Where is the quantum system prior to measurement?

[votingmachine]

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

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

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

 

[Morbert]

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

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

 

[StevieTNZ]

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

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

 

[StevieTNZ]

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

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

 

[StevieTNZ]

What did you mean by it then?

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

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

 

[jbergman]

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

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

 

[Lynch101]

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

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

Is my amendment here correct?

 

[Lynch101]

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

You said:

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

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

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

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

 

[Lynch101]

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

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

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

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

 

[hutchphd]

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

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

 

[Lynch101]

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

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

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

 

[Morbert]

Is my amendment here correct?

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

 

[EPR]

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

 

[Lynch101]

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

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

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

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

 

[votingmachine]

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

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

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

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

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

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

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

 

[Lynch101]

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

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

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

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

 

[Morbert]

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

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

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

 

[EPR]

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

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

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

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

 

[Lynch101]

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

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

Edit: not trying to be facetious

 

[EPR]

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

 

[EPR]

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

 

[Morbert]

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

Edit: not trying to be facetious

Yes.

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

 

[Lynch101]

Yes.

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

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

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

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

View attachment 288604

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

 

[Lynch101]

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

I appreciate the input but reasoned arguments are preferable.

 

[Lynch101]

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

*Rhetorical

 

[Morbert]

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

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

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

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

 

[Lynch101]

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

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

 

[Morbert]

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

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

 

[Lynch101]

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

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

 

[Morbert]

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

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

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

 

[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'.