Is Bohmian mechanics a convenient ontological overcommitment?

[gentzen]

Collapse theories (like GRW) only need extremely few collapses to reproduce macroscopic observations, and actually must limit themselves to extremely view collapses to avoid being experimentally distinguishable with current technology from standard QM. Being too generous with world splitting in MWI is also a (not uncommon) mistake, as Lev Vaidman indicates with words like "has been justly criticized".

Therefore, the fact that Bohmian mechanics can get away with having a precise trajectory for every particle fascinates me. When I first became familiar with Bohmian mechanics, it was rather the opposite: I found it confusing why Bohmian mechanics doesn't need trajectories for inner degrees of freedom of the particles like spin. Today, I rather wonder whether Bohmian mechanics could not easily get away with ommiting some of its precise trajectories, for example all trajectories for photons. This is what I mean by my question whether Bohmian mechanics a convenient ontological overcommitment.

However, the reason why I ask this question now is that Demystifier's paper Solipsistic hidden variables also seems to raise this question: what happens if many of the precise trajectories are omitted from Bohmian mechanics? But the paper seems mostly concerned about what can be gained by omitting trajectories, for example in terms of reducing the non-locality of the theory. I would rather like to know what is lost by omitting (a subset of the) trajectories, and whether anything important is lost at all, i.e. whether is it just a matter of convenience that every particle has a trajectory?

 

[Demystifier]

You can omit some trajectories, e.g. those of photons as you suggested, without loosing much. But if you omit all trajectories, then you have to explain why measurements have outcomes at all.

 

[vanhees71]

Photons cannot have trajectories. They don't even have a position observable. I don't think that we have a convincing Bohmian reinterpretation of local relativistic QFT yet. For non-relativistic QT in the first-quantization formulation BM is a consistent theory without much additional merit compared to standard statistically interpreted QT. At least I've not seen any experiment that depicts the Bohmian trajectories of slow massive particles, e.g., in a double-slit experiment or something equivalent.

 

[Demystifier]

Photons cannot have trajectories.

http://materias.df.uba.ar/labo5Aa2012c2/files/2012/10/Weak-measurement.pdf

 

[gentzen]

You can omit some trajectories, e.g. those of photons as you suggested, without loosing much.

Do I just lose some convenience and elegance, or also something more substantial. For example, the trajectories in BM are continuous (probably even infinitely differentiable) and deterministic. (Those properties would be hard to recovered, if you start with the consistent histories framework, and then try to complete it by position based refinements.) And there is a canonical probability distribution on the particle positions in BM, plus typicality arguments why we are allowed to assume that the actual particle positions are consistent with that distribution, if the system is sufficiently big. (Those properties are absent in some other "deterministic non-local hidden variable" interpretations.)

But if you omit all trajectories, then you have to explain why measurements have outcomes at all.

My purpose with this question is not to omit all trajectories, or mutilate BM in other ways. It is rather the opposite: how much would I mutilate BM, if I just tried to omit a subset of the trajectories. The example with the photons was just to make the question more concrete.

 

[WernerQH]

I would rather like to know what is lost by omitting trajectories, and whether anything important is lost at all, i.e. whether is it just a matter of convenience that every particle has a trajectory?

Strange question. What is lost by dropping superfluous metaphysical baggage? Trajectories are (occasionally useful) classical fiction, but they are also a burden. How can you make sense of the idea that electrons are identical, when each has its own trajectory? Nature would always "know" which electron interacted with which photon. But there are no such facts of the matter. Nature uses a different kind of bookkeeping.

 

[vanhees71]

http://materias.df.uba.ar/labo5Aa2012c2/files/2012/10/Weak-measurement.pdf

As expected they measure the position of photon-detection events. There is no photon-position observable you can measure.

 

[gentzen]

Strange question. What is lost by dropping superfluous metaphysical baggage?

Well, the mathematical model might become more complicated. From my perspective, analyzing fictional mathematical models can provide useful insight:

I believe in a principle of 'conservation of difficulty'. This allows me to believe that mathematics stays useful, even if it would be fictional. I believe that often the main difficulties of a real world problem will still be present in a fictional mathematical model. Therefore analyzing that model and understanding the difficulties in that context will provide useful insight into the real world problem.
... physicists ... trust in 'conservation of difficulty' is often less pronounced. As a consequence, physics fictionalism has a hard time (...). So instead of accepting Bohmian mechanics as a useful fictional model with huge potential for analyzing various difficulties of quantum mechanics (and extracting insights about the real world from it), it was initially dismissed for being too obviously fictional.

How can you make sense of the idea that electrons are identical, when each has its own trajectory?

Well, BM provides you a model were the QM predictions are still satisfied, despite this paradox. So it provides you the opportunity to analyse how that is possible, in one specific fictional model. (I am a bit less keen on creating or destroying particles, because the original BM proposal doesn't include those effects.)

 

[Demystifier]

It is rather the opposite: how much would I mutilate BM, if I just tried to omit a subset of the trajectories. The example with the photons was just to make the question more concrete.

