Where is the quantum system prior to measurement?

[Lynch101]

TL;DR Summary

To explore the idea that the system has location/position* prior to measurement which requires description for a theory/interpretation to be considered complete.

*Not necessarily a single, pre-defined value.

Continuing the discussion in the 'Assumptions of Bell's Theorem' thread, I'm hoping to explore the question of the location/position of the QM system prior to measurement.

I may have some bias or underlying assumption that is affecting the conclusion that I am drawing and, by exploring this question, my bias might become clear - or the alternative .

There are a probably a number of different ways to explore this question, but I'm hopeful that by making some general statements and asking some general questions (and having those probed, questioned, and challenged) the discussion will develop organically.I think the following are the only necessary assumptions but, as I say, there might be some hidden assumptions I am making:

Assumptions
1. The universe is spatially extended.
2. The system [we prepare and consider] is a subset of the universe i.e. it is not the entire universe*.Is it the case that one of the two following propositions must be true:
1) Location/position is an 'element of reality' of the system, prior to measurement.
2) Location/position is not an 'element of reality' of the system, prior to measurement.

Do the following make sense:
A) If someone tells you that they have hidden something 'somewhere in the field over there'. Would you know where to look for that 'something'?

B) Does the idea of being somewhere in the universe make sense?

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

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

 

[gentzen]

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

Yes, it makes sense to say that the system is located somewhere in the lab in Paris. I would be more careful with the negative assertion "and not in the lab in Rome". There might be nonlocal correlations that make negative assertion dangerous, at least sometimes. Positive assertions on the other hand are normally unproblematic.

 

[Lynch101]

Yes, it makes sense to say that the system is located somewhere in the lab in Paris. I would be more careful with the negative assertion "and not in the lab in Rome". There might be nonlocal correlations that make negative assertion dangerous, at least sometimes. Positive assertions on the other hand are normally unproblematic.

Would it be safe to say that the system is not everywhere in the universe?

 

[gentzen]

Would it be safe to say that the system is not everywhere in the universe?

I don't want to be drawn into your discussion with PeterDonis. Your assertion is so weak that I believe the only reason why you wanted to say it was your discussion with PeterDonis. It is simply not a useful assertion, because it has no chance to imply any observable consequences.

 

[Lynch101]

I don't want to be drawn into your discussion with PeterDonis. Your assertion is so weak that I believe the only reason why you wanted to say it was your discussion with PeterDonis. It is simply not a useful assertion, because it has no chance to imply any observable consequences.

The discussion isn't exclusively between PeterDonis and I. It's open to anyone.

The assertion is indeed quite weak. I don't believe it needs to be any stronger to draw the inferences I believe can be drawn.

The consequences need not necessarily be observable in order to draw the conclusion of incompleteness.

 

[PeterDonis]

I don't want to be drawn into your discussion with PeterDonis.

The discussion isn't exclusively between PeterDonis and I. It's open to anyone.

More than that, I am intentionally not posting in this separate thread, so that other people can have a discussion with @Lynch101 without being influenced by my particular opinions. I have already said all that I can usefully say in the previous thread. So everyone please feel free to post here about the OP question; that is the purpose of having this separate thread.

 

[msumm21]

Summary:: To explore the idea that the system has location/position* prior to measurement which requires description for a theory/interpretation to be considered complete.

*Not necessarily a single, pre-defined value.

A) If someone tells you that they have hidden something 'somewhere in the field over there'. Would you know where to look for that 'something'?

B) Does the idea of being somewhere in the universe make sense?

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

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

I’m not an expert and I haven’t read the other forum where this originated, but it seems like your questions are ones that nobody knows the answer to. Does something “have a location” when it’s not “measured”? Is that a core question here? Some interpretations of QT (e.g. pilot-wave) say yes, others say no, right? I realize I’m probably missing a deeper question here, maybe you could clarify?

Regarding C, I assume you are aware of Bell experiments? You could measure/prepare something in Paris from a lab in Rome, but only if very carefully setup that way.

