Where is the quantum system prior to measurement?

[Morbert]

If by a complete description of physical reality you mean an ontological account that renders all that exists thoroughly intelligible, then the statistical interpretation does not claim to offer a complete description of reality.

 

[Lynch101]

If by a complete description of physical reality you mean an ontological account that renders all that exists thoroughly intelligible, then the statistical interpretation does not claim to offer a complete description of reality.

I would be more inclined to say a specification of the state of the system prior to measurement, as opposed a complete list of all possible measurement outcomes (together with their probabilities). Because the list of all possible measurement outcomes could be explained by the system being in one of several different states prior to measurement.

EDIT: In terms of the die, it would be specifying whether the die was in:
1) a single valued state
2) mutli-valued state

prior to observation. As opposed to giving a complete list of all the possible values we could observe (1-6) along with the probability of observing them.

 

[Morbert]

I would be more inclined to say a specification of the state of the system prior to measurement

What do you mean by the state of the system? In the statistical interpretation, the state of the system is not an ontological account. It codifies a preparation of the system such that we can expect the corresponding statistical distributions in data generated by an apparatus repeatedly measuring members of an ensemble of the system. So e.g. by "specifying the state of the system prior to measurement", do you mean this? Or do you mean a thorough ontological account rendering of all existing elements of the system intelligible?

 

[hutchphd]

Failure to proffer an interpretation/explanation would leave us with an incomplete 'description of physical reality', which the statistical interpretation appears to do.

Physics is inherently phenomenological. Attempts to expand it beyond that realm are enticing but not required. Your suppositions really have nothing to do with physics. I defer to Dr Eddington and suggest his counsel:

Sir Arthur Eddington and the Foundations of Modern Physics​

The essential point is that, although we seem to have very definite conceptions of objects in the external world, those conceptions do not enter into exact science and are not in any way confirmed by it. Before exact science can begin to handle the problem they must be replaced by quantities representing the results of physical measurement..

 

[Fra]

1) The die had a pre-defined value which is why we observe it in a single, well defined position.
2) The die was, physically, in a multi-valued state prior to observation. This would require some form of spontaneous, physical collapse to explain the observation of a single value.

It must be the case then, that the system goes through either:
1) Slit A
2) Slit B
3) Slit A & B

Because if it goes through neither 1, 2, nor 3 then it cannot 'imprint' on the measurement device.

I would be more inclined to say a specification of the state of the system prior to measurement, as opposed a complete list of all possible measurement outcomes (together with their probabilities). Because the list of all possible measurement outcomes could be explained by the system being in one of several different states prior to measurement.

EDIT: In terms of the die, it would be specifying whether the die was in:
1) a single valued state
2) mutli-valued state

prior to observation. As opposed to giving a complete list of all the possible values we could observe (1-6) along with the probability of observing them.

My impression is that implicit in your reasoning - just like there is in the original EPR papers, as revealed in the form of the ansatz - there is a hidden association between your ontological "options", and the causation mechanisms following assuming each ontology has it's own kind of "mechanics". This is as I see it, the core of the matter and where the resolution lies.

But how well do we really understand the "mechanisms" of ANY physical interaction, ie action and reaction?
Is the abstraction that two systems "make contact" in a background space adequate? Or how do we cast action and reaction into a more information theoretic, background independent form?

/Fredrik

 

[Lynch101]

What do you mean by the state of the system? In the statistical interpretation, the state of the system is not an ontological account. It codifies a preparation of the system such that we can expect the corresponding statistical distributions in data generated by an apparatus repeatedly measuring members of an ensemble of the system. So e.g. by "specifying the state of the system prior to measurement", do you mean this? Or do you mean a thorough ontological account rendering of all existing elements of the system intelligible?

By 'the state of the system' I'm referring to (or trying to) 'every element of the physical reality' à la EPR.

It might be helpful to put it another way. Usually, a complete description would include the path an object/system takes through 3D space. This path would be a function of its position over a specified period of time. I know this is not possible for very complex systems such as atoms/molecules of gas. However, we do at least say that the particles of gas behave in a certain way that doesn't necessarily need any further explanation. We say they follow well defined trajectories in the given space, even if we cannot specify exactly what they are.

