How do deterministic Bohmian/Pilot Wave Theories Handle These?

[DrChinese]

How do "deterministic" Bohmian/Pilot Wave Theories Handle These?

We are fortunate to have Demystifier and several others on this board who are very involved in research into Bohmian Mechanics/dBB/Pilot Wave theory. I have a couple of questions I am hoping someone can discuss.

(I will use the term BM here to represent this general class of theories, knowing that there are differences between some of the leading versions and that some tend to prefer one name or another... although I am not trying to push in one direction or another. Also, these questions should not be thought of as any kind of critique. I am interested in learning more about BM, and I am sure there are others who share this interest. I hope this does not become a thread discussing the pros and cons of one interpretation or another, as there are plenty of those going on elsewhere at any time.)

One of the hallmarks of BM is that the pilot wave guides the particle in a deterministic fashion. Initial (unknown) positions x of particles in the wave equation provide an unknown dispersion of values which mirror standard quantum uncertainty. Since those are, in principle, unknowable, there are limits on our knowledge. Were it not for that, the outcomes of observations could be predicted with certainty.

So here are a couple of questions:

A. We know there is a powerful background field of quantum fluctuations which produces virtual particle pairs which interact with "real" particles. Does current BM theory have an analog of this? If so, how is it expressed? Is the existence of a particular virtual particle pair (pre-)determined? At what point does a virtual particle, during its brief existence, figure into the global equation along with other "real" particles?

B. An unbound neutron has a half-life of perhaps 15 minutes. At some point, a down quark decays to an up quark plus byproducts. This is mediated by the weak force. I realize that BM has not moved to a comprehensive description of this process, and I am not criticizing it for that. I did have this question: would BM ultimately be expected to provide an answer to the question: why does a particle exhibit decay due to the weak force? Is this something that BM would ultimately consider (pre-)determined?

Thanks in advance.

-DrC

 

[Ilja]

So here are a couple of questions:

A. We know there is a powerful background field of quantum fluctuations which produces virtual particle pairs which interact with "real" particles. Does current BM theory have an analog of this? If so, how is it expressed? Is the existence of a particular virtual particle pair (pre-)determined? At what point does a virtual particle, during its brief existence, figure into the global equation along with other "real" particles?

This is something depending on the particular pilot wave model. One has to fix some configuration space to define a pilot wave theory. In case of field theories, the appropriate choice of the configuration space is a field ontology.

If we make this choice, there will be no answer to your question, or, more accurate, one can answer this question in the same way as in condensed matter physics, described by some atomic model, one can answer such questions about pseudo-particles like phonons.

"Virtual particles" are sloppy language for some terms in the pertubation expansion, so it seems better not to assign them too much reality.

On the other hand, there are approaches to field theory, in particular for fermions, which are based on a particle picture with variable particle number.

B. An unbound neutron has a half-life of perhaps 15 minutes. At some point, a down quark decays to an up quark plus byproducts. This is mediated by the weak force. I realize that BM has not moved to a comprehensive description of this process, and I am not criticizing it for that. I did have this question: would BM ultimately be expected to provide an answer to the question: why does a particle exhibit decay due to the weak force? Is this something that BM would ultimately consider (pre-)determined?

If we use a field ontology, we should not expect an answer. For a theory with particle ontology, we would like to have such an answer. And the theory with variable particle number gives such an answer: It is a stochastic theory, and there is some good argument for its stochastic character. Else, a one-particle state would be bounded by a deterministic evolution to some one-dimensional subset of the set with larger particle numbers.

 

[ZapperZ]

This is something depending on the particular pilot wave model. One has to fix some configuration space to define a pilot wave theory. In case of field theories, the appropriate choice of the configuration space is a field ontology.

If we make this choice, there will be no answer to your question, or, more accurate, one can answer this question in the same way as in condensed matter physics, described by some atomic model, one can answer such questions about pseudo-particles like phonons.