 

[Lynch101]

I’m not an expert and I haven’t read the other forum where this originated, but it seems like your questions are ones that nobody knows the answer to. Does something “have a location” when it’s not “measured”? Is that a core question here? Some interpretations of QT (e.g. pilot-wave) say yes, others say no, right? I realize I’m probably missing a deeper question here, maybe you could clarify?

Yep. The original discussion stemmed from a claim I made, that those interpretations which only provide statistical predictions for the outcomes of measurements i.e. only tell us the probability of what we will observe on measurement devices are, by definition, incomplete descriptions of physical reality because they do not describe the quantum system prior to measurement. To my mind this seems pretty obvious but I might be making an invalid assumption somewhere.

There are a couple of different arguments, all of which are pretty simple and straightforward:

The argument from Somewhere
1) The quantum system must be located somewhere in the universe prior to measurement.
2) A complete 'description of physical reality' must provide a description of the location of the system prior
to measurement.
3) The description of the location/position of the system does not need to be a single, pre-defined value.
4) Given 3) we don't need a single, pre-defined value for position but we do need some description of
location/position.

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.

The argument from Near here
7) The QM probability distribution tells us the probability of measuring the system in a given spatial location.
8) One of the following propositions must be true:
- The QM system is located in (or adjacent to) the given spatial region.
- The QM system is not located in (or adjacent to) in the given spatial region.
9) If the QM system is not located (or adjacent to) in the given spatial region then it cannot interact with the
measurement device.

The argument from Everywhere
10) To have the possibility of interacting with a measurement device, the QM system must be located in (or
adjacent to) the given spatial region, otherwise see 9) above.
11) If the probability distribution is not the result of a lack of information and there is a genuine possibility
of measuring the system in a spatial region with a zero-probability, then the system must be located in
all of those locations with a non-zero probability.
12) If the system is located in all of those spatial regions, then some form of FTL 'collapse' must occur to
give rise to a single measurement outcome.

Regarding C, I assume you are aware of Bell experiments? You could measure/prepare something in Paris from a lab in Rome, but only if very carefully setup that way.

I am aware of Bell experiments msumm. The point I am trying to get at is, is it possible to say that there is somewhere that the system is not?

If we prepare a system in Paris from a lab in Rome, is it possible to say that the system is not on the moon?

The point I am trying to make is:
1) If the system is not located everywhere, and we can state where it is not located then, by the process of
elimination we could [theoretically] have a description of where the system
is located, prior to measurement.

 

[EPR]

The quantum system is mostly around the peak of the probability amplitude.

 

[Lynch101]

The quantum system is mostly around the peak of the probability amplitude.

But also partially around the spatial regions with non-zero probabilities of measurement?

 

[EPR]

But also partially around the spatial regions with non-zero probabilities of measurement?

Of course.

You should disregard the other worlds as they don't affect yours.

 

[vanhees71]

I’m not an expert and I haven’t read the other forum where this originated, but it seems like your questions are ones that nobody knows the answer to. Does something “have a location” when it’s not “measured”? Is that a core question here? Some interpretations of QT (e.g. pilot-wave) say yes, others say no, right? I realize I’m probably missing a deeper question here, maybe you could clarify?

Regarding C, I assume you are aware of Bell experiments? You could measure/prepare something in Paris from a lab in Rome, but only if very carefully setup that way.

If you have a quantum system for which a position obsevable exists (e.g., all massive particles as well as massless particles with spin 0 or spin 1/2), then you can measure the position of this system/particle. Position, as a then necessarily continuous observable is never exactly determined but a particle can be principally localized in a small region (but usually not smaller than its Compton wavelength, because if you try to localize it even better you'll create rather more particles than localizing the single particle better). The only meaningful statement you can make is that when measuring the position of the system, you'll find it witin a volume $\mathrm{d} V$ at a given place with a probability $\rho(t,x,x) \mathrm{d} V$, where $\rho(t,x,x')$ are the position matrix elements of the statistical operator describing the state of the particle.