If you do that, it's still (a version of) Bohmian mechanics.

 

[Demystifier]

As expected they measure the position of photon-detection events. There is no photon-position observable you can measure.

So what? Are you saying that what they measure is not a trajectory?

 

[WernerQH]

Well, the mathematical model might become more complicated.

Wouldn't you call Minkowski's formulation of electrodynamics simpler than Maxwell's? Of course, the actual calculations remain essentially the same.

 

[gentzen]

Wouldn't you call Minkowski's formulation of electrodynamics simpler than Maxwell's? Of course, the actual calculations remain essentially the same.

I have now edited the question to make it even clearer that I was only talking about omitting a subset of the trajectories, not of omitting all trajectories. (Even Demystifier himself also included that interpretation of my question in his answer, so apparently it was not clear enough from context.)

The point of having the trajectories in the model is that it allows you to get rid of the concept of "objective randomness" in your model. So you reduced mysterious "quantum randomness" to familiar "classical randomness". But interestingly, your model became quite non-local by doing so. So by "conservation of difficulty", you might start to wonder whether this connection between non-locality and randomness is also important for the real world problem. And answering that question is what Bell did.

 

[vanhees71]

So what? Are you saying that what they measure is not a trajectory?

How can something have a trajectory which doesn't even have a position observable? To think about photons as little particle-like bullets is always wrong!

 

[Demystifier]

How can something have a trajectory which doesn't even have a position observable? To think about photons as little particle-like bullets is always wrong!

So no experimental result could refute your theoretical argument that photon can't have a trajectory? Then your theoretical argument is not falsifiable in the Popper sense, and hence it's not scientific.

 

[vanhees71]

If cannot measure something it's simply not defined. In this sense it's not scientific indeed, and that's my argument all the time.

 

[Demystifier]

If cannot measure something it's simply not defined.

But they measured something. And that something is even theoretically defined. It's just not defined the way you are used to.

 

[WernerQH]

It's just another interference pattern. But if you are so inclined, you see photon trajectories. It's a kind of Rohrschach test. ;-)

 

[Sunil]

Photons cannot have trajectories. They don't even have a position observable. I don't think that we have a convincing Bohmian reinterpretation of local relativistic QFT yet.

For fields a field ontology is more appropriate. The standard reference is

Bohm.D., Hiley, B.J., Kaloyerou, P.N. (1987). An ontological basis for the quantum theory, Phys. Reports 144(6), 321-375.

For a field ontology, the photons are similar to phonons in condensed matter theory, and nobody cares if they have position operators or not. What should have a trajectory is the field itself, $u(x)$, and its trajectory with be $u(x,t)$.

For non-relativistic QT in the first-quantization formulation BM is a consistent theory without much additional merit compared to standard statistically interpreted QT.

Except that it solves all the conceptual problems like the measurement problem.

 

[Sunil]

To the original question:

What is lost is some simplicity. What is gained is that it will not matter to you if you don't know how to define the ontology. Say, if you have no idea how to handle fermion fields, because you don't like the particle picture but are influenced too much by the idea that fermion fields themselves are something completely non-classical, you simply don't have to care, the fields where it is already known what to do are sufficient for this variant of Bohmian theory. All what you need is that the measurement devices are visible enough if you can see only those fields where you know how to define the ontology.

So I think this ugly variant is only useful as such an excuse, but has no value as an ultimate theory.

 

[Sunil]

Wouldn't you call Minkowski's formulation of electrodynamics simpler than Maxwell's? Of course, the actual calculations remain essentially the same.

The 4-dimensional denotations are a little bit simpler, computations are essentially the same, conceptually it is more complicate because you have to understand how that 4-dimensional formalism translates into what we observe in our 3-dimensional world.

 

[Demystifier]

How can you make sense of the idea that electrons are identical, when each has its own trajectory?

The idea that "electrons are identical" really means (in Bohmian interpretation) that the pilot wave does not distinguish particles, not that the particles are identical by themselves.

 

[WernerQH]

The idea that "electrons are identical" really means (in Bohmian interpretation) that the pilot wave does not distinguish particles, not that the particles are identical by themselves.

Of course you can have the personal belief that electrons are distinguishable, that you could label them uniquely, and that these labels would have an objective meaning. But in view of the fact that the wave functions are constructed as determinants (where any dependence on these labels is carefully removed), it strikes me as a strangely uneconomical description.

 

[Demystifier]

it strikes me as a strangely uneconomical description.

Do you have any idea why Bohmian mechanics is studied in the first place? Certainly not for economic reasons.

 

[WernerQH]

Do you have any idea why Bohmian mechanics is studied in the first place?

Of course. The plethora of interpretations of QM is a strong indication that we lack true understanding. And I share the view that it is yet to be found. I cannot accept Bohr's philosophy that QM cannot be formulated without the complementary concepts of classical physics, which has somehow rendered fundamental physics as transcendental, beyond human understanding.

Bohmian mechanics, in my opinion, is not radical enough. Its adherents are too strongly tied to the classical concepts of particles and fields.

