Undergrad Understanding the Fundamental Difference in Interpretations of QM

[Lynch101]

You're not "probing the features of instrumentalist interpretations". You're just describing the actual process of measurement, which is the same for all QM interpretations, and putting your preferred interpretation on it.

It is probably fair to say that I am not "probing the features of instrumentalist interpretations", and equally so that I am describing the actual process of measurement, but I think when we probe the actual process of measurement we are - I would say - forced down the road of determinism - which I will try to outline below.

Sure, but that doesn't mean it was deterministically caused by the particle.
...
The lack of predictability could be because the fundamental process involved is truly indeterministic--it is literally impossible, even in principle, to know which way the result will come out until it happens;

I think how we analyse the notion of determinism is a key factor here. We often tend to think about it in terms of predictability, moving from cause to effect, and saying that given the state of the system at time t, there can only be one possible outcome. In practice, of course, we can't always make such predictions with a probability of 1.

Another way to think about it is going the other way, from cause to effect, and establishing a causally deterministic chain. In this sense we think about states of the world being caused by antecedent events. It is when we apply this to quantum experiments that, I believe, we are forced down (or back up) the road of determinism.

the result is truly not determined by the previous state.

It is this idea that the result is not truly determined by the previous state which I can't make sense of. To my mind, an event which is not caused by antecedent events happens completely spontaneously, for no reason whatsoever, and requires that something (the event) appears out of absolutely nothing, completely unconnected to anything else in the Universe.

If we take the exposure on the SG plate, if the exposure event is not caused by an antecedent event, then the exposure happens completely spontaneously and which would seem to mean that it was only a matter of coincidence that it occurs during the experiment.

If we say that the exposure was caused by the particle, then the particle interacting with the SG plate is the antecedent event. This is where things seem to get murky, because there is very little we can say about the particle, in terms of position and momentum, prior to its interaction with the plate. I fell, however, that we can talk about it in the broadest possible terms saying that the particle (or whatever it is that interacts with the SG plate) is in the Universe and probably within the region of space where we are conducting the experiment.

In these very broad terms we could, I think, establish a causally deterministic chain from the effect - the exposure event - back to the cause - the device we use to prepare the particle.

Or the lack of predictability could be only because we do not have a sufficiently exact knowledge of the initial conditions:

That we do not have sufficient knowledge of initial conditions is a given from the outset isn't it? Would the Heisenberg uncertainty principle not necessitate this?

 

[Lynch101]

Here is Mermin’s take on QBism. https://arxiv.org/abs/1809.01639 It’s an essay accessible to the general reader.

Thanks Ruta. I'll certainly give this a read.

 

[PeterDonis]

We often tend to think about it in terms of predictability, moving from cause to effect

Another way to think about it is going the other way, from cause to effect, and establishing a causally deterministic chain.

Determinism as it is usually understood implies both of these.

It is this idea that the result is not truly determined by the previous state which I can't make sense of.

Yes, obviously. But this is not an argument for us being "forced" to determinism. It is simply a statement that you can't make sense of the alternative. So what? The fact that you can't make sense of it is not an argument for anything. It's just a statement of your state of mind.

an event which is not caused by antecedent events

I did not say the result of the S-G measurement was not caused by an antecedent event. In fact I explicitly said the opposite:

that in no way prevents me from saying that, once the result is observed (a spot on the detector in either the "up" location or the "down" location), that result was caused by the particle.

You are simply conflating "caused by an antecedent event" with "determined by the previous state", which is not valid; it is possible for the first to be true while the second is not true. The fact that you are unable to conceive of such a possibility does not mean the possibility does not exist.

That we do not have sufficient knowledge of initial conditions is a given from the outset isn't it?

It's a given if we accept the limitations of standard QM. But a deterministic interpretation of QM like the Bohmian interpretation is perfectly consistent with the view that, at some time in the future, we might figure out how to gain more information about the initial conditions than standard QM allows us to. Or, to put it another way, that standard QM is not the final fundamental theory, so its limitations are not fundamental limitations.

 

[Demystifier]

What would you say the biggest criticisms of Bohmian mechanics would be?

