I Where is the quantum system prior to measurement?

[PeterDonis]

A conclusion is either valid or it is invalid

Only if the proposition itself is well defined in the domain of discussion. In QM, many of the propositions you are making claims about simply are not well defined in the domain of discussion.

It sounds to me like you are confusing the 'map' with the 'territory' here.

No, I am pointing out to you that interpretations of QM exist in which the wave function is a direct description of the physical reality, the same way the position of a point particle is in classical Newtonian mechanics. You are simply ignoring such interpretations and assuming that the wave function is not a direct description of physical reality.

If you mean the physical system to which the wave function corresponds is localized in the finite region of space

No, I don't mean that. Nor do I mean that the wave function is just a mathematical artifact. I mean that the implicit assumptions you are making about "localization" do not apply to wave functions; wave functions are not like classical point particles or finitely extended objects, and the concept of "localization" that works for classical point particles or finitely extended objects does not work for wave functions. So in QM interpretations in which the wave function is a direct representation of the physical reality, your concept of "localization" is simply not well-defined, and the questions you are trying to ask can't even be asked.

It might very well be the case that these matters cannot be resolved by appeal to experiment and must remain in the domain of interpretation. That doesn't mean, however, that we cannot deduce or infer the necessary consequences of a given position or determine what implications they imply.

This is true, but it also means we have to accept the limitations of deduction and inference, and we have to carefully check our premises and whether they even make sense in the domain of discussion before we try to make any deductions or inferences.

 

[Lynch101]

No, I am pointing out to you that interpretations of QM exist in which the wave function is a direct description of the physical reality, the same way the position of a point particle is in classical Newtonian mechanics. You are simply ignoring such interpretations and assuming that the wave function is not a direct description of physical reality.

OK, we appear to be talking at cross purposes here because I am specifically talking about the statistical interpretation.

Only if the proposition itself is well defined in the domain of discussion. In QM, many of the propositions you are making claims about simply are not well defined in the domain of discussion.

Such as what? You have suggested previously that 'location' is ill-defined but I have been using that instead of the term 'position' because there is a danger of people interpreting 'position' to mean 'single, well- or pre-defined value'. Everything else I am talking about are well defined and are objects we use in real world experiments; the equipment used in a stern gerlach experiment, magnetic fields and finite regions of space.

We can instead talk about the 'position' of the system being narrowed down to the finite region of space occupied by the magnetic field. Just as long as people don't assume 'position' means ''single, well- or pre-defined value'.

No, I don't mean that. Nor do I mean that the wave function is just a mathematical artifact. I mean that the implicit assumptions you are making about "localization" do not apply to wave functions; wave functions are not like classical point particles or finitely extended objects, and the concept of "localization" that works for classical point particles or finitely extended objects does not work for wave functions. So in QM interpretations in which the wave function is a direct representation of the physical reality, your concept of "localization" is simply not well-defined, and the questions you are trying to ask can't even be asked.

They can of course be asked. That doesn't mean to that the answer will be the classical answer we expect, but the answers (or non-answers) to the question have implications for how the system behaves.

The concept of localisation does apply to the magnetic fields however, since it occupies a finite region of space. If the physical quantum system (not the mathematical description of it) passes through the finite region of space occupied by the magnetic field then this means that at some time, the quantum system was localized within that region of space. We're not specifying a 'single, pre-defined value' for it, but we have narrowed down its position(s)/location(s).

The only other alternative is that it doesn't pass through the magnetic field. One way in which this might be done is to challenge what it means to pass through a finite region of space but we have existing models which define finite regions of 3D space and what it means to pass through them. Appealing to other dimensions might be one such way of re-defining what it means to pass through a region of space.

This is true, but it also means we have to accept the limitations of deduction and inference, and we have to carefully check our premises and whether they even make sense in the domain of discussion before we try to make any deductions or inferences.

Indeed, as we have been doing.