 

[Sunil]

Bohmian mechanics, in my opinion, is not radical enough. Its adherents are too strongly tied to the classical concepts of particles and fields.

I think they are not strong enough ties to classical concepts. Classical concepts should never be given up without strong enough evidence.

 

[vanhees71]

Of course. The plethora of interpretations of QM is a strong indication that we lack true understanding. And I share the view that it is yet to be found. I cannot accept Bohr's philosophy that QM cannot be formulated without the complementary concepts of classical physics, which has somehow rendered fundamental physics as transcendental, beyond human understanding.

Bohmian mechanics, in my opinion, is not radical enough. Its adherents are too strongly tied to the classical concepts of particles and fields.

All you need from classical physics for the physics of QT are the spacetime symmetries of Newtonian or special relativistic physics and the general structure of QT as defined on (rigged) Hilbert space and the observable algebras, whose concrete structure follows from the spacetime symmetries. There's nothing transcentdental but just a "symbolism of atomistic measurements", as Schwinger puts it.

That many people after 100 years of modern QT still have a problem to accept that Nature is behaving fundamentally random is not a problem of physics but rather of psychology and philosophy of these individual people. The natural sciences are not to please your epistemological prejudices but to figure out how Nature behaves as objectively and quantitatively observed.

 

[WernerQH]

The natural sciences are not to please your epistemological prejudices but to figure out how Nature behaves as objectively and quantitatively observed.

I fully agree. I also believe that Nature behaves fundamentally random, although "randomness" is something that can never be strictly defined. But probability theory and statistics are invaluable.

What Q(F)T is still lacking is a convincing ontology. We disagree what it is about. I think "measurements" cannot be the answer. The formal structure is here to stay, but as physicists we should not only consider the relations between the basic concepts of the theory, but how they relate to the real world.

 

[Demystifier]

Bohmian mechanics, in my opinion, is not radical enough.

What's your favored interpretation?

 

[gentzen]

although "randomness" is something that can never be strictly defined. But probability theory and statistics are invaluable.

What Q(F)T is still lacking is a convincing ontology.

I guess that "randomness" can still be a bit better defined than in the currently dominant frequentist interpretations and subjective Bayesian interpretations.

For a convincing ontology, accepting true indistinguishabiliy and developping appropriate mental images for both bosons and fermions seems crucial to me. You argued against the Bohmian ontology on that basis, but I believe that trying to understand how this paradox is solved in the Bohmian ontology would actually bring you closer to your goal. (My guess is that if you would do the computation, it is the forced symmetry of the wavefunction together with the non-locality of the particles that restores indistinguishability. Would be interesting whether there is a difference between particles that had a close interaction before, and arbitrary particles.)

 

[vanhees71]

What do you need an "ontology"? At the end you can only observe what you can observe. It's at least not subject of the natural sciences to speculate what further may be "behind" that observable facts.

 

[Demystifier]

What do you need an "ontology"?

It helps to develop an intuitive mental image. It's a very useful thinking tool.

 

[gentzen]

What do you need an "ontology"?

For me, the original Bohmian mechanics is an existence proof of a mathematical model. In a sense this is the minimal requirement for an "ontology", but some people expect more.
But not all mathematical models are equally nice as an "ontology". Often mathematical models contain quotient structures. If too much work is hidden in those implicit equivalence relations, then the model risks to become trivial and meaningless. But some of those quotient structures are there to stay, especially those caused by topological constraints.

Understanding such details can give hints why certain things are difficult. For example, A. Neumaier thinks it is possible that non-separable Hilbert spaces might be required for QFT. But that non-separability could also be a hint that some topological information is missing (for example the surfaces in solid state physics), and that different possibilities for that missing information could lead to different results.

 

[WernerQH]

At the end you can only observe what you can observe. It's at least not subject of the natural sciences to speculate what further may be "behind" that observable facts.

Also experiments need interpretation! It is not clear what exactly the observable facts are in experiments that claim to simulate "Wigner's friend" or reveal "photon trajectories".

 

[Sunil]

That many people after 100 years of modern QT still have a problem to accept that Nature is behaving fundamentally random is not a problem of physics but rather of psychology and philosophy of these individual people.

Essentially nobody has a problem with Nature behaving random. I have never seen anybody with conceptual problems in thermodynamics because of randomness.

You seem to have a problem not understanding that your "fundamentally" is your personal metaphysical preference, nothing more. This can be even proven: There exists a deterministic interpretation, thus, fundamental randomness is not interpretation-independent, thus, a metaphysical preference.

The natural sciences are not to please your epistemological prejudices but to figure out how Nature behaves as objectively and quantitatively observed.

Looks more like you think they have to please, instead, your own epistemological prejudices.

 

[WernerQH]

What's your favored interpretation?

It's a blend of the statistical and the transactional interpretation. But without the "offer" and "confirmation" waves, and also without particles. In my view, it's only the interactions between photons and electrons (events) that are real. As John Bell once wrote:

A piece of matter then is a galaxy of such events.

("Are there quantum jumps?")