This part, I don't understand. How is the Bohmian approach to that problem be the same as condensed matter approach, especially when the condensed matter approach, in this case, is nothing more than standard field theoretic method? The exchange particle can be anything, not just "pseudo-particles".

Zz.

 

[Ilja]

This part, I don't understand. How is the Bohmian approach to that problem be the same as condensed matter approach, especially when the condensed matter approach, in this case, is nothing more than standard field theoretic method? The exchange particle can be anything, not just "pseudo-particles".

Ok, let's put it slightly different: For atoms in a lattice, we can, in some approximation, which is sufficient for all (or almost all) condensed matter theory, replace the atoms with point particles with appropriate interaction potential and use standard multi-particle Bohmian theory.

There will be, of course, phonons in the resulting condensed matter theory too. But one would not expect that that the Bohmian trajectories of the atoms give us any information about the phonons.

In a similar way, a Bohmian theory with fields or something more fundamental than the fields as the ontology will not give anything new about the usual elementary particles.

 

[Demystifier]

A. We know there is a powerful background field of quantum fluctuations which produces virtual particle pairs which interact with "real" particles. Does current BM theory have an analog of this? If so, how is it expressed? Is the existence of a particular virtual particle pair (pre-)determined? At what point does a virtual particle, during its brief existence, figure into the global equation along with other "real" particles?

B. An unbound neutron has a half-life of perhaps 15 minutes. At some point, a down quark decays to an up quark plus byproducts. This is mediated by the weak force. I realize that BM has not moved to a comprehensive description of this process, and I am not criticizing it for that. I did have this question: would BM ultimately be expected to provide an answer to the question: why does a particle exhibit decay due to the weak force? Is this something that BM would ultimately consider (pre-)determined?

First, it should be said that a satisfying Bohmian interpretation of quantum field theory does not exist yet. (In fact, I am currently writing a paper in which I believe the main framework for a satisfying Bohmian interpretation of QFT will be formulated. I expect the paper to be finished in 10 days or so.) Still, answers to your questions can be made even without the complete theory.

A. Even in standard QFT, vacuum fluctuations do NOT produce virtual particles. The vacuum is an eigenstate of the operator of the number of particles, so there are no particle fluctuations in the vacuum. What fluctuates in the vacuum is the value of field. Virtual particles are something different, they are artefact of a specific mathematical method of treating interactions, based on perturbation method. If you use some other method, such as numerical path integration on the lattice, then nothing analogous to virtual particles exists. For more details see e.g. Secs. 9.3. and 9.4. in
http://xxx.lanl.gov/abs/quant-ph/0609163 [Found.Phys.37:1563-1611,2007]

B. In the version of BM on which I am currently writing the paper, the decay of the particle by weak force is predetermined. This is also so in most other versions of BM that attempt to include the effects of QFT.

 

[Dmitry67]

Could anyone explain to me, what are the reasons to discuss the interpretation so retarded that it even is not compatible with QFT and only recently, if I am not wrong, became relativistic.

Before I started to read this forum Bohmian Int. for me was like... ether or something. A desperate attempt to restore 'classical' vision of the world and of a particle

 

[ZapperZ]

Ok, let's put it slightly different: For atoms in a lattice, we can, in some approximation, which is sufficient for all (or almost all) condensed matter theory, replace the atoms with point particles with appropriate interaction potential and use standard multi-particle Bohmian theory.

There will be, of course, phonons in the resulting condensed matter theory too. But one would not expect that that the Bohmian trajectories of the atoms give us any information about the phonons.

In a similar way, a Bohmian theory with fields or something more fundamental than the fields as the ontology will not give anything new about the usual elementary particles.

I still don't understand this.

You do know that "condensed matter physics" does not just deal with "atoms in a lattice", don't you?

I wish you give specific references to what you are trying to explain here so that I know what exactly is the piece of "condensed matter physics" that you are claiming to be similar to Bohmian mechanics. If you need one, I can point out to one of the most obvious and one that typically every condensed matter physicist would know - the Fermi Liquid model. Can you, for example, show how in that model, which renormalizes the many-body interactions into single-particle quasiparticles, the physics is similar to Bohmian mechanics?

