Is BM Bohmian Local actually Local

[RandallB]

Is BM “Bohmian Local” actually Local

Is BM “Bohmian Local” actually Local

The debate over “local” as defined by Bohmian Mechanics compared to the “local” described by “Einstein Local” and “Bell Local” constantly invades and disrupts the discussions of various threads. This thread is to provide a place to discuses this issue without the need to cluttering other threads with multiple versions of the same argument being rehashed.

If I understood you correctly, you claim that Bohmian mechanics is actually local? I strongly disagree.

Note, on addition, that Bell was inspired by Bohmian mechanics when he discovered his famous theorem on the relation between QM and local hidden variables.

1. The universal wave function, given by Wheeler-De Witt equation is stationary.
2. The initial particle configuration at big-bang is a constant.
3. The trajectory of any particle can be described in terms of the two constant terms above.

In other words, by introducing the initial conditions in the particle's law of motion one can avoid non-locality. Is this wrong?

I both disagree and agree with Demystifier.
BM is “local” within the rules described by Bohm.
However, these are not the same rules and expectation of local held by Einstein! That strict version of Einstein Local uses determinate values from the point when an entity (Photon or Particle) is created up to the point that value can be measured by some form of detection.
That is the only type of local that Bell Theorem can test for, and must treat “BM Local” as “non-local”, which might be better described as not “Local & Realistic”. That is “not realistic” meaning not classically real. Such as when BM reality coordinates extraordinary information about the past history prior to the creation of photon into some type of synchronization with any future possible detection device and the history of that divice.

The famous tests using the Bell Theorem no not apply to BM as BM can successfully resolve the EPR-Bell paradox as a “Non-Bell Local” theory just as other “Non-Bell Local” theories can. Bell cannot help with picking the best theory between BM QM or any other “Non-Bell Local” theories. Just as BM is powerless to critique how Bell evaluates the possibility of the existence of a Hidden Variable that is Einstein Local, Bell Local.

Anyway, that is my opinion.
For those that feel “BM Local” is the same as Bell Local,
and those that feel BM should make no claim of any type as to being local in any sense of form please detail your points here in this thread.

Thanks

 

[Demystifier]

Ueit, before discussing the Wheeler-DeWitt equation, I would like if we could first discuss the simplest case, that is BM for nonrelativistic QM of particles. So, in your opinion, is it local or not?

 

[ueit]

Ueit, before discussing the Wheeler-DeWitt equation, I would like if we could first discuss the simplest case, that is BM for nonrelativistic QM of particles. So, in your opinion, is it local or not?

As far as we use the conditional wavefunction (CWF), BM is non-local.

In a double-slit experiment, for example, closing one slit produce an instantaneous change of the wavefunction.

On the other hand, the universal wavefunction (UWF) does not change, so no information need to be instantly transmitted from the slit to the particle. Both the slit (actualy the particles the wall is build of) and the particle, follow the same, changeless field, UWF.

 

[Demystifier]

As far as we use the conditional wavefunction (CWF), BM is non-local.

In a double-slit experiment, for example, closing one slit produce an instantaneous change of the wavefunction.

On the other hand, the universal wavefunction (UWF) does not change, so no information need to be instantly transmitted from the slit to the particle. Both the slit (actualy the particles the wall is build of) and the particle, follow the same, changeless field, UWF.

But if UWF does not contain gravity (or contains it, but gravity is quantized in a different way, not by using the Wheeler-DeWitt equation), then UWF does depend on time, so it is not changeless.

If you still view such BM as being local, would you say that Newton's law of gravity is also local?

 

[ueit]

But if UWF does not contain gravity (or contains it, but gravity is quantized in a different way, not by using the Wheeler-DeWitt equation), then UWF does depend on time, so it is not changeless.

Yeah, but this should not be a problem as long as UWF evolves deterministically.

If you still view such BM as being local, would you say that Newton's law of gravity is also local?

Yes, it can be interpreted like that, just like any other deterministic theory. Now, I'm not saying that Newton's gravity is necessarily local, only that it is not necessarily non-local. While the non-local description is certainly much more simple, intuitive and elegant than the local one, it is not compulsory. This is what I'm saying about BM too.

 

[Demystifier]

Yeah, but this should not be a problem as long as UWF evolves deterministically.

Yes, it can be interpreted like that, just like any other deterministic theory. Now, I'm not saying that Newton's gravity is necessarily local, only that it is not necessarily non-local. While the non-local description is certainly much more simple, intuitive and elegant than the local one, it is not compulsory. This is what I'm saying about BM too.