 

[hutchphd]

The concept of localisation does apply to the magnetic fields however, since it occupies a finite region of space.

The only other alternative is that it doesn't pass through the magnetic field. One way in which this might be done is to challenge what it means to pass through a finite region of space but we have existing models which define finite regions of 3D space and what it means to pass through them.

Can we not obfuscate here? How does your '"region of magnetic field" differ from one of the slits in a two slit experiment?

.

 

[Lynch101]

Can we not obfuscate here? How does your '"region of magnetic field" differ from one of the slits in a two slit experiment?

I really don't think there should be any confusion here. I am working on the assumption that you are familiar with magnetic fields and slits in screen.

The diagram below has an example of both. #2 would be an example of a slit in a screen, while #3 is the Stern Gerlach machine which creates a magnetic field.

 

[hutchphd]

I asked a simple question. I have previously read and understand your description. You really needn't show it a third time.
Everything you say should be true of archetypal two slit diffraction. Is it?
Edit: I guess you are aware that this is a well studied question in the realm of the S where care must be taken to "adiabatically" turn on (and off) the interaction.

 

[StevieTNZ]

OK, then if this is true we must have some form of spontaneous FTL collapse to explain how the system then localises to a single position.

There may, of course, be alternative explanations. Again, if there are, we can explore their consequences. It might be the case that the idea of the system as being a separate 'thing' from the universe is challenged.

Perhaps. I don't know. Does 'collapse of the wave function' mean physical collapse, or merely we perceive the system in one state but remains, according to QM, in a superposition? I choose the latter - because, at all times, the system is described by QM and is in a superposition state.

 

[Lynch101]

I asked a simple question. I have previously read and understand your description. You really needn't show it a third time.
Everything you say should be true of archetypal two slit diffraction. Is it?
Edit: I guess you are aware that this is a well studied question in the realm of the S where care must be taken to "adiabatically" turn on (and off) the interaction.

And I gave a simple answer.

Unless you are using an SG magnet in a two slit experiment then no, we can't narrow it down to the finite region of space occupied by the SG magnetic field.

However, we could still narrow down the position(s)/location(s) in a two slit experiment.

If we call the point of emission from the electron beam gun A and the measured position on the detector screen B, then we can map all the possible geometric paths from A to B.

There are an infinite number of paths from A to B. However, there are only a finite number of possible paths that the electrons can take. This is because some possible paths extend out to distant regions of the universe and back and if the electrons were to follow those paths it would require FTL travel.

So, we can define the sum of all possible paths, which will represent a finite region of space in itself. At some time during the experiment the electron will have to have been located within that finite region of space. It may even have occupied that entire region of space. If it did occupy that entire region of space, however, we would require spontaneous, physical collapse to explain how it localized to a single position.

 

[Lynch101]

Perhaps. I don't know. Does 'collapse of the wave function' mean physical collapse, or merely we perceive the system in one state but remains, according to QM, in a superposition? I choose the latter - because, at all times, the system is described by QM and is in a superposition state.

If the physical system is everywhere in the physical universe, then we require physical collapse.

 

[StevieTNZ]

If the physical system is everywhere in the physical universe, then we require physical collapse.

I would answer that with 'not necessarily'. Remember we are dealing with potentialities when we talk about the system being everywhere in the universe. Don't think of the system being in a classical state.

 

[Lynch101]

I would answer that with 'not necessarily'. Remember we are dealing with potentialities when we talk about the system being everywhere in the universe. Don't think of the system being in a classical state.

Being everywhere in the universe isn't how classical objects behave. But, the quantum system is either physically everywhere in the universe, or it is not.

If it is, then we require physical collapse.

If by potentialities you mean there is the potential to measure it anywhere in the universe but in a single, localized position then that is not the same as saying the system is everywhere in the universe.

 

[hutchphd]

If by potentialities you mean there is the potential to measure it anywhere in the universe but in a single, localized position then that is not the same as saying the system is everywhere in the universe.