Concerning C: That's right. You can prepare, say, an entangled photon pair by parametric downconversion in the polarization-singlet state and direct one of them to Rome. If you make sure that this photon is not interacting with anything on its way then by measuring the other photon in Paris and let the other photon only go to Rome if your photon is horizontally polarized, then you know with certainty that the experimentalist measuring the polarization in Rome in precisely the same direction, he or she will find the photon to be vertically polarized.

 

[Lynch101]

Concerning C: That's right. You can prepare, say, an entangled photon pair by parametric downconversion in the polarization-singlet state and direct one of them to Rome. If you make sure that this photon is not interacting with anything on its way then by measuring the other photon in Paris and let the other photon only go to Rome if your photon is horizontally polarized, then you know with certainty that the experimentalist measuring the polarization in Rome in precisely the same direction, he or she will find the photon to be vertically polarized.

Does this not imply that there is a time when the system is not in Rome then?

 

[vanhees71]

Since photons don't have a position observable it doesn't even make sense to ask where they are. You can only give a probability distribution for detecting them at a place defined by the location of the detector.

 

[Lynch101]

Since photons don't have a position observable it doesn't even make sense to ask where they are. You can only give a probability distribution for detecting them at a place defined by the location of the detector.

I think this is where we are in disagreement because I think it does make sense to ask where they are. The answer may not be a single, pre-defined value but, to my mind, it makes sense to say that the system must be located (or have position) somewhere in the universe.

I think you said that this is a trivial point and that the probability of it being somewhere in the universe is 1.

 

[gentzen]

I think it does make sense to ask where they are. The answer may not be a single, pre-defined value

Your terminology is slightly dangerous here, because asking and getting answers is often associated with measurements, but that is probably not what you want.
It seemed to me that what you want is more to make certain assertions about a system that may be true independent of whether you make a specific measurement to check them.

 

[Lynch101]

Your terminology is slightly dangerous here, because asking and getting answers is often associated with measurements, but that is probably not what you want.
It seemed to me that what you want is more to make certain assertions about a system that may be true independent of whether you make a specific measurement to check them.

I understand that it usually is associated with measurements but I don't think it necessarily needs to be. As PeterDonis mentioned in the 'Assumptions' thread.

The hidden variables do not even have to be observables, and they certainly do not have to contain all possible observables. They just have to contain enough information to determine the results of the measurements being conducted.

It seemed to me that what you want is more to make certain assertions about a system that may be true independent of whether you make a specific measurement to check them.

I think it is, or at least should be, possible to make certain deductions about nature that are not limited to what we can observe.

It might actually be more accurate to say that we can make certain deductions about different models of nature based on a given set of principles, as per the arguments above.

For example, if our model says the universe is spatially extended and the quantum system is a subsystem of the universe i.e. it is not everywhere in the universe then, we should be able to make the deduction that the system has a location in the universe which a full and complete description would describe.

Similarly, if we can say that the model is not located in a given spatial region e.g. the moon, then we should be able to conclude, by the process of elimination, where the system is located, in principle at least.What form this description takes is completely open, and it seems as though some interpretations do indeed have such a description. Not providing such a description, to my mind, renders a model/interpretation incomplete.

 

[vanhees71]

I think this is where we are in disagreement because I think it does make sense to ask where they are. The answer may not be a single, pre-defined value but, to my mind, it makes sense to say that the system must be located (or have position) somewhere in the universe.

I think you said that this is a trivial point and that the probability of it being somewhere in the universe is 1.

If something doesn't have a position variable, how can it then be located? The important point is that you cannot locate a photon. All there is are probabilities to register a photon with a detector, which is located somewhere, and you can locate the detector, because it has a well-defined (macroscopic) position observable. Of course everything is somwhere in the universe.

 

[Lynch101]

If something doesn't have a position variable, how can it then be located?

That is what I think we can deduce. It doesn't necessarily have to have a single, pre-defined value for location, but that doesn't mean that it isn't located anywhere nor have any position whatsoever.

