Can the PBR Theorem Prove the Reality of Quantum States?

[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...

 

[Demystifier]

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...

I'm not claiming that Bohmian particles can be measured easily. I am just claiming that there is no exact absolute principle which forbids it. They are not measurable in the simplest minimal version of the theory, but the general framework is flexible enough to create a modified theory in which they can become measurable. The "problem" is that Bohmians (unlike BSM physicists) are typically not phenomenologists, so they are not much interested in producing an ad hoc modification just to make the theory testable. Yet, some ad hoc proposals exist.

 

[vanhees71]

Well, then they are mathematicians and no physicists!

 

[Demystifier]

Well, then they are mathematicians and no physicists!

Mathematicians would probably disagree, but I guess you think the same about string theorists.

 

[fanieh]

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.

Bohmians make the particle local.. but why don't Bohmians make the guiding wave real too? Even if the guiding wave is made real.. it should still follow the rule of the wave function that guiding waves (or wave function) of different objects are separate.. and entangled subsystem won't have wave function or guiding wave but only one guiding wave for the entire entangled system so this won't make the guiding wave superluminal violating relativity (or would it?) But yet the Bohmians don't want to make the guiding wave real or objective but only math. Is the reason because of relativity? But if there was a preferred frame of reference (for example the preferred frame uses some adS/CFT surface as preferred), then that means you can make the guiding wave objective too? Or still not and why not?I'd like to ask you something separate to the above. According to a pilot wave researcher, he uses the concept of duplex Reference Frame where there are two subspaces one of which is spacetime. Thus, as an approximation, one might consider it as a member of the general, eight-dimensional space. In this concept, the thing that makes this duplex RF unique and specific is that the other subspace is a reciprocal subspace to spacetime (imagine the momentum-space or Fourier transform of space and time function). Thus we have two potential four-dimensional subspaces; one is spacetime, the other is an actual reciprocal space (again composing of actual momentum space or Fourier transform of space and time function)...

Now in the double slit experiment and using that model. He suggested that in this duplex-space perspective, the slit structure itself, without the light waves, already has a Reciprocal space substance interference pattern existing around the slit regions of the ordinary spacetime structure. The model is that it is this reciprocal space pattern that guides the light into its maxima and minima ordinary space intensity locations behind the slits? Can you refute this? Or give other arguments that can refute this model? Thanks.

 

[Demystifier]

Bohmians make the particle local.. but why don't Bohmians make the guiding wave real too?

Because the wave does not live in ordinary 3-dimensional space. Analogy with HJ S-function or Newton gravity potential is again useful.

 

[fanieh]

Because the wave does not live in ordinary 3-dimensional space. Analogy with HJ S-function or Newton gravity potential is again useful.

Hamilton phase space doesn't live in ordinary 3-dimensional space too.. it's just a way to arrange information.. so for the BM guiding wave.. we can call it perhaps a force or something that is 3D yet described by wave function like any classical object can be described by Hamilton 3N phase space. so why can't the guiding force exist?

About the reciprocal space thing. The pilot wave author said every object has a reciprocal duplicate. I've been thinking about it for 12 years so if you have arguments that can refute it.. would thanks you hundredtimes.. thanks:)

 

[Demystifier]

Hamilton phase space doesn't live in ordinary 3-dimensional space too.. it's just a way to arrange information.. so for the BM guiding wave.. we can call it perhaps a force or something that is 3D yet described by wave function like any classical object can be described by Hamilton 3N phase space. so why can't the guiding force exist?

The guiding force exists. But just as in classical mechanics, the force is not a part of primitive ontology.

About the reciprocal space thing. The pilot wave author said every object has a reciprocal duplicate. I've been thinking about it for 12 years so if you have arguments that can refute it.. would thanks you hundredtimes.. thanks:)

I have no idea what is reciprocal duplicate.

 

[fanieh]

The guiding force exists. But just as in classical mechanics, the force is not a part of primitive ontology.

Hmm.. that's why we must make it QFT based so the force can be described. In classical mechanics, there is no strong force.. and even in QM, it can't be described. It can only be described by QFT.. you saying the guiding force is like this? Also are you simply referring to the guiding force as quantum potential?

I have no idea what is reciprocal duplicate.

It's simple. The inverse of distance is number per unit distance is spatial frequency, and the inverse of time is number per unit time is a temporal frequency.

You can you turn them into a four-dimensional subspace reference frame called wave number space and denoted by the vector Kx, Ky, Kz, Kt? The condense matter physicist with Ph.d. suggested there is an actual wave number space connected to our spacetime.. so every object has it.. and in the double slit experiment.. it has that actual wave number space too and the intereference patterns in the screen is simply the Fourier transform of the slits.. is this true?

 

[Demystifier]

Hmm.. that's why we must make it QFT based so the force can be described. In classical mechanics, there is no strong force.. and even in QM, it can't be described. It can only be described by QFT.. you saying the guiding force is like this?

Sort of.

Also are you simply referring to the guiding force as quantum potential?

Negative divergence of the quantum potential, to be more precise.

It's simple. The inverse of distance is number per unit distance is spatial frequency, and the inverse of time is number per unit time is a temporal frequency.

You can you turn them into a four-dimensional subspace reference frame called wave number space and denoted by the vector Kx, Ky, Kz, Kt? The condense matter physicist with Ph.d. suggested there is an actual wave number space connected to our spacetime.. so every object has it.. and in the double slit experiment.. it has that actual wave number space too and the intereference patterns in the screen is simply the Fourier transform of the slits.. is this true?

It is true that more-or-less any function f(x,t) can be Fourier transformed, but I'm not sure that it answers your question.

 

[fanieh]

Sort of.Negative divergence of the quantum potential, to be more precise.It is true that more-or-less any function f(x,t) can be Fourier transformed, but I'm not sure that it answers your question.

He is suggesting the pilot wave of our physical object is connected to another space (actual momentum space).. here are some illustrations:

Is it really true the interference pattern of the screen is the Fourier transform of the slits? If not true.. then it is refuted.. please let me know.. many thanks.