I guess we'll take your word for it. That is a polite way of bowing out of this particular monolog. But I really do appreciate you not using a bunch of jargon in your arguments.

 

[StevieTNZ]

If it is, then we require physical collapse.

There is no collapse in QM formalism.

 

[StevieTNZ]

If by potentialities you mean there is the potential to measure it anywhere in the universe but in a single, localized position then that is not the same as saying the system is everywhere in the universe.

Definitely not what I meant.

 

[physika]

Does something “have a location” when it’s not “measured”?

..and the inverse, how does know, that don't have it a location/ position?

 

[PeterDonis]

we appear to be talking at cross purposes here because I am specifically talking about the statistical interpretation.

No, you're not. You're talking about your concept of "location". But as far as the statistical interpretation is concerned, your concept of "location" doesn't apply to it either.

You have suggested previously that 'location' is ill-defined

I'm basing that on what is implicit in how you have been using the term "location". If you want to offer an explicit, rigorous definition of "location" instead of making me have to infer what you mean by it, by all means do so.

They can of course be asked.

Not in the cases I have described. In order for a question to even be asked in the first place, the concepts it is making use of have to make sense in the domain of discussion. Yours don't.

At this point I don't think I have anything further that is useful to contribute to this discussion.

 

[Lynch101]

I guess we'll take your word for it. That is a polite way of bowing out of this particular monolog. But I really do appreciate you not using a bunch of jargon in your arguments.

Yes, such impenetrable jargon as 'location', 'position', 'within', and 'finite region of space'.

But don't take my word for it, apply the simplest of basic reasoning.

Saying: we have the potential (there is a non-zero probability) to measure the system anywhere in the universe, is not the same as saying: the system is everywhere in the universe.

 

[Lynch101]

There is no collapse in QM formalism.

If the physical system is located everywhere in the physical universe, then collapse is required to explain our observations. This is entirely contingent on the proposition, 'the physical system is located everywhere in the physical universe'.

 

[Lynch101]

No, you're not. You're talking about your concept of "location". But as far as the statistical interpretation is concerned, your concept of "location" doesn't apply to it either.

I'm basing that on what is implicit in how you have been using the term "location". If you want to offer an explicit, rigorous definition of "location" instead of making me have to infer what you mean by it, by all means do so.Not in the cases I have described. In order for a question to even be asked in the first place, the concepts it is making use of have to make sense in the domain of discussion. Yours don't.

At this point I don't think I have anything further that is useful to contribute to this discussion.

Perhaps I am placing undue burden on others to infer what is meant. I have been working on the assumption that everyone is familiar with the idea of a 'finite region of space', and the notion of being 'within' that 'finite region of space'.

If at any point I am assuming too much, let me know and I can define what is meant more rigorously.

I'm going to assume that you are familiar with the concept of '3 dimensional space' and how to model/graph that using X, Y, and Z axes. I'm also assuming that , at some point during the course of your life you have made one, if not several, observations of boxes, be they cardboard or otherwise.

Now, we can model the 3D space of the box in the broader 3D space in which we find it. I'm assuming you know how to draw a 3D box on a graph using X, Y, and Z axes.

When we have the box drawn we can shade it in, so that it is a different colour from the rest of the 3D space on the graph. Let's say we shade the box blue and leave the rest of the space white.

Now, what is meant by 'located within a finite region of space' with regard to the box is, simply, somewhere on the part that is shaded blue. While 'not located within that finite region of space' would be somewhere on the part that is shaded white.

Is there anything there that is not clear?

 

[Lynch101]

Definitely not what I meant.

What did you mean by it then?

There are different ways to interpret what you said. I outlined one possible interpretation.

 

[physika]

There is no collapse in QM formalism.

However, exists collapse models and are testable.

 

[votingmachine]

The argument from Nowhere
5) If the system is not located anywhere in the universe then it is not in/part of the universe.
6) If the system is not in/part of the universe then it cannot interact with measurement devices which are in/
part of the universe.

