Why is the pilot-wave theory controversial ? Is it?

[nonequilibrium]

Why is the pilot-wave theory "controversial"? Is it?

The wikipedia page on the pilot-wave theory (aka the de Broglie-Bohm interpretation of QM), being http://en.wikipedia.org/wiki/Pilot_wave , says things like

[...] remains a controversial attempt to interpret quantum mechanics as a deterministic theory [...]

The de Broglie-Bohm theory is now considered by some to be a valid challenge to the prevailing orthodoxy of the Copenhagen Interpretation, but it remains controversial.

According to whom is this not a valid challenge? Of course, that there are people who do not accept it as their interpretaion, I'm fully aware of, but are there any respectable physicists who actually deny it being a valid challenge? That implies the idea of it not being consistent and/or not reproducing regular QM predictions (which is simply not true)...

EDIT (mostly for mods): see my 2nd post here for a justification for posting this in the science forum (as opposed to the philosophy forum)

 

[Maui]

Anything unobservable is controversial, even unscientific. As an extention, all hidden variable theories are controversial.

 

[nonequilibrium]

Hm, I definitely don't want to make this a thread about philosophy of science, but I'll respond in the way that I think stays on-topic. I hope to stay on the "science" track in my answer.

The view you express seems very naive to me. The best reply I can think of is Einstein saying "it's the theory which determines what is measurable". This is a subtle quote, but what lies at its core is the realisation that what is "observable" or not is actually a very subtle matter. Two points:

* In one sense according to your logic any interpretation is controversial since they all differ on matters not directly "observable" (that's what makes them interpretations), and if you truly stand by that, then I think we're talking past each other (i.e. then it's becoming a semantics issue);

* In another sense (and more importantly!) every observation is embedded in a theory; in other words, you cannot meaningfully talk about the result of a measurement without associating to it an underlying theory, and in this process even elements which are naively regarded as "unobservable" are crucial. This is what the Einstein quote is talking about and I think it's most clearest with an example: the Copenhangen interpretation says "one cannot tell which slit the particle went through" (without adding extra measurement devices beyond the slits) whereas, rather surprisingly, in the pilot-wave theory you can always say which slit the particle went through (specifically: if you measure it at the lower side of the slit, it went through the bottom slit, and vice versa). This example indicates that the whole notion of "observation" is far more subtle (i.e. theory-dependent) than a naive interpretation might suggest.

---

DISCLAIMER

Note in all this that my intention is not convincing anybody of the de Broglie-Bohm interpretation as such (although, of course, I would welcome that) --otherwise this should go into the philosophy of science forum--, I just want to debate about its validity as an interpretation among the other interpretations (which seems to be debated by the wikipedia article).

Specifically, I don't want to talk about arguments concerning the metaphysical niceness of the pilot-wave theory or whatever, I want to talk about facts (as I believe this post is trying to do) such as issues of "observability" or "consistency" etc. That's why I believe it belongs in the science forum.

 

[Maui]

* In one sense according to your logic any interpretation is controversial since they all differ on matters not directly "observable" (that's what makes them interpretations), and if you truly stand by that, then I think we're talking past each other (i.e. then it's becoming a semantics issue);

Well, yes... the relationship between qm and the outside world is rather controversial, so the interpretations are not to blame. However, some interpretations are more scientific than others - e.g. the standard minimalist interpretation is closer to the "shut up and calculate" approach without positing unobservable influences to please someone's pre-conceived notions of reality.

* In another sense (and more importantly!) every observation is embedded in a theory; in other words, you cannot meaningfully talk about the result of a measurement without associating to it an underlying theory, and in this process even elements which are naively regarded as "unobservable" are crucial.

No. The point of a theory is to make predictions, what underllies them is currently too big of a question. The rest is philosophy.

 

[nonequilibrium]

You can't just say "No" when I've given an explicit example. At least address the example. Or did you not read the whole part of my second point?

EDIT: and by the way your first paragraph indicates you deem pretty much all interpretations (except what you regard as the minimalist interpretation) controversial. In that case you're talking about preferring one interpretation over another, that's not what I'm talking about (that would be a philosophical discussion, I'm having a scientific discussion). Then again, your objection about observability is on-topic, and regarding that I stand by what I said in this post (i.e. before the "EDIT").

 

[Maui]

the Copenhangen interpretation says "one cannot tell which slit the particle went through" (without adding extra measurement devices beyond the slits) whereas, rather surprisingly, in the pilot-wave theory you can always say which slit the particle went through (specifically: if you measure it at the lower side of the slit, it went through the bottom slit, and vice versa). This example indicates that the whole notion of "observation" is far more subtle (i.e. theory-dependent) than a naive interpretation might suggest.

It's hard for me to see your point, given the commonly accepted ambiguity of the term 'measurement'. What does this prove or imply?

 

[nonequilibrium]

It's hard for me to see your point, given the commonly accepted ambiguity of the term 'measurement'. What does this prove or imply?

That the interpretation has an effect on what you observe.

For example, according to the pilot-wave theory, the two-slit experiment (the standard set-up) can be seen as a measurement of "through which slit did the particle pass". This is not the case according to the orthodox interpretation, where the measurement of the position of the particle on the screen does not tell you which slit it went through.

My intention is to back up my claim that your view is too naive: you say the Bohmian particles are not observable, indicating they have no influence on what you measure. The above convinces me, and hopefully you too, that it does. Hence the argument in your first post is not valid.

 

[Maui]

That the interpretation has an effect on what you observe.

For example, according to the pilot-wave theory, the two-slit experiment (the standard set-up) can be seen as a measurement of "through which slit did the particle pass". This is not the case according to the orthodox interpretation, where the measurement of the position of the particle on the screen does not tell you which slit it went through.

