the many/infinite number of measurement basis choices) are simultaneously real. Bell precludes that, because there is no such set that reproduces the QM expectation values.

So you MUST consider both a) and b) when talking about this. It is easy to jump past one or the other. Your model must reproduce perfect correlations, and statistical percentages at other times. (Of course the perfect correlations are also a subset of the statistical percentages, where the percentage is either 0% or 100%.)

 

[Lynch101]

Reality as understood by humans is comprised of macroscopic objects. I would need to first understand macroscopic objects in terms of QM to answer this question. A quantum measurement is itself a macroscopic object comprised of an initially isolated quantum system evolving via hamiltonian, $H_{S}$ , which at the time of measurement, $t$, interacts via an interaction hamiltonian, $H_I(t)$, with a macroscopic detector, $D$. The question is what is $H_D$ and what are its internal micro states? How do the micro state effect $H_I$? When there are an astronomical sized set of possible states all recognized as the very same macroscopic object what is done with $|D\rangle$? Clearly a two level system, $|\text{alive}\rangle$ and $|\text{dead}\rangle$ is a comical over simplification.

Thanks for this breakdown Paul. I find posts like this very helpful.

I think, perhaps, thinking of reality in terms of macroscopic objects can be somewhat of a hindrance. It is entirely natural and almost impossible not to do, but the idea that I have in mind tries to get away from that. I'm trying to use very broad terms such as "anything" and "something" to try and circumvent this tendency.

The issue - on my part - with the above, is that I am taking it in the context of what other members have said also. @Morbert made a distinction that helped me to see an issue with how I was interpreting the anti-realist position. I was taking the anti-realist position to mean a denial of the existence of the quantum system prior to measurement, but he clarified:

anti-realist is agnostic towards the nature of the reality of quantum systems, and rejects physical properties in our models as real

In relation to the role of the mathematical formalism he says:

Quantum theory in a strict sense is nothing more than the set of rules whereby physicists compute probabilities of the outcomes of macroscopic tests.

This is in keeping with what I had generally understood and what you and others have reiterated.

If I interpret your post above, with regard to the Hamiltonians, in the context of the statement about computing the probabilities of outcomes, it appears to say that the mathematics only gives us the probabilities for the outcomes of experiments. In terms of the analogy I've used, it only tells us the probability of which window will get broken and tell us nothing at all about what happens inside the building.

I understand that the phrase "what happens inside the building" is not very precise but if we agree that there is a building and that there is a quantum system prior to measurement, then I would reason that, in order for our model of nature to be complete, it would have to model the system inside the building prior to measurement.

If it doesn't, then I'm inclined to think that our model of nature is incomplete. If it simply isn't possible to model inside the building then it means that we cannot have a complete model of nature. Either way, the conclusion would be that the model is not a complete model of nature. That doesn't make it any less effective in what it does, but that is the conclusion I find myself arriving at.

 

[Lynch101]

What you are calling "predefined values" are an example of what Bell called "hidden variables". Bell's theorem shows that any hidden variable model that satisfies his assumptions (which include what you are calling "local realism" and "statistical independence") must obey the Bell inequalities and therefore cannot account for the actual experimental data that violates them.

Thanks Peter. I follow the logic of Bell's theorem and how the violation of the inequality in experiments rules out local hidden variables. In my mind I am making a distinction between the system having properties with predefined values and the system simply having properties.

It's the idea I'm trying to get at by saying there must be something or anything inside the building or prior to measurement. That is what is leading me to the conclusion that any model which doesn't model the system prior to measurement must be incomplete.

 

[Lynch101]

You use the words "no properties whatsoever" and those have no connection to what is being assumed by EPR or Bell.

a) EPR says that if any value can be predicted in advance, it must be pre-existing (and therefore QM is incomplete). Entangled particle pairs demonstrate this feature as EPR believed in 1935. It is sometimes called "perfect correlations" as there is 100% agreement when appropriate measurement settings are chosen.

b) The question Bell asked was: If there are values prior to measurement, then are the values INDEPENDENT of measurement? I.e. are they objectively real? I.e. are they observer independent? I.e. are values for all possible measurement settings predetermined? Bell showed that this extension to a) was NOT possible.