A system that is not within a plane can interact with the plane. I'm not sure that #6 is a meaningful statement.

It either is a tautalogy, which then contradicts #5, since there is nothing that is not in/part of the universe, or it makes an unsupported statement that things not in/part of the universe cannot interact with the universe. I see no reason why a thing NOT IN the universe is forbidden to interact with a measuring device IN the universe

 

[Morbert]

I'm going to indulge myself and give the consistent histories answer.

We have a quantum system $s$ and measurement apparatus $M$ prepared in some initial state $\rho=\rho_s\otimes\rho_M$. The apparatus measures some observable $O$ at time $t_1$, with possible results $\{\epsilon_i\}$. We want to ask where the system is immediately prior to measurement, at time $t_1-\delta t$. We can model the location of the system with the observable $X$ and a suitably coarse-grained decomposition corresponding to possible position volumes $\{x_j\}$, such that $X$ and $O$ commute. We construct a state space $\mathcal{H}_{t_1-\delta t} \otimes \mathcal{H}_{t_1}$ as well as a suitable set of consistent histories $\mathcal{F}$. This set let's us extract quantities like $p(x_j|\epsilon_i)$. E.g. If our measurement result is $\epsilon_i$ then we can say that right before our measurement the system was located in the volume $x_j$ with probability $p(x_j|\epsilon_i)$.

 

[StevieTNZ]

If the physical system is located everywhere in the physical universe, then collapse is required to explain our observations. This is entirely contingent on the proposition, 'the physical system is located everywhere in the physical universe'.

Again, not necessarily. QM formalism doesn't have a non-linear attribute to the Schrodinger equation.

 

[StevieTNZ]

If the physical system is located everywhere in the physical universe, then collapse is required to explain our observations. This is entirely contingent on the proposition, 'the physical system is located everywhere in the physical universe'.

That's a very materialism kind of view. I subscribe to idealism.

 

[StevieTNZ]

What did you mean by it then?

There are different ways to interpret what you said. I outlined one possible interpretation.

Your supposed interpretation doesn't even read coherently, so I'm not sure what your view about my view is.

 

[jbergman]

This all strikes me as a somewhat bizarre discussion, Lynch101, and I agree with some of what you say. I have problems with the statistical interpretation and many others do too, as evidenced by the different interpretations.

That said, I don't understand the point of your questions. Are you trying to convince others of something? If so maybe a more direct route of laying out which interpretation you prefer might be more effective.

 

[Lynch101]

I'm going to indulge myself and give the consistent histories answer.

we can say that right before our measurement the probability of measuring the system in the volume $x_j$ is $p(x_j|\epsilon_i)$.

Is my amendment here correct?

 

[Lynch101]

Your supposed interpretation doesn't even read coherently, so I'm not sure what your view about my view is.

You said:

I would answer that with 'not necessarily'. Remember we are dealing with potentialities when we talk about the system being everywhere in the universe. Don't think of the system being in a classical state.

The system is either every everywhere in the universe or it is not. This is different from saying there is the potential to measure it everywhere (or anywhere) in the universe

That's a very materialism kind of view. I subscribe to idealism.

How does the 3 dimensional universe differ according to idealism, other than metaphysically?

 

[Lynch101]

This all strikes me as a somewhat bizarre discussion, Lynch101, and I agree with some of what you say. I have problems with the statistical interpretation and many others do too, as evidenced by the different interpretations.

That said, I don't understand the point of your questions. Are you trying to convince others of something? If so maybe a more direct route of laying out which interpretation you prefer might be more effective.

I don't necessarily have a preferred interpretation. I'm just trying to explore what QM tells us about the universe. I'm laying out my understanding as it currently is, with regard to the completeness* of the statistical interpretation. I am open to having that changed by way of reasoned discussion, or the unlikely alternative.