We cannot necessarily say the same thing about quantum systems. However, that doesn't mean that we can't say anything at all.

The quantum system must take some path, through 3D space, to get from the preparation device to the measurement apparatus. Some interpretations such as Bohmian Mechanics, Many Worlds, and objective collapse theories make statements about the path that the system takes from preparation to measurement devices. They are therefore, potentially, complete descriptions.

As you have said, the statistical interpretation makes no such statement about the path the system takes from preparation to measurement devices. Therefore, by my reasoning, it defines itself as being incomplete.

 

[Lynch101]

Physics is inherently phenomenological. Attempts to expand it beyond that realm are enticing but not required. Your suppositions really have nothing to do with physics. I defer to Dr Eddington and suggest his counsel:

Sir Arthur Eddington and the Foundations of Modern Physics​

The essential point is that, although we seem to have very definite conceptions of objects in the external world, those conceptions do not enter into exact science and are not in any way confirmed by it. Before exact science can begin to handle the problem they must be replaced by quantities representing the results of physical measurement..

There is nothing wrong with shutting up and calculating but there are many physicists for whom this is not entirely satisfactory.

 

[Morbert]

The quantum system must take some path, through 3D space

Again, you are assuming a thoroughgoing intelligibility. QM might completely characterise all that is intelligible about the system.

 

[Lynch101]

My impression is that implicit in your reasoning - just like there is in the original EPR papers, as revealed in the form of the ansatz - there is a hidden association between your ontological "options", and the causation mechanisms following assuming each ontology has it's own kind of "mechanics". This is as I see it, the core of the matter and where the resolution lies.

But how well do we really understand the "mechanisms" of ANY physical interaction, ie action and reaction?
Is the abstraction that two systems "make contact" in a background space adequate? Or how do we cast action and reaction into a more information theoretic, background independent form?

/Fredrik

I think the issue can probably be boiled down to the following. My reasoning is as follows:

1) The system must take some path through 3D space from preparation device to measurement apparatus.
2) A 'complete description of the physical reality' would include a definitive statement on the path taken.
3) The statistical interpretation remains completely agnostic on this point.
4) Therefore, the statistical interpretation does not give a 'complete description of the physical reality'.

 

[Lynch101]

Again, you are assuming a thoroughgoing intelligibility. QM might completely characterise all that is intelligible about the system.

We need to be careful here when we talk about QM. I know this because, previously, I haven't been and it can cause confusion. I am talking specifically about the statistical interpretation here.

'All that is intelligible' is the key qualifier here. This is effectively the point that 'a more complete description may not be possible'. That may very well be the case, but that does not render the statistical interpretation complete. Some interpretations of QM are potentially complete.In the above, I am assuming 3D space, which we can model graphically. Our models allow us to identify some very basic rules that must apply at the noumenological level. For example, where we have a preparation device in one location and a measurement device in another (both represented graphically), according to the rules of 3D space, to get from one to the other some path through 3D space must be taken.

Where we have a barrier erected à la the screen, there is no way for something to move from the 'preparation device' to the 'measurement apparatus'. If 'slits' are put in the barrier, there is then a possible route but anything passing from one to the other must pass through these 'slits'. Those are the rules of moving in 3D space.

EDIT: By my reasoning, remaining agnostic on that point renders an interpretation incomplete, by definition.

 

[Morbert]

'All that is intelligible' is the key qualifier here. This is effectively the point that 'a more complete description may not be possible'. That may very well be the case, but that does not render the statistical interpretation complete. Some interpretations of QM are potentially complete.

The statistical interpretation is motivated by the charge that it is problematic to assume the quantum state completely describes the physical system. If all you are saying is the statistical interpretation as put forth by Ballentine in the 1970s is motivated by a sentiment that a quantum state cannot completely describe an individual system, then that isn't very controversial.

But there has been plenty of literature since the 1970s defending Copenhagen interpretations, and a lot of that literature interrogates the term complete.