OK, I agree that BM is not more (and not less) nonlocal than Newton's gravity.

 

[ueit]

OK, I agree that BM is not more (and not less) nonlocal than Newton's gravity.

But would you also agree that a deterministic theory cannot be mathematically proven as being non-local, that the local or non-local character is a matter of interpretation of the mathematical formalism?

 

[Demystifier]

But would you also agree that a deterministic theory cannot be mathematically proven as being non-local, that the local or non-local character is a matter of interpretation of the mathematical formalism?

I agree that the notion of (non)locality can be defined in many inequivalent ways. So, in a sense, it is a matter of definition. Once you fix your definition, you can prove that a deterministic theory is either local or nonlocal.

 

[RandallB]

But would you also agree that a deterministic theory cannot be mathematically proven as being non-local, that the local or non-local character is a matter of interpretation of the mathematical formalism?

It’s not a matter of mathematically proving a deterministic theory non-local or local. It is a matter of definitions. The Bohm interpretation of QM or Boh(e)mian Mechanics is free to define a form of “Local” just a MWI can do so as well. MWI can assume two photons separating in all 3 dimensions and time, but still remaining “local” or next to each other in some another dimension(s) in a meaningful way. At least until “entanglement” is broken in such a way that the “World” they live in is un-split & synchronized till then, thus accounting for entanglement.

BM-Local just uses a synchronized past history of photons and detectors to duplicate the results predicted by QM and MWI.
Both BM and MWI can resolve “entanglement” not because they are BM-local or MWI-local, but because both theories can successfully establish an analogy to the HUP results found with QM. They are both interpretations of QM that may or may not be correct or even useful.

Neither can use the fact that they can resolve Bell Theorem Entanglement, to declare themselves superior to QM or any other Non-Bell Local theory, because BM-local and MWI-local are not Bell Local.

And as far as I know the only kind of local anyone really cares about how it applies to the Bell Theorem in an effort to declare themselfs the better theory. Therefore I see no purpose discribing alternate versions of local at all. Just theories that are not Bell-Local like BM WMI QM String etc. Those theories are just interpretations of QM that would need something other than Bell to show which of the non-local ones is the better theory.

If there is topic other than Bell & HV's that cares about "Local" what is it?

 

[Demystifier]

I The Bohm interpretation of QM or Bohemian Mechanics

Mechanics is Bohmian, Bohemian is Rhapsody. Nevertheless, there is a deep relation between them. See the lyrics after the Abstract in
http://xxx.lanl.gov/abs/physics/0702069

 

[RandallB]

Mechanics is Bohmian, Bohemian is Rhapsody. Nevertheless, there is a deep relation between them. See the lyrics after the Abstract in
http://xxx.lanl.gov/abs/physics/0702069

Great link and reference to the “Queen” lyrics by F. Mercury. I was going to correct my spelling error but how can I edited it out after seeing that.

Another part of his lyrics also said
"I sometimes wish I'd never been born at all,"
This could put a whole new slant on this Rock Ballad, could Freddie have been singing about a frustrated physicist that wished they’d never been part of the “Born probabilistic interpretation” !

As to the link content; it referred to the various alternatives to QM such as :
“statistical ensemble interpretation, Bohm (pilotwave) interpretation, Nelson (stochastic dynamics) interpretation, Ghirardi-Rimini-Weber (spontaneous collapse) interpretation, quantum logic interpretation, information theoretic interpretation, consistent histories interpretation, many-world (relative state) interpretation, relational interpretation, etc.”

And I realized these all differ from Copenhagen Interpretation in that they trying to define some hidden structure or mechanism to explain the results QM was getting. But they did not expect that “hidden structure or mechanism” to satisfy EPR. They were not trying to satisfy Einstein, they wanted to describe a reality of some kind behind the “probabilistic HUP”, which they already expected to be non-EPR & therefore Non-Local. Even Bohm himself called his a interpretation of QM with a hidden variable, in the context of some hidden structure or mechanism to explain QM/HUP. Not some classical variable to satisfy Einstein and "local".

I suspect the constant haranguing we see over “Local” is just the result of people seeing the phrase “hidden variable” used by Bohm, and jumping to the incorrect conclusion that it was intended to be the same thing as Einstein’s Local Hidden Variable. Big mistake, which lead them to thinking Bell has something to say about ‘their favorite theory’. While the Bell Theorem can only test the credibility of a Classically Local EPR Hidden Variable vs. the successful predictions of ALL the various and non-local “Born probabilistic interpretations” from Copenhagen to relational interpretation, BM included.

