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

[martinbn]

Translation symmetry, rotation symmetry, the usual discrete symmetries, ...

Is that true? In what sense are they present? Consider a spherically symmetric source and detector. In QM this is truly symmetric. In BM the particle has a trajectory from the source to a point on the sphere of the detector. That is not spherically symmetric. It only looks like it because the trajectory is undetectable and over a large number of trials the results have agree with QM, so one says that the initial data is symmetric.

 

[martinbn]

You both seem to have a very strong tendency to "reify" mathematical concepts, or at least the tendency to belief that bohmians would "reify" their mathematical concepts.
N David Mermin is very skeptical of that tendency, especially with respect to MWI proponents.

Am I right that you accuse bohmians of having metaphysical prejudices, because you belief that they mistake their mathematical concept for the true physical reality?

Yes, but not in this discussion.

 

[martinbn]

The only thing that Bohmians a priori believe, without actual evidence, is that nature can be described mathematically even in situations when it is not measured.

You say this, but it is not true. Because QM has that property and yet bohmians are unhappy with it.

Everything else, like nonlocality, trajectories, violation of certain symmetries, preferred frame, etc. are a posteriori properties of specific mathematical models that satisfy the a priori belief above in a way compatible with observations. There are Lorentz-covariant Bohm-like models without a preferred frame, there are even local Bohm-like models, but such models are less popular because they seem more contrived and complicated.

You have given references for those, but so far I haven't seen one that does anything more than wishful thinking.

 

[Demystifier]

In BM the particle has a trajectory from the source to a point on the sphere of the detector. That is not spherically symmetric.

In physics symmetry refers to the laws (equations of motion), not to particular solutions.

 

[Demystifier]

You say this, but it is not true. Because QM has that property and yet bohmians are unhappy with it.

No, standard QM does not describe nature in the absence of measurement. Neither in a probabilistic sense (because the Born rule in arbitrary basis is only valid when an observable is measured, it cannot be universally valid due to the contextuality theorems), nor in a deterministic sense (Schrodinger equation is deterministic, but standard QM insists that nature is not deterministic).

Indeed, adherents of standard QM often emphasize that a physical theory should not describe nature in the absence of measurement, because any such description would necessarily be metaphysical. This fact (that standard QM does not describe nature in the absence of measurement) they see as a strength of standard QM, not as its weakness.

 

[Demystifier]

You have given references for those, but so far I haven't seen one that does anything more than wishful thinking.

Can you be more precise? What exactly is missing in these models to be more than "wishful thinking"?

 

[vanhees71]

Define "true". It is true in the same sense in which it is true that EM potential in the Coulomb gauge is not Lorentz invariant. Those who can't think of Bohmian trajectories as something "real" may still think of them as something analogous to gauge potentials.

They are not observable, and so are the electromagnetic potentials, no matter in which gauge you work. That's a mathematical fact, independent of any interpretation.

 

[Demystifier]

They are not observable, and so are the electromagnetic potentials, no matter in which gauge you work. That's a mathematical fact, independent of any interpretation.

You mean empirical fact, not "mathematical". And yes, Bohmians of course agree that trajectories are not observable. But the point is that even unobservable things have a role in theoretical physics, gauge potentials are an obvious example. Once we agree that unobservable things can have some role in physics, we can discuss what exactly is the role of the trajectories.

 

[Quantum Waver]

Indeed, adherents of standard QM often emphasize that a physical theory should not describe nature in the absence of measurement, because any such description would necessarily be metaphysical.

Isn't the point of measurement to figure out what nature is doing all the time? What makes a measurement special such that nature would behave differently? The standard CI inspired approach is deeply dissatisfying. Is there another scientific field that has this approach to measurement, other than psychology or sociology?

 

[vanhees71]

You mean empirical fact, not "mathematical". And yes, Bohmians of course agree that trajectories are not observable. But the point is that even unobservable things have a role in theoretical physics, gauge potentials are an obvious example. Once we agree that unobservable things can have some role in physics, we can discuss what exactly is the role of the trajectories.

No it's a mathematical fact, because gauge invariance means redundance, i.e., the same physical situation is described by different gauge potentials, and thus the gauge potential cannot be local observables already in the classical theory. At the QFT level in addition the gauge potentials do not obey the microcausality constraint and thus again cannot represent local observables. At least for these mathematical reasons the assumption that the em. potentials would represent observables, makes no sense. That's independent of any interpretation.

 

[Demystifier]

Isn't the point of measurement to figure out what nature is doing all the time? What makes a measurement special such that nature would behave differently? The standard CI inspired approach is deeply dissatisfying. Is there another scientific field that has this approach to measurement, other than psychology or sociology?