In the language of EPR: the question was whether the values (for each of the many/infinite number of measurement basis choices) are simultaneously real. Bell precludes that, because there is no such set that reproduces the QM expectation values.

So you MUST consider both a) and b) when talking about this. It is easy to jump past one or the other. Your model must reproduce perfect correlations, and statistical percentages at other times. (Of course the perfect correlations are also a subset of the statistical percentages, where the percentage is either 0% or 100%.)

Thanks Dr.Chinese, I think I understand that part of Bell.

I guess the distinction I am trying to make is between the idea of the properties of the system having predefined values prior to measurement and the idea of the system simply having properties prior to measurement.

My reasoning is that the system must have physical properties prior to measurement, if we are to consider it in the context of the materialist paradigm. A model which doesn't or cannot model the system prior to measurement would, to my mind, have to be considered an incomplete model of nature.

 

[Lynch101]

I think they can't, but I don't have a particularly enlightening way to articulate it.

Just thinking about this further. Do you need to find a way to articulate it? Does the materialist paradigm not articulate it already?

Well, concepts the meaning of which is intuitive but cannot be defined precisely are called primitive. Similarly, claims the truth of which seems obvious but can be neither proved nor disproved are called axioms. Any system of thought must contain some primitive concepts and some axioms. Once one realizes that, it's no longer infuriating.

Is the idea that every part of nature must have physical properties an axiom of the materialist paradigm?

 

[PeterDonis]

In my mind I am making a distinction between the system having properties with predefined values and the system simply having properties.

Instead of just waving your hands, you should look for some actual model that has this distinction. Vague ordinary language is not a good tool to use for physics.

It's the idea I'm trying to get at by saying there must be something or anything inside the building or prior to measurement.

"Something" and "anything" are so vague that they effectively have zero content for this purpose.

 

[DrChinese]

A model which doesn't or cannot model the system prior to measurement would, to my mind, have to be considered an incomplete model of nature.

Except that there is evidence that there is no such model. What you are describing is a non-contextual model. Which is one which is observation independent. You could say MWI is such a model, I guess, although all possibilities are realized with that rather than none. Not sure that actually solves your quandary.

Past that, pretty much everything is contextual. Which is precisely the opposite - the property & value only come into focus when the measurement is performed.

 

[Lynch101]

Instead of just waving your hands, you should look for some actual model that has this distinction. Vague ordinary language is not a good tool to use for physics.

"Something" and "anything" are so vague that they effectively have zero content for this purpose.

I completely accept that. I guess I'm fumbling about trying to get my meaning across and relying on a common understanding of those words.

Ultimately, the point I am trying to make is, my understanding leads me to the conclusion that if there is a quantum system prior to measurement but our models do not or cannot describe the quantum system prior to measurement, then our models cannot be considered complete models of the system itself or of nature.

I had been misinterpreting the anti-realist position as making a more definitive statement, that it doesn't actually make, but that part of the conclusion appears to remain unchanged.

 

[Lynch101]

Except that there is evidence that there is no such model. What you are describing is a non-contextual model. Which is one which is observation independent. You could say MWI is such a model, I guess, although all possibilities are realized with that rather than none. Not sure that actually solves your quandary.

Past that, pretty much everything is contextual. Which is precisely the opposite - the property & value only come into focus when the measurement is performed.

Thanks for that clarification. I have come across the tern contextual in the context of QM and had a rough understanding of it, but this has given me a clearer understanding of the term.

If there is a quantum system prior to measurement but our models do not or cannot describe it prior to measurement, does that mean that our models are necessarily incomplete? Incomplete models of the system/nature, I mean.

