I Understanding the Fundamental Difference in Interpretations of QM

[martinbn]

But if you knew all positions at all times, then you could predict the outcomes deterministically, so you would no longer need the probabilistic Born rule.

Or if you want to restrict to one time only, if you know all positions at that time, then you don't need Born rule at that time. To make an analogy, if you know that the coin is in the head state, then you don't need to know that the probability of head is 1/2.

But if you know the coordinates at one time, can you predict anything in the future. Say one particle, you measure, it happens to be at the origin. Are you saying that according to BM you will know with certainty where it will be in the future? That would make BM different from QM.

Then answer this: What is the state in the Hamilton-Jacobi formulation of classical mechanics?

Is there a formulation where only the Hamilton-Jacobi function is the initial data and that gives the same predictions?

I think it cannot be answered from how you formulated the question. You formulated it as nothing but a set of equations. Foundations of physics is more than a set of equations.

Now you are avoiding the question.

 

[PeterDonis]

If it doesn't describe the physically real state of the system, there must be a difference between the two

You're assuming there is a physically real state of the system that you could in principle compare with the quantum state. In some interpretations, there isn't; it's simply meaningless to ask what the "physically real state of the system" is. All you can ask is what the probabilities are for future measurements you could make.

Why isn't there an experiment where the results don't match the predictions?

Some interpretations would say it's simply because we haven't figured out how to run such an experiment yet.

 

[martinbn]

You're assuming there is a physically real state of the system that you could in principle compare with the quantum state. In some interpretations, there isn't; it's simply meaningless to ask what the "physically real state of the system" is. All you can ask is what the probabilities are for future measurements you could make.

Well, yes, and any interpretation that says that it isn't the real state must say what the real state is and then the difference will be apparent. That is what confuses me, how can there be such an interpretation without different predictions.

Some interpretations would say it's simply because we haven't figured out how to run such an experiment yet.

But the interpretation must provide such an experiment at least in principle, no? Which interpretations do that? And if they do, are they still interpretations or different theories?

 

[PeterDonis]

To me it seems reasonable to conclude that, previous to the effect on the SG plate, the particle must have been in some state - any state - sufficient for it to interact with the SG plate to cause that effect. If it was in no state whatsoever, then it couldn't interact with the SG plate and there would be no exposure event in the first place.

First, however reasonable this might seem to you, it's not valid as a matter of logic. It's perfectly possible, logically, for the particle to not have any "state" prior to a measurement result being observed. Indeed, this was the viewpoint (as far as I can tell) of Bohr and others in the quantum debates that took place in the 1920s and 1930s.

Second, suppose I agree for the sake of argument that your claim is true. How does it help in proving determinism? Saying that the particle was in some state prior to the measurement result, and that the particle caused the measurement result we observed, does not in any way require that it was impossible, before the result was observed, that some other result could have been observed. The latter claim is just you assuming that determinism is the only possible way for the particle to cause the measurement result, i.e., you arguing in a circle.

It sounds as though, "accepting the limitations of standard QM" means accepting that we cannot have full knowledge of the initial conditions of an experiment.

It means accepting that the quantum state captures everything we can know that is relevant to making predictions about future measurement results, since that is what standard QM uses the quantum state for.

This would seem to tacitly suggest that there are such initial conditions that we cannot know, which account for our indeterminate predictions. Am I right in thinking this is essentially referring to hidden variables?

Hidden variable hypotheses fall into this category, yes. I don't know that hidden variable hypotheses are the only possible ones in this category.

Would this, therefore imply determinism?

All of the hidden variable hypotheses I'm aware of are deterministic. I don't know that hidden variable hypotheses have to be deterministic.

Note, btw, that "deterministic" is not the same as "local". Bohmian mechanics, for example, is highly nonlocal: the quantum potential is determined by the configuration of particles in the entire universe at an instant, not just at one location.

The alternative here, that the process is truly indeterministic, would seems to imply that there are no initial conditions that we are unaware of i.e. we are aware of all the initial conditions that are present. The indeterminism is then attributed, not to a lack of information but, to the complete absence of that information in the first place. Am I correct in that summation?

Yes.