Zz.

 

[Demystifier]

Could anyone explain to me, what are the reasons to discuss the interpretation ...

The main reason is assumption that reality (more precisely, single reality) exists even when nobody observes it.

 

[Dmitry67]

I believe that such hope should be abandoned. Check the Unruh effect: different observers even don't agree with the number of particles.

I mean, don't you see that the Bohmian Int is UGLY? Yes, QM is weird, but that craziness has its charm. It is very beautiful madness. I think that any attemps to put QM back into the classical procrustean bed are doomed.

 

[Demystifier]

Check the Unruh effect: different observers even don't agree with the number of particles.

I believe that the usual definition of particles in curved spacetime is physically wrong. After all, no existing experiment confirms that it is correct.

 

[Demystifier]

I mean, don't you see that the Bohmian Int is UGLY? Yes, QM is weird, but that craziness has its charm. It is very beautiful madness. I think that any attemps to put QM back into the classical procrustean bed are doomed.

Let me ask you only one question: Do you really believe that the Moon is not there when nobody looks?

 

[Demystifier]

I mean, don't you see that the Bohmian Int is UGLY?

So? The Standard Model of elementary particles is ugly too. Quantum electrodynamics is much more beautiful. Sometimes ugly theories are closer to the final theory than the beautiful ones.

For me, it is a challenge to start from an ugly theory and to reformulate it such that it becomes much more beautiful. For example, string theory is an attempt (not yet successfull) to replace the ugly Standard Model with something really beautiful. Another example is my recent result that transforms ugly BM with a preferred time into something much more beautiful:
http://xxx.lanl.gov/abs/0811.1905 [accepted for publication in Int. J. Quantum Inf]

 

[Dmitry67]

It has just hit me on the way home: the importance of the Unruh effect for the understanding the realism. What is reality? Something all observers agree upon.

So, if the very existence of particles is observer-dependent, are they real?

After all these efforts you could make Bohmian Int relativistic and may be QFT-compatible (how many artificial thing you need to add to achieve that?)

But still it is far behind the 'pure' QM - because we already have some progress on the QM in curved times and accelerated frames. THe semi-classical approach, Hawking and Unruh radiation.

So how can one, in principle, explain Unruh effect in terms of Bohmians Int, assigning something realistic behind the QM, when particles exist only for SOME observers?

 

[Demystifier]

So how can one, in principle, explain Unruh effect in terms of Bohmians Int, assigning something realistic behind the QM, when particles exist only for SOME observers?

Given the fact that the Unruh effect is not an experimentally confirmed effect, one could also ask the following:
How can one believe that the Unruh effect exists, when the number of particles does not depend on observers?

And again, do you really believe that the Moon is not there when nobody looks?

And one additional question: If the Unruh effect is true, does it mean that the black hole does not evaporate for some observers?

 

[Dmitry67]

1 Given the fact that the Unruh effect is not an experimentally confirmed effect, one could also ask the following: How can one believe that the Unruh effect exists, when the number of particles does not depend on observers?

2 And again, do you really believe that the Moon is not there when nobody looks?

3 And one additional question: If the Unruh effect is true, does it mean that the black hole does not evaporate for some observers?

1 Well, it is based on the same idea as Hawking radiation. Do you think that Hawking is wrong? isn't it a federal offence? :)

2 I think the really is something all obserers agree on, so the macroscopic (irreversible) events are real, but what they consist of is not. Therefore Moon is real.

3 No, it means that they evaporate differently for the different observers, as the location of the Black Hole horizon is observer-dependent.

 

[DrChinese]

Could anyone explain to me, what are the reasons to discuss the interpretation so retarded that it even is not compatible with QFT and only recently, if I am not wrong, became relativistic.

Before I started to read this forum Bohmian Int. for me was like... ether or something. A desperate attempt to restore 'classical' vision of the world and of a particle

I don't think that BM should be considered "retarded". Give it a chance. There are pluses and minuses for each interpretation out there. As to "ugly": beauty is in the eye of the beholder, as I think we have proven on this board MANY times.