 

[Paul Colby]

I think, perhaps, thinking of reality in terms of macroscopic objects can be somewhat of a hindrance. It is entirely natural and almost impossible not to do, but the idea that I have in mind tries to get away from that.

I think this is the same mistake so many people make. Independent of my opinion, you will need much more than philosophy to resolve such a problem.

 

[DrChinese]

If there is a quantum system prior to measurement but our models do not or cannot describe it prior to measurement, does that mean that our models are necessarily incomplete? Incomplete models of the system/nature, I mean.

No one is questioning that the quantum system exists, let's agree on this point. The moon is there when you are not looking at it. What's missing - to continue the analogy - is whether the moon is yellow (thinking of this as an observable property) when it is not observed. Of course the moon is macroscopic, so I don't really believe that it is not yellow when scientists don't look at it.

Is the model complete? Well sure it is. That is, that which the model attempts to map is complete. But no model is "true". Models are useful tools. Better models normally require more inputs to prove better output descriptions. In the case of Bohmian Mechanics, as Demystifier will tell you, he is missing key input variables to enable him to predict the outcome of a quantum measurement in advance.

In the case of the antirealist position, there is no such missing variable. A system in a superposition of states lacks any local property whatsoever that would predetermine the outcome of a quantum measurement of that superposition.

So our quantum model is complete as is. Can a new model be created that relies on more information?

a) The answer is YES if you look for the added information non-locally. Bohmians follow this line. However, their improved model cannot operate simply because that added information they need is NOT available, even in principle.

b) The answer is NO if you are an antirealist. The current model is the best there is precisely because there are no additional variables to tap.

Again, the interpretations attempt to address this question - with varying results that are not fully satisfying* to anyone.*To be fully satisfying, an interpretation would need to be convincing to most other scientists. That probably means it would need to be falsifiable by experiment, and then said experiment performed with a favorable outcome. 90 years later... good luck with that!

 

[Lynch101]

No one is questioning that the quantum system exists, let's agree on this point. The moon is there when you are not looking at it. What's missing - to continue the analogy - is whether the moon is yellow (thinking of this as an observable property) when it is not observed. Of course the moon is macroscopic, so I don't really believe that it is not yellow when scientists don't look at it.

I think we might still be talking at cross purposes a little. I'll try to pin point what I see as the issue.

Initially, I was of the [mis]understanding that the anti-realist theory said, to stick with the analogy, that the moon was not there when no one is looking at it. I understand now that was a misinterpretation on my part. There seems to be agreement that the moon exists prior to measurement.

Is the model complete? Well sure it is. That is, that which the model attempts to map is complete.

This is where I think we are talking at cross purposes, the sense in which the model is complete.

@Morbert clarified a couple of points that I had been misunderstanding, when he said.

Quantum theory in a strict sense is nothing more than the set of rules whereby physicists compute probabilities of the outcomes of macroscopic tests.

anti-realist is agnostic towards the nature of the reality of quantum systems, and rejects physical properties in our models as real

Following on with the analogy, there might be agreement that the moon is there whether we look at it or not, but the above seems to say that our model only describes the part of the moon we can see [from Earth, let's say]. If the purpose of the model is to only map the part of the moon that we can see, then it is complete in what it sets out to do.

We can, however, distinguish a complete model of the part of the moon we can see from a complete model of the moon itself, and there seems to be agreement there that there is a part of the moon that we cannot see. It is in this sense, that I am reasoning that our model is not a complete model of nature.

I thought this was fundamentally what Einstein was driving at when he made his statement in relation to the moon. I know the EPR paper was based on certain classical preconceptions which Bell subsequently ruled out, but I feel like there was a more fundamental point as demonstrated by saying that the moon is there whether we look at it or not.

Now, it might be the case that it simply isn't possible, even in principle, to develop a complete model of the moon, but that would just mean that we can never have a completed model of nature.