The important point is that you cannot locate a photon. All there is are probabilities to register a photon with a detector, which is located somewhere, and you can locate the detector, because it has a well-defined (macroscopic) position observable.

And there are a number of ways we can interpret what the probabilities tell us. One such way is that the system has a definite position, we just don't know what it is. Under this scenario, only one possible outcome for the measurement is ever possible. There is only the seeming possibility that spatial regions with a non-zero probability can register the photon, but in truth there is not a genuine possibility for each region with a non-zero probability.

If we reject this idea and we say that there is a genuine possibility that the measurement device can register the photon in any spatial region with a non-zero probability, then we can ask what this tells us about the system. How is it a genuine possibility, as opposed to a seeming possibility?

And, if there is a genuine possibility that the photon will register in spatial regions with a non-zero probability, why is it that we only ever observe the photon in one spatial region? What happens to 'make nature choose' one over the others?

Of course everything is somwhere in the universe.

Is the system everywhere in the universe?

 

[PeterDonis]

That is what I think we can deduce.

Moderator's comment: Please bear in mind that "I think" is not an acceptable argument here. You should be able to either make an argument yourself showing how this can be deduced from the basic math and principles of QM, or give a reference that makes such an argument.

 

[StevieTNZ]

You might find this paragraph helpful:

If an electron is expelled from a nucleus, Schrodinger's equation predicts that the ψ wave spreads out evenly through space. But when the electron is revealed, by a detector for instance, or by a TV screen, its arrives at one point only, not spatially spread out.

-- pg 25 of 'Helgoland: Making Sense of the Quantum Revolution' by Carlo Rovelli.

 

[Lynch101]

You might find this paragraph helpful:

-- pg 25 of 'Helgoland: Making Sense of the Quantum Revolution' by Carlo Rovelli.

thank you Stevie, I must give Helgoland a read.

There appears to be different ways of interpreting the idea that 'the ψ wave spreads out evenly through space'. Some physicists ascribe an ontology to the wave function, while others treat it instrumentally.

We can explore the implications of both these possibilities and see what inferences/deductions we can make.

 

[vanhees71]

BTW: Does Rovelli explain what Heisenberg wanted to tell us with this paper? I never could understand its logic. Only the follow-up papers by Born and Jordan and by Born, Jordan, and Heisenberg ("Dreimännerarbeit") make an understandable theory for me, though the Helgoland paper is of course the result of Heisenberg's original idea.

 

[Lynch101]

In the other thread you mentioned:

An experiment consists of a preparation procedure followed by a measurement. E.g. in the SG experiment you put silver vapor into an oven at a given temperature and let out the silver atoms through a little hole.
...
Then you let this stream of Ag atoms go through a nicely tailored inhomogeneous magnetic field.

Presumably the 'little hole' that the atoms go through is a finite region of space. Can we not then conclude that the system, at some time, had a position within this little hole? Otherwise, in what sense do the atoms 'go through the little hole'?

Similarly, the 'nicely tailored inhomogeneous magnetic field', presumably, represents a finite region of space. Can we not, therefore, narrow down the position of the system (at some time during the experiement) to 'somewhere in that field'?

Can we set up a similar magnetic field with a detection plate in another location? Either, in the same room in the laboratory; a different room in the laboratory; a different building; a different town; etc. etc. and say that the quantum system doesn't go through those other magnetic fields? In this way can we rule out possible locations/positions of the quantum system? If so, this too would help us narrow down the location/position of the quantum system.If not, then in what sense does the quantum system 'go through the magnetic field'?

 

[vanhees71]

Well, all our observations are localized by the equipment we use. I don't understand your problem with that.

 

[Lynch101]

Well, all our observations are localized by the equipment we use. I don't understand your problem with that.

I'm just saying, if we can say the system passes through a 'little hole' or passes through one magnetic field but not the other, then we are necessarily saying the system is located in some finite region of space.

 

[vanhees71]

Sure. So what?

 

[Lynch101]

Sure. So what?