 

[Demystifier]

I just had a read of the paper in your signature and, although I am clearly in no position to evaluate it for myself, I certainly found it very interesting. I was wondering if there is any similarity between the point I am trying to make (below) and the point you make in the paper.

Yes, the two points of view are very similar.

 

[Demystifier]

Are you saying that according to BM you will know with certainty where it will be in the future? That would make BM different from QM.

I am saying that, according to BM, I can know it in principle but not in practice. So in principle BM is very different from QM, but in practice it's not. See also Sec. 2.1 in my paper.

 

[PeterDonis]

any interpretation that says that it isn't the real state must say what the real state is

This is clearly not true since there are interpretations that explicitly refuse to say what you say they "must" say.

Again, I understand that you find it hard to wrap your mind around such interpretations. But that doesn't mean they don't exist.

the interpretation must provide such an experiment at least in principle, no?

I don't see why they "must".

 

[Demystifier]

All of the hidden variable hypotheses I'm aware of are deterministic.

Nelson interpretation is a counterexample. It's like Bohmian theory with trajectories, but the equation of motion for trajectories has an additional stochastic term.

 

[PeterDonis]

Nelson interpretation

Do you have a reference that describes this? It looks interesting.

 

[Demystifier]

Well, yes, and any interpretation that says that it isn't the real state must say what the real state

QBism, for instance, explicitly refuses to say what the real state is.

 

[Demystifier]

Do you have a reference that describes this? It looks interesting.

You can find references here https://en.wikipedia.org/wiki/Stochastic_quantum_mechanics

 

[martinbn]

This is clearly not true since there are interpretations that explicitly refuse to say what you say they "must" say.

Again, I understand that you find it hard to wrap your mind around such interpretations. But that doesn't mean they don't exist.
I don't see why they "must".

I think I see it now. Some interpretations in category (1) say that the wave function is not the real state and that there is a real state but we don't know what it is. Is that correct? What is the use of that?

 

[PeterDonis]

Some interpretations in category (1) say that the wave function is not the real state and that there is a real state but we don't know what it is.

Some category (1) interpretations say that. Others say there is no "real state" or that the concept of "real state" is meaningless.

What is the use of that?

What is the use of saying there is a "real state" if we don't know what it is and can't use it to make any predictions?

 

[Lynch101]

First, however reasonable this might seem to you, it's not valid as a matter of logic. It's perfectly possible, logically, for the particle to not have any "state" prior to a measurement result being observed. Indeed, this was the viewpoint (as far as I can tell) of Bohr and others in the quantum debates that took place in the 1920s and 1930s.

The point I am trying to make is similar to a point @Demystifier makes in the paper in his signature (emphasis is mine).

Intuitively, it says that the precise particle positions are not very much important to make measurable predictions. It is important that particles have some positions (for otherwise it is not clear how can a perceptible exist)

Here @Demystifier talks about "positions" but I'm suggesting we can talk in even broader terms, avoiding specifics like positions. Perhaps we can talk about the very broad category of "properties" and say that it must have some properties that enable it to interact with the measurement device. We don't need to be able to specify what exact properties it has, we can simply consider the alternative, that it has absolutely no properties whatsoever. If it has no properties whatsoever, then it simply would not interact with the measurement device and there would be no observable outcome, or "preceptible".

Second, suppose I agree for the sake of argument that your claim is true. How does it help in proving determinism? Saying that the particle was in some state prior to the measurement result, and that the particle caused the measurement result we observed, does not in any way require that it was impossible, before the result was observed, that some other result could have been observed. The latter claim is just you assuming that determinism is the only possible way for the particle to cause the measurement result, i.e., you arguing in a circle.

If we establish that the particle has some (or any) properties prior to the exposure event i.e. it was in some "state" prior to the event, then we can establish a causally deterministic chain from the effect back to the cause i.e. the device used to create the particle. Every step in this chain would be the result of the antecedent state, making the outcome deterministic.

To posit that any other outcome was possible would require either breaking the causal chain or positing some hidden feature that allows a deterministic chain of causality to be indeterministic.

Breaking the chain of causality carries its own implications. It would require, obviously, that a given state is not the result of an antecedent state, which would mean that a given state arises out of absolute nothing and is unconnected to anything in the Universe. This would mean that the experimental result is just a matter of the purest coincidence and just happens to occur when we do the experimental run, for no reason whatsoever.