My intention is to back up my claim that your view is too naive: you say the Bohmian particles are not observable, indicating they have no influence on what you measure. The above convinces me, and hopefully you too, that it does. Hence the argument in your first post is not valid.

No, you are misunderstaning. The unobservable part(and controversial) is the implicate order that Bohm talked about(the hidden variable). See here

Anything that's not observable cannot be regarded as scientific, hence it's a philosophical position.

 

[nonequilibrium]

You seem to be mixing things. The words "the implicate order" are indeed words used by Bohm but are totally not necessary for the pilot-wave theory; they're just extra philosophical baggage which do not translate into any math (and let's subsequently ignore those words since they're not relevant in a physics forum). The "hidden variables" however refer to the postulated point particles, which are essential to the pilot-wave theory. As is often noted (e.g. by J.S. Bell), "hidden variable" is a misnomer, since according to the pilot-wave theory they're actually the measurable thing, and more concretely my aforementioned example shows the so-called "hidden variable" does have an influence on observation.

Anyway, to keep it more precise, generally under "the de Broglie-Bohm interpretation of QM" or "the pilot-wave theory" one understands the two axioms that associated to any (one-particle) system there is
A) a wavefunction \psi(\mathbf x,t) = R e^{iS} (using complex notation), governed by the Schrödinger equation;
B) a point particle with position \mathbf X(t) and with law of motion m \mathbf{ \dot X} (t) = \nabla S(\mathbf x,t) |_{\mathbf x = \mathbf X(t)}

(sometimes Born's rule, i.e. that the modulus squared gives the probability of finding a particle, is listed too, but most pilot-wave theorists agree that this is actually a theorem derivable from the previous two axioms)

I understood your first post as saying that the entities listed in axiom B are "not observable and hence have no influence on matters of observation" and my subsequent posts were an attempt to convince you otherwise. I hope there's no mix-up.

 

[madness]

No, you are misunderstaning. The unobservable part(and controversial) is the implicate order that Bohm talked about(the hidden variable). See here

Anything that's not observable cannot be regarded as scientific, hence it's a philosophical position.

I think you're treading on thin ice here. As Mr.Vodka said, quantities are only observable within a theory. To measure distance with a metre stick you need certain assumptions about space (e.g. that a metre here is the same as a metre somewhere else).

 

[Demystifier]

Any interpretation of QM is controversial, simply because we don't have a proof that it is THE right interpretation.

 

[nonequilibrium]

Demystifier, I don't think you've read it carefully. It says that even the fact that it's a valid challenge as an interpretation is controversial. This has nothing to do with accepting it as a correct interpretation or not, but more fundamentally with its validity as an interpretation. The former is a more philosophical matter, the latter a more scientific matter.

 

[bohm2]

I thought it was because non-locality is more explicit in pilot-wave theories (moreso than the more popular orthodox/epistemic view) and since it is directly in conflict with relativity then it's more controversial? Personally, I don't see any problem with non-locality or whatever stuff a future physics may need to postulate in order to explain phenomena.

 

[nonequilibrium]

Ah yes that makes more sense.

EDIT: on the other hand, since QM is a non-relativistic theory, why should anyone use relativistic arguments in discussions about its interpretation?

 

[Maui]

You seem to be mixing things. The words "the implicate order" are indeed words used by Bohm but are totally not necessary for the pilot-wave theory; they're just extra philosophical baggage which do not translate into any math (and let's subsequently ignore those words since they're not relevant in a physics forum).

How does the math matter in ANY interpretation, instead to match predictions with experiment?? Remember that's an interpretation we are talking about.

The "hidden variables" however refer to the postulated point particles, which are essential to the pilot-wave theory. As is often noted (e.g. by J.S. Bell), "hidden variable" is a misnomer, since according to the pilot-wave theory they're actually the measurable thing, and more concretely my aforementioned example shows the so-called "hidden variable" does have an influence on observation.

Then we are indead talking of completely different things. I was pointing out that the question of whether a random outcome is predetermined by a nonlocal theory is philosophical, and it can be potentially intractable. I have no idea what you mean by hidden variables being observable/measureable.

Anyway, to keep it more precise, generally under "the de Broglie-Bohm interpretation of QM" or "the pilot-wave theory" one understands the two axioms that associated to any (one-particle) system there is
A) a wavefunction \psi(\mathbf x,t) = R e^{iS} (using complex notation), governed by the Schrödinger equation;
B) a point particle with position \mathbf X(t) and with law of motion m \mathbf{ \dot X} (t) = \nabla S(\mathbf x,t) |_{\mathbf x = \mathbf X(t)}

(sometimes Born's rule, i.e. that the modulus squared gives the probability of finding a particle, is listed too, but most pilot-wave theorists agree that this is actually a theorem derivable from the previous two axioms)

I understood your first post as saying that the entities listed in axiom B are "not observable and hence have no influence on matters of observation" and my subsequent posts were an attempt to convince you otherwise. I hope there's no mix-up.

No, that's not what i meant to say. Particles are of course observable and have observable influence on measurement results. The way i understand the BI(and i believe it's not controversial at all) is that the behaviour of particles is fundamentally deterministic(as opposed to in qm) and the determinism stems from hidden variables(unobservable hidden reality - hence my comment of the implicate deterministic order that manifests as random). The motivation for this weird interpretation was to show that it is in principle possible, not that it's correct or sound or reasonable. It's not otherwise possible to directly reconcile realism with probabilities(later attempts like MWI seem to do better than BI but it also has its share of issues).

 

[bhobba]

Any interpretation of QM is controversial, simply because we don't have a proof that it is THE right interpretation.

Exactly. All interpretations of QM suck - but in their own special way - you simply pick the one that to you sucks the least. To me the pilot wave theory sucks at a number of levels - an inherently unobservable pilot wave, the reintroduction of a preferred frame, and the difficulty extending it to QFT. But having discussed it extensively in the past the reasons it sucks for me are precisely the reason others like it - to each his/her own.