Just was we have narrowed down the location of the system to some finite region of space, we can try to narrow it's location down further within that finite region of space. We can ask, is the quantum system everywhere in that finite region of space?

 

[Lynch101]

Reasoning might lead us to the following conclusions. This is by no means an exhaustive list but it allows us to explore the implications:
1) The system is spatially extended to occupy the entire spatial region.
2) The system is spatially extended but doesn't occupy the entire spatial region.
3) The system is localised and occupies a single pre-defined position.
4) The system is localised but occupies multiple positions.

We can rule out the possibility that the system is not located anywhere in the given spatial region, since we have agreed that the system is located somewhere in that finite region of space.

All but #3 above would necessitate some form of spontaneous and/or FTL 'collapse' of the system to a single well-defined position.

If there are other possibilities, other that 1-4 above, we can explore the implications of those also.

 

[gentzen]

BTW: Does Rovelli explain what Heisenberg wanted to tell us with this paper? I never could understand its logic.

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

It is very simple: the forces are the same as in classical physics; the equations are the same as those of classical physics. But the variables are replaced by tables of numbers, or "matrices."

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:

We cannot find new laws of motion to account for Bohr’s orbits and his “leaps”? Fine, let’s stick with the laws of motion that we’re familiar with, without altering them.

Let’s change, instead, our way of thinking about the electron. Let’s give up describing its movement.

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."

 

[PeterDonis]

Just was we have narrowed down the location of the system to some finite region of space, we can try to narrow it's location down further within that finite region of space.

In order to narrow down the location further, you would have to use a device that is smaller. And at some point you will run into the fact that, according to quantum field theory, to confine a quantum object into a smaller space requires more energy, and at some point you have pumped enough energy into the system to create more particles, so you're no longer measuring just the original system.

This illustrates the more general point that you can't just wave your hands and say "we can try" to do something. You have to actually specify how you are going to try, and then you have to ask what QM tells you about what will happen when you do that.

 

[Lynch101]

In order to narrow down the location further, you would have to use a device that is smaller. And at some point you will run into the fact that, according to quantum field theory, to confine a quantum object into a smaller space requires more energy, and at some point you have pumped enough energy into the system to create more particles, so you're no longer measuring just the original system.

This illustrates the more general point that you can't just wave your hands and say "we can try" to do something. You have to actually specify how you are going to try, and then you have to ask what QM tells you about what will happen when you do that.

But there we've gone from not being able to say anything about the location/position of the system prior to measurement to narrowing it down to a very specific, finite region of space. We don't need to physically narrow down the location any further to draw the conclusions from propositions 1-4 above.

But we could narrow it down as much as possible, to that limit you've specified, and conclude that the system is located in that finite region of space. Here, again, we are saying that the system has location/position prior to measurement. Again ask if it is located everywhere in that smaller, finite region of space. Again, we will arrive at the same conclusions.

If the description does not specify that the system is:
A) everywhere in the finite region of space
B) not-everywhere in the finite region of space

then it does not give a complete description of the system. If it specifies B above, but does not then specify where in the region of space it is (or where it is not), it cannot be said to give a complete description of the system.

 

[PeterDonis]

we could narrow it down as much as possible, to that limit you've specified, and conclude that the system is located in that finite region of space at the instant the measurement is made.

See my qualifier in bold above. It makes a big difference.

 

[PeterDonis]

If the description does not specify that the system is:
A) everywhere in the finite region of space
B) not-everywhere in the finite region of space

then it does not give a complete description of the system.

This is not physics. It's your personal opinion. That will remain true no matter how many times you repeat it.

 

[Lynch101]

See my qualifier in bold above. It makes a big difference.

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.

Having narrowed down the possible location(s)/position(s) of the system to some finite region of space we can then ask if the system was located everywhere in that finite region of space. From there, we can draw the conclusions outlined above.

This is not physics. It's your personal opinion. That will remain true no matter how many times you repeat it.

This is interpreting what the physics tells us, which you seem to categorise as 'not physics'. Which is fair enough. But, that doesn't invalidate the conclusions drawn.