Also, I don't think the idea of an ether is so strange. It does NOT need to be classical in any way. If space-time itself is expanding (as experimental evidence indicates), perhaps we should re-consider our notions of a background of some type. I realize that the term "ether" itself may have classical notions associated with it, but perhaps there is an absolute something. It is at least worth considering.

Also, regarding the Unruh effect: as I mention in the original post, I am interested in learning about how BM addresses several specific issues. I selected these items because they are key elements of our existing understanding of the quantum world. Eventually, BM will need to fill in these elements of the story. I think there are any number of additional effects out there that will need filling in too - such as the Unruh effect you mention. Not sure what order these will be addressed, but clearly Demystifier and others are working on improving our understanding in these areas.

 

[DrChinese]

First, it should be said that a satisfying Bohmian interpretation of quantum field theory does not exist yet. (In fact, I am currently writing a paper in which I believe the main framework for a satisfying Bohmian interpretation of QFT will be formulated. I expect the paper to be finished in 10 days or so.) Still, answers to your questions can be made even without the complete theory.

A. Even in standard QFT, vacuum fluctuations do NOT produce virtual particles. The vacuum is an eigenstate of the operator of the number of particles, so there are no particle fluctuations in the vacuum. What fluctuates in the vacuum is the value of field. Virtual particles are something different, they are artefact of a specific mathematical method of treating interactions, based on perturbation method. If you use some other method, such as numerical path integration on the lattice, then nothing analogous to virtual particles exists. For more details see e.g. Secs. 9.3. and 9.4. in
http://xxx.lanl.gov/abs/quant-ph/0609163 [Found.Phys.37:1563-1611,2007]

B. In the version of BM on which I am currently writing the paper, the decay of the particle by weak force is predetermined. This is also so in most other versions of BM that attempt to include the effects of QFT.

Thanks, Demystifier. Please don't rush on your work, though of course I am interested in seeing more on the subject. :)

I will look through some of what you mention for a follow-up question.

 

[Ilja]

Could anyone explain to me, what are the reasons to discuss the interpretation so retarded that it even is not compatible with QFT and only recently, if I am not wrong, became relativistic.

Before I started to read this forum Bohmian Int. for me was like... ether or something. A desperate attempt to restore 'classical' vision of the world and of a particle

It is compatible with QFT, extensions to relativistic bosonic field theories are even straigthforward, and has been already relativistic long time. Distortions of this have been common and are even popular today.

It has introduced unitary evolution without collapse long before many worlds, has a much easier classical limit, allows to derive quantum measurement theory, is deterministic, realistic, causal, and therefore shows that all the quantum mystery claims about the impossibility of all this is metaphysical nonsense.

Restoring the notion of particle is irrelevant, pilot wave theory works on abstract configuration spaces, like the Lagrange formalism or the Hamilton-Jacobi theory.

The main argument against it is that it needs a hidden preferred frame. Why a hidden preferred frame is an argument against a hidden variable theory is something I don't understand.

 

[Ilja]

I still don't understand this.

You do know that "condensed matter physics" does not just deal with "atoms in a lattice", don't you?

I wish you give specific references to what you are trying to explain here so that I know what exactly is the piece of "condensed matter physics" that you are claiming to be similar to Bohmian mechanics. If you need one, I can point out to one of the most obvious and one that typically every condensed matter physicist would know - the Fermi Liquid model. Can you, for example, show how in that model, which renormalizes the many-body interactions into single-particle quasiparticles, the physics is similar to Bohmian mechanics?

Zz.

It was not my aim to claim that the physics of Fermi liquids are similar to BM.

My analogy was much weaker: Assume we can use standard multi-particle Schroedinger theory for the atoms of the lattice to describe some condensed matter effects involving quasiparticles. Then, replacing the quantum theory with its Bohmian version introduces trajectories for the atoms of the lattice. But it does not give anything new about the quasiparticles. In particular, it does not introduce any trajectories of quasiparticles.
That's all I wanted to say.