Thanks
Bill

 

[bhobba]

It's not otherwise possible to directly reconcile realism with probabilities(later attempts like MWI seem to do better than BI but it also has its share of issues).

There is no conflict between realism and probabilities. A world out there external and independent of us can be probabilistic. If you flip a coin and cover it with your hand you know it is heads or tails - just not which it is. The issue with realism and QM is the superposition principle where a particle for example can literally be in two positions at once which is the antithesis of any sane view of reality - and even logic. It's not like flipping a coin - it's not in one position or the other but you don't know which - it literally is in both positions. However now we understand QM better, especially decoherence, how the world of everday experience with its usual rules of logic and probability emerge is not as big an issue and I believe with further research will eventually be totally resolved - it almost is now - evidently anyway - I am delving into the full detail of decoherence right now to discover what the unresolved issues are - as far as I can tell its simply a few technical issues of how it works in all situations - the current models are not as general as they should/could be.

What you may be referring to is what is called naive realism where the world is both non contextual and value definite - that has been dealt a harsh blow - but not reality per se:
http://en.wikipedia.org/wiki/Naïve_realism

Thanks
Bill

 

[nonequilibrium]

Exactly. All interpretations of QM suck - but in their own special way - you simply pick the one that to you sucks the least. To me the pilot wave theory sucks at a number of levels - an inherently unobservable pilot wave, the reintroduction of a preferred frame, and the difficulty extending it to QFT. But having discussed it extensively in the past the reasons it sucks for me are precisely the reason others like t - to each hisher own.

Thanks
Bill

It's getting kind of boring having to repeat the same thing over and over, but: you're missing the point, indicating you haven't read properly what you're replying to. The "controversial" comment is concerning the validity of it being an interpretation. Please try to respect the distinction between this and actually preferring a specific interpretation. It's the same distinction between "this sentence is nice to read" and "this sentence is not a correct sentence" (e.g. due to grammatical issues).

And as for your other comment: isn't it rather inconsistent to label the pilot-wave unobservable since the pilot-wave is actually the well-known \psi? I might agree with the statement that the psi function is not directly observable, however this would actually be an argument pro the pilot-wave theory, since it's the only interpretation that does not just consist of a psi function. Perhaps you meant the postulated point particles are unobservable, as opposed to the pilot-wave. In that case I redirect you to my 2nd post in this thread where I try to argue that it does have observable consequences, in a sense.

 

[bhobba]

It's getting kind of boring having to repeat the same thing over and over, but: you're missing the point, indicating you haven't read properly what you're replying to. The "controversial" comment is concerning the validity of it being an interpretation. Please try to respect the distinction between this and actually preferring a specific interpretation. It's the same distinction between "this sentence is nice to read" and "this sentence is not a correct sentence" (e.g. due to grammatical issues).

I thought my reply was perfectly clear and directly related to the quote I replied to - its a valid interpretartion - but like all interpretations sucks in some way. The controversy is the same controversy any interpretation has - how to decide via experiment which is correct. Until you can do that its simply which appeals to your aesthetics of science better. Personally I think the pilot wave interpretation is a load of rubbish - its like a re-introduction of an aether and a step backwards - but opinions are like bums - everyone has one - it doesn't make it correct.

And as for your other comment: isn't it rather inconsistent to label the pilot-wave unobservable since the pilot-wave is actually the well-known \psi? I might agree with the statement that the psi function is not directly observable, however this would actually be an argument pro the pilot-wave theory, since it's the only interpretation that does not just consist of a psi function. Perhaps you meant the postulated point particles are unobservable, as opposed to the pilot-wave. In that case I redirect you to my 2nd post in this thread where I try to argue that it does have observable consequences, in a sense.

According to the pilot wave theory it really exists out there - and guides a real particle with a real and actual position - but so far no one has ever figured out how to directly observe it - that is not generally considered a good scientific ontology. It's like the aether of LET compared to SR. Both theories are valid but most people reject LET because of the inherently unobservable aether. A few still cling to it because they like physical causes for things like length shortening rather than it simply being the result of geometry like it is in SR. In the ensemble interpretation it simply is a device for calculating probabilities. Other interpretations have a different view as well - but the most common view is its simply a calculational device not having any direct existence eg Copenhagen and Consistent Histories view it that way.

Thanks
Bill

 

[nonequilibrium]

I thought my reply was perfectly clear - its a valid interpretartion - but like all interpretations sucks is some way.

Alright, then it was just off-topic.

According to the pilot wave theory it really exists out there - and guides a real particle with a real and actual position - but so far no one has ever figured out how to directly observe it - that is not generally considered a good scientific ontology. It's like the aether of LET compared to SR. Both theories are valid but most people reject LET because of the inherently unobservable aether. A few still cling to it because they like physical causes for things like length shortening rather than it simply being the result of geometry like it is in SR. In the ensemble interpretation it simply is a device for calculating probabilities. Other interpretations have a different view as well - but the most common view is its simply a calculational device not having any direct existence eg Copenhagen and Consistent Histories view it that way.

I see what you mean now. I think that's a good argument (although it's still off-topic, since it then becomes about preferring a certain interpretation, and that brings in the danger of getting this thread moved over to the philosophy forum). However, viewing the pilot-wave as physical is not a necessary part of the pilot-wave theory. Actually, I think it's more logical to say it's not physical. One argument is that it is not acted back upon (no action-reaction principle) by the point particle; this is not a very strong argument, but it's an intuitive one. In this sense the role of the pilot-wave is like that of the Hamiltonian function in classical mechanics: it determines the evolution without it being influenced by that evolution. A stronger argument is that the pilot-wave is a function on \mathbb R^{3N} (for N spin zero point particles in 3D). In the general N particle case this cannot be interpreted as a function on space, unlike for example the electric field, which can indeed be interpreted as physical. (This makes the pilot-wave look even more like the Hamiltonian in classical mechanics.)

