Where is the quantum system prior to measurement?

[PeterDonis]

If it passes through these finite regions of space then we can conclude that, at some time during the experiment the system was located somewhere in those finite regions of space.

Not with the meaning you are giving to the term "located", no. What @vanhees71 means by "passes through" is that the wave function is localized to that finite region of space. But you are trying to use a definition of "located" that will say more than that. So you are going beyond what @vanhees71 is saying.

This is interpreting what the physics tells us, which you seem to categorise as 'not physics'.

That is an acceptable paraphrase of what I said, given what you are using "interpreting" to mean, yes.

that doesn't invalidate the conclusions drawn.

It's not my job to "invalidate" the claims you are making. It is your job to either make physics claims, or not have this discussion in a physics forum. Granted, this particular forum, the QM interpretations forum, has somewhat looser rules; but along with those looser rules you must accept the fact that many discussions in this forum cannot be resolved because they come down to one person's opinion or preference vs. another's. That's basically where we are with your preferred concept of "location".

 

[PeterDonis]

that doesn't invalidate the conclusions drawn.

Conclusions are not valid until proven otherwise. They are invalid until evidence otherwise is presented; and they can never be "proven" valid because it is always possible that more evidence could either falsify them or limit their domain of validity in a way not previously considered. That's how science works.

 

[StevieTNZ]

Given the quote I provided, I'd say the quantum system is everywhere in the universe before measurement. This is further emphasised by Stephen Hawking in his book 'The Grand Design'.

 

[hutchphd]

Vanhees said that, when we prepare the system, it passes through a 'little hole' and it passes through a 'nicely tailored inhomogeneous magnetic field'. If it passes through these finite regions of space then we can conclude that, at some time during the experiment the system was located somewhere in those finite regions of space

This is a bad way to look at it. You have simply enlarged your detector. Before you had just a particle detector. Now you have a particle detector with a magnet in front of it. That doesn't change the behavior of the electron. Same for the slit and the photon.

 

[vanhees71]

Yes, Rovelli tries to explain it. But if you already read the paper yourself, you will probably be disappointed by explanations like:

I guess what confuses you is that Heisenberg's tables of numbers or "matrices" seem to be just as unobservable as the position of an electron or its time of circulation. Yet the abstract says: "In der Arbeit soll versucht werden, Grundlagen zu gewinnen für eine quantentheoretische Mechanik, die ausschließlich auf Beziehungen zwischen prinzipiell beobachtbaren Größen basiert ist." Not sure whether an explanation like the following would help you:After trying to read the paper, my guess is that the logic is to give up describing the time dependence. Because that is what Heisenberg does: He looks at the Fourier expansion in time of the classical variable, replaces that infinite series of Fourier coefficients by an infinite matrix, and then explains how to replace the expressions for the Fourier series of $x^2$, $x^3$ and $f(x)$ for general analytic functions $f$ by corresponding expressions for his infinite matrix. Then he notices that the expression for $xy$ is not commutative and therefore more problematic, suggests that the classical expression $v\dot{v}$ should probably be replaced by $(v\dot{v}+\dot{v}v)/2$ because it is the derivative of $v^2/2$, but that it is less clear what to do with more general terms.

So it looks like Heisenberg is trying to find out how to keep the equations of motion, but reinterpret their "mathematical" meaning for his matrices (which he obtained by giving up attempts to descibe a time dependence). This guess matches well with the title "Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen."

The problem is not to understand matrix mechanics, which is just one representation of QT, and it's well understandable reading the papers by Born&Jordan and Born&Jordan&Heisenberg written shortly after the Helgoland paper, where of course also the Heisenberg picture of time evolution was established, which indeed is the most natural description: the state (statistical operator) describes the initial preparation and the time-evolution of the operators representing observables determines the time evolution of the corresponding eigenvectors and then together with the statistical operator you get the probabilities/probability distributions as a function of time, containing all the physical probabilistic content of the quantum formalism.

The interesting point of the Helgoland paper is more to learn, how Heisenberg got to his profound new idea and the logic used to derive the matrix representation. It's obviously very heuristic and based on intuition. This was Heisenberg's strength. His weakness was to formulate these things in a deductive way. This was done by his collaborators, particularly Pauli and Born and Jordan.

 

[Lynch101]

Conclusions are not valid until proven otherwise. They are invalid until evidence otherwise is presented; and they can never be "proven" valid because it is always possible that more evidence could either falsify them or limit their domain of validity in a way not previously considered. That's how science works.

A conclusion is either valid or it is invalid i.e. it is either true or it is false*. On this basis we can explore the consequences of it being true and the consequences of it being false.

So, if it is true that the system passes through one 'nicely tailored inhomogeneous magnetic field' but does not pass through a separate magnetic field (which we have set-up either in the same room in the lab or another room) then we can narrow down the location of the system at some time to having been located in the finite region of space associated with the magnetic field through which it did pass.

This is either true or it is false.