Or, more simply, it would require the conclusion that it seemed like another outcome was possible because we were not in possession of all of the relevant information, something which standard QM says is the case anyway.

It means accepting that the quantum state captures everything we can know that is relevant to making predictions about future measurement results, since that is what standard QM uses the quantum state for.

It seems that there are two ways to interpret this.
1) Everything we can know does not represent all that there is i.e. there are hidden variables that we are unaware of. This incomplete information about the system is what gives rise to our probabilistic predictions.

This first way of interpreting it appears to fall into the category of deterministic interpretations (until such time as an indeterministic interpretation of this type is formulated).

The second way of interpreting it appears to be:
2) There is no additional information. Not that there is no additional information because it's not possible for us to know it, but that there is no additional information [period].

The third approach, 3) "shut up and calculate" doesn't seek to interpret the mathematical formalism at all, instead choosing to ignore it. Am I correct in saying that instrumentalists fall into categories 2) and 3)?

Note, btw, that "deterministic" is not the same as "local". Bohmian mechanics, for example, is highly nonlocal: the quantum potential is determined by the configuration of particles in the entire universe at an instant, not just at one location.

Thank you. I've come across statements like this before but I'm not certain that I understand it. I have an understanding of why this might be true in a deterministic universe, but I'm not certain it is the right understanding, not least because I'm unclear about the term "quantum potential".

It would make sense to me that, in a deterministic Universe, [what I imagine] the quantum potential [to be],would depend on the configuration of particles in the entire Universe, because all of those particles "arrive" at their locations by way of the same causally deterministic process that causes the particle in our experiment to arrive at its specific location.

 

[Lynch101]

@PeterDonis
Just to add to a point in the previous post:

To posit that any other outcome was possible would require either breaking the causal chain or positing some hidden feature that allows a deterministic chain of causality to be indeterministic.

Breaking the chain of causality is not possible, I don't think, if we grant that the quantum system has any properties whatsoever.

 

[PeterDonis]

Perhaps we can talk about the very broad category of "properties" and say that it must have some properties that enable it to interact with the measurement device.

This is not an argument for anything, it's just a definition of what you mean by "properties".

If we establish that the particle has some (or any) properties prior to the exposure event i.e. it was in some "state" prior to the event

Now you are assuming without proof or argument that "having properties" must mean "in some state". Suppose whatever "properties" are required to interact with the measurement device don't include a "state"? You have not excluded this possibility at all.

Similar remarks apply to your claims about a "causal chain"; suppose whatever "properties" are required to interact with the measurement device don't include a "deterministic causal chain", but allow either no "causal chain" at all, or one that is not deterministic? You have not excluded these possibilities either.

Basically, at this point I think you are just throwing undefined terms around based on your intuition, not making arguments based on commonly accepted premises.

Breaking the chain of causality carries its own implications. It would require, obviously, that a given state is not the result of an antecedent state, which would mean that a given state arises out of absolute nothing and is unconnected to anything in the Universe. This would mean that the experimental result is just a matter of the purest coincidence and just happens to occur when we do the experimental run, for no reason whatsoever.

It requires no such thing. First, you are assuming again, without proof or argument, that a "state" must be involved. Second, you are assuming that the only way to have "causality" at all is to have "causal chains". What if there are other ways?

It seems that there are two ways to interpret this.
1) Everything we can know does not represent all that there is i.e. there are hidden variables that we are unaware of. This incomplete information about the system is what gives rise to our probabilistic predictions.

This first way of interpreting it appears to fall into the category of deterministic interpretations (until such time as an indeterministic interpretation of this type is formulated).

The second way of interpreting it appears to be:
2) There is no additional information. Not that there is no additional information because it's not possible for us to know it, but that there is no additional information [period].

Your two ways are fine except that the first kind of interpretation does not have to be deterministic. We already have at least one example of an indeterministic interpretation of this type: the stochastic version of the Bohmian interpretation that @Demystifier referred to.

The third approach, 3) "shut up and calculate" doesn't seek to interpret the mathematical formalism at all, instead choosing to ignore it.