 

[bhobba]

Alright, then it was just off-topic.However, viewing the pilot-wave as physical is not a necessary part of the pilot-wave theory. Actually, I think it's more logical to say it's not physical. One argument is that it is not acted back upon (no action-reaction principle) by the point particle; this is not a very strong argument, but it's an intuitive one. In this sense the role of the pilot-wave is like that of the Hamiltonian function in classical mechanics: it determines the evolution without it being influenced by that evolution. A stronger argument is that the pilot-wave is a function on \mathbb R^{3N} (for N spin zero point particles in 3D). In the general N particle case this cannot be interpreted as a function on space, unlike for example the electric field, which can indeed be interpreted as physical. (This makes the pilot-wave look even more like the Hamiltonian in classical mechanics.)

Interesting view. I would just like to mention that, it would seem, strictly speaking, the reason an electric field exists is QM in origin. Feynman actually developed a version of EM without fields where everything was direct action at a distance. The problem was he, and as far as I know no one else either, has been able to figure out a QM version - it seems QM really does require the existence of EM fields. Exactly what that is trying to tell us I don't really know - maybe you have an idea.

Thanks
Bill

 

[bohm2]

However, viewing the pilot-wave as physical is not a necessary part of the pilot-wave theory. Actually, I think it's more logical to say it's not physical.

Here's a criticism of this view in another post on this topic:

There is a very serious and obvious problem with their interpretation; in claiming that the wavefunction is nomological (a law-like entity like the Hamiltonian as you said), and because they want to claim deBB is a fundamentally complete formulation of QM, they also claim that there are no underlying physical fields/variables/mediums in 3-space that the wavefunction is only a mathematical approximation to (unlike in classical mechanics where that is the case with the Hamiltonian or even statistical mechanics where that is the case with the transition probability solution to the N-particle diffusion equation). For these reasons, they either refuse to answer the question of what physical field/variable/entity is causing the physically real particles in the world to move with a velocity field so accurately prescribed by this strictly mathematical wavefunction, or, when pressed on this issue (I have discussed this issue before with DGZ), they simply deny that this question is meaningful. The only possiblity on their view then is that the particles, being the only physically real things in the world (along with their mass and charge properties of course), just somehow spontaneously move on their own in such a way that this law-like wavefunction perfectly prescribes via the guiding equation. This is totally unconvincing, in addition to being quite a bizarre view of physics, in my opinion, and is counter to all the evidence that the equations and dynamics from deBB theory are suggesting, namely that the wavefunction is either a physically real field on its own or is a mathematical approximation to an underlying and physically real sort of field/variable/medium, such as in a stochastic mechanical type of theory.

http://74.86.200.109/showthread.php?t=247367&page=2

In case you haven't read it, a really good summary of this criticism can be found on p.136 of:

Formalism, Ontology and Methodology in Bohmian Mechanics
https://springerlink3.metapress.com...b5nwspxhjssd4c5c3cpgr&sh=www.springerlink.com

 

[Maui]

What you may be referring to is what is called naive realism where the world is both non contextual and value definite - that has been dealt a harsh blow - but not reality per se:
http://en.wikipedia.org/wiki/Naïve_realism

Thanks
Bill

This is exactly what i was referring to. The only way to fully get back to the preconceived notion of a world independetly existing out there with fixed values and properties is the Bohmian interpretation. Naive or not, it's the classical world of objects existing, not objects happening. Even though objects happening(decohering) are observationally real, this speaks more of a world of events. Certainly an issue that is not there in the BI.

 

[rocket123456]

Any theory proclaiming a phenomenon as being invincible is rather annoying.

That being said the interpretation might very well be correct since it's compatible with Einsteins special relativity.

We couldn't see any atoms back in the day so surely such things did not exist but of course they did!

John Bell who was famous for discrediting the local hidden variables was an avid defender of the pilot-wave theory with it's non-local hidden variables. So there is at least one heavyweight in the science community concidering it to be the correct description of QM.

 

[audioloop]

This is exactly what i was referring to the notion of a world independetly existing out there

Reality is the state of things as they actually exist (that is, with or without values or properties).

and counterfactual in physics refers to the fact that any physical system must have definite properties whether measured/observed or not.

 

[Demystifier]

Demystifier, I don't think you've read it carefully. It says that even the fact that it's a valid challenge as an interpretation is controversial. This has nothing to do with accepting it as a correct interpretation or not, but more fundamentally with its validity as an interpretation. The former is a more philosophical matter, the latter a more scientific matter.

You are right that these two types of controversy should be distinguished. But other interpretations are also controversial in that sense that there are people who are not convinced that it is consistent even as an interpretation.

But your question is what exactly is controversial about Bohmian interpretation, not about some other interpretation. I would leave the answer to those who actually think that it is controversial.

 

[f95toli]

Ah yes that makes more sense.

EDIT: on the other hand, since QM is a non-relativistic theory, why should anyone use relativistic arguments in discussions about its interpretation?

Standard QM is fully relativistic, SR was "incorporated" in QM in the early days of the development of the theory (by Dirac and others); the fact that there is no theory that unifies QM and GR is not really relevant here.

 

[nonequilibrium]

@ Demystifier: thanks for claring that up

Standard QM is fully relativistic, SR was "incorporated" in QM in the early days of the development of the theory (by Dirac and others); the fact that there is no theory that unifies QM and GR is not really relevant here.

Oh okay we're having a semantics issue: by QM I mean the non-relativistic version, i.e. not quantum field theory, which you seem to be talking about. The pilot-wave theory as usually presented is an interpretation for "ordinary"/non-relativistic QM. Concerning pilot-wave theories for QFT: I think there are multiple candidates at the moment. Then again, I think non-locality is also present there, so it seems your argument holds true.