 

[Lynch101]

I think this is the same mistake so many people make. Independent of my opinion, you will need much more than philosophy to resolve such a problem.

Is there a consensus [among anti-realists] that it is not possible, even in principle, to distinguish between the various interpretations on the basis of experiment? If so, would that not mean that philosophy is the only way to probe the question further? I'm not necessarily saying to resolve it, because it philsophy might not be able to resolve it, but it might be possible to draw certain conclusions or consequences which help to frame the different interpretations.

 

[PeterDonis]

Is there a consensus [among anti-realists] that it is not possible, even in principle, to distinguish between the various interpretations on the basis of experiment?

This is what "interpretations" means. If you have something that makes different experimental predictions from standard QM, it isn't an interpretation of QM, it's a different theory.

If so, would that not mean that philosophy is the only way to probe the question further?

No, it means you can't probe the question further at all unless and until you find some different theory from standard QM that can be tested experimentally against it.

 

[PeterDonis]

it might be possible to draw certain conclusions or consequences which help to frame the different interpretations

If this were going to be helpful, one would expect that the voluminous literature over the past century or so that has attempted to do this would have had some effect. But it doesn't appear that it has. Everything that has happened up to now indicates that a priori reasoning in the absence of any possible experimental test simply doesn't help us humans to find better theories or better interpretations of theories.

 

[DrChinese]

Now, it might be the case that it simply isn't possible, even in principle, to develop a complete model of the moon, but that would just mean that we can never have a completed model of nature.

As mentioned, there is nothing incomplete in the current model(s).

EPR (1935) postulated a more complete specification of the system was possible, since it is possible to predict in advance the outcome of certain quantum measurements (allegedly) without disturbing that system. They assumed if you could predict any property's value and predict it in advance, then they must all exist in advance. This position was soundly rejected by most, but it remained feasible until Bell and Aspect. Now we know better.

I think if you worked through a Bell test example, you would understand better why my statement above generally matches the position of most physicists. Because we only have measurements to tell us anything about what is going on; and we know the statistical rules for the results of those measurements; and they cannot be modeled by having values prior to measurement due to Bell: we have enough to conclude that anything left to add is just a philosophical or interpretational point. Even an interpretation does not purport that there is more; they merely purport to explain a mechanism whereby the measurement results in a value. (That usually being the measurement of an entangled system, which is why I suggest working through the math of Bell Test.)

Try imagining pairs of hypothetical entangled photon pairs, and how they end up with values that match the statistical predictions of QM. Consider examples at 0 degrees difference, and 120 degrees difference, but otherwise at all different angles. You will quickly see that to be statistically correct, you MUST know the measurement setting(s) in advance. That is exactly the requirement of ANY contextual model. But it is NOT allowed in any non-contextual model.

 

[DrChinese]

@Lynch101

Putting that a little differently: Nothing BEFORE the measurement is missing or incomplete. Possibilities for completion exist at the time of measurement. Different interpretations explain to varying degrees how that happens, but the additional input variables are in the form of the complete context. Which includes the measurement settings. There still appears to be random elements which appear in the equation, the origin of which (again) is explained in varying degrees by each interpretation.

There essentially aren't any interpretations filling in the blanks BEFORE a measurement occurs. That this is the case is one of the strange attributes of QM. But there is definitely no basis for insisting there is something missing, other than to simply adopt that position and not move off of it. Which is what Einstein did (no criticism intended, he did not have the benefit of what we know today).

 

[RUTA]

Try imagining pairs of hypothetical entangled photon pairs, and how they end up with values that match the statistical predictions of QM. Consider examples at 0 degrees difference, and 120 degrees difference, but otherwise at all different angles. You will quickly see that to be statistically correct, you MUST know the measurement setting(s) in advance. That is exactly the requirement of ANY contextual model. But it is NOT allowed in any non-contextual model.

