Undergrad Can the PBR Theorem Prove the Reality of Quantum States?

[Demystifier]

In the other thread you also said 'yes' to the question 'So nothing more than an equation that gives the result...' Then my question is what is the point of BM?

Ontology.

https://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/files/duerr_ontology.pdf

And by the way, the point of PBR theorem is also ontology, as is the point of most non-minimal interpretations of QM.

 

[martinbn]

What is the ontology? When I asked you, you said that the wave function is not like the electric field, I took it to mean that there is no ontology for the wave function?

 

[Demystifier]

What is the ontology? When I asked you, you said that the wave function is not like the electric field, I took it to mean that there is no ontology for the wave function?

According to BM, the only primitive ontology is particle positions. In that sense, it is just like classical mechanics. All other mathematical objects (Hamiltonians, HJ S-functions, wave functions) are only auxiliary nomological objects. Classical and Bohmian mechanics have different nomologies, but the same ontologies.

Talking about physical laws without talking about ontology is like talking about legal laws without talking about humans. A professional can do it to make the laws more efficient, but then one can miss what the laws are really about.

 

[stevendaryl]

Ontology.

https://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/files/duerr_ontology.pdf

And by the way, the point of PBR theorem is also ontology, as is the point of most non-minimal interpretations of QM.

Okay, but this sort of gets to what I don't like about Bohmian mechanics. It restores ontology, in the sense of now we can think of particles having definite positions moving along definite trajectories. But as we have been discussing, those particles don't actually have any effect on anything. To me, a large part of wanting an ontology is to understand what's going on in terms of cause and effect--explaining appearances in terms of an underlying reality. But if the reality has no causal power...

I guess an analogy might be something like watching a planetarium show. Looking up, you see stars and planets doing interesting things. Those celestial objects are real, in the sense that they are actually spots of light on a ceiling. But the dynamics of them can't be understood by studying the objects themselves, because they are just projections. All the "physics" is in the projector. In Bohmian mechanics, the particles might be real, but all the physics is in the wave function (or pilot wave, or whatever it's called).

 

[vanhees71]

All that's really interesting is, whether the trajectories in configuration space claimed to be "ontic" in BM are observable. For me it's a contradiction to say something is "ontic" and at the same time claiming it's unobservable. The only true "ontology" of any physical theory is whether it describes quantitatively and at least to the precision available in experiment what's observable. The mathematical "world" is epistemic, and just a construct of the human mind (I'm very anti-Platonic in this sense, although of course Platon's obsession with symmetries sounds very modern to physicists) and for some reason very suitable to describe observations in nature.

 

[zonde]

Well, at least endpoint of trajectory, where particle deposits it's energy in detector, is observable. Empty branch does not produce "click" in detector.
And when experimentalist rotates polarizer or SG apparatus wave function changes. Well if we can assume that there is supperposition of "experimentalist rotating apparatus by angle $\alpha$" and (plus or minus) "experimentalist rotating apparatus by angle $\beta$" then only non empty branch changes wavefunction.
So it's not quite convincing that particles can play only passive role in dynamics.

 

[Demystifier]

But as we have been discussing, those particles don't actually have any effect on anything.

That's not true, particles have effect on other particles.

I guess an analogy might be something like watching a planetarium show. Looking up, you see stars and planets doing interesting things. Those celestial objects are real, in the sense that they are actually spots of light on a ceiling. But the dynamics of them can't be understood by studying the objects themselves, because they are just projections. All the "physics" is in the projector. In Bohmian mechanics, the particles might be real, but all the physics is in the wave function (or pilot wave, or whatever it's called).

This is like saying that in classical Hamiltonian mechanics (CHM), all physics is in Hamiltonian. It's simply wrong, in order to determine particle trajectories you also need to know the initial conditions (positions and momenta in CHM or positions only in BM). This is more like a planetarium in which you can change initial positions and velocities of planets at will.

 

[vanhees71]

Well, all we observe is a particle hitting the screen and no trajectory. Using many equally prepared particles we get a statistics according to Born's rule. That's all there is standard minimally interpreted QT. If you claim there are trajectories, you should be able to construct an experimental setup to verify their existence and show that your theory are able to quantitatively predict their shape.

All dynamics there is is given by the Schrödinger equation of the statistical operator. BM puts some (imho unobservable) trajectories on top without any consequences to the predicted probabilistic description of observable facts. Thus it's an empty mathematical game without any physical content.

 

[zonde]

If you claim there are trajectories, you should be able to construct an experimental setup to verify their existence and show that your theory are able to quantitatively predict their shape.

