Understanding Bohmian Mechanics of Instrumentalists

[Demystifier]

Just looking more into this now. Is Brownian motion a representative example of a stochastic process, that would be analogous in this case?

Yes.

 

[Elias1960]

Is that interpretation of QFT, with particles being created and destroyed, necessary to maintain a fundamentally indeterministic interpretation? To me the alternative would seem to be deterministic, where particles are just a different state of an underlying field, with particles "emerging" from and "returning" to that field.

Particles being something completely irrelevant, like phonons, the "particles of sound", is the other possibility. In this case, the fundamental thing is the field, and it cannot be created or destroyed. But because of the interaction with other fields, it can change its own part of energy, and the quantum energy levels are simply the "numbers" of those "particles", so that such pseudo-particles can be created or destroyed.

If the field changes in a deterministic or in a random way is a completely different question, there is dBB where it is deterministic, and other realistic interpretations (Nelson, Caticha) where it is some variant of Brownian motion.

 

[user30]

I have heard previously in relation to deterministic interpretations of QM, that they do not give rise to the same predictions.

Then you heard wrong. Hence it's not meaningful to speak of deterministic vs indeterministic interpretations.

"Attempts to explain these conundrums fall into two broad categories, Weinberg said: “instrumentalist” and “realist.” Instrumentalists contend that the wave function is merely a tool for calculating the results of experiments — there’s no way to know anything more about reality. Devotees of the realist approach contend that the wave function is a real thing out in the world, evolving over time, and at a fundamental level it is responsible for what’s really happening"

https://www.sciencenews.org/blog/context/why-quantum-mechanics-might-need-overhaul

 

[user30]

For an example, the explanation many worlds gives for quantum mechanics has very little in common with the Bohm interpretation, yet they are both called "deterministic". Their explanations are in many ways polar opposites of each other.

 

[Lynch101]

Yes.

If the field changes in a deterministic or in a random way is a completely different question, there is dBB where it is deterministic, and other realistic interpretations (Nelson, Caticha) where it is some variant of Brownian motion.

Is Brownian motion not attributable to a fundamentally deterministic process though? With the apparent randomness being due to a lack of information on our part, but the underlying particle collisions being, themselves, deterministic?

Particles being something completely irrelevant, like phonons, the "particles of sound", is the other possibility. In this case, the fundamental thing is the field, and it cannot be created or destroyed. But because of the interaction with other fields, it can change its own part of energy, and the quantum energy levels are simply the "numbers" of those "particles", so that such pseudo-particles can be created or destroyed.

This is more the picture I have in mind. To put a very, very crude analogy on it, I would imagine a field to be like a sheet spread out in space (or the field could be viewed as space itself) with, to stick with the crude analogy, ripples or waves in the sheet interacting with other fields and giving rise to what we measure as "particles". This would still be a fundamentally deterministic picture, however, with the indeterminism being a result of a lack of information on our part.

 

[Lynch101]

Then you heard wrong. Hence it's not meaningful to speak of deterministic vs indeterministic interpretations.

"Attempts to explain these conundrums fall into two broad categories, Weinberg said: “instrumentalist” and “realist.” Instrumentalists contend that the wave function is merely a tool for calculating the results of experiments — there’s no way to know anything more about reality. Devotees of the realist approach contend that the wave function is a real thing out in the world, evolving over time, and at a fundamental level it is responsible for what’s really happening"

https://www.sciencenews.org/blog/context/why-quantum-mechanics-might-need-overhaul

Thanks User30. I think there is a third category with relation to the above - "realists", "instrumentalists", and "anti-realists".

Strict instrumentalists are those that advocate a "shut up and calculate" approach to QM and so, technically, instrumentalism isn't a foundational interpretation of QM. Realists, as you say, tend to take the position that the wave function is a real thing out in the world, evolving over time, and at a fundamental level it is responsible for what’s really happening. Those who prefer deterministic interpretations of QM tend to be realists, from what I can gather. I think, but I am open to correction, that deterministic interpretations necessitate realism. @Demystifier has suggested that it is possible to have a real yet indeterministic interpretation also.

Anti-realists then, tend to adopt an intepretation that closely resembles instrumentalism. The anti-realist position differs from instrumentalism in that, instead of adopting a "shut up and calculate" approach, the anti-realist makes definitive claims about the underlying ontology. Given that fundamentally deterministic interpretations necessitate realism, anti-realist interpretations eschew determinsim and adopt a position which says that the universe is fundamentally indeterministic.

It's a seemingly subtle difference, but instrumentalists say that the mathematics is just a tool for calculating predictions. Some might say that it doesn't give us any information about the underling ontology. While the anti-realist would say that the mathematics does tell us something about the underlying ontology and it tells us that it is fundamentally indeterministic.