*By completeness I mean a complete description of the universe ala EPR's 'complete description of physical reality'.

 

[hutchphd]

The system is either every everywhere in the universe or it is not. This is different from saying there is the potential to measure it everywhere (or anywhere) in the universe

The cat is either alive or not. Same old stuff.
These are not new ideas, and restating them in different circumstances simply obfuscates

 

[Lynch101]

The cat is either alive or not. Same old stuff.
These are not new ideas, and restating them in different circumstances simply obfuscates

We might be talking at cross purposes here bcos we're in agreement on one point. The cat is either alive or dead. It is either alive or dead prior to opening the box.

An interpretation which only says, prior to opening the box, there is a 0.5 probability the cat is alive and a 0.5 probability the cat is dead, gives an incomplete description precisely because the cat is either definitely alive or definitely dead.

 

[Morbert]

Is my amendment here correct?

The amendment is fine, but not necessary. Consistent histories let's us make claims about the past not predicated on some counterfactual case where an additional measurement was performed at some point in the past. If we open the box and find a live cat, we can infer that the cat was alive and in the box before we opened it.

 

[EPR]

4 pages of idle discussion of layperson classical ideas and reasoning on quantum theory. If quantum systems behaved classically, there would be no separate theory.
I, and many others here, disagree that quantum theory is not a complete description of reality.
The quantum system is an integral part of the relative quantum field. Before measuring, there is only the field. The basic ingredient of the universe are not solid balls that you can assign a location to, but fields. Before you ask - fields are everywhere, because they are everything. They are the cat.

 

[Lynch101]

The amendment is fine, but not necessary. Consistent histories let's us make claims about the past not predicated on some counterfactual case where an additional measurement was performed at some point in the past. If we open the box and find a live cat, we can infer that the cat was alive and in the box before we opened it.

Can the same be said for the position of the system? You're statement said that it was located in the given volume with a probability $p(x_j|\epsilon_i)$. Does that probability equate to 1 after we make the measurement? i.e. does it say that the system always had a definite position? I'm guessing that the answer is no.

For any given region of space, the probability that the system is positioned in that region is either 1 or 0. That is, the set of values that comprise its position (it doesn't necessarily need to be one single value) includes that value with a probability of 1 or 0. The system is either in that position or it isn't, but it doesn't necessarily have to be in that position only.

This is a separate proposition to saying there is a probability $p(x_j|\X)$ that when measured it will be return a single value X.

 

[votingmachine]

*By completeness I mean a complete description of the universe ala EPR's 'complete description of physical reality'.

EPR was a clever proposal for an experimental setup to measure things beyond the allowances of Heisenberg's uncertainty. A way to demonstrate that uncertainty is JUST a necessary measurement error.

The experimental setup does not show that. It leads to the puzzling results that show (conclusively) that a complete description does not exist.

I too am puzzled by your arguments. It seems that you use want to use the knowledge gained as the result of a measurement as an argument that the universe knew, but we did not. The introduction of subsets seems puzzling and unnecessary.

I learned uncertainty as a measurement error (1970's). If you measure a baseball's position and momentum with a radar gun, the radar bouncing off the ball matters to the balls position and momentum. If the ball was thrown at night and we only had radar, we would necessarily have uncertainty imposed by the measurement process. But for macroscopic things, we generally have experimental errors much larger than the limits of uncertainty. With better equipment, we can get closer to the correct value. We add significant figures, and it is tempting to think we could arrive at a terminal decimal, beyond which it is all zeroes.

The complete descriptive set of information for that baseball does not exist. You can arbitrarily talk about the baseball being in subsets of the universe, but the complete descriptive set still does not exist. The part limited by uncertainty simply does not exist.

Maybe you have some other point by dicing up the universe, which I am not following.