I suppose I understand some people saying pilot-wave theory is invalid since it does not respect locality... I do think it deserves a nota bene (and I hope you agree), also being the reason why I don't find that argument too convincing: although the pilot-wave theory supports a non-local image of the universe, none of it predictions violate special relativity. This is because Einstein's special relativity emerges as an effective theory, much like how time-irreversibility is effective in a Newtonian theory (a better word is perhaps "illusory", but it is prone to misinterpretation).

Hence in my view the objection of non-locality might be a sensible thing to reflect upon when deciding to adhere to the interpretation or not, although it has no bearing on its validity as an interpretation per se.

 

[DrewD]

I think you are correct that there are no valid experimental ways to refute pilot wave theory. The argument is that it adds nothing and requires more assumptions. That bothers a lot of physicists. Physicists like simplicity which is why theories like SR and GR are so highly regarded. Not because they are simple to calculate, but because the initial assumptions are very simple and from only those assumptions, very precise predictions can be made.

My brief reading of Wiki didn't give me the impression that physicist thought that the pilot wave theory was wrong.

It uses the same mathematics as other interpretations of quantum mechanics; consequently, it is also supported by the current experimental evidence to the same extent as the other interpretations.

Maybe somebody rewrote it after this thread!

Frankly, I don't think most people care except here. There are a handful of good physicist out there that are trying to see if pilot wave theory will make any predictions that make it observationally different from standard QM. Right now there are no proposed experiments that would separate the two interpretations that I know of. It will be interesting if somebody comes up with something.

My answer to your question of "scientific controversy" is that most scientist include simple derivation and interpretation as a part of science when choosing an interpretation. If experimental predictions are the only issue, I think that there is no controversy.

 

[nonequilibrium]

Drew, pilot-wave theory requires actually less assumptions than the orthodox interpretation! Sure you need an extra assumption of point particles, but you get two other assumptions for free: Born's rule (i.e. that the modulus squared gives the probability) is a consequence, as is collapse! Both of these are extra assumptions in the orthodox interpretation.

However, something tells me that even though you now know this you still won't adhere to the pilot-wave interpretation (although according to your last post you should). People are weird like that.

 

[Demystifier]

Drew, pilot-wave theory requires actually less assumptions than the orthodox interpretation! Sure you need an extra assumption of point particles, but you get two other assumptions for free: Born's rule (i.e. that the modulus squared gives the probability) is a consequence, as is collapse! Both of these are extra assumptions in the orthodox interpretation.

However, something tells me that even though you now know this you still won't adhere to the pilot-wave interpretation (although according to your last post you should). People are weird like that.

Simplicity is a subjective concept. There is no objective measure of simplicity of a theory.

For PRACTICAL physicists, which most physicists are, the standard interpretation is still simpler because it requires a smaller amount of CALCULATION. It is simpler to calculate psi and probability density |psi|^2 then to calculate psi and a large ensemble of trajectories. Practical physicists are more interested in ability to efficiently calculate than in ability to intuitively explain.

But still, there are even situations in which it is PRACTICALLY SIMPLER to calculate the trajectories and the probability density than to calculate psi. See e.g.
Phys. Rev. Lett. 82, 5190–5193 (1999) [http://prl.aps.org/abstract/PRL/v82/i26/p5190_1]
In such situations, even for practical physicists Bohmian QM is really simpler than standard QM.

Other practical uses of Bohmian particle trajectories are discussed in a recent book
https://www.amazon.com/dp/9814316393/?tag=pfamazon01-20

 

[DrewD]

There are more physical assumptions. You need an unmeasurable pilot wave that controls the trajectories of real particles that have a physical position and momentum but, despite these being well defined, they cannot be simultaneously measured. I don't like that. I didn't say it was wrong.

You are right, I will not start using Bohmian mechanics because my research is in quantum information and nobody uses this interpretation because it provides nothing new (that's actually not true, but there has been no experimental confirmation of the one new prediction that I know of). It might be a nice way to think about things, and I often do imagine quantum particles to be somewhat like the Bohm interpretation, but until there is a reason to follow a less common interpretation that would make reading QM papers more difficult, you are correct.

You will probably continue to adhere to the pilot-wave interpretation, which is equally valid but provides nothing new, despite the fact that the rest of the physics community uses a different formality. This will make your research in anything except re-deriving QM difficult, but people are weird like that. Maybe you will make a breakthrough. Good luck.

 

[Demystifier]

There are more physical assumptions. You need an unmeasurable pilot wave ...

But standard QM also needs THE SAME unmeasurable wave (which is not called "pilot", but is mathematically the same anyway).

 

[nonequilibrium]

Simplicity is a subjective concept. There is no objective measure of simplicity of a theory.

For PRACTICAL physicists, which most physicists are, the standard interpretation is still simpler because it requires a smaller amount of CALCULATION. It is simpler to calculate psi and probability density |psi|^2 then to calculate psi and a large ensemble of trajectories. Practical physicists are more interested in ability to efficiently calculate than in ability to intuitively explain.

But still, there are even situations in which it is PRACTICALLY SIMPLER to calculate the trajectories and the probability density than to calculate psi. See e.g.
Phys. Rev. Lett. 82, 5190–5193 (1999) [http://prl.aps.org/abstract/PRL/v82/i26/p5190_1]
In such situations, even for practical physicists Bohmian QM is really simpler than standard QM.

Other practical uses of Bohmian particle trajectories are discussed in a recent book
https://www.amazon.com/dp/9814316393/?tag=pfamazon01-20

But when simply calculating the wavefunction suffices (due to only being interested in averaged behaviour), why can't the pilot-wave theorist also be satisfied with just calculating the wavefuntion in those cases? Why would he go through the trouble of the extra calculations? Concerning practical issues, I see the explicit trajectories more like an add-on which can be helpful in numerical simulations but are not important for predicting observations (of course they're important for understanding observations). Am I missing your point? More succinctly: can you think of a case where a pilot-wave theorist is obliged to go through more trouble than, say, someone adhering to the Copenhagen interpretation?