I believe that it's enough to claim that reality is consistent with trajectories.

All dynamics there is is given by the Schrödinger equation of the statistical operator.

Schrödinger equation gives only statistics about dynamics. But individual "clicks" in detectors are observable. And Schrödinger equation have nothing to say about that while BM says at least something.

 

[martinbn]

To me it seems like an incomplete ontology. In classical physics it is not just particles moving on a well define trajectories, there are also interactions, which explain the behavior and the mathematics models that as well. It could be mediating fields or forces at a distance or what not, but there is something. In BM it seems like magic, and BM stubbornly refuses to say anything about it except here are the equations. Looks a lot like shut up and calculate.

 

[Demystifier]

To me it seems like an incomplete ontology. In classical physics it is not just particles moving on a well define trajectories, there are also interactions, which explain the behavior and the mathematics models that as well. It could be mediating fields or forces at a distance or what not, but there is something. In BM it seems like magic, and BM stubbornly refuses to say anything about it except here are the equations. Looks a lot like shut up and calculate.

I agree with you that BM is probably incomplete. It this respect it is very similar to Newton theory of gravity, which is also non-local. Incompleteness is not a reason for a rejection.

 

[Boing3000]

Well, all we observe is a particle hitting the screen and no trajectory

And in what sense is it different from not observing wave functions in Hilbert spaces ?

Using many equally prepared particles we get a statistics according to Born's rule. That's all there is standard minimally interpreted QT. If you claim there are trajectories, you should be able to construct an experimental setup to verify their existence and show that your theory are able to quantitatively predict their shape.

Is it formally forbidden by some theoretical part of the BM framework to be able two physically obtain knowledge of "initial position" ?
I was under the impression the BM goals was to be able to further discriminate between "equally" prepared state, making it falsifiable...

All dynamics there is is given by the Schrödinger equation of the statistical operator. BM puts some (imho unobservable) trajectories on top without any consequences to the predicted probabilistic description of observable facts. Thus it's an empty mathematical game without any physical content.

I can only conclude from this statement that there is no correlation between differences in initial positions, and difference in final positions in BM. Rendering it un-physical/ un-falsifiable

 

[martinbn]

I agree with you that BM is probably incomplete. It this respect it is very similar to Newton theory of gravity, which is also non-local. Incompleteness is not a reason for a rejection.

It looks different to me, perhaps because I am unfamiliar with it. Newtonian gravity says that each body acts on the other bodies in a certain way, which completely describes their motion. Does BM say anything of that sort? It seems that it says that particles act on each other, but that is not enough for the description. There is more to it, but no other particles or fields are present to do the job, all we have is the mathematical model. That's why I think the ontology is not complete.

 

[vanhees71]

I'm not a Bohmian. That's why I keep asking the Bohm proponents about the observability of their claimed trajectories. If they are not observable, there's not even a motivation to calculate them!

 

[Boing3000]

I'm not a Bohmian. That's why I keep asking the Bohm proponents about the observability of their claimed trajectories. If they are not observable, there's not even a motivation to calculate them!

Fair enough. I hope Demystifier will mystify us once more

The PBR theorem seems to at least give some more tool to distinguish between theories. I will try to go through this paper which seem to address the problem...

 

[Demystifier]

Newtonian gravity says that each body acts on the other bodies in a certain way, which completely describes their motion. Does BM say anything of that sort?

Yes.

 

[Demystifier]

That's why I keep asking the Bohm proponents about the observability of their claimed trajectories.

I already told you several times that their unobservability is analogous to unobservability of dark matter. Yet, not many physicists have problems with accepting dark matter as physical.

 

[martinbn]

Yes.

:) I expected you to elaborate. Ok, I'll ask. What does BM say that is comparable to Newton's gravity?

 

[Demystifier]

:) I expected you to elaborate. Ok, I'll ask. What does BM say that is comparable to Newton's gravity?

Newton's gravity for two massive particles says that force between them is given by the non-local potential of the form
$$V({\bf x}_1,{\bf x}_2)=\frac{c m_1m_2}{|{\bf x}_1-{\bf x}_2|}$$
Similarly, BM for two entangled particles says that force between them is given by the non-local potential $Q({\bf x}_1,{\bf x}_2)$, the explicit form of which can be calculated explicitly from the wave function.

 

[martinbn]

This helps a bit. Can I look at it this way? In Newtonian gravity of point particles the theory says that each particle has a mass, which characterizes the particle's ability to interact with other particles, particles act on each other through forces, which depend on the masses and positions of the particles, the forces force the particles to move about on their trajectories and so on. In BM there are particles which together have a wave function, which is in some sense analogous to the masses, they act on each other via forces, which depend on the wave function in some way possibly on other things as well, those forces push the particles around on their trajectories and so on.