For example, where we have a preparation device in one location and a measurement device in another (both represented graphically), according to the rules of 3D space, to get from one to the other some path through 3D space must be taken.

Here you are assuming an some intelligible substance propagating from one component of the system (the electron gun) to another (a detector screen). You are also assuming this intelligibility is sufficiently fine grained that a statement like "the system must travel through both slits" is a necessary conclusion.

 

[gentzen]

1) The system must take some path through 3D space from preparation device to measurement apparatus.
2) A 'complete description of the physical reality' would include a definitive statement on the path taken.
3) The statistical interpretation remains completely agnostic on this point.
4) Therefore, the statistical interpretation does not give a 'complete description of the physical reality'.

1) Statements about what a system must do only make sense to me with respect to some specific interpretation. The orthodox interpretation (basically Copenhagen) is slightly agnostic at this point, but not completely. A beam of light in an interferometer can travel on multiple distinct paths from the source to the detector, and claiming that a photon in the beam must have traveled on some speficic of those distinct paths is simply wrong with respect to the orthodox interpretation. Already talking of "a photon" is wrong, because photons don't have individuality. The photons in the beam are indistinguishable (even that word is too weak, they are inseparable) from one another.
2) Could you please stop to damage the tricky word "complete" and stop to associate it to unclear concepts like "physical reality". And how can you extract anything from such an unclear concept, like that it would include something definitive.
4) Even so it is an interesting question whether the (minimal) statistical interpretation is complete, the result of an investigation into whether it is or not would be more convincing, without the impression that the words preceeding the "therefore" were biased from the start.

 

[hutchphd]

1) The system must take some path through 3D space from preparation device to measurement apparatus.

What is the "system"? What constitutes a "path"? Does it include the measurement device? The slits? Alpha centauri?
I don't see that you have defined anything

 

[Lynch101]

Here you are assuming an some intelligible substance propagating from one component of the system (the electron gun) to another (a detector screen). You are also assuming this intelligibility is sufficiently fine grained that a statement like "the system must travel through both slits" is a necessary conclusion.

We don't need to assume some intelligible substance. It's more a statement about 3 dimensional space and the rules that apply to anything operating within 3 dimensions, including the system. We can represent 3 dimensional space graphically and our reasoning will apply at the noumenological level also.

Where we have two spatially separated 'things' or regions of space. In order for anything to start in one region and end up in the other region, it must follow some path between the two. We don't need to be able to specify the exact path taken, we only need to specify that some path must, indeed, be taken. This is just 'a rule of the game' where 3D space is concerned. Remaining agnostic on this point would render an interpretation incomplete.

 

[Morbert]

We don't need to assume some intelligible substance. It's more a statement about 3 dimensional space and the rules that apply to anything operating within 3 dimensions, including the system. We can represent 3 dimensional space graphically and our reasoning will apply at the noumenological level also.

Where we have two spatially separated 'things' or regions of space. In order for anything to start in one region and end up in the other region, it must follow some path between the two. We don't need to be able to specify the exact path taken, we only need to specify that some path must, indeed, be taken. This is just 'a rule of the game' where 3D space is concerned. Remaining agnostic on this point would render an interpretation incomplete.

Space might be transcendental in this context, but you are positing a thing moving in it, distinct from the preparation and the measurement outcome.

 

[Lynch101]

We're in agreement on some key points here, particularly with regard to certain things being interpretation dependent. But, if we unpack some of your statements here, we might be able to find agreement.

1) Statements about what a system must do only make sense to me with respect to some specific interpretation. The orthodox interpretation (basically Copenhagen) is slightly agnostic at this point, but not completely.

It is the agnosticism that would render it incomplete. We can unpack some of what you say to explore in what sense it is agnostic and therefore, potentially, incomplete.

A beam of light in an interferometer can travel on multiple distinct paths from the source to the detector, and claiming that a photon in the beam must have traveled on some speficic of those distinct paths is simply wrong with respect to the orthodox interpretation.

Let's unpack the idea that the system 'can travel on multiple distinct paths'. I can see two ways of interpreting this:
1) There are multiple distinct paths that the system can travel and it travels on one of those. This would imply the system has a definite position and follows one single path.