If it is false, then we have to look at our premises.Evidence is the means by which we confirm the truth or falsity of a conclusion for us. Our finding evidence for a proposition does not make the proposition true, since it must have been true in the first place for us to be able to find evidence for it - unless this particular claim is false, in which case we can explore the consequences of that.*The conclusion 'X is valid in a limited domain' is a different conclusion to 'X is valid'.

 

[Lynch101]

Given the quote I provided, I'd say the quantum system is everywhere in the universe before measurement. This is further emphasised by Stephen Hawking in his book 'The Grand Design'.

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.

 

[Lynch101]

This is a bad way to look at it. You have simply enlarged your detector. Before you had just a particle detector. Now you have a particle detector with a magnet in front of it. That doesn't change the behavior of the electron. Same for the slit and the photon.

It doesn't matter if we make the set-up more complicated, particularly if it reveals more information to us. If we do have such a set up then:

If it is true that the system passes through one 'nicely tailored inhomogeneous magnetic field' but does not pass through a separate magnetic field (which we have set-up either in the same room in the lab or another room) then we can narrow down the location of the system at some time to having been located in the finite region of space associated with the magnetic field through which it did pass.

 

[gentzen]

The interesting point of the Helgoland paper is more to learn, how Heisenberg got to his profound new idea and the logic used to derive the matrix representation. It's obviously very heuristic and based on intuition. This was Heisenberg's strength. His weakness was to formulate these things in a deductive way. This was done by his collaborators, particularly Pauli and Born and Jordan.

Born and Jordan definitively were true collaborators. Pauli is different, but not in the way you would expect. Pauli was a troubled soul, more than anyone can imagine who has never read more about the details of his life. Here is an example from Arthur I. Miller's book 137: Ralf Kronig first had the idea that each electron also has an angular momentum of its own. But Bohr and Pauli dismissed his proposal, and Kronig dropped the idea. Then, nine months later, two Dutch physicists, George Uhlenbeck and Samuel Goudsmith, rediscovered spin and stacked their claim in print, warning that one should not visualize the electron as a spinning top. Pauli was deeply embarrased at having discouraged Kronig from publishing his idea and thereafter always spoke highly of him. And similarly, Pauli had also dismissed Heisenberg's idea, but both Heisenberg and Born were "sufficiently experienced" with how to handle Pauli's reactions and how to even "help" him.

Anyway, let me have another try at providing more information about "how Heisenberg got to his profound new idea". The most relevant words from
3. The Development of Quantum Mechanics (1925 – 1927)
3. Die Entstehung der Quantenmechanik (1925 – 1927)
are probably:

Nevertheless, his latest calculations in Copenhagen on dispersion theory and on complex spectra, especially the principle of “sharpened” correspondence applied in these works, seemed to point toward a future satisfactory theory.

With characteristic optimism the Göttingen Privatdozent took on a new and difficult problem at the beginning of May 1925, the calculation of the line intensities in the hydrogen spectrum. Heisenberg began with a Fourier analysis of the classical hydrogen orbits, intending to translate them into a quantum theoretical scheme – just as he had done with Kramers for the dispersion of light by atoms. But the hydrogen problem proved much too difficult, and he replaced it with the simpler one of an anharmonic oscillator. With the help of a new multiplication rule for a quantum-theoretical Fourier series he succeeded in writing down a solution for the equations of motion for this system. On 7 June 1925 he went to the island of Helgoland to recover from a severe attack of hay fever. There he completed the calculation of the anharmonic oscillator, determining all the constants of the motion. He made use, in particular, of a modified quantum condition that was later called by Born, Pascual Jordan and himself a “commutation relation”, and he proved that the new theory yielded stationary states (conservation of energy).

(Of course, I can also imagine that your real question is something else, but that you don't want to state it explicitly, because on the one hand you could just work it out yourself if that question were really sufficiently important to you, and on the other hand you don't expect that anybody could really answer that question for you, at least not without you also investing quite some work into trying to understand that answer.)

 

[hutchphd]

If it is true that the system passes through one 'nicely tailored inhomogeneous magnetic field' but does not pass through a separate magnetic field (which we have set-up either in the same room in the lab or another room) then we can narrow down the location of the system at some time to having been located in the finite region of space associated with the magnetic field through which it did pass.

Sorry I don't even know what hypothetical experiment you are talking about now. It is equivalent to two slits I believe, so perhaps we could simplify to that and you can restate your thesis.
It is clear from Feynman's formulation of the path integral that a particle samples all paths the most likely being where the action is stationary. At some level of approximation we concentrate only on likely paths.
Any other formulation is similar and one always tacitly works with a truncated hamiltonian $H_{local}+H_{rest~of~ universe}$. Whether a door is ajar in the lab down the hall seldom makes a difference to the experimental outcome but there is a tiny finite probability to detect the particle there.

 

[Lynch101]

Not with the meaning you are giving to the term "located", no. What @vanhees71 means by "passes through" is that the wave function is localized to that finite region of space. But you are trying to use a definition of "located" that will say more than that. So you are going beyond what @vanhees71 is saying.

