Undergrad Where is the quantum system prior to measurement?

[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.

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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
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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.

 

[Lynch101]

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.

I understand that different interpretations say different things. I'm focusing solely on those statistical interpretations which say that the mathematics only gives probabilistic predictions for measurement outcomes. Those are generally the interpretations which don't make ontic commitments, am I correct in saying that? The 'anti-realist'/instrumental/minimal statistical interpretations.

In the physical experimental set-up the system has to either pass through:
1) Slit A
2) Slit B
3) Slit A & B

Any description which does not specify that one of these three scenarios occurs, with a probability of 1, cannot be a complete description. It doesn't even have to pick which one is the case, it just has to allow that one of the 3 scenarios happens with certainty.

If we say that #1 or #2 is the case then, by my reasoning, we have to accept that the particle had a definite positon during the experiment and that FTL influences occur ala Bohmian Mechanics and Many Worlds.

If #3 is the case, then we require some form of physical collapse to say how the system has a definite position when measured.

By my reasoning, remaining agnostic on those simply leaves us with an incomplete description.

 

[Morbert]

Actual minimalist interpretations would treat the system as a Kantian-like thing-in-itself, imprinting on our experimental apparatus when we probe, but not subject to any thoroughgoing intelligibility. Your three alternatives assume an intelligibility a hardcore minimalist would not commit to.

 

[Lynch101]

Actual minimalist interpretations would treat the system as a Kantian-like thing-in-itself, imprinting on our experimental apparatus when we probe, but not subject to any thoroughgoing intelligibility. Your three alternatives assume an intelligibility a hardcore minimalist would not commit to.

Would the rules of 3 dimensional space not still apply though, as represented by the graphical representation. 'Slits' would still be required on the noumenological level for the system to 'pass through' and imprint itself on the experimental apparatus. Because if we remove the slits on the phenomenolgical level the system doesn't imprint itself on the measurement apparatus.

Also, would those mimimalist statistical interpretations also say that the mathematical formalism doesn't correspond to the physical reality?

 

[Morbert]

Would the rules of 3 dimensional space not still apply though, as represented by the graphical representation. 'Slits' would still be required on the noumenological level for the system to 'pass through' and imprint itself on the experimental apparatus. Because if we remove the slits on the phenomenolgical level the system doesn't imprint itself on the measurement apparatus.

Also, would those mimimalist statistical interpretations also say that the mathematical formalism doesn't correspond to the physical reality?

The statistical interpretation does not assert a system passing through slits. It asserts a statistical distribution of measurement outcomes that follow from a preparation.

 

[Lynch101]

The statistical interpretation does not assert a system passing through slits. It asserts a statistical distribution of measurement outcomes that follow from a preparation.

I understand that. That is part of the point I am trying to make. The general point is about the incompleteness of the statistical interpretation, as a 'description of physical reality'. It seems that for some of the points being made, the response is, '...but there are other interpretations which say...'. I am trying to focus on the completeness of the statistical interpretation, as 'description of physical reality'.

You seem to be making the point that the statistical interpretation is complete because it gives a complete list of all possible observations, à la giving a complete list of all the possible outcomes for the roll of a die, along with their probability.

What I am saying, and I believe others* have said, is that there are only a limited number of possibilities for explaining the probabilistic predictions and reconciling those with the observation of single, well-defined values, thereby giving a complete 'description of physical reality. With regard to the roll of a die, the possible options are:

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


As you say, the statistical interpretation does not assert a system passing through slits, it asserts a statistical distribution of measurement outcomes that follow from a preparation. But, in the physical set-up, the system must pass through slits in order to 'imprint' on our measuring apparatus. This must be true at the noumenological ('thing-in-itself') level also, since there must be something corresponding to 'slits' at that level - as represented graphically. If there were no 'noumenological slits' then the system could not 'imprint' on the measurement device.

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

Because if it goes through neither 1, 2, nor 3 then it cannot 'imprint' on the measurement device.By my reasoning, any interpretation which does not assert a system passing through slits but instead, asserts only a statistical distribution of measurement outcomes does not, by its own definition, give a complete description of physical reality.Given that options 1-3 are the only possible options in 3D space the conclusions which follow would be:
1) The system always has a definite position which explains why we observe it in a single, well-defined position.
2) The system always has a definite position, which explains why we observe it in a single, well-defined position.
3) The system was, physically, in a multi-valued state prior to observation.

For options 1&2 we would require an interpretation à laBohmian Mechanics or Many Worlds. For option 3 we would require some form of physical, spontaneous collapse. Are there interpretations which posit additional dimensions?

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

*others who question the completeness of the statistical interpretation as a 'complete description of physical reality'.

 

[Morbert]

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

 

[Lynch101]

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

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

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

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

 

[Morbert]

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

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

 

[hutchphd]

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

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

Sir Arthur Eddington and the Foundations of Modern Physics​

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

 

[Fra]

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

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

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

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

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

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

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

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

/Fredrik

 

[Lynch101]

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

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

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

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

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

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

 

[Lynch101]

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

Sir Arthur Eddington and the Foundations of Modern Physics​

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

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

 

[Morbert]

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

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

 

[Lynch101]

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

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

/Fredrik

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

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

 

[Lynch101]

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

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

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

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

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

 

[Morbert]

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

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

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

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

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

 

[gentzen]

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

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

 

[hutchphd]

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

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

 

[Lynch101]

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

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

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

 

[Morbert]

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

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

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