No, it doesn't ignore it; it uses it to make predictions and stops there. Many physicists feel that since the predictions are all we can test against experiment, going beyond that is not physics, but something else, like "philosophy", which they are happy to leave to philosophers.

Am I correct in saying that instrumentalists fall into categories 2) and 3)?

As far as I can tell, yes.

I'm unclear about the term "quantum potential".

It's a particular term in the Hamiltonian in the Bohmian interpretation, when that interpretation is done using a particular mathematical framework that is equivalent to the usual one in QM, but which rearranges the terms in a way that Bohmians prefer. It can be thought of as part of the potential energy.

It would make sense to me that, in a deterministic Universe, [what I imagine] the quantum potential [to be],would depend on the configuration of particles in the entire Universe, because all of those particles "arrive" at their locations by way of the same causally deterministic process that causes the particle in our experiment to arrive at its specific location.

It's simpler than that. The quantum potential is nonlocal for the same reason that the Coulomb potential between charged particles is nonlocal. The Coulomb potential depends on the positions of two particles (since it involves the distance between the particles, which is the difference in their positions). The quantum potential depends on the positions of all the particles in whatever quantum system you are describing; ultimately, on all the particles in the universe. Depending on more than one position is what makes the potential nonlocal.

 

[Lynch101]

Basically, at this point I think you are just throwing undefined terms around based on your intuition, not making arguments based on commonly accepted premises.

I am mindful of the fact that my use of terminology is probably imprecise, so I try to clarify my understanding as best I can using the language as I understand it. In doing so, I hope to portray my point in a manner that can be understood and hopefully refine my statements along the way. Discussions like this are a helpful part of that process as members such as yourself usually help to clarify where a term is being used incorrectly or a meaning is misunderstood - unfortunately, the benefit gleamed from discussions such as this tend to be very one-sided, in that I gain all the benefit of improving my understanding; even if it often appears to be at a glacial pace.

This is not an argument for anything, it's just a definition of what you mean by "properties".

Now you are assuming without proof or argument that "having properties" must mean "in some state". Suppose whatever "properties" are required to interact with the measurement device don't include a "state"? You have not excluded this possibility at all.

I am also mindful of the possibility that the way in which the term "state" is used, in the context of quantum mechanics, is not necessarily the same as how it was used by Laplace when he said

We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow.

This can possibly lead to us talking past each other, so I am keen to avoid that. That is why I am trying to find the correct term.

In @Demystifier's paper he talks about the property of "particle positions" and says,

It is important that particles have some positions (for otherwise it is not clear how can a perceptible exist)

Here, he is talking about a very specific property associated with particles and talks about the point I am trying to make, the idea that it is unclear how an observable, experimental outcome i.e. perceptible is possible if particles do not have specific properties, such as position.

The point I am trying to make is effectively the same, but I am suggesting we don't need to talk about specific properties, such as position, instead we can talk about properties simpliciter*; we can talk in the broadest possible terms about properties.

Instead of saying it is unclear how a perceptible can occur if particles don't have position, we can speak in even more general terms and question how measurements can happen if particles have absolutely no properties whatsoever?

If the use of the term "state" is an issue, we can replace it with the word "properties" and still get a clear statement about determinism, from Laplace's original statement:

We ought to regard the present [properties] of the universe as the effect of its antecedent [properties] and as the cause of the [properties] that [are] to follow.

*I'm not sure if I have used the term "simpliciter" correctly in this context.

Similar remarks apply to your claims about a "causal chain"; suppose whatever "properties" are required to interact with the measurement device don't include a "deterministic causal chain", but allow either no "causal chain" at all, or one that is not deterministic? You have not excluded these possibilities either.

This is essentially the point in question.

To me, it seems axiomatic that things in the Universe have properties - or at least one property - and that only things with properties can interact with other things that have properties. If something has no properties whatsoever, I cannot see how it can interact with anything else.

If we grant that the exposure event, on the SG plate, is caused by something with properties then we can establish that the properties of the Universe at the moment of the exposure event, is the effect of the antecedent properties of the Universe - I would be inclined to use the term "state" here instead of properties, but I don't think it is strictly necessary. That much allows us to establish a causally deterministic chain starting at the exposure event. It doesn't yet stretch back to the device used to prepare the "particle", but we can apply similar reasoning to get us there.