Here is an interesting paper on the contextuality inherent in QM that is valid for retrocausation or
non-local constraints, which are not handled by Kochen-Specker type no-go theorems. They write:

The rationale in both cases is that non-contextuality could emerge naturally in such models: physical properties might well be “real” and “counterfactually definite”, but depend on future or distant measurements because of some physically motivated—although radically novel—causal influence. Such proposals do not fit neatly within the classical causal modelling framework, and so are not ruled out by recent work in this direction [9,22], nor by any of the existing no-go theorems.

In this paper, we characterise a new ontological models framework to prove that even if one allows for arbitrary causal structure, ontological models of quantum experiments are necessarily contextual. Crucially, what is contextual is not just the traditional notion of “state”, but any supposedly objective feature of the theory, such as a dynamical law or boundary condition. Our finding suggests that any model that posits unusual causal relations in the hope of saving “reality” will necessarily be contextual.

 

[RUTA]

In an earlier post, someone classified Relational Blockworld (RBW) as anti-realist. We are not realists about the wavefunction, but we classify RBW as realist because there simply are no hidden "quantum entities" to be a realist about. What we have access to (classical reality) is certainly "real" and there are no other ontological entities in the RBW interpretation. That does not entail instrumentalism either :-) Here is our latest paper whereby physics is understood to be the study of certain constraints on experience. You only need to read Section 3 "Neutral Monism and the Axioms of Physics" to see what I mean. If you're interested in how it relates to entanglement, you can read Section 4 "The Axioms Reveal QM’s Completeness and Coherence." If you're interested in how it explains delayed-choice experiments, you can read Section 5 "QM and Experience."

 

[Lynch101]

EPR (1935) postulated a more complete specification of the system was possible, since it is possible to predict in advance the outcome of certain quantum measurements (allegedly) without disturbing that system. They assumed if you could predict any property's value and predict it in advance, then they must all exist in advance. This position was soundly rejected by most, but it remained feasible until Bell and Aspect. Now we know better.

I think if you worked through a Bell test example, you would understand better why my statement above generally matches the position of most physicists.

I think we're still talking past each other here. I'm not advocating the idea that a more complete specification of the system is possible. I can understand that a more complete specification might even be impossible in principle. But that we cannot have a more complete specification of the system doesn't mean that the specification we have is a complete specification of that system.

Because we only have measurements to tell us anything about what is going on; and we know the statistical rules for the results of those measurements; and they cannot be modeled by having values prior to measurement due to Bell:

I follow that, and I'm not objecting to it. This is the crux of what I'm trying to get at. We have statistical rules which tell us the probability of measurement outcomes but those rules don't appear to tell us about the system prior to measurement. If we agree that there is a system prior to measurement, then surely we must also agree that a model which only gives us predictions about measurements is not a complete specification of the system?

we have enough to conclude that anything left to add is just a philosophical or interpretational point.

This is essentially the point I am trying to get at, the idea that there is something left or that there must be something left to add because the model is not a complete specification of the system. If there is a system prior to measurement and our model only models measurements, then the system prior to measurement is the part to add. Yes, it may only be possible to speculate about it philosophically or by way of an interpretational point, but it highlights an incompleteness in the specification of the system.

In the analogy I used in response to Paul, where we have a building and we are looking at the outside wall with 5 windows. If I tell you the probability for each window to be broken and over a number of trials those probabilities turn out to be flawlessly accurate then that is undoubtedly a very useful model. But it only tells you which window will be broken, it doesn't provide a complete specification of what happens inside the building that causes the windows to break.

We might agree that the system which we prepared causes the windows to break, but only predicting which windows will break doesn't give a complete specification of the system.

 

[Demystifier]

Just thinking about this further. Do you need to find a way to articulate it? Does the materialist paradigm not articulate it already?

Is the idea that every part of nature must have physical properties an axiom of the materialist paradigm?

Maybe, but I think "matter" is another primitive notion that cannot be defined precisely.