2) There are multiple paths and the system travels along more than one simultaneously. This would seem to necessitate some form of physical collapse.

By my reasoning, either 1 or 2 must be true. Remaining agnostic on which it is would render an interpretation incomplete.

Already talking of "a photon" is wrong, because photons don't have individuality. The photons in the beam are indistinguishable (even that word is too weak, they are inseparable) from one another.

We don't need to talk about 'photons', we can talk more generally about any system whatsoever with any characteristics whatsoever. If it operates in 3D space then there are certain rules it has to follow.

2) Could you please stop to damage the tricky word "complete" and stop to associate it to unclear concepts like "physical reality". And how can you extract anything from such an unclear concept, like that it would include something definitive.

I am referencing the EPR paper titled, 'Can quantum mechanical description of physical reality be considered complete?'.

4) Even so it is an interesting question whether the (minimal) statistical interpretation is complete, the result of an investigation into whether it is or not would be more convincing, without the impression that the words preceeding the "therefore" were biased from the start.

If we think in terms of 3D space and the basic rules that apply to traveling from one region of 3D space to another, and then consider the agnosticism of the minimal statistical interpretation, we arrive at the conclusion that it is incomplete. By my reasoning.

 

[Lynch101]

Space might be transcendental in this context, but you are positing a thing moving in it, distinct from the preparation and the measurement outcome.

The nature of space doesn't really matter here, as long as it can be represented 3 dimensionally.

We can create a graphical 3 dimensional model. We can then represent the the experiment within this graphical representation, in accordance with these 3 dimensions. The preparation device will have a position in one 3D region while the measurement apparatus will have a position in another, spatially separated region.

If something starts in the region of the preparation device and ends up in the region of the measurement device, how does it get there?

By my reasoning, it must traverse a path through the intervening 3D region. We can discard our intuitive ideas about the specific path it takes, but it must take a unique path through that region. That unique path could have it in multiple places at once, it could be everywhere in the finite 3D region, but it must travel a unique path through that space. Remaining agnostic on which path it takes would leave us with an incomplete description.

 

[Morbert]

If something starts in the region of the preparation device and ends up in the region of the measurement device, how does it get there?

You are again supposing the underlying reality can be made intelligible by concepts like a definite path. I think interpretations like consistent histories can help make this kind of intuition sharp and reliable, but a hardcore Copenhagenist defending themselves against Ballentine's charges would not necessarily grant you this level of intelligibility.

 

[gentzen]

Let's unpack the idea that the system 'can travel on multiple distinct paths'. ...

2) There are multiple paths and the system travels along more than one simultaneously. This would seem to necessitate some form of physical collapse.

Well, it can travel along more than one path in the othodox interpretation, and there is a collapse postulate in that interpretation. But I neither see why that collapse has to be a physical collapse, nor why a collapse would have to be present in any interpretation allowing this.

We don't need to talk about 'photons', we can talk more generally about any system whatsoever with any characteristics whatsoever.

We can talk of photons, electrons, atoms, ions, or molecules. The fact that things can be indistinguishable/inseparable remains, and any reasoning trying to negate this fundamental truth risks being inapplicable in discussions about quantum physics.
Maybe try to appreciate some of the consequences of that fact, like Fermi-Dirac statistics, and Bose-Einstein statistics. And also why insisting on a single continuous path with definite a position at all times would be incompatible with such inseparability.

I am referencing the EPR paper titled

Well, that paper presents a paradox. Using a paradox to make definite conclusions is tricky business. The irony is that Bohr loved paradoxes, and Einstein was great at inventing paradoxes. But Bohr's resolutions of Einstein's paradoxes were often just as disappointing as Alexander the Great slicing the Gordian know instead of untying it. I think Einstein's paradoxes deserved better than Bohr's resolutions.

then consider the agnosticism of the minimal statistical interpretation, we arrive at the conclusion that it is incomplete. By my reasoning.