 

[Dmitry67]

The main argument against it is that it needs a hidden preferred frame. Why a hidden preferred frame is an argument against a hidden variable theory is something I don't understand.

I can understand how you can define a hidden preferred frame in falt spacetime. It is the same in LET (Lorentz Ether Theory, compatible with SR).

But how can you do the same for the black hole metric? Can you define a single frame common to space inside and outside the horizon?

 

[Fra]

I believe that such hope should be abandoned. Check the Unruh effect: different observers even don't agree with the number of particles.

Even though I do not share the realist dream, please note that in the end, the standard resolution to various observer dependent notions, to "restore reality" is by means of a symmetry.

If we expect a coherent reasoning here, why would we expect symmetries to be real, even when no one is there to observe it? :)

From the perspective of science as something that deals with observations, this distinction is highly doubtful IMHO.

So while I do not share Demystifiers realist resolution, I think that at minimum he puts the finger on an inconsistency.

To me, a symmetry contains information, and I'd say usually it's information a real observer doesn't hold. This is why the use of symmetry arguments, takes the form of realist reasoning, although the analogy is at a more subtle level.

/Fredrik

 

[Demystifier]

1 Well, it is based on the same idea as Hawking radiation. Do you think that Hawking is wrong? isn't it a federal offence? :)

Yes, I do. But at the same time, I do believe that black holes radiate. Moreover, I have almost no doubts that if it radiates, then the spectrum is approximately thermal. In other words, I believe that the main Hawking conclusion that black holes radiate is correct, but that the details of his formal description of that phenomenon is incorrect. I think that a correct description can be done only with fully quantized gravity, not with semiclassical gravity. For one of my attempts to contribute in that direction see
http://xxx.lanl.gov/abs/0708.0729 [Eur.Phys.J.C54:319-323,2008]

2 I think the really is something all obserers agree on, so the macroscopic (irreversible) events are real, but what they consist of is not. Therefore Moon is real.

If I understood you correctly, you say that macroscopic events are real, while microscopic are not. But where is the boundary between macroscopic and microscopic? If there is no strict boundary, does it mean that some events are semi-real? Is Schrodinger cat alive/dead before one opens the box?

3 No, it means that they evaporate differently for the different observers, as the location of the Black Hole horizon is observer-dependent.

But for some observers there is no horizon at all. Does it mean that for such observers the black hole does not radiate at all?

 

[ZapperZ]

It was not my aim to claim that the physics of Fermi liquids are similar to BM.

My analogy was much weaker: Assume we can use standard multi-particle Schroedinger theory for the atoms of the lattice to describe some condensed matter effects involving quasiparticles. Then, replacing the quantum theory with its Bohmian version introduces trajectories for the atoms of the lattice. But it does not give anything new about the quasiparticles. In particular, it does not introduce any trajectories of quasiparticles.
That's all I wanted to say.

Hum... then all I wanted to say is that, that is not condensed matter physics.

Zz.

 

[Dmitry67]

1
If I understood you correctly, you say that macroscopic events are real, while microscopic are not. But where is the boundary between macroscopic and microscopic? If there is no strict boundary, does it mean that some events are semi-real? Is Schrodinger cat alive/dead before one opens the box?

2
But for some observers there is no horizon at all. Does it mean that for such observers the black hole does not radiate at all?

1 I really like realism. I believe that wavefunction is real. But the way how it is interpreted as particles is incorrect. Particles are not real. Microscopic events (the ones which are subject to the quantum decoherence) are real, but the way how they are decomposed into particles is not.

To give an analogy, imagine a surface of the sea. The sea itself (wavefunction) is real, but the notion of an individual wave is not (depends on your movement, angle etc). But big events, like a storm, are real for all observers.

2 yeap.
For such observers the real particles of the hawking radiation are virtual.
Exactly like in Unruh effect: for an accelerating observer there is a horizon and particles are real, in the inertial frame there is no horizon and particles are virtual.