There is no simple extension to relativistic QFT. There are various ways to make that extension (even though many wrongly claim that there isn't any), but neither of them is simple.

 

[martinbn]

That it doesn't describe the physically real state of the individual quantum system. On this kind of interpretation, if I have a device that prepares qubits in the quantum state "spin-z up", that does not mean that state describes the physically real state of each individual qubit. The state only allows me to make claims about the statistics of the results I will get if I measure a stream of qubits from the device with Stern-Gerlach measurements oriented in various directions.

What I don't understand is the following. If it doesn't describe the physically real state of the system, there must be a difference between the two, and yet in terms of predictions this tool only state gives the best possible predictions. Why isn't there an experiment where the results don't match the predictions? After all if the real state is different then the results must differ too.

Um, by not being more than that according to that particular interpretation?

Basically, it seems like you are simply denying that interpretations in category (1) are even possible. That does not seem to me to be a viable position. You might think such interpretations are wrong, but I don't see how you can say they're impossible.

I know that there are interpretations of this type. I just don't understand them to the point where it seems that they are impossible.

No, ensemble is not the only type of interpretation that is not in category (2). @Demystifier gave QBism as another example. At least some versions of Copenhagen are also not in category (2) (I say "some versions" because the term "Copenhagen" doesn't really name one particular interpretation).

This is related to my misunderstanding of (1), because to me it seems that they all belong to (2).

 

[Demystifier]

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

I give a detailed answer to this question in the Bohmian case, in my "Bohmian mechanics for instrumentalists".

 

[martinbn]

I give a detailed answer to this question in the Bohmian case, in my "Bohmian mechanics for instrumentalists".

Can tell me where, or do I have to read the whole thing again?

 

[Demystifier]

Can tell me where, or do I have to read the whole thing again?

The whole paper should be read for a closed picture, but the central part is Sec. 4.4, which cannot be completely understood without understanding at least Secs. 3.2 and 4.1.

 

[Lynch101]

Determinism as it is usually understood implies both of these.

Yes, obviously. But this is not an argument for us being "forced" to determinism. It is simply a statement that you can't make sense of the alternative. So what? The fact that you can't make sense of it is not an argument for anything. It's just a statement of your state of mind.

I agree, we usually take it to imply both, but the predictability criterion is not always possible in practice; as in, it is not always possible to predict the exact outcome, perhaps due to a lack of information. I think, however, if we reason backwards from the effect i.e. the exposure event in a quantum experiment, we are left with two choices, only one of which, I feel makes sense. Not just intuitively (but because, to me at least) the consequences of the other are such that they cannot work, as they require events to occur in a Universe without being in contact with anything else in the Universe.

Hopefully, I will be able to articulate this more clearly below.

I did not say the result of the S-G measurement was not caused by an antecedent event. In fact I explicitly said the opposite:

You are simply conflating "caused by an antecedent event" with "determined by the previous state", which is not valid; it is possible for the first to be true while the second is not true. The fact that you are unable to conceive of such a possibility does not mean the possibility does not exist.

My use of terminology here might be getting in the way of the point I am trying to make. The event in question is the SG exposure. The question I am trying to get at is, what caused the SG exposure? As you have said, the particle causes the exposure. The question then becomes whether the particle was in any state previous to the exposure event. The key thing here, as I see it, is that we do not need to define exactly what state the particle was in prior to the event, we only need to establish that it was in some undefined state or, in the broadest possible terms, any state whatsoever. This I believe we can do.

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.

If we can establish that very broad condition, it seems - to me - sufficient to establish a causally deterministic chain from the outcome of the experiment back to the preparation device.

It's a given if we accept the limitations of standard QM. But a deterministic interpretation of QM like the Bohmian interpretation is perfectly consistent with the view that, at some time in the future, we might figure out how to gain more information about the initial conditions than standard QM allows us to. Or, to put it another way, that standard QM is not the final fundamental theory, so its limitations are not fundamental limitations.

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. 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? Would this, therefore imply determinism?

The alternatives you mentioned:

The lack of predictability could be because the fundamental process involved is truly indeterministic...Or the lack of predictability could be only because we do not have a sufficiently exact knowledge of the initial conditions

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?