Your reasoning and your conclusion are too trivial. I tried to explain before how such overly trivial reasoning can have negative impact. The question whether the minimal statistical interpretation is incomplete is an interesting and subtle question. It deserves better than a trivial misunderstanding of what is meant by being complete.

And as I said above, Einstein's paradoxes would have deserved better too. And thanks to Bell, at least one of them also got what it deserved. Demystifier has a paper that tries to do justice to another one of Einstein's paradoxes.

 

[Lynch101]

You are again supposing the underlying reality can be made intelligible by concepts like a definite path. I think interpretations like consistent histories can help make this kind of intuition sharp and reliable, but a hardcore Copenhagenist defending themselves against Ballentine's charges would not necessarily grant you this level of intelligibility.

No, I'm saying that if the system is operating in 3 dimensions then there are certain rules that apply to it. Taking a unique* path through the 3D region between the devices is one such rule.

Remaining agnostic on the path taken would render the description incomplete, by definition.

*it doesn't have to be our intuitive idea of a path which is a function of a single, well-defined value for position,

 

[hutchphd]

*it doesn't have to be our intuitive idea of a path which is a function of a single, well-defined value for position,

? Sorry, what then is a path?

 

[Lynch101]

Well, it can travel along more than one path in the othodox interpretation, and there is a collapse postulate in that interpretation. But I neither see why that collapse has to be a physical collapse, nor why a collapse would have to be present in any interpretation allowing this.

Again, we have to unpack what is meant by, 'travel along more than one path in the othodox interpretation'.

The 'physical reality' that EPR are referring to is nothing more than the experimental set-up in the lab, as opposed to the mathematical representation of it. The physical preparation device occupies a 3D region which we can represent graphically, as does the measurement apparatus. The physical preparation device prepares a physical system which interacts with the physical measurement apparatus. For something to get from the physical preparation device to the physical measurement device it must take a path through the intervening 3D region in the 'physical reality'.

If it takes more than one path through the 3D space and arrives at the measurement device, we should have more than one detection event, but we don't. We only have one. Therefore, the physical system which took multiple paths through the 3D region of 'physical reality' must physically collapse to a single, well-defined position.

We can talk of photons, electrons, atoms, ions, or molecules.

We can, but we don't need to. We can talk even more generally.

insisting on a single continuous path with definite a position at all times would be incompatible with such inseparability.

OK, we're obviously talking past each other here because I am not insisting on a 'continuous path with definite a position at all times'. I have been at pains to try and emphasise that is not what I am talking about.

I am talking about a unique path/route, but that unique path/route can be a combination of multiple 'continuous path with definite position at all times' (as you have mentioned previously). It might be more helpful to call it a 'route' for the purpose of this point.

If we imagine the various possible 'continuous path with definite position at all times'. Let's call them:
Path1
Path 2
Path 3

The unique route taken by the system could be a combination of the different paths:
Path 1 + Path 2
Path 1+ Path 3
Path 2 + Path 3
Path 1 + Path 2 + Path 3

It must take some route through the 3D space to get from the preparation device to the measurement apparatus. Remaining agnostic on which route is taken would render an interpretation incomplete, which is what the statistical interpretation appears to do.

Well, that paper presents a paradox. Using a paradox to make definite conclusions is tricky business. The irony is that Bohr loved paradoxes, and Einstein was great at inventing paradoxes. But Bohr's resolutions of Einstein's paradoxes were often just as disappointing as Alexander the Great slicing the Gordian know instead of untying it. I think Einstein's paradoxes deserved better than Bohr's resolutions.

I have read a few accounts which would agree with you on that point.

But, just to re-iterate the point. The 'physical reality' that EPR are referring to is simply the experiment which takes place in the physical world, as opposed to the mathematical description of it.

 

[Lynch101]

? Sorry, what then is a path?

The path taken by a quantum system could be a multi-valued path. It could be the idea of the system going through two slits instead of just one.

 

[hutchphd]

The unique route taken by the system could be a combination of the different paths:
Path 1 + Path 2
Path 1+ Path 3
Path 2 + Path 3
Path 1 + Path 2 + Path 3

Feynman says it is the sum of all available paths (modulated by the path integral of the action). So you are saying what?