Essentially, either the universe is fundamentally deterministic and real* or it is fundamentally indeterministic and not real, or there is a third, as of yet undiscovered, paradigm for how the Universe is.

The anti-realist position seems somewhat problematic to me because it would seem to require an explanation for how a system can have absolutely no properties whatsoever and still interact with measurement devices. A more fundamental question would be how a system with absolutely no properties whatsoever can even be said to be a part of the Universe in the first place.

*As I mentiond, @Demystifier has suggested that an indeterministic, yet real, interpretation is possible. I have asked a further question on that, in this thread.

 

[PeterDonis]

Is Brownian motion not attributable to a fundamentally deterministic process though? With the apparent randomness being due to a lack of information on our part, but the underlying particle collisions being, themselves, deterministic?

The usual statistical mechanics explanation of Brownian motion is consistent with a deterministic underlying dynamics (and in fact it was originally formulated, by Einstein, using statistical mechanics based on deterministic Newtonian mechanics). However, it is equally compatible with an indeterministic underlying dynamics. So we can't tell from Brownian motion whether the underlying dynamics is deterministic or not.

 

[Lynch101]

The usual statistical mechanics explanation of Brownian motion is consistent with a deterministic underlying dynamics (and in fact it was originally formulated, by Einstein, using statistical mechanics based on deterministic Newtonian mechanics). However, it is equally compatible with an indeterministic underlying dynamics. So we can't tell from Brownian motion whether the underlying dynamics is deterministic or not.

Thanks for that Peter.

I think an underlying deterministic dynamics is probably much more intuitive than an underlying indeterministic dynamics. I would imagine a fundamentally deterministic process would involve particles (or perhaps just "things") colliding with each other or influencing each other in some way, which then gives rise to a seemingly "random walk".

EDIT: Essentially, the current state of a system would be causally connected to the antecedent state, as per Laplace's definition.

How would a fundamentally indeterministic process work?

 

[mattt]

How would a fundamentally indeterministic process work?

https://en.m.wikipedia.org/wiki/Stochastic_process

 

[Lynch101]

https://en.m.wikipedia.org/wiki/Stochastic_process

Thanks mattt. I've had a look at that page previously and I'll have another read of it, but I wasn't able to glean an explanation of how a physical process can be truly indeterminate, but that could be down to my level of understanding of the information in the page.

If determinism is that case where the current state of a system is causally connected to its antecedent state, then a truly indeterminate or stochastic system would seem to require that the current state of the system be causally disconnected from its antecedent state. Just thinking about it now, this would almost seem to necessitate the total absence of causality with events occurring without reference to a prior cause.

In the above sense of the terms, a fundamentally deterministic process could appear stochastic as a result of a lack of information, but a truly stochastic process would seem to require the total absence of causality.

 

[PeterDonis]

a truly indeterminate or stochastic system would seem to require that the current state of the system be causally disconnected from its antecedent state

No, it wouldn't. Causality could still determine the possible results of a particular stochastic "jump" (such as the result of a quantum measurement). Saying that the result is not determined is not at all the same as saying the result is totally disconnected from everything that has gone before.

 

[user30]

Thanks User30. I think there is a third category with relation to the above - "realists", "instrumentalists", and "anti-realists".

Strict instrumentalists are those that advocate a "shut up and calculate" approach to QM and so, technically, instrumentalism isn't a foundational interpretation of QM. Realists, as you say, tend to take the position that the wave function is a real thing out in the world, evolving over time, and at a fundamental level it is responsible for what’s really happening. Those who prefer deterministic interpretations of QM tend to be realists, from what I can gather. I think, but I am open to correction, that deterministic interpretations necessitate realism. @Demystifier has suggested that it is possible to have a real yet indeterministic interpretation also.

Anti-realists then, tend to adopt an intepretation that closely resembles instrumentalism. The anti-realist position differs from instrumentalism in that, instead of adopting a "shut up and calculate" approach, the anti-realist makes definitive claims about the underlying ontology. Given that fundamentally deterministic interpretations necessitate realism, anti-realist interpretations eschew determinsim and adopt a position which says that the universe is fundamentally indeterministic.

It's a seemingly subtle difference, but instrumentalists say that the mathematics is just a tool for calculating predictions. Some might say that it doesn't give us any information about the underling ontology. While the anti-realist would say that the mathematics does tell us something about the underlying ontology and it tells us that it is fundamentally indeterministic.

Essentially, either the universe is fundamentally deterministic and real* or it is fundamentally indeterministic and not real, or there is a third, as of yet undiscovered, paradigm for how the Universe is.

The anti-realist position seems somewhat problematic to me because it would seem to require an explanation for how a system can have absolutely no properties whatsoever and still interact with measurement devices. A more fundamental question would be how a system with absolutely no properties whatsoever can even be said to be a part of the Universe in the first place.