By the way, interesting book! I didn't know there was one like that out there.

There are more physical assumptions. You need an unmeasurable pilot wave that controls the trajectories of real particles that have a physical position and momentum but, despite these being well defined, they cannot be simultaneously measured. I don't like that. I didn't say it was wrong.

You are right, I will not start using Bohmian mechanics because my research is in quantum information and nobody uses this interpretation because it provides nothing new (that's actually not true, but there has been no experimental confirmation of the one new prediction that I know of). It might be a nice way to think about things, and I often do imagine quantum particles to be somewhat like the Bohm interpretation, but until there is a reason to follow a less common interpretation that would make reading QM papers more difficult, you are correct.

You will probably continue to adhere to the pilot-wave interpretation, which is equally valid but provides nothing new, despite the fact that the rest of the physics community uses a different formality. This will make your research in anything except re-deriving QM difficult, but people are weird like that. Maybe you will make a breakthrough. Good luck.

I don't follow you when you say "there are more physical assumptions" or "it adds nothing new". These words are probably too subjective in a sense. In my view, for example, the pilot-wave theory requires less physical assumptions, since collapse and Born's rule are physical. Unless you don't call them physical, in which case you're thinking in an interpretation where hardly anything is physical, and I've never quite understood that reasoning, but maybe that's my bad. As for providing "nothing new": surely we all agree it adds a lot on the theoretical level? In the sense that: it explains collapse, it explains Born's rule, it explains the time-dependent Schrödinger equation form the time-independent one etc. Most importantly, in my case, it is clear about what it's talking about, but it seems like most people don't have that problem with other interpretations, so it seems to be an iffy topic. In case you're talking about practical issues: even there it adds some new things. As you may have heard of, there is the concept of quantum non-equilibrium. Indeed, this has not been confirmed, so it's not an argument pro the pilot-wave theory, but it is an argument against the statement that it brings nothing new. More importantly, for real pratical issues, it leads to new methods of numerical simulations (I can provide links if you're truly interested) which seem to improve on the older methods. Maybe there are more such new practical effects in pilot-wave theory, but I'm not an expert on it.

As concerning your statement that pilot-wave theory works with an undetectable pilot-wave: I've encountered this statement before, even in this thread (and responded to it then in more depth). But as Demystifier just posted: I don't understand why you have such problems with it since it's the same wavefunction you're used to.

 

[Demystifier]

... it explains the time-dependent Schrödinger equation form the time-independent one etc. ...

Are you sure about that? Can you explain it or give a reference?

 

[nonequilibrium]

Are you sure about that? Can you explain it or give a reference?

Sure, it's really a nice little idea. From the little I know of quantum gravity, it seems the interest originates from there, in an attempt to derive the time-dependent Schrödinger equation from a time-independent universal wavefunction, this by treating spacetime as a macroscopic quantity.

Let's keep it simple, keeping the idea clear: the set-up is a two-particle system, the first with coordinates q, the latter with coordinates Q. The "universal" wavefunction is the time-independent \Psi(Q,q) satisfying E \Psi = \hat H \Psi. We now suppose that the Q-particle is macroscopic, such that we know its (Bohmian) position Q(t) at all times. We now want to treat the subsystem q quantum-mechanically. To do this, it is logical to define the conditional wavefunction \psi(q,t) := \Psi(Q(t),q). Note that the conditional wavefunction is now time-dependent since we've evaluated the universal wavefunction in the Bohmian trajectory for the macroscopic particle. It's not hard to prove/see that this conditional wavefunction and the universal wavefunction predict the same physics for the small particle.

Now due to the postulates of pilot-wave theory we know \dot Q(t) in terms of \Psi. Consequently, using the chain rule, we can calculate i\partial_t \psi(q,t). One gets that in highest order of M, being the mass of the macroscopic particle Q, we get that i\partial_t \psi = \hat H' \psi where \hat H' denotes the appropriate Hamiltonian for the subsystem. The math is a bit cumbersome, however I worked it out in a bachelor (i.e. undergraduate) project I made; I will PM it to you.

Summarizing, in the case of a time-independent Schrödinger equation, we can derive the time-dependent Schrödinger equation for a subsystem in case the environment is macroscopic.

Another, in my view less compelling, approach is taken by Goldstein in e.g. http://arxiv.org/pdf/quant-ph/0308039v1.pdf (page 21). The above approach, the one I outlined, I haven't seen as such in print. I think perhaps Kittel talks about it in his quantum gravity book, but I'm really not sure, this is more of a guess. Anyway I don't claim priority on this one, the suggestion mainly came from my advisor for the project (Ward Struyve), and I don't know where he got his juice, although there is a link with Tejinder Pal Singh as I outline in my project. I'll send the PM in a moment. (Anyone else interested is free to PM me, of course.)

NB: you are of course aware, Demystifier, but for other readers of this post I might note that the concept of conditional wavefunction is not new at all and can be read about in many papers/books about pilot-wave theory, e.g. Bohmian Mechanics by Dürr and Teufel. It's a nice new concept that pilot-wave theory brings in and seems to be fertile.

 

[nonequilibrium]

EDIT: the post I replied to seems to have been snipped

 

[bhobba]

But standard QM also needs THE SAME unmeasurable wave (which is not called "pilot", but is mathematically the same anyway).

Yea, but its ontological status is different. In most other interpretations (not all but most) of QM its purely a device for calculating probabilities, in BM it is supposed to actually exist out there and have physical effects that guide the actual particle that also exists - is like the aether in LET - and most physicists reject it for the same reason the aether is rejected. Like I say all interpretations suck in their own special way and the existence of the pilot wave that can not be detected is one way BM sucks.