If the properties of the particle are the effect of its antecedent properties, then a causally deterministic chain is a given.

If the the properties of the particle are not the effect of its antecedent properties, then it means that the particle can have properties and then have absolutely no properties and then acquire properties again, ad infinitum. Or it can start without any properties and have the reverse happen, having absolutely none, then acquiring some, then losing them again, ad infinitum. This in itself would require an explanation.

The other alternative, one which appears to have been favoured by some instrumentalists, is the idea that the act of measurement is what bestows the particle with its properties, implying that it had absolutely no properties prior to measurement.

That just brings us back to our question of how something with absolutely no properties whatsoever, can interact with something that does have properties? A more fundamental question would be, how can something without any properties whatsoever be said to be in, or part of, the Universe in the first place?

As soon as we grant that things in the Universe have properties and that the exposure event was caused by something with some property - any property whatsoever - it seems difficult to avoid the conclusion of casual determinism, that the present properties/state of the universe as the effect of its antecedent properties/state.

Your two ways are fine except that the first kind of interpretation does not have to be deterministic. We already have at least one example of an indeterministic interpretation of this type: the stochastic version of the Bohmian interpretation that @Demystifier referred to.

I must check that out, thanks Peter.

No, it doesn't ignore it; it uses it to make predictions and stops there. Many physicists feel that since the predictions are all we can test against experiment, going beyond that is not physics, but something else, like "philosophy", which they are happy to leave to philosophers.

I didn't mean it in the pejorative sense, I simply meant it as you outline above. They ignore it insofar as they don't engage in what they feel amounts to nothing more than philosophy. It's a perfectly reasonable position if one is not interested in the fundamental questions.

It's a particular term in the Hamiltonian in the Bohmian interpretation, when that interpretation is done using a particular mathematical framework that is equivalent to the usual one in QM, but which rearranges the terms in a way that Bohmians prefer. It can be thought of as part of the potential energy.

Thank you. Clarifications like this really help to break down the conceptual barrier I sometimes face when reading papers and articles on the subject.

It's simpler than that. The quantum potential is nonlocal for the same reason that the Coulomb potential between charged particles is nonlocal. The Coulomb potential depends on the positions of two particles (since it involves the distance between the particles, which is the difference in their positions). The quantum potential depends on the positions of all the particles in whatever quantum system you are describing; ultimately, on all the particles in the universe. Depending on more than one position is what makes the potential nonlocal.

So, non-locality is not really that "spooky" at all but rather quite pedestrian and dare I say, intuitive?

 

[PeterDonis]

Instead of saying it is unclear how a perceptible can occur if particles don't have position, we can speak in even more general terms and question how measurements can happen if particles have absolutely no properties whatsoever

Asking this question is one thing. Proponents of interpretations where it is an issue might be able to answer it. There is quite a lot of literature on the various interpretations, and that's where you should look for the answer.

However, asking the question does not in itself mean there is only one possible answer, let alone that that answer is the one you favor. Asking the question, in itself, doesn't even guarantee that the question has an answer.

I don't think that is something we are going to resolve here. I think the best we can do is to say that, ok, this is a question you have, that you'll need to spend time with the literature on QM interpretations to investigate.

To me, it seems axiomatic that things in the Universe have properties

Ok, fine. That seems axiomatic to you. We get that.

And it's not an argument for anything. It's just a statement of your state of mind. As I've already pointed out before.

Again, I don't think this is something we are going to resolve here.

So, non-locality is not really that "spooky" at all but rather quite pedestrian and dare I say, intuitive?

Only if you think violations of the Bell inequalities are "pedestrian" and "intuitive". Bear in mind that we've only been talking about the simple cases so far: single measurements on single particles. We haven't even gotten into the additional complexities that arise when you start talking about measurements on multiple particles that are entangled.

 

[Lynch101]

Asking this question is one thing. Proponents of interpretations where it is an issue might be able to answer it. There is quite a lot of literature on the various interpretations, and that's where you should look for the answer.

However, asking the question does not in itself mean there is only one possible answer, let alone that that answer is the one you favor. Asking the question, in itself, doesn't even guarantee that the question has an answer.