*As I mentiond, @Demystifier has suggested that an indeterministic, yet real, interpretation is possible. I have asked a further question on that, in this thread.

I'm not so sure they that they do view the universe as indeterministic. Every physicist that I know of contends that the laws of physics are deterministic, and rely on it to do meaningful physics. It's hard to envision a functional alternative. You will note that Bell himself viewed inanimate matter as deterministic in his superdeterminism quote.

The QM correlations in action at a distance are very hard, if not impossible, to reconcile with a stochastic model, because stochastic models contain noise and unknown variables by definition.

The problem is that they can't be explained by a deterministic model alone either because they lack discernable causality.

 

[user30]

EDIT: Essentially, the current state of a system would be causally connected to the antecedent state, as per Laplace's definition.

That is one version of determinism, not the only one. Determinism has different definitions depending on the context. In computer science it means getting the same output for the same input. In mathematics it's equations with one consistent solution, always. In physics it's that each state in a given physical world was always a fact and could never have been differently if you rewind the tape with the same initial conditions.

 

[user30]

Here is a very good account of how the Bohm interpretation explains action at a distance. As we established in the superdeterminism thread, determinism has no answer to why there are non causal correlations.
Even in a timeless universe with no events unfolding, it would still be a complete mystery why things are correlated that show no causal connection.

https://www.quora.com/How-does-the-pilot-wave-theory-explain-spooky-action-at-a-distance

"The important point is how any of this works, not in detail, but in principle.

And the “in principle” bit is fairly simple. The “mystery” in an EPR or Bell test of entanglement is how the statistics of a particle in place A manages to be correlated with free choices of measurements in place B at a rate higher than is possible by common cause alone.

In the pilot wave picture, you have a particle — which responds locally, by riding on a wave — which can be influenced non-locally. So, it comes as no surprise that the explanation in de Broglie-Bohm terms is that the choice of measurement axis by the experimenter at B affects the wave there, and that this effect is transmitted non-locally (and faster than light) to the part of the wave at A, where the particle at A can be guided by it."

 

[user30]

So the easiest way to account for quantum correlations would be too reinstate casuality. The problem is that any such causality would according to Bells theorem be non local. Hence why Bohm mechanics is non local.

MWI interpretation tries to explain it as a function of branching worlds but I have not quite understood the connection and how that would work in practise.

 

[user30]

No, it wouldn't. Causality could still determine the possible results of a particular stochastic "jump" (such as the result of a quantum measurement). Saying that the result is not determined is not at all the same as saying the result is totally disconnected from everything that has gone before.

But a QM measurement does not cause a "jump" anymore than when you try to find your lost keys and based on past events, you deduce the probability of finding it at certain place. Compared to when you look for your keys and you know where you put them.

 

[PeterDonis]

a QM measurement does not cause a "jump"

In a stochastic underlying model, it might.

 

[user30]

In a stochastic underlying model, it might.

How does that same model account for QM correlations?

 

[PeterDonis]

How does that same model account for QM correlations?

I said "a" model, not "the" model. Different models would do this in different ways. For example, the following two models are both stochastic, but are very different in how they arrive at standard QM in an appropriate approximation:

https://en.wikipedia.org/wiki/Ghirardi–Rimini–Weber_theory

https://en.wikipedia.org/wiki/Stochastic_quantum_mechanics

 

[Lynch101]

I said "a" model, not "the" model. Different models would do this in different ways. For example, the following two models are both stochastic, but are very different in how they arrive at standard QM in an appropriate approximation:

https://en.wikipedia.org/wiki/Ghirardi–Rimini–Weber_theory

https://en.wikipedia.org/wiki/Stochastic_quantum_mechanics

Do these models involve "jumps"?

 

[Lynch101]

I said "a" model, not "the" model. Different models would do this in different ways. For example, the following two models are both stochastic, but are very different in how they arrive at standard QM in an appropriate approximation:

https://en.wikipedia.org/wiki/Ghirardi–Rimini–Weber_theory

https://en.wikipedia.org/wiki/Stochastic_quantum_mechanics

Just having a read of these now. In the GRW page it mentions "each particle of a system described by the multi-particle wave function $|\psi \rangle$ independently undergoes a spontaneous localisation process (or jump)"

Is a "jump" the same thing as the "collapse of the wave function"?

 

[PeterDonis]

Do these models involve "jumps"?

In the sense of discontinuous changes in the quantum state, yes.

 

[PeterDonis]

Is a "jump" the same thing as the "collapse of the wave function"?

In the GRW model, yes, the "spontaneous localization process" is the model's version of collapse of the wave function. So in this model, the collapse is a real physical process.