 

[martinbn]

The whole paper should be read for a closed picture, but the central part is Sec. 4.4, which cannot be completely understood without understanding at least Secs. 3.2 and 4.1.

So, what is the state in BM? Is it $\psi$ and all $Q_i$ together? But the $Q_i$ are not ralevant to any prediction!

Let me give you an example to illustrate how I understand the situation in BM, and you can tell me if it is right.

In classical mechanics of a single particle the state is a six-tuple of numbers (or functions of $t$ if you prefer) say $(x, y, z, p_x, p_y, p_z)$. The observables are functions of those. The evolution is given by certain equations.

Now I can modify that by saying that the six-tuple $(x, y, z, p_x, p_y, p_z)$ is just a tool for calculating predictions and the real physical state of the particle is described by $(x, y, z, p_x, p_y, p_z, a, b, c)$, where $a=xy+z^2$ and something like that for the other new parameters. I can add equations as well. The predictions will be identical although the state of the system is different. That of course is nothing new, the so called real state is just a different way of representing the just a tool state. My guess is that this doesn't count as an example of interpretation of type (1) from the first post.

Another way i can modify the original theory is to add independent parameters $a, b, c$ to the state but posit the the observables are functions only of $(x, y, z, p_x, p_y, p_z)$. Same conclusions here.

In both examples I can add as much metaphysics about the real state, but the truth is that I haven't done anything essentially different.

My guess is the BM is not just a variation of my examples, but it is hard for me to see what it is.

 

[Demystifier]

My guess is the BM is not just a variation of my examples, but it is hard for me to see what it is.

Your guess is right. I don't know how to explain it to you, in a way you would find comprehensible. Some people get it, some don't.

 

[martinbn]

Your guess is right. I don't know how to explain it to you, in a way you would find comprehensible. Some people get it, some don't.

Ok, fine, I can live with my limitations, but can you at least answer my question. What is the state of a quantum system in BM?

 

[Demystifier]

Ok, fine, I can live with my limitations, but can you at least answer my question. What is the state of a quantum system in BM?

The state (at a given time) is the positions of all particles. Some would say that the wave function is also a part of the state, but in my opinion it's misleading in the same sense it would be misleading to say that the Hamilton-Jacobi function $S(x,t)$ is a part of the state in classical mechanics.

 

[Demystifier]

So, what is the state in BM? Is it ψ and all Qi together? But the Qi are not ralevant to any prediction!

If you just knew all $Q_i$ at all times, without knowing $\psi$, then you could make all the predictions.

 

[martinbn]

The state (at a given time) is the positions of all particles. Some would say that the wave function is also a part of the state, but in my opinion it's misleading in the same sense it would be misleading to say that the Hamilton-Jacobi function $S(x,t)$ is a part of the state in classical mechanics.

That seems incomplete. Given the positions of all the particles at a given time is not enough initial data for the evolution problem. Also the observables are not functions (maps, operator valued maps/distributions ect) on the phase space. That seems like unusual use of terminology.

Let me ask you this then. In the examples above, do you consider those modifications to be interpretations of type (1) or not, and why?

 

[martinbn]

If you just knew all $Q_i$ at all times, without knowing $\psi$, then you could make all the predictions.

Hm, how? In your article you need the $\psi$ for the Born rule.

 

[Demystifier]

Hm, how? In your article you need the $\psi$ for the Born rule.

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.

 

[Demystifier]

That seems incomplete. Given the positions of all the particles at a given time is not enough initial data for the evolution problem. Also the observables are not functions (maps, operator valued maps/distributions ect) on the phase space. That seems like unusual use of terminology.

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

 

[Demystifier]

Let me ask you this then. In the examples above, do you consider those modifications to be interpretations of type (1) or not, and why?

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.

 

[Lynch101]

There is no simple extension to relativistic QFT. There are various ways to make that extension (even though many wrongly claim that there isn't any), but neither of them is simple.

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.

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)

The key thing here, as I see it, is that we do not need to define exactly what state the particle was in prior to the event, we only need to establish that it was in some undefined state or, in the broadest possible terms, any state whatsoever. This I believe we can do.

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.

 

[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.