 

[Demystifier]

This helps a bit. Can I look at it this way? In Newtonian gravity of point particles the theory says that each particle has a mass, which characterizes the particle's ability to interact with other particles, particles act on each other through forces, which depend on the masses and positions of the particles, the forces force the particles to move about on their trajectories and so on. In BM there are particles which together have a wave function, which is in some sense analogous to the masses, they act on each other via forces, which depend on the wave function in some way possibly on other things as well, those forces push the particles around on their trajectories and so on.

Yes, that's a nice way to look at it.

 

[Demystifier]

I hope Demystifier will mystify us once more

There is no demystification without prior mystification.

BTW, that's my 8000th post.

 

[vanhees71]

I already told you several times that their unobservability is analogous to unobservability of dark matter. Yet, not many physicists have problems with accepting dark matter as physical.

Wait, I thought it's NOT analogous. The hypothesis of the existence of dark matter is at least in principle subject to observational tests in the sense that you can find corresponding particles, and that's why there are many attempts to find such particles like WIMPs etc.

In BM, afaik the trajectories (in configuration space) are not observable in principle, and thus they cannot be subject to empirical testing to begin with. Otherwise BM gives the same probabilistic predictions as minimally interpreted QM. Thus the assumption of unobservable trajectories are just a philosohpical addition to make the theory look in some way "ontic", but there's no physics content in addition to QM in it.

 

[Boing3000]

BTW, that's my 8000th post.

And I hope not the last !

Can I ask you if my remarks in post #41 were missguided ?

 

[Demystifier]

Can I ask you if my remarks in post #41 were missguided ?

If your thoughts about BM are guided by claims of non-experts, then they are probably missguided.

 

[Demystifier]

Wait, I thought it's NOT analogous. The hypothesis of the existence of dark matter is at least in principle subject to observational tests in the sense that you can find corresponding particles, and that's why there are many attempts to find such particles like WIMPs etc.

If dark matter interacts only gravitationally, which is compatible with present observations, how would you observe them in principle?

In BM, afaik the trajectories (in configuration space) are not observable in principle,

Where does this principle come from? Do you think that it is a fundamental principle (like energy conservation) or emergent principle (like 2nd law of thermodynamics)? How robust do you think this principle is? ... And if your answer is "I don't know, I'm not an expert", then why are you so confident that they are not observable in principle?

 

[Boing3000]

No, they were OK. I didn't react because they were not addressed to me.

So I will assume that BM goal is to be more falsifiable than QM,making it a possibly more precise/complete theory...

I can only conclude from this statement that there is no correlation between differences in initial positions, and difference in final positions in BM. Rendering it un-physical/ un-falsifiable

Thus my conclusion must be false, meaning even if the correlation between initial (sensitivity to precision) and final position is chaotic (are they ?), they are in principle distinguishable from "true" randomness ?

 

[Boing3000]

If dark matter interacts only gravitationally, which is compatible with present observations, how would you observe them in principle?

You cannot observe it per say, but still can falsify it, by observing some configuration of matter that no amount of "dark" one would explain. But than GR is falsified too...

 

[Demystifier]

So I will assume that BM goal is to be more falsifiable than QM,making it a possibly more precise/complete theory...Thus my conclusion must be false, meaning even if the correlation between initial (sensitivity to precision) and final position is chaotic (are they ?), they are in principle distinguishable from "true" randomness ?

Sorry, my first reading of your text was not careful. In the meantime I totally changed my post #54. Yes, one of the motivations for BM is to have more precise/complete theory, but it does not necessarily mean more falsifiable. And yes, Bohmian trajectories are somewhat unpredictable in practice due to chaos-like reasons (even if this is not chaos in a strict technical sense).

 

[vanhees71]

Where does this principle come from? Do you think that it is a fundamental principle (like energy conservation) or emergent principle (like 2nd law of thermodynamics)? How robust do you think this principle is? ... And if your answer is "I don't know, I'm not an expert", then why are you so confident that they are not observable in principle?

Ok, then I misunderstood BM all my life. So do you say the trajectories are observable according to BM? Than it's clearly a different theory than QM and not the same as QM. I thought it was the point of de Broglie and Bohm, to provide just an alternative interpretation with keeping the physical outcome, i.e., observable predictions unaltered? I'm getting more and more confused.

I also wonder then, why nobody has ever tried to measure Bohm trajectories and test BM against QM then. Perhaps I should read a bit more in the book by Dürr et al...