I QFT made Bohmian mechanics a non-starter: missed opportunities?

[gentzen]

You are absolutely right, that's a description and Bohmians are not satisfied with it. The reason why they are not satisfied is because this description is mathematically incomplete, in the sense that it does not contain a mathematical definition of measurement.

So it turns out that I am definitively not a Bohmian. But I find it instructive nevertheless to try to understand the mathematical and physical properties of BM.

 

[Structure seeker]

What we can mathematically describe

Presupposing what we can and cannot mathematically describe is exactly the problem. One thing the CI doesn't describe is what happens at wavefunction collapse. Then it is like a gravity model that describes everything except black holes. Bohmians want to understand wavefunction collapse as well.

It's just that IMO the idea that a particle is hiding somewhere in the wave before measurement reduces the geniously devised quantum field waves to background influence rather than these waves being the actual form of the particle before measurement. I'd like these geniously devised fields to be accessible rather than an ethereal background

 

[Demystifier]

The wave function evolves according to all interactions of the system described by it, including its interaction with the measurement device. At this moment the time evolution is of course not described any longer by the wave function but by the corresponding reduced density matrix since now the system is an open system, and the time evolution is rather described by master equations than unitary time evolution.

But the open system is a part of the larger closed system, and the full closed system should be described by the wave function.

 

[Demystifier]

So it turns out that I am definitively not a Bohmian. But I find it instructive nevertheless to try to understand the mathematical and physical properties of BM.

Fair enough. What's your favored interpretation of QM?

 

[Demystifier]

Science is about the objectively observable facts about Nature

No, that's just your wishful thinking, to use the favored phrase of @martinbn. In reality, science is much more than that. It's an empirical fact that scientific journals publish a lot of research which are not only about observable facts. After all, the Bohm's paper is published in one such journal (Physical Review). By insisting that science is only about observable facts you deny observable facts.

 

[martinbn]

No, that's just your wishful thinking, to use the favored phrase of @martinbn. In reality, science is much more than that. It's an empirical fact that scientific journals publish a lot of research which are not only about observable facts. After all, the Bohm's paper is published in one such journal (Physical Review). By insisting that science is only about observable facts you deny observable facts.

What is your definition of science? What is published in journals?

 

[Demystifier]

What is your definition of science? What is published in journals?

Science is any research the results of which is publishable in scientific journals. To avoid circularity, scientific journal is any journal that the society proclaims to be so.

 

[martinbn]

Science is any research the results of which is publishable in scientific journals. To avoid circularity, scientific journal is any journal that the society proclaims to be so.

That is too restrictive, what about the times before journals. It is also too generous, there is a lot of cr@p that gets published.

 

[Demystifier]

That is too restrictive, what about the times before journals.

My definition refers to present times.

It is also too generous, there is a lot of cr@p that gets published.

Crap science is also science.

But I admit that my definition of science is not perfect. Do you have a better one?

 

[Demystifier]

How is a mathematical description of nature possible "in absence of measurement"? What we can mathematically describe are quantified phenomena, i.e., phenomena which can be described by numerical data, and the mapping of properties of natural phenomena to numbers involves an operational definition of observables, i.e., some measurement procedure.

The gauge potential is mathematical, it is even expressed in physical units, and yet the gauge potential is not measurable.

 

[gentzen]

Fair enough. What's your favored interpretation of QM?

I guess in the end I am still an instrumentalist, just like I was in Jan '17 when I reacted with huge anger against Steven Weinberg's "The Trouble With Quantum Mechanics" and his unfair characterization of instrumentalism.

I don't remember exactly when I learned about the Hanbury Brown effect (from Feynman's QED book), at least I know that in Oct '19 I tried to recall the name of that effect after "I talked with a colleague about interpretation of mathematics and physics, and I claimed that mathematics must secretly always be interpreted instrumentalistically. He said that this would be the same for physics, so I tried to remember the name of that effect"

which shows that my preferred instrumentalistic interpretation of QM is insufficient, and that there is some reality of the wavefunction with observable effects (a systematic pattern instead of mere noise) deep below the predictions of my instrumentalistic interpretation.

Maybe I could fix this specific defect, maybe not. But in the end it is also part of the instrumentalistic philosophy that I don't care too much that my intuitions and "interpretation miniatures" are not fully consistent, and that it may be impossible to make them fully consistent, even if I tried.

After the death of Steven Weinberg, I learned more about his motivation(s) for his attack against instrumentalism, and that he even had the audacity to compute "relaxation times" for specific scenarios in his QM textbook, and suggest that them being much bigger than the age of the universe had consequences like ... well, I don't want to dive into that sort of discussion here.
Let me just say that he cared deeper about that stuff than I do.

 

[Demystifier]

I guess in the end I am still an instrumentalist

So I guess you have seen my "Bohmian mechanics for instrumentalists".

"interpretation miniatures"

I guess you have seen that one too.

 

[vanhees71]

The gauge potential is mathematical, it is even expressed in physical units, and yet the gauge potential is not measurable.

So?

 

[Demystifier]

So?

So it answers your question "How is a mathematical description of nature possible in absence of measurement?".

 

[vanhees71]

No, it doesn't. The physical meaning of the electromagnetic field is given operationally, i.e., by giving a relation between what's described by the mathematics to quantitatively observable phenomena. The electromagnetic potentials themselves are not directly observable. They are not even uniquely determined by a given physical phenomenon but only "modulo arbitrary gauge transformations". They can be used, of course, to derive observables like the electromagnetic field.