 

[Morbert]

Unless I don't understand your comment, Bell precludes that.

There are no data sets or statistical averages for quantum spins independent of the measurement setting(s). Keeping in mind that there are a multitude of statistical requirements due to the multitude of possible settings (thinking of typical Bell tests here).

It's true that there's no sample space that is, even in principle, appropriate for all observables. But we can still build models that reference the values of observables before measurement. E.g. Take a typical EPRB experiment: Alice and Bob each have one of a pair of entangled particles. At time $t_1$ Alice measures her particle (particle a) in the basis $|\uparrow_x^a\rangle,|\downarrow_x^a\rangle$ and at the same time Bob measures his particle (particle b) in the basis $|\uparrow_z^b\rangle,|\downarrow_z^b\rangle$. A typical sample space of outcomes for this experiment could be built from the projective decomposition of the identity on $\mathcal{H}_{t_1}$
$$\begin{eqnarray*} I &=& |\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow\rangle\langle\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow|_{t_1} + \\
&& |\downarrow_x^a,A_\downarrow,\uparrow_z^b,B_\uparrow\rangle\langle\downarrow_x^a,A_\downarrow,\uparrow_z^b,B_\uparrow|_{t_1} + \\
&&|\uparrow_x^a,A_\uparrow,\downarrow_z^b,B_\downarrow\rangle\langle\uparrow_x^a,A_\uparrow,\downarrow_z^b,B_\downarrow|_{t_1} + \\
&& |\downarrow_x^a,A_\downarrow,\downarrow_z^b,B_\downarrow\rangle\langle\downarrow_x^a,A_\downarrow,\downarrow_z^b,B_\downarrow|_{t_1}
\end{eqnarray*}$$
where A and B are Alice and Bob's measuring devices respectively, and each of the four projectors above represents one of the four possible experimental outcomes.

But we could also construct an alternative model that includes statements about the spin of the particle at time $t_0$ before measurement. This times we consider the projective decomposition* of the identity on $\mathcal{H}_{t_0}\otimes\mathcal{H}_{t_1}$

$$\begin{eqnarray*} I &=& |\uparrow_x^a,\uparrow_z^b\rangle\langle \uparrow_x^a,\uparrow_z^b|_{t_0}\otimes|\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow\rangle\langle\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow|_{t_1} + \\
&& |\downarrow_x^a,\uparrow_z^b\rangle\langle \downarrow_x^a,\uparrow_z^b|_{t_0}\otimes|\downarrow_x^a,A_\downarrow,\uparrow_z^b,B_\uparrow\rangle\langle\downarrow_x^a,A_\downarrow,\uparrow_z^b,B_\uparrow|_{t_1} + \\
&&|\uparrow_x^a,\downarrow_z^b\rangle\langle \uparrow_x^a,\downarrow_z^b|_{t_0}\otimes|\uparrow_x^a,A_\uparrow,\downarrow_z^b,B_\downarrow\rangle\langle\uparrow_x^a,A_\uparrow,\downarrow_z^b,B_\downarrow|_{t_1} + \\
&& |\downarrow_x^a,\downarrow_z^b\rangle\langle \downarrow_x^a,\downarrow_z^b|_{t_0}\otimes|\downarrow_x^a,A_\downarrow,\downarrow_z^b,B_\downarrow\rangle\langle\downarrow_x^a,A_\downarrow,\downarrow_z^b,B_\downarrow|_{t_1}
\end{eqnarray*}$$
Here, we model the measured properties at $t_0$ before the measurement has occurred. All the inferences from this model would be just as valid as from the previous model.

tl;dr The formalism doesn't seem to privilege properties after measurement over properties before measurement. Whether or not these properties are real, they seem to be just as real/not real before and after measurement.