.

 

[gentzen]

If it takes more than one path through the 3D space and arrives at the measurement device, we should have more than one detection event, but we don't. We only have one. Therefore, ...

OK, we're obviously talking past each other here because I am not insisting on a 'continuous path with definite a position at all times'. I have been at pains to try and emphasise that is not what I am talking about.

I am talking about a unique path/route, but that unique path/route can be a combination of multiple 'continuous path with definite position at all times' (as you have mentioned previously).

For me, your arguments give me the impression that you are simultaneously arguing that there would be some serious consequences if the system would take more than one path, and that simulataneously you are perfectly fine with it taking more than one path.

So maybe you hope that I will protest that you should decide for one position or the other. But if I would do so, you would say "see, similarly the system must decide for one path or the other". So I won't protest, and just accept that this is the way you argue.

My protest therefore remains that you risk to damage the tricky word "complete", and that your reasoning and conclusions are too trivial.

 

[Lynch101]

Feynman says it is the sum of all available paths (modulated by the path integral of the action). So you are saying what?.

The sum of all available paths through the 3D region of 'physical reality' i.e. the 3D region in the physical experimental set-up?

If that is the case, then a physical collapse is required to explain why we only observe a single well-defined position. Failure to specify a unique path leaves us with an incomplete description.

 

[PeterDonis]

By 'the state of the system' I'm referring to (or trying to) 'every element of the physical reality' à la EPR.

You can't just wave your hands and say this. You need to show us in a specific model how "the state of the system" is represented. For example, in Bohmian mechanics, "the state of the system" is the wave function plus the positions of all particles.

If no model meeting your requirements exists, then you have no basis for any of the claims you have been making. Even in this forum, where the rules are somewhat looser than in the regular QM forum, you still have to have some valid basis for discussion other than your personal opinion or preference.

 

[Lynch101]

For me, your arguments give me the impression that you are simultaneously arguing that there would be some serious consequences if the system would take more than one path, and that simulataneously you are perfectly fine with it taking more than one path.

Nothing more serious than has already been postulated by collapse theories.

If the system takes more than one path simultaneously, we require physical collapse to account for the observation in a single, well-defined position. If the path has a well-defined position at all times we have:
1) Bohmian Mechanics
2) Many Worlds
3) [Insert other interpretation]

Remaining agnostic on this question renders an interpretation an incomplete description of 'the physical reality'.

So maybe you hope that I will protest that you should decide for one position or the other. But if I would do so, you would say "see, similarly the system must decide for one path or the other". So I won't protest, and just accept that this is the way you argue.

The system doesn't necessarily need to take a 'single valued path', however, it must take either a 'single-valued path' or a 'multi-valued path'. Remaining agnostic on this question, as the minimal statistical interpretation appears to do, renders it an incomplete description of 'the physical reality'

My protest therefore remains that you risk to damage the tricky word "complete", and that your reasoning and conclusions are too trivial.

That's fair enough. I am inclined to disagree on that point.

 

[Lynch101]

You can't just wave your hands and say this. You need to show us in a specific model how "the state of the system" is represented. For example, in Bohmian mechanics, "the state of the system" is the wave function plus the positions of all particles.

If no model meeting your requirements exists, then you have no basis for any of the claims you have been making. Even in this forum, where the rules are somewhat looser than in the regular QM forum, you still have to have some valid basis for discussion other than your personal opinion or preference.

Bohmian Mechanics and Many Worlds specify that the system has a well-defined position at all times. Collapse theories posit physical collapse. I'm simply saying that remaining agnostic on that question renders an interpretation incomplete as description of 'the physical reality', to use the words of EPR. Which the minimal statistical interpretation appears to do.

 

[vanhees71]

Feynman says it is the sum of all available paths (modulated by the path integral of the action). So you are saying what?

.