 

[Morbert]

@vanhees71 everyone presumably agrees that physical theories have to ultimately make contact with measurement. But this does not mean measurement must have a foundational significance, with no ontic conceptualization preceding it.

 

[vanhees71]

What ontic conceptualization do you have in mind?

 

[Morbert]

What ontic conceptualization do you have in mind?

E.g. Instead of interpreting a quantum theory as a theory of measurement outcomes. We might first interpret it as a theory of possible events and their likelihoods, and then identify measurement outcomes with correlations between certain events.

 

[vanhees71]

Sure, you can use different words for observables, and call them events. What does this change?

 

[Morbert]

Not all events would be measurement events though. We would give significance to the an event like a microscopic system's angular momentum obtaining some value, even if no measurement is made.

As for what changes, my opinion is that probably not much changes. Instrumentalism is a defensible position for a quantum physicist even if it is not for a paleontologist. As a foundational project, it is probably the most complete.

At the same time it's also my opinion that it doesn't fully capture the modes of thinking quantum chemists and applied quantum physicists use in their day-to-day. Consistent histories seems to better capture convention here, even if the number of applied physicists who identify as CH proponents is approximately 0.

 

[Demystifier]

a microscopic system's angular momentum obtaining some value, even if no measurement is made.

Consistent histories seems to better capture convention here

But consistent history depends on the choice of framework. We cannot say that the microscopic angular momentum obtains some value, period. Instead, we say that the microscopic angular momentum obtains some value in one framework, and does not obtain any value in another framework. Different frameworks, in my understanding, are just different modes of thinking. In this sense the CH interpretation is not one interpretation, but a large class of interpretations. Each framework can be thought of as another interpretation. The frameworks do not exist out there in nature itself, without physicists who apply them as their way of thinking. Does it make sense to you?

 

[Demystifier]

Sure, you can use different words for observables, and call them events. What does this change?

Are there microscopic events, which do not involve any macroscopic apparatuses or macroscopic environments? Is it possible to have an event in a system with only two particles, completely isolated from the environment?

 

[Demystifier]

This is more belief than what you addmitted initially.

Only a little bit more. Bohmians assume that a mathematical description of nature in the absence of measurement is possible (as I said before), and they also assume that measurement is not primitive (i.e. they assume that measurement can be explained in terms of something more fundamental).

 

[vanhees71]

Are there microscopic events, which do not involve any macroscopic apparatuses or macroscopic environments? Is it possible to have an event in a system with only two particles, completely isolated from the environment?

You can detect single particles/quanta, but of course it involves "macroscopic" equipment. The detection events are due to local interactions of the quanta with a small part of the macroscopic device, and the rest of it you can describe as "environment".

 

[martinbn]

Only a little bit more. Bohmians assume that a mathematical description of nature in the absence of measurement is possible (as I said before), and they also assume that measurement is not primitive (i.e. they assume that measurement can be explained in terms of something more fundamental).

And how does it follow from this that there are point particles, trajectories, preferred frame and so on?

 

[vanhees71]

Hm, are there point particles, trajectories or even a preferred frame? For me from Faraday on, physics teaches us that at the most fundamental level Nature is described by (local) quantum field theories rather than Newtonian point-particle mechanics. That we prefer point-particle pictures so much is most probably, because any systematic physics teaching starts with Newtonian point-particle mechanics, because it's the conceptually most simple and most "intuitive" picture. Also it has an amazing realm of applicability.

Then usually, we don't treat the trouble of the point-particle picture in much detail. At best you mention in passing that the radiation-reaction problem in classical point-particle electrodynamics (Lorentz's classical "electron theory") is plagued by inconsistencies and problems. The best one can do at this level is to use the 1st order perturbative implementation of radiation reaction/self-energies, aka the Landau-Lifhitz approximation of the Lorentz-Abraham-Dirac equation. I think a the classical level that's the best you can do, and it's not too bad in comparison with continuum-mechanical treatments (magneto-hydrodynamics, transport theory), which are much better suited, because more in the spirit of continuum/field descriptions, which seem to be more appropriate already at the classical level of relativsitic physics than the point-particle paradigm.

Finally, the best we have is local relativistic QFT, and even that it's not completely satisfactory from a mathematical point of view ("axiomatic QFT" in 1+3 dimensions hasn't delivered much more than a rigorous description of free quantum fields) as well as a physics point of view since it still lacks a satisfactory quantum description of the gravitational field/aka spacetime geometrodynamics.

 

[Demystifier]

You can detect single particles/quanta, but of course it involves "macroscopic" equipment. The detection events are due to local interactions of the quanta with a small part of the macroscopic device, and the rest of it you can describe as "environment".

I guess it means that the answer to my question is no. There are no events if the small part above is isolated from the rest of the environment. Right?

 

[vanhees71]

Yes, or do you have a counter example?

 

[Demystifier]

And how does it follow from this that there are point particles, trajectories, preferred frame and so on?

It doesn't follow. The point particles, trajectories, preferred frames and so on are just the simplest model that Bohmians found, which satisfies the mentioned assumptions. And of course, the notion of simplicity is subjective. If you have another model, which seems simpler to you, I would be truly happy to learn about that model.

 

[Demystifier]

Yes, or do you have a counter example?

I don't, I just wanted to be sure that I understood what you mean by "event". It's now clear that event, in your understanding of that word, cannot be purely microscopic. By contrast, @Morbert had a different meaning of the word "event" in mind, as something that can be purely microscopic.