Thanks
Bill

 

[nonequilibrium]

Bhobba, what is it then, according to you, that one measures, as viewed from the orthodox interpretation (or whatever interpretation you feel comfortable with). Apparently it cannot be the wavefunction, since you say that those interpretations treat it as unphysical. It can't be a point particle since then you'd have the pilot-wave theory, since any theory with point particles and wavefunctions can be shown to be the usual de Broglie-Bohm theory. Unless, of course, you deny the physical reality of anything in between measurements, "measurements" just being blips on a machine meaning nothing else, in which case I wonder why you would use the word "measurement" at all. This question is probably too philosophical, but I feel as though without your answer on it, I can't understand the other things you say (at least I can't understand your view on the matter so far, although I'd like to).

 

[bhobba]

Bhobba, what is it then, according to you, that one measures, as viewed from the orthodox interpretation (or whatever interpretation you feel comfortable with).

One doesn't 'measure' anything because that tacitly assumes what is being measured and what is doing the measurement is independent. What interpretations such as the Ensemble interpretation, Copenhagen, Consistent Histories etc provide is a prediction of the probabilities of what the outcome of a system and measurement apparatus is. Specifically the basis vectors one expands a state into varies from experimental, measurement, observational - whatever words you want to use - setup, apparatus etc etc - it's inherently contextually dependent.

That is why decoherence is so important because it gives a physical explanation for this state of affairs - exactly how the state is decohered by interaction with the environment depends on the environment - ie the overall observational situation.

In such a view a state doesn't physically exist out there - it simply codifies in a mathematical entity what the outcome of a system and observational apparatus is ie its purely a theoretical device.

Thanks
Bill

 

[nonequilibrium]

I've often heard decoherence explains collapse, but I've never seen it done (without some invalid argument along the road). Can you give me a reference? (Specifically I understand how decoherence leads to non-interfering components, but I don't understand how one specific component is selected out in such interpretations as you mention.)

Anyway you seem to be implying that every element of a theory is directly observable seems like a necessary part of a good theory/interpretation? Wouldn't you say "understanding" is equally important as "predicting"? Anyway, more importantly, do you have a clear notion of what you mean by "directly observable"? Indirectly, everything is observable in a theory, otherwise it wouldn't be in the theory.

 

[bohm2]

Anyway you seem to be implying that every element of a theory is directly observable seems like a necessary part of a good theory/interpretation? Wouldn't you say "understanding" is equally important as "predicting"?

I'm sympathetic to this view and I'm guessing this is the reason why I find Valentini's and Bohm's/Hiley's Bohmian approach more "understandable"/"explanatory" than DGZs minimalist Bohmian interpretation. Now we have sub-interpretations within interpretations. Belousak writes it like this:

On the DGZ view, then, the guidance equation allows for only the prediction of particle trajectories. And while correct numerical prediction via mathematical deduction is constitutive of a good physical explanation, it is not by itself exhaustive thereof, for equations are themselves 'causes' (in some sense) of only their mathematical-logical consequences and not of the phenomena they predict. So we are left with just particles and their trajectories as the basis within the DGZ view of Bohmian mechanics. But, again, are particle trajectories by themselves sufficient to explain quantum phenomena? Or, rather are particle trajectories, considered from the point of view of Bohmian mechanics itself, as much a part of the quantum phenomena that needs to be explained?...the mere existence of those trajectories is by itself insufficient for explanation. For example, to simply specify correctly the motion of a body with a certain mass and distance from the sun in terms of elliptical space-time orbit is not to explain the Earth's revolving around the sun but rather to redescribe that state of affairs in a mathematically precise way. What remains to be explained is how it is that the Earth revolves around the sun in that way, and within classical mechanics, Newton's law of universal gravitation and second law provide that explanation.

The author then goes on to argue for favouring the non-minimalist Bohmian model (e.g. quantum potential, etc.). I found that argument kind of persuasive for the same reason I found your argument above persuasive.

 

[nonequilibrium]

Bohm2, thank you for your posts (incl #22). They are certainly interesting remarks. I have two questions:

* One minor one: you seem to imply Valentini favours interpreting the quantum potential as a causal agent (instead of just a handy mathematical similarity with the Hamilton-Jacobi formalism of classical mechanics). However, I remember reading some passages of his work where he definitely implies the reverse, more in the line of what you seem to call the minimalist Bohmian interpretation. Does this claim seem odd to you? (if so I'll dig up the exact reference) If not, in what way did I misunderstand you?

* More importantly: although I'm in principle not against the kind of argument you bring forth (regarding explaining the trajectories) I can't find it very convincing. If I understand correctly, you're not satisfied with predicting the trajectories, but also want to find a causal agent. Indeed this is in line with my own comment regarding "understanding". But I'm having trouble with how one determines what does not need to be explained, trajectory-wise. In Newtonian mechanics, linear motion at constant speed needs not be explained (first law of Newton). How is it obvious that in the dBB case we still regard this as the case that needs no further explanation?

I'm trying to understand your point of view. Which is it that you want to interpret physically: the wavefunction, or the quantum potential? Perhaps the quantum force? Or all of them? And for any: how do you circumvent the seemingly fundamental problem concerning them being functions on configuration space? Actually, I suppose this only a problem if one tries to interpret the wavefunction physically; it's less of a problem for the quantum potential, say. After all, that case is reminiscent of electrodynamics. Do point out of I'm being inconsistent with this view.

 

[bhobba]

I've often heard decoherence explains collapse, but I've never seen it done (without some invalid argument along the road). Can you give me a reference? (Specifically I understand how decoherence leads to non-interfering components, but I don't understand how one specific component is selected out in such interpretations as you mention.)