What Feynman or rather his path integral says that in non-relativistic (sic!) quantum mechanics the transition probability amplitude (or more formally the propagator) is schematically given by
$$G(t,x;t_0,x_0)=F \sum_{\text{paths}} \exp(\mathrm{i} S[q,\dot{q}]/\hbar).$$
The sum (or rather functional integral) runs over all paths in configuration space with fixed boundary points $q(t)=x$ and $q(t_0)=x_0$. It's equivalent to solving the time-dependent Schrödinger equation for the corresponding Green's function.

This tells you that in the general case there's no specific path the particle is taking. That's in full accordance with standard quantum mechanics. The path integral is anyway just one more different way to formulate orthodox quantum theory.

It also tells you that you get the classical trajectory as the dominating contribution, if $|S-S_{\text{cl}}|/\hbar$ is rapidly rising when the paths are deviating from the classical trajectory, because the classical trajectory is determined by the stationary point of the action functional, and then you can use the approximation of the steepest-descend method to approximately evaluate the path integral.

 

[PeterDonis]

Bohmian Mechanics and Many Worlds specify that the system has a well-defined position at all times.

Bohmian mechanics does, yes. But not MWI. MWI says that "the state of the system" is the wave function, period. That's all there is.

I'm simply saying that remaining agnostic on that question renders an interpretation incomplete as description of 'the physical reality', to use the words of EPR.

And this, by itself, is just a statement of opinion, even for EPR. Others might have different opinions. There is no way to resolve such a dispute, so arguing about it is rather pointless.

 

[Morbert]

No, I'm saying that if the system is operating in 3 dimensions then there are certain rules that apply to it. Taking a unique* path through the 3D region between the devices is one such rule.

Remaining agnostic on the path taken would render the description incomplete, by definition.

*it doesn't have to be our intuitive idea of a path which is a function of a single, well-defined value for position,

Again, the only system a physicist commits to is the preparation and the measurement outcome. You are supposing some additional process made intelligible by e.g. some physical state $\lambda$, distinct from the preparation $\rho$, which has a direct ontological interpretation at all times between the preparation and measurement.

 

[Lord Jestocost]

I'm simply saying that remaining agnostic on that question renders an interpretation incomplete as description of 'the physical reality', to use the words of EPR.

In case I understand you correctly, you are believing that a “complete” theory must provide some picturization as, for example: “… for something to get from the physical preparation device to the physical measurement device it must take a path through the intervening 3D region in the 'physical reality'.”

Why?

P. A. M Dirac in “THE PRINCIPLES OF QUANTUM MECHANICS” (third edition, page 10) :

"...the main object of physical science is not the provision of pictures, but is the formulation of laws governing phenomena and application of these laws to the discovery of new phenomena. If a picture exists, so much the better; but whether a picture exists or not is a matter of only secondary importance. In the case of atomic phenomena no picture can be expected to exist in the usual sense of the word 'picture', by which is meant a model functioning essentially on classical lines.“

 

[jbergman]

Bohmian Mechanics and Many Worlds specify that the system has a well-defined position at all times. Collapse theories posit physical collapse. I'm simply saying that remaining agnostic on that question renders an interpretation incomplete as description of 'the physical reality', to use the words of EPR. Which the minimal statistical interpretation appears to do.

I think there are some interesting questions here but I am not sure I agree with your framing of them in terms of complete and incomplete.

Really, what you are positing is that a complete theory must provide some physical explanation of the wave function outside of the context of measurements.

In the double slit experiment, we cannot "measure" whether a particle passes through one slit or both slits. We only know that if we measure the particle going through a slit then the interference pattern disappears.

So all we really know is that the wave function describes the probabilities we will measure for an ensemble of particles prepared in the same state.

Anything beyond that is speculation.

 

[Killtech]

In the double slit experiment, we cannot "measure" whether a particle passes through one slit or both slits. We only know that if we measure the particle going through a slit then the interference pattern disappears.

Out of curiosity, is that statement formally true?

Assume $|L>$ be the state of an particle passing left slit and $|R>$ the right one. Then the projection operator onto the state $\frac {1} {\sqrt 2} (|L> +|R>)$ suffices the axiomatic requirements for an observable. Therefore we can (at least formally) measure that observable and thus in theory give an answer within the framework of the theory.