 

[user30]

I said "a" model, not "the" model. Different models would do this in different ways. For example, the following two models are both stochastic, but are very different in how they arrive at standard QM in an appropriate approximation:

https://en.wikipedia.org/wiki/Ghirardi–Rimini–Weber_theory

https://en.wikipedia.org/wiki/Stochastic_quantum_mechanics

It does not say how those models account for action at a distance.

 

[PeterDonis]

It does not say how those models account for action at a distance.

As far as I know, mathematically they do it the same way standard QM does; their predictions don't differ from standard QM in that respect. But I have not spent a lot of time digging into the details. You would have to do that to figure out in detail how they arrive at predictions for things like correlations in Bell-type experiments.

As a matter of interpretation, I don't know that these models resolve the open issues. But deterministic models don't either.

 

[user30]

E

As far as I know, mathematically they do it the same way standard QM does; their predictions don't differ from standard QM in that respect. But I have not spent a lot of time digging into the details. You would have to do that to figure out in detail how they arrive at predictions for things like correlations in Bell-type experiments.

As a matter of interpretation, I don't know that these models resolve the open issues. But deterministic models don't either.

The math isn't the question, it's the conceptual inconsistency.

It should also be noted

"The GRW theory differs from standard quantum mechanics for the dynamical principles according to which the wave function evolves[10][11]."

So perhaps not appropriate to discuss in this forum since it is not a main stream view.

 

[PeterDonis]

The math isn't the question, it's the conceptual inconsistency.

What conceptual inconsistency?

it is not a main stream view

There isn't really a "mainstream view" as far as QM interpretation is concerned. That's why we have this forum separate from the plain QM one, to allow for the fact that discussions of QM interpretations are different in that respect.

That said, the GRW model is not really a QM interpretation, it's an alternative theory, since it does make different predictions from standard QM in some respects (for example, it predicts that there should be limits on how long, even in principle, quantum coherence can be maintained in a system, whereas standard QM says there is no limit to that in principle, the only limits are practical). But AFAIK it does not make different predictions about things like EPR correlations and violations of the Bell inequalities.

 

[user30]

What conceptual inconsistency?
There isn't really a "mainstream view" as far as QM interpretation is concerned.

According to the quote there is. Quantum jumps are exclusively in stochastic models, and not part of the standard view, and is thus an obscure model of quantum mechanics that is yet to gain traction.

 

[PeterDonis]

Quantum jumps are exclusively in stochastic models, and not part of the standard view

I get that, but I don't get how it's a conceptual inconsistency. The "standard view" is just the basic math of QM, which takes no position at all on whether the quantum state is "real" or whether the collapse that happens in the math when you make a measurement corresponds to a "real" process or not. So the "standard" view is consistent conceptually with a model like the GRW model.

It is true that the GRW model is not consistent with interpretations that do not treat the quantum state as "real", but that is a property of those particular interpretations of QM, not of QM itself.

 

[user30]

I get that, but I don't get how it's a conceptual inconsistency.

I was referring to quantum correlations only, since these indicate the very opposite of a stochastic world, and instead complete reliability and repeatability.

 

[PeterDonis]

I was referring to quantum correlations only, since these indicate the very opposite of a stochastic world

No, they don't. They just indicate that whatever stochastic processes might be involved have to be able to produce such correlations.

and instead complete reliability and repeatability.

Quantum correlations indicate no such thing, since the results of the experiments involved are not completely reliable and repeatable. The correlations can be repeatably observed, within experimental error, but the individual results of the individual measurements are not repeatable. If Alice and Bob are each measuring one of a pair of entangled photons, and their measurement angles differ by, say, 30 degrees, the individual measurement results, and whether they are the same or opposite, are not repeatable. Only the correlations shown in the statistics of a large number of repetitions are.

 

[Lynch101]

In the GRW model, yes, the "spontaneous localization process" is the model's version of collapse of the wave function. So in this model, the collapse is a real physical process.

Is it in anyway accurate to think that the wave function, in this case, represents a real physical thing, as in a field or a particle? I'm thinking of a particle or field spread out over some area but then spontaneously localising to a single location before it interacts with the measurement device.

 

[PeterDonis]

Is it in anyway accurate to think that the wave function, in this case, represents a real physical thing, as in a field or a particle?

In the GRW model, yes.

 

[Lynch101]

In the GRW model, yes.

Thanks Peter.

Would it then be fair to amend the previous statement and say: interpretations that are truly indeterminate/ stochastic AND not based in realism, would seem to require that the current state of the system be causally disconnected from its antecedent state. This would seem to necessitate the total absence of causality with events occurring without reference to a prior cause?

 

[PeterDonis]

interpretations that are truly indeterminate/ stochastic AND not based in realism

Are there any?