Anyway you seem to be implying that every element of a theory is directly observable seems like a necessary part of a good theory/interpretation? Wouldn't you say "understanding" is equally important as "predicting"? Anyway, more importantly, do you have a clear notion of what you mean by "directly observable"? Indirectly, everything is observable in a theory, otherwise it wouldn't be in the theory.

The reason you have not seen decoherence explaining the measurement problem is because it strictly speaking doesn't - it explains it only for all practical purposes. It explains how a superposition is transformed into a mixed state but where each pure state of the mixed state is an eigenstate of what is being measured. This means the usual rules of probability apply where you can consider it in an actual state that the measurement reveals rather than some kind of weird superposition where it is literally in a number of states simultaneously eg literally being in two positions at the same time. The ensembles of the ensemble interpretation then actually exist and you simply pick out one of them. Here is the textbook I am studying right now about it:
https://www.amazon.com/dp/3642071422/?tag=pfamazon01-20

Why do you want to use terminology like directly observable for a situation when it is the system AND observational apparatus that the theory describes?

Sure understanding is important and I think I understand the interpretations I mentioned better than an inherently unobservable pilot wave that strongly reminds me of an aether.

Don't be fooled by statements of guys like Feynman who say no one understands QM - in the context of what he was writing about it is 100% true - but that context is in terms of everyday pictures where you simply can not picture a particle taking two paths simultaneously. If you refuse to think in terms like that - no problem. If you try to then you will as he said go down a hole that no one has ever escaped from. You can also ascribe to BM if you like - but I personally think this unobservable pilot wave is a crock of crap - but to each his/her own. I personally have no problem with viewing the world in ways different from everyday experience. I recently heard an audiobook on entanglement where they talked about a discussion Feynman and Bohm had while they were in Brazil. Dave was really proud of BM claiming it solves all sorts of problems but, Dick explained - basically - it only solved those problems if you think they are problems - he had zero issues with interpretations that refused to think in terms of ordinary everyday pictures - it worked perfectly OK for him that way - as it does for me.

Thanks
Bill

 

[Demystifier]

Bhobba, I could appreciate your quite orthodox view of QM, provided that you give me straight answers to the following questions:
1. Does anything exist before we observe it?
2. If yes, then what it is?
3. If you don't know what it is, then do you think physics should try to find it out?

 

[bhobba]

Bhobba, I could appreciate your quite orthodox view of QM, provided that you give me straight answers to the following questions:
1. Does anything exist before we observe it?
2. If yes, then what it is?
3. If you don't know what it is, then do you think physics should try to find it out?

Without decoherence then it does not exist before you observe it - the act of observation causes it to exist. With the ensemble interpretation the naive view is it really does exist in that state prior to observation but the Kocken-Sprecker theorem says - no way. Ballentine was fouled up by this and resorted to the belief some sub quantum process meant it really did exist - and this was Einsteins view - QM was incomplete. However since it is really a theory about the results of observation ie information - there is nothing physically going on so the act of observation causing it to exist is not really a problem. But it does whisper in your ear - something else is going on here.

I believe that something else is decoherence. It causes a superposition to become a mixed state where each pure state of a mixed state is an eigenvector of what is being observed so no collapse occurs - observation does not change a state - it reveals what is really there. A mixed state is in one of its pure states - we simply do not know which one. This is completely different from a superposition. It does not solve the measurement problem because it does not say how a particular eigenstate is selected (there are other issues such as what can we say before the environment quickly decoheres it - but that is the main one) - what it does however is explain how it is in an eigenstate before observation - it really is in a definite eigenstate before observation. Schrodinger's cat really is alive or dead - not some weird state where it is both alive and dead.

To be 100% sure my answers to your questions are:

1. Yes
2. We don't know - but it is a definite outcome 100% for sure - we simply do not know which one.
3. I have zero problems with a system being in a definite state and not knowing what it is and physicists should not worry about it. But if they want to - well as one wag once said - free scientific inquiry - the first part is redundant.

Thanks
Bill

 

[Demystifier]

For bhobba, mr. vodka, and bohm2:
I don't think that wave function in BM is more real than in standard QM.

In standard QM, one may (or may not) think of psi merely as a mathematical tool to compute the probability.
Likewise, in BM one may (or may not) think of psi merely as a mathematical tool to compute the particle trajectories.

Both in standard-QM camp and in BM camp there are people who disagree on how "real" the wave function is. But in both camps, this question is NOT considered to be a crucial one.

 

[Demystifier]

Without decoherence then it does not exist before you observe it - the act of observation causes it to exist.

1. Yes
2. We don't know - but it is a definite outcome 100% for sure - we simply do not know which one.
3. I have zero problems with a system being in a definite state and not knowing what it is and physicists should not worry about it. But if they want to - well as one wag once said - free scientific inquiry - the first part is redundant.

I would like to remind you that questions 1. 2. and 3. were referring to reality BEFORE observation. So perhaps you would like to rewrite your answers to 1. 2. and 3., because in the present form it doesn't make sense.

 

[bhobba]

For bhobba, mr. vodka, and bohm2:
Both in standard-QM camp and in BM camp there are people who disagree on how "real" the wave function is. But in both camps, this question is NOT considered to be a crucial one.

I agree that there is disagreement on how real the potential that determines the position of the particle is is in BM. But I do not agree this issue is not crucial - I believe you really must consider it real or how else does it determine the position of the particle. I think there was a post earlier on in this thread that explained the issue.

Thanks
Bill

 

[bhobba]

I would like to remind you that questions 1. 2. and 3. were referring to reality BEFORE observation. So perhaps you would like to rewrite your answers to 1. 2. and 3., because in the present form it doesn't make sense.

I would like to remind you that a mixed state is in a particular pure state prior to observation - we simply do not know which one. Schrodengers cat is definitely alive or dead prior to observation with decoherence.

Thanks
Bill