 

[Lynch101]

4 pages of idle discussion of layperson classical ideas and reasoning on quantum theory. If quantum systems behaved classically, there would be no separate theory.
I, and many others here, disagree that quantum theory is not a complete description of reality.
The quantum system is an integral part of the relative quantum field. Before measuring, there is only the field. The basic ingredient of the universe are not solid balls that you can assign a location to, but fields. Before you ask - fields are everywhere, because they are everything. They are the cat.

You seem to be using the terminology a little loosely here. You say that the quantum system is an integral part of the relative quantum field [singular] and that, before measuring, there is only the field [singular]. Then you change to the plural when you say fields [plural] are everywhere.

We're talking about the quantum system prepared in the experiment. Is this part of the quantum system everywhere? If it were, then we should be able to measure it everywhere, with a probability of 1. If it isn't everywhere, but it is extended then we should be able to measure it everywhere it is, with a probability of 1. We don't however. This is part of what needs explaining.

There is no appeal to 'classical solid balls' here, since classical solid balls are not usually everywhere.

 

[Morbert]

Can the same be said for the position of the system? You're statement said that it was located in the given volume with a probability $p(x_j|\epsilon_i)$. Does that probability equate to 1 after we make the measurement? i.e. does it say that the system always had a definite position? I'm guessing that the answer is no.

So long as we partition the volumes accordingly, such that the observables $X$ and $O$ commute, we can say the system (or the centre of mass of the system or whatever) was definitely located in one of the volumes $\{x_j\}$. Though this is not the same as $p(x_j|\epsilon_i) = 1$. Instead it's $\sum_j p(x_j|\epsilon_i) = 1$

The commutation is important though. We cannot e.g. arbitrarily refine the possibilities $\{x_j\}$ into smaller and smaller volumes.

 

[EPR]

You seem to be using the terminology a little loosely here. You say that the quantum system is an integral part of the relative quantum field [singular] and that, before measuring, there is only the field [singular]. Then you change to the plural when you say fields [plural] are everywhere.

We're talking about the quantum system prepared in the experiment. Is this part of the quantum system everywhere? If it were, then we should be able to measure it everywhere, with a probability of 1. If it isn't everywhere, but it is extended then we should be able to measure it everywhere it is, with a probability of 1. We don't however. This is part of what needs explaining.

There is no appeal to 'classical solid balls' here, since classical solid balls are not usually everywhere.

Yes, the quantum field is everywhere. This is the only thing that is everywhere. Not "the quantum system" but the relative quantum field. You don't seem to grasp this and won't spend time as others did countering stubborn pedestrian reasoning.

 

[Lynch101]

So long as we partition the volumes accordingly, such that the observables $X$ and $O$ commute, we can say the system (or the centre of mass of the system or whatever) was definitely located in one of the volumes ##\

Am I interpreting this correctly when I liken it to saying, we can definitely say a dice is in one of its 6 positions?

Edit: not trying to be facetious

 

[EPR]

You are asking a nonsensical question in this thread which kind of gives away your incomplete knowledge of QT, rather than the incompleteness of QM. This naive question was asked in 1935 - but the theory has moved on and advanced immensely since then. It was relevant in the beginning when evidence of the correctness of QT wasn't as overwhelming as it is today and physicists were naturally still thinking in classical terms(like you). Not anymore. This question makes no sense in 2021.

 

[EPR]

You don't poke fun at classical physics, despite its blatant shootings and wrong predictions. Is classical physics a complete theory and description of reality? Rithorical question

 

[Morbert]

Am I interpreting this correctly when I liken it to saying, we can definitely say a dice is in one of its 6 positions?

Edit: not trying to be facetious

Yes.

Now if we suppose some experiment where $X$ and $O$ don't commute, then we have to be careful. E.g. In a setup like this, where the location of the particle striking the screen does not commute with the "which slit" observable, we cannot make a claim like "the particle that landed on the screen at some position x definitely passed through one of the slits"

 

[Lynch101]

Yes.