I don't think that is something we are going to resolve here. I think the best we can do is to say that, ok, this is a question you have, that you'll need to spend time with the literature on QM interpretations to investigate.
Ok, fine. That seems axiomatic to you. We get that.

And it's not an argument for anything. It's just a statement of your state of mind. As I've already pointed out before.

Again, I don't think this is something we are going to resolve here.

That's fair enough. I appreciate your taking the time to discuss it this far. Would you have any suggestions for papers/articles/books that might address this point? I am perhaps over-reliant on platforms such as this because I find that I struggle to clearly interpret the technical language in papers, specifically, so I often need analogies and explanations to help develop a better understanding.

That is why I am genuinely appreciative of sites like this and members such as yourself who take the time to engage in these discussions. I know it might seem like you are banging your head against a brick wall at times, but on the other side, I know that my understanding of physical theories is miles ahead of where it was because of discussions like this.

Only if you think violations of the Bell inequalities are "pedestrian" and "intuitive". Bear in mind that we've only been talking about the simple cases so far: single measurements on single particles. We haven't even gotten into the additional complexities that arise when you start talking about measurements on multiple particles that are entangled.

A clear example of the Dunning-Kruger effect here, I would say

I do find your previous explanation to be a lot more intuitive than the original impression I had of non-locality, though.

 

[PeterDonis]

I do find your previous explanation to be a lot more intuitive than the original impression I had of non-locality, though.

My explanation was only of why the quantum potential in Bohmian mechanics is nonlocal. That in turn explains why, even though Bohmian mechanics is a hidden variable theory (the positions of the particles are hidden variables that determine the outcomes of experiments), it can still predict violations of the Bell inequalities: because it's a nonlocal hidden variable theory, and Bell's theorem only says that local hidden variable theories can't predict violations of the Bell inequalities.

 

[Lord Jestocost]

Here, he is talking about a very specific property associated with particles and talks about the point I am trying to make, the idea that it is unclear how an observable, experimental outcome i.e. perceptible is possible if particles do not have specific properties, such as position.

The fundamental “stuff” underlying our world and which we seem to “perceive” (the experience of observation) cannot be characterized in terms of classical notions like “particles” or “waves”. And more important:

“It is not true that the underlying stuff sometimes behaves like a wave and sometimes like a particle. It always behaves like itself, but we sometimes choose to measure one property, sometimes another. When we choose to measure momentum, we find momentum clicks. When we choose to measure position, we find position clicks.” (John Marburger)

 

[Lynch101]

My explanation was only of why the quantum potential in Bohmian mechanics is nonlocal. That in turn explains why, even though Bohmian mechanics is a hidden variable theory (the positions of the particles are hidden variables that determine the outcomes of experiments), it can still predict violations of the Bell inequalities: because it's a nonlocal hidden variable theory, and Bell's theorem only says that local hidden variable theories can't predict violations of the Bell inequalities.

Ah, I see. Thank you for that clarification.

 

[Lynch101]

The fundamental “stuff” underlying our world and which we seem to “perceive” (the experience of observation) cannot be characterized in terms of classical notions like “particles” or “waves”. And more important:

“It is not true that the underlying stuff sometimes behaves like a wave and sometimes like a particle. It always behaves like itself, but we sometimes choose to measure one property, sometimes another. When we choose to measure momentum, we find momentum clicks. When we choose to measure position, we find position clicks.” (John Marburger)

Thank you LJ. This seems to echo sentiments like, the map is not the territory and the Zen Buddhist saying that "the finger pointing to the moon is not the moon".

 

[Lynch101]

@Demystifier would you have any suggestions for resources (books/articles/papers/videos) that address the point you raise in your paper, namely (emphasis is mine obviously):

Intuitively, it says that the precise particle positions are not very much important to make measurable predictions. It is important that particles have some positions (for otherwise it is not clear how can a perceptible exist) .

 

[Demystifier]

@Demystifier would you have any suggestions for resources (books/articles/papers/videos) that address the point you raise in your paper, namely (emphasis is mine obviously):

Try "Against Realism" by Norsen:
https://arxiv.org/abs/quant-ph/0607057

 

[Lynch101]

Try "Against Realism" by Norsen:
https://arxiv.org/abs/quant-ph/0607057

Thank you.

 

[PeterDonis]

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