 

[Demystifier]

1 I really like realism. I believe that wavefunction is real. But the way how it is interpreted as particles is incorrect. Particles are not real. Microscopic events (the ones which are subject to the quantum decoherence) are real, but the way how they are decomposed into particles is not.

To give an analogy, imagine a surface of the sea. The sea itself (wavefunction) is real, but the notion of an individual wave is not (depends on your movement, angle etc). But big events, like a storm, are real for all observers.

So essentially, you adopt some version of the many-world interpretation, right?
That is fine, but as we already discussed, MWI suffers from a frog problem, because it needs frogs to explain why only one of the possibilities (allowed by the decohered density matrix) is observed. MWI does not contain a mathematical theory of frogs. From this perspective, I view Bohmian particles as a mathematical theory of frogs.

 

[Dmitry67]

only one of the possibilities (allowed by the decohered density matrix) is observed

yes, sure, I am MWI fan.
I don't see any problems with a frog.
the key concept of MWI is that both possibilities are observed.

 

[ueit]

IMHO the main problem of MWI is that it seem to postulate the entire reality (starting with our 3D world, objects, etc.) when it should derive these observations from the theory's beable (the wave-function).

 

[Dmitry67]

The observable reality is derived from pure QM using Quantum Decoherence.

 

[ueit]

The observable reality is derived from pure QM using Quantum Decoherence.

I am not sure what "pure QM" is supposed to be but the orthodox interpretation assumes the existence of a classical world with observers, instruments and all that. In BM you also work on a 3D space background so one does not need to explain it. The issue is different in MWI where all reality is supposed to somehow emerge from a wavefunction. Decoherence does not explain this.

 

[Demystifier]

I don't see any problems with a frog.

As long as you don't see any problems with a frog, you will never understand why some people see advantages of the Bohmian approach. Otherwise, MWI and BM are very similar, in the sense that they both postulate that the wave function is real and that it never collapses.

 

[Demystifier]

the key concept of MWI is that both possibilities are observed.

... but by different frogs, right?

 

[Dmitry67]

... but by different frogs, right?

Yes, non-interacting branches of the same frog. Each frog remembers the same past, having an illusion that it is the only frog.

And yes, I know that there is a duality between BI and MWI. But can I ask, what makes BI so attractive to you?

 

[Dmitry67]

The issue is different in MWI where all reality is supposed to somehow emerge from a wavefunction. Decoherence does not explain this.

Well, as your claim contradicts with Wiki:

Quantum decoherence gives the appearance of wave function collapse and justifies the framework and intuition of classical physics as an acceptable approximation: decoherence is the mechanism by which the classical limit emerges out of a quantum starting point and it determines the location of the quantum-classical boundary

As a consequence, the system behaves as a classical statistical ensemble of the different elements rather than as a single coherent quantum superposition of them. From the perspective of each ensemble member's measuring device, the system appears to have irreversibly collapsed onto a state with a precise value for the measured attributes, relative to that element.

the burden of proof is yours

 

[jnorman]

a small quibble, inre: "B. An unbound neutron has a half-life of perhaps 15 minutes."

a single neutron does not have a half-life.

 

[ueit]

Well, as your claim contradicts with Wiki:

Quantum decoherence gives the appearance of wave function collapse and justifies the framework and intuition of classical physics as an acceptable approximation: decoherence is the mechanism by which the classical limit emerges out of a quantum starting point and it determines the location of the quantum-classical boundary

As a consequence, the system behaves as a classical statistical ensemble of the different elements rather than as a single coherent quantum superposition of them. From the perspective of each ensemble member's measuring device, the system appears to have irreversibly collapsed onto a state with a precise value for the measured attributes, relative to that element.

the burden of proof is yours

The quote refers to the orthodox interpretation (MWI does not have a quantum-classical boundary).

To clarify this issue, can you point me at a set of postulates that define MWI so I can refer to them?