*neglecting projections that would give zero probability, like $|\downarrow_x^a,\uparrow_z^b\rangle\langle \downarrow_x^a,\uparrow_z^b|_{t_0}\otimes|\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow\rangle\langle\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow|_{t_1}$

 

[DrChinese]

But we could also construct an alternative model that includes statements about the spin of the particle at time $t_0$ before measurement. This times we consider the projective decomposition* of the identity on $\mathcal{H}_{t_0}\otimes\mathcal{H}_{t_1}$

$$\begin{eqnarray*} I &=& |\uparrow_x^a,\uparrow_z^b\rangle\langle \uparrow_x^a,\uparrow_z^b|_{t_0}\otimes|\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow\rangle\langle\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow|_{t_1} + \\
&& |\downarrow_x^a,\uparrow_z^b\rangle\langle \downarrow_x^a,\uparrow_z^b|_{t_0}\otimes|\downarrow_x^a,A_\downarrow,\uparrow_z^b,B_\uparrow\rangle\langle\downarrow_x^a,A_\downarrow,\uparrow_z^b,B_\uparrow|_{t_1} + \\
&&|\uparrow_x^a,\downarrow_z^b\rangle\langle \uparrow_x^a,\downarrow_z^b|_{t_0}\otimes|\uparrow_x^a,A_\uparrow,\downarrow_z^b,B_\downarrow\rangle\langle\uparrow_x^a,A_\uparrow,\downarrow_z^b,B_\downarrow|_{t_1} + \\
&& |\downarrow_x^a,\downarrow_z^b\rangle\langle \downarrow_x^a,\downarrow_z^b|_{t_0}\otimes|\downarrow_x^a,A_\downarrow,\downarrow_z^b,B_\downarrow\rangle\langle\downarrow_x^a,A_\downarrow,\downarrow_z^b,B_\downarrow|_{t_1}
\end{eqnarray*}$$
Here, we model the measured properties at $t_0$ before the measurement has occurred. All the inferences from this model would be just as valid as from the previous model.

tl;dr The formalism doesn't seem to privilege properties after measurement over properties before measurement. Whether or not these properties are real, they seem to be just as real/not real before and after measurement.

Assuming I understand what you are saying: Your model provides that it has properties at t0 (before measurement) that are like its properties at t1 (at measurement). I guess that would literally meet the criteria you set, but wouldn't really be useful at any level that I can see.

 

[DrChinese]

I think we're still talking past each other here. I'm not advocating the idea that a more complete specification of the system is possible. I can understand that a more complete specification might even be impossible in principle. But that we cannot have a more complete specification of the system doesn't mean that the specification we have is a complete specification of that system.

I guess I dispute your idea that we DON'T have a complete specification of the system. If we agree no greater detail is possible, we're done. And the reason we feel there is no greater detail possible is because it would lead to statistical contradictions. The property is fully blurred prior to measurement, and has no preferred value or basis that is in any way related to the outcome of a specific future measurement.

What CAN be said, for an entangled system, is that there is a conservation rule at play in that system. Such that A+B=k or A-B=k (k being some constant or initial value).

Of course, some interpretations say more detail exists, but it is unknowable in principle. So if you are tilting in that direction, all is good.

 

[Lynch101]

I guess I dispute your idea that we DON'T have a complete specification of the system. If we agree no greater detail is possible, we're done. And the reason we feel there is no greater detail possible is because it would lead to statistical contradictions.

My thinking is that there is a difference between 1) no greater detail being possible and 2) there being no greater detail period.

A possible explanation for 1) is that there is a limit beyond which we cannot probe. There would be further to probe, but we simply cannot probe that far due to limitations of our instruments or a fundamental limit in nature.

This is contrasted with 2) the idea that there is nothing whatsoever there to probe.

In the context of the moon analogy, it sounds a little to me like seeing a reflection of the moon and concluding that the reflection is a complete model of the moon. The reflection is a complete specification of what it is possible to see but it isn't a complete model of the moon itself.

The property is fully blurred prior to measurement, and has no preferred value or basis that is in any way related to the outcome of a specific future measurement.