It sounds to me like you are confusing the 'map' with the 'territory' here. The finite region of space which the magnetic field occupies is not the same as the mathematical description of the magnetic field.

So, if by the wave function is localized to that finite region of space you mean the mathematical artefact that is the 'wave function' is localized in the mathematical description of the finite region of space that is one thing. We can examine how this corresponds to 'physical reality'.

The 'wave function' [as the mathematical description of the system] cannot be localized in a finite region of space [in physical reality] because it is a mathematical artefact. If you mean the physical system to which the wave function corresponds is localized in the finite region of space, then that is precisely the point I am making.

It's not my job to "invalidate" the claims you are making. It is your job to either make physics claims, or not have this discussion in a physics forum. Granted, this particular forum, the QM interpretations forum, has somewhat looser rules; but along with those looser rules you must accept the fact that many discussions in this forum cannot be resolved because they come down to one person's opinion or preference vs. another's. That's basically where we are with your preferred concept of "location".

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.

It's also not simply a matter of opinion, they are matters of reason based on premises and conclusions. A conclusion is either true or it is false. We can explore the consequences of it being true and the consequences of it being false.

If we deny the conclusion presented then we must be denying the premises from which it follows. You have attempted this above by questioning what we mean by 'passes through'. Doing this has implications for any given position. We can explore these implications by presenting reasoned arguments which follow from the physics or which interpret the physics.

 

[Lynch101]

Sorry I don't even know what hypothetical experiment you are talking about now. It is equivalent to two slits I believe, so perhaps we could simplify to that and you can restate your thesis.
It is clear from Feynman's formulation of the path integral that a particle samples all paths the most likely being where the action is stationary. At some level of approximation we concentrate only on likely paths.
Any other formulation is similar and one always tacitly works with a truncated hamiltonian $H_{local}+H_{rest~of~ universe}$. Whether a door is ajar in the lab down the hall seldom makes a difference to the experimental outcome but there is a tiny finite probability to detect the particle there.

I believe an experimental set-up like the following:

#3 is what creates the inhomogenous magnetic field.

If, the magnetic field occupies a finite region of space and the system 'passes through' this region of space, then we have narrowed down the possible location(s)/position(s) of the system.

Now imagine, in the same room we also have an identical set-up but instead of sending particles through the second apparatus we simply turn on the magnetic field. So, now we've got two magnetic fields occupying two separate finite regions of space. If we can say that the system 'passes through' one magnetic field but not the other, then we can narrow down the locations(s)/position(s) of the system [at some time during the experiment] to the finite region of space through which it did pass.

 

[vanhees71]

Born and Jordan definitively were true collaborators. Pauli is different, but not in the way you would expect. Pauli was a troubled soul, more than anyone can imagine who has never read more about the details of his life. Here is an example from Arthur I. Miller's book 137: Ralf Kronig first had the idea that each electron also has an angular momentum of its own. But Bohr and Pauli dismissed his proposal, and Kronig dropped the idea. Then, nine months later, two Dutch physicists, George Uhlenbeck and Samuel Goudsmith, rediscovered spin and stacked their claim in print, warning that one should not visualize the electron as a spinning top. Pauli was deeply embarrased at having discouraged Kronig from publishing his idea and thereafter always spoke highly of him. And similarly, Pauli had also dismissed Heisenberg's idea, but both Heisenberg and Born were "sufficiently experienced" with how to handle Pauli's reactions and how to even "help" him.

Anyway, let me have another try at providing more information about "how Heisenberg got to his profound new idea". The most relevant words from
3. The Development of Quantum Mechanics (1925 – 1927)
3. Die Entstehung der Quantenmechanik (1925 – 1927)
are probably:

(Of course, I can also imagine that your real question is something else, but that you don't want to state it explicitly, because on the one hand you could just work it out yourself if that question were really sufficiently important to you, and on the other hand you don't expect that anybody could really answer that question for you, at least not without you also investing quite some work into trying to understand that answer.)

Well, I don't think it's so important concerning physics, because we have the fully developed theory today. It's just interesting historically to get the idea, how the original ideas developed. This is not so easy with the Helgoland paper.

It's even more difficult for Newton's Principia or Maxwell's Treatise. The content we learn of course today in a much more digestible form, going back to Euler and Heaviside, respectively.

 

[hutchphd]

If, the magnetic field occupies a finite region of space and the system 'passes through' this region of space, then we have narrowed down the possible location(s)/position(s) of the system.

This is just a slightly complicated two slit experiment. What is the surprise here?
Clearly particles can be localized more or less I do not understand the point you are trying to make

 

[Lynch101]

This is just a slightly complicated two slit experiment. What is the surprise here?
Clearly particles can be localized more or less I do not understand the point you are trying to make

The general point is that those interpretations which only predict the outcomes of an ensemble of experiments do not give a complete description of the system because they do not describe, in any way, where the system is 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.