Those are indeed excellent questions! Most scientists would like to know what nature is doing all the time. However, the measurement by itself, obviously, cannot say what is nature doing in the absence of measurement. This is why science also has theories. The theories are guided by experiments, but they are really extrapolations from experiments. It is the scientific theories (or at least some of them) that tell us something about what is nature doing all the time.

 

[vanhees71]

This doesn't make sense. Science is about the objectively observable facts about Nature not some fictitious behavior of Nature, when it's "not observed". You can claim anything about this. To verify it, you have to observe it, and then it's not "not observed" any longer. Of course, philosophers love such oddities ;-)).

 

[gentzen]

Isn't the point of measurement to figure out what nature is doing all the time? What makes a measurement special such that nature would behave differently?

Neither measurements nor nature is special. What is special is that you have a theory whose predictions consists mostly of statistics. Like I explained to vanhees71 earlier in this thread:

I guess your basic problem is that you don't understand why you have to first fix a context before applying statistics. Many scientists in the "softer sciences" ran into the practical consequences of this misunderstanding. The currently favored solution is to preregister (i.e. fix a context for) studies that would risk to get into trouble with this.

In the end, you need stuff which can be reliably described and reproduced. At least, if the results of your experiment consists mostly of statistics.

 

[vanhees71]

Of course the context of the statistics is given by the measurement device used to measure some observable(s). That's what I always try to make clear: Nature doesn't consist of a rigged Hilbert space and self-adjoint operators!

 

[martinbn]

No, standard QM does not describe nature in the absence of measurement. Neither in a probabilistic sense (because the Born rule in arbitrary basis is only valid when an observable is measured, it cannot be universally valid due to the contextuality theorems), nor in a deterministic sense (Schrodinger equation is deterministic, but standard QM insists that nature is not deterministic).

Indeed, adherents of standard QM often emphasize that a physical theory should not describe nature in the absence of measurement, because any such description would necessarily be metaphysical. This fact (that standard QM does not describe nature in the absence of measurement) they see as a strength of standard QM, not as its weakness.

Come on! Standard QM says that each QM system is described mathematically by a wave function, which in the absence of measurement evolves according to the Schrodinger equation.

 

[martinbn]

Can you be more precise? What exactly is missing in these models to be more than "wishful thinking"?

I can, but you would have to give a specific paper.

 

[martinbn]

In physics symmetry refers to the laws (equations of motion), not to particular solutions.

But BM includes equations for the trajectories, right?

 

[gentzen]

But BM includes equations for the trajectories, right?

Violation of symmetry typically leads to violation of associated conservation laws. I strongly doubt that you will find violation of angular momentum convervation in BM. But for the symmetries that BM actually violates, you also find violations of some exact conservation laws, so that you are left with conservation only on average.

 

[Demystifier]

Come on! Standard QM says that each QM system is described mathematically by a wave function, which in the absence of measurement evolves according to the Schrodinger equation.

And what happens with the wave function at the time of measurement? Collapse? But collapse is non-local, and yet standard QM insists that Nature is local. Do you see a contradiction?

 

[Demystifier]

But BM includes equations for the trajectories, right?

Yes, and these equations have symmetries that I mentioned.

 

[Quantum Waver]

This doesn't make sense. Science is about the objectively observable facts about Nature not some fictitious behavior of Nature, when it's "not observed". You can claim anything about this. To verify it, you have to observe it, and then it's not "not observed" any longer. Of course, philosophers love such oddities ;-)).

Why would the observable facts of nature change just because we stopped observing? Shouldn't they remain the same, given all the observed regularities not just on Earth but throughout the cosmos? There's all sorts of things happening all the time that go unobserved, but we have a good scientific understanding for how stars are fusing hydrogen into helium far away or ants are building ant hills deep in the woods. It all hangs together. You slam the breaks and feel the inertia of all the mass in the universe acting on you.

 

[gentzen]

I can, but you would have to give a specific paper.

I can lookup the specific paper (or papers) which caused me to start this thread:

Even classically, we talk about the electromagnetic field instead of saying that a particle here interacts with a particle there. So the question should rather be whether we favor photons over configurations of an electromagnetic field to just keep things local.

I read in "Do We Really Understand Quantum Mechanics?" by Franck Laloë that a version of Bohmian mechanics using field configuration trajectories for the electromagnetic field and particle trajectories for Fermions (with stochastic creation and annihilation events) works actually quite well. One of the main drawbacks of Bohmian mechanics (including this version) is its non-locality, so the answer to the adjusted question about keeping things local could actually be yes, in a certain sense.

Maybe you know those anyway, so I don't need to select some specific paper, or decide which was the paper with the initial proposal, and which were papers only ment for people like me that "sometimes need to update their knowledge" before they can continue a discussion.

 

[Quantum Waver]

Of course the context of the statistics is given by the measurement device used to measure some observable(s). That's what I always try to make clear: Nature doesn't consist of a rigged Hilbert space and self-adjoint operators!