My initial understanding of the anti-realist position was that it denied even the blurred property prior to measurement, but my interpretation of what @Morbert said previously is that it doesn't even talk about the blurred property prior to measurement, it only models the measurement outcome.

It's the idea that there is a blurred property prior to measurement, which isn't modeled in the anti-realist interpretation (and perhaps cannot even be modeled in principle) which is leading me to conclude the model is not a complete description of the system. If the property cannot be modeled even in principle then would seem to suggest that no complete model of the system is possible.

Of course, some interpretations say more detail exists, but it is unknowable in principle. So if you are tilting in that direction, all is good.

I think this is the direction I'm tilting but my reasoning is that this is the only direction that we can tilt.

The idea that there is no more detail whatsoever, sounds like the initial interpretation I had of anti-realism.

 

[Lynch101]

Maybe, but I think "matter" is another primitive notion that cannot be defined precisely.

This is probably true but I think it can be juxtaposed with [Cartesian] dualism, or other paradigms, to suggest what the alternatives might be and what the consequences of those are.

The materialist paradigm is generally juxtaposed with other paradigms which posit the existence of the supernatural entities or substances, such as "the soul". So, if we say that the quantum system doesn't have physical properties prior to measurement we must necessarily invoke a different paradigm and the consequences that flow from that.

On a separate but related note, does the point I am trying to make about the incompleteness of the anti-realist interpretation make sense to you or can you see what part of the argument I am missing?

 

[PeterDonis]

The materialist paradigm is generally juxtaposed with other paradigms which posit the existence of the supernatural entities or substances

It is? I thought the whole point of the materialist paradigm was to not posit the existence of supernatural entities or substances. See, for example, here:

https://plato.stanford.edu/entries/physicalism/

(As this article notes, "physicalism" is a synonym for "materialism".)

 

[Lynch101]

It is? I thought the whole point of the materialist paradigm was to not posit the existence of supernatural entities or substances. See, for example, here:

https://plato.stanford.edu/entries/physicalism/

(As this article notes, "physicalism" is a synonym for "materialism".)

Apologies, I could have worded that more clearly. It is the "other paradigms" which posit the supernatural. It is with those that materialism is usually juxtaposed to deny the supernatural.

 

[physika]

Would objects which exist and are real not have properties by necessity? Would real and existing not be properties in and of themselves?

.
Aristotle.
Properties; are characteristic qualities that are not truly required for the continued existence of an entity ((object, thing...) but are, nevertheless, possessed by the entity (object, thing...)

.

.

 

[Morbert]

Assuming I understand what you are saying: Your model provides that it has properties at t0 (before measurement) that are like its properties at t1 (at measurement). I guess that would literally meet the criteria you set, but wouldn't really be useful at any level that I can see.

The 2nd model isn't particularly useful, but it at least illustrates that the formalism does not privilege predictions over retrodictions. It's just the case that physicists are more interested in predictions.

(Though with that said retrodictions can be useful when reasoning through scenarios like the Vaidman bomb, or when reasoning about the trajectory of emitted particles.)

 

[RUTA]

I guess I dispute your idea that we DON'T have a complete specification of the system. If we agree no greater detail is possible, we're done. And the reason we feel there is no greater detail possible is because it would lead to statistical contradictions. The property is fully blurred prior to measurement, and has no preferred value or basis that is in any way related to the outcome of a specific future measurement.

What CAN be said, for an entangled system, is that there is a conservation rule at play in that system. Such that A+B=k or A-B=k (k being some constant or initial value).

Of course, some interpretations say more detail exists, but it is unknowable in principle. So if you are tilting in that direction, all is good.

Here is my Insight explaining the type of conservation at work for the Bell spin states. [I don't know why so many of the equation numbers have turned into ? when referenced and a couple of equations are cut in half. Hopefully, a Moderator can explain how to fix those.]