Just to unpack the analogy a little further. We have the following statements which could apply:
1) When we observe the die, we will definitely observe it with a value of 1-6.
2) There is a probability of 1/6 of observing the die with each value.
3) Prior to observation the die is, with certainty, in one of the states with a value of 1-6

#3 here would suggest that the die had a pre-defined value.

It seems as though, according to the statistical interpretation, we cannot say make statement #3. We cannot say that the system had a pre-defined value. By my reasoning then, we must conclude that it is in a state with multiple values prior to measurement. The permutation of possible states would be given by all possible 2, 3, 4, 5, and 6 value sates, with the system being in one of those multi-valued states.

Now if we suppose some experiment where $X$ and $O$ don't commute, then we have to be careful. E.g. In a setup like this, where the location of the particle striking the screen does not commute with the "which slit" observable, we cannot make a claim like "the particle that landed on the screen at some position x definitely passed through one of the slits"

View attachment 288604

But presumably we could say that X passed through slit A with a probability of 1 or 0 and/or slit B with a probability of 1 or 0. Where we can't have a value of 0 for both, however, we could have a value of 1 for both.

 

[Lynch101]

You are asking a nonsensical question in this thread which kind of gives away your incomplete knowledge of QT, rather than the incompleteness of QM. This naive question was asked in 1935 - but the theory has moved on and advanced immensely since then. It was relevant in the beginning when evidence of the correctness of QT wasn't as overwhelming as it is today and physicists were naturally still thinking in classical terms(like you). Not anymore. This question makes no sense in 2021.

I appreciate the input but reasoned arguments are preferable.

 

[Lynch101]

You don't poke fun at classical physics, despite its blatant shootings and wrong predictions. Is classical physics a complete theory and description of reality? Rithorical question

*Rhetorical

 

[Morbert]

I'll leave the statistical interpretation stuff for someone else.

But presumably we could say that X passed through slit A with a probability of 1 or 0 and/or slit B with a probability of 1 or 0. Where we can't have a value of 0 for both, however, we could have a value of 1 for both.

This is where QM gets subtle. If we have some unitary partition of a volume C that spans the slits, we can say the particle that struck the screen at position x passed through volume C.

-
However, if we refine this volume into volumes A and B like so, we cannot make a claim like "the particle that struck the screen at position x passed through either volume A or volume B", as we would break our probability calculus. If we had a classical theory we could, we we can't with a quantum theory.

 

[Lynch101]

I'll leave the statistical interpretation stuff for someone else.This is where QM gets subtle. If we have some unitary partition of a volume C that spans the slits, we can say the particle that struck the screen at position x passed through volume C. View attachment 288611
-
However, if we refine this volume into volumes A and B like so, we cannot make a claim like "the particle that struck the screen at position x passed through either volume A or volume B", as we would break our probability calculus. If we had a classical theory we could, we we can't with a quantum theory.
View attachment 288613

But, in the physical set-up, does the system not have to pass through the slits in order to hit the detector screen? If we had a screen with no slits, would we still have particles being observed on the detection plate? My presumption would be no, but I know that my presumptions are prone to error.

 

[Morbert]

But, in the physical set-up, does the system not have to pass through the slits in order to hit the detector screen? If we had a screen with no slits, would we still have particles being observed on the detection plate? My presumption would be no, but I know that my presumptions are prone to error.

Yes, the slits, but not "either one slit or the other".

 

[Lynch101]

Yes, the slits, but not "either one slit or the other".

Then it must be 'both slits' because it can't be neither.

 

[Morbert]

Then it must be 'both slits' because it can't be neither.

There are interpretations which say a particle passes through both slits. There are interpretations which invoke some primitive field ontology such that a particle only manifests at the point of detection on the screen. There is an "extended probability" interpretation with attempts to recover the notion of "either one slit or the other". There is an interpretations which do not make ontic commitments.

Ultimately, the formalism just says your space of possibilities have to be sufficiently coarse-grained for your purposes.