Then what does nature consist of? What is the mathematics describing and how is it predictive?

 

[gentzen]

Why would the observable facts of nature change just because we stopped observing?

Are you sure that you are not arguing against a strawman here? Einstein accused his opponents of that mindset, but I have yet to see somebody who really takes that position.

 

[gentzen]

Then what does nature consist of?

What sort of answer do you expect? An answer like Descartes dualism, that you can "prove" that you yourself exists, and then hope that somehing similar can be proved about the "external world" too?
Maybe have a look at my answer
https://philosophy.stackexchange.co...rgo-sum-that-we-can-be-certain-of/14461#14461
and especially try to think about what I wanted to communicate with that answer.

 

[Quantum Waver]

Are you sure that you are not arguing against a strawman here? Einstein accused his opponents of that mindset, but I have yet to see somebody who really takes that position.

I may not be phrasing it generously. What I'm arguing against is that the wave equation is just a predictive tool which doesn't describe what's happening to the unobserved system, because science can't say what happens in between observations. I disagree, because science offers explanations for all sorts of things happening around us which may go unobserved, like the chemistry in our bodies or solar radiation.

There are anti-realists who argue that unobservables are theoretical fictions used to make models work, and models are predictive of experimental results, not descriptive of nature.

 

[gentzen]

because science can't say what happens in between observations. I disagree, because science offers explanations for all sorts of things happening around us which may go unobserved.

I agree that QM also makes prediction which are not purely statistical. But those are not predictions about a naive "external world" either. So we test QM mostly with experiments that can only be interpreted statistically, but we deduce from this that also the non-statistical predictions of QM are reliable.

 

[Quantum Waver]

What sort of answer do you expect?

A physics answer like MWI or BM. One that's realist about the wave equation. I'm not really following your ontological commitment answer. I would say science is a guide to ontological commitments, within the limits of the scientific method.

 

[martinbn]

And what happens with the wave function at the time of measurement? Collapse? But collapse is non-local, and yet standard QM insists that Nature is local. Do you see a contradiction?

Why are you changing the subject! Is standard textbook QM a mathematical description or not?

 

[gentzen]

A physics answer like MWI or BM. One that's realist about the wave equation. I'm not really following your ontological commitment answer. I would say science is a guide to ontological commitments, within the limits of the scientific method.

I disagree with the naive conclusion of 'cogito ergo sum' as a proposition proved beyond doubt in some absolute sense, or otherwise of exceptional status. I suggested that it may just be a normal case of ontological commitment. (I later gave another more charitable answer that does grant some special status to it.)

With respect to Descartes, his dualism was a huge part of the revolution in mathematics and the sciences more general. But in the end, his dualism is probably not correct, and at some point it started to limit further scientific progress.

 

[gentzen]

Why are you changing the subject! Is standard textbook QM a mathematical description or not?

Some textbooks like Griffiths teach a literal collapse interpretation which is indeed non-local. It is true that he explains his (pedagocial) reasons for doing so in the book itself, but it still means that the simplest "calculation first" version of (nonrelativistic) QM is non-local.

You have to work much harder to avoid that straightforward non-locality, and risk that only very few people will understand what you are trying to communicate.

 

[martinbn]

Some textbooks like Griffiths teach a literal collapse interpretation which is indeed non-local. It is true that he explains his (pedagocial) reasons for doing so in the book itself, but it still means that the simplest "calculation first" version of (nonrelativistic) QM is non-local.

You have to work much harder to avoid that straightforward non-locality, and risk that only very few people will understand what you are trying to communicate.

But we are not diacussing locality! We are disagreeing on wether QM is a mathimatical discription of nature.

 

[gentzen]

But we are not diacussing locality! We are disagreeing on wether QM is a mathimatical discription of nature.

I agree that nonrelativistic QM is a mathematical description of many important features of nature, which goes far beyond classical physics. I don't want to deny QFT a similar status, but I am not expert enough in that subject to judge for myself.

 

[Structure seeker]

This doesn't make sense. Science is about the objectively observable facts about Nature not some fictitious behavior of Nature, when it's "not observed". You can claim anything about this. To verify it, you have to observe it, and then it's not "not observed" any longer.

Nothing is objectively observable by humans, it is only independently of researcher, time and place observable. And claims aren't proven by verification, they are made reasonable by passing multiple falsification possibilities again and again.

 

[vanhees71]

And what happens with the wave function at the time of measurement? Collapse? But collapse is non-local, and yet standard QM insists that Nature is local. Do you see a contradiction?

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. For me the best description is via the Kadanoff-Baym equations, but there are many more equations, using other and different approximation schemes like the Lindblad equations (with a lot of trouble like the lack of the correct thermalization in the long-time limit) describing a Markov approximation etc. etc.