RB

 

[ueit]

I agree that the notion of (non)locality can be defined in many inequivalent ways. So, in a sense, it is a matter of definition. Once you fix your definition, you can prove that a deterministic theory is either local or nonlocal.

By local theory I mean a theory that doesn't allow a causal connection to exceed c.

I think that the local or non-local character of a deterministic theory is a matter of interpretation. In Newtonian mechanics one can deny that the instantaneous gravitational force really exists and the non-local appearance is a result of a past interaction. In other words, A accelerates towards B's instantaneous position not because there is a non-local force between A and B but because A and B used the old information, available through a past, local interaction, to mimic this behavior. You can calculate where Pluto will be 1 year from now, based on the information you've got by local means, you don't need a time machine to go into the future to find that out. In the same way, A can "calculate" where B is now and accelerate towards that position.

 

[Demystifier]

Another part of his lyrics also said
"I sometimes wish I'd never been born at all,"
This could put a whole new slant on this Rock Ballad, could Freddie have been singing about a frustrated physicist that wished they’d never been part of the “Born probabilistic interpretation” !

Another interesting fact is that one of the QUEEN members is a physicist. Actually, he said recently now he will finish his PhD dissertation.

 

[RandallB]

By local theory I mean a theory that doesn't allow a causal connection to exceed c.

But that is pointless and NOT the way you have been have been using the term. With this definition of “local” any “Born probabilistic interpretation” can be considered local, QM & BM included. With this kind of “local” any QM style interpretation can fabricate a ‘hidden variable’ to solve “Weird Actions at a distance” without information or individual causal actions to exceed c.

QM >> uses a HUP version of ‘HV’
Bohm Interpretation >> uses a pilotwave / guidewave ‘HV’
WMI >> uses the relative state of Many Worlds that are selected somehow
Consistent Histories Interpretation >> defines a ‘HV’ of particle histories that are somehow manipulated to effect the appropriate results.

BUT none of these provide a complete explanation of how those results are achieved, including BM which seems to be described as some kind of combination of the Bohm Interpretation & Consistent Histories Interpretation. All contain an unexplained probabilistic element that must be accepted as a real active function without provable explanation.
[As to using Pluto for an example, add one more planet and refer to the orbital three body problem]

None of these versions of “local” is what is intended by most people when they say “Local”. They mean LOCAL as Einstein intended in EPR and what the Bell theorem tests for. Meaning a “Local” solution that can be described in classical understandable terms sometimes also referred to as “Local & Realistic” and the possibility of Classically describable HV, not some abstract function declared a ‘HV’. Anyone can “open their mind” in a metaphysical way to visualize a “Non-local” that does not make that interpretation “Bell-Local”. They are variations of the “Born probabilistic interpretation”.

So far I’ve only seen how the interpretation of BM can visualize a solution to no better level of understanding than any other QM like “Born probabilistic interpretation”.

Therefore, in the sense that most understand the term local; “BM local” should be considered Non-Local (i.e. not Bell Local).

 

[Demystifier]

B All contain an unexplained probabilistic element that must be accepted as a real active function without provable explanation.

Nice post, but I do not understand this particular sentence. What would be the unexplained PROBABILISTIC element for BM?

 

[ueit]

But that is pointless and NOT the way you have been have been using the term. With this definition of “local” any “Born probabilistic interpretation” can be considered local, QM & BM included. With this kind of “local” any QM style interpretation can fabricate a ‘hidden variable’ to solve “Weird Actions at a distance” without information or individual causal actions to exceed c.
QM >> uses a HUP version of ‘HV’
Bohm Interpretation >> uses a pilotwave / guidewave ‘HV’
WMI >> uses the relative state of Many Worlds that are selected somehow
Consistent Histories Interpretation >> defines a ‘HV’ of particle histories that are somehow manipulated to effect the appropriate results.

Let me give you a quote from Bell's book, " Speakable and Unspeakable in Quantum Mechanics", p. 54. The name of the chapter is "Local causality":

Consider a theory in which the assignment of values to some beables "lambda" implies, not necessarely a particular value, but a probability distribution, for another beable A. (...)
Let A be localized in the space-time region 1. Let B be a second beable localized in a second region 2 separated from 1 in a spacelike way. Now my intuitive notion of local causality is that events in 2 should not be causes of events in 1, and vice versa.

I think this is pretty close to my (shorter) definition of locality. Anyway, I assume you agree that the above quote clearly explains what Bell-local means and this is what I intend when using the word "local".

Now, one can see that in order to speak about the local or non-local character of a theory, that theory must clearly specify its beables and the mechanism by which they are related (in other words it must be a realistic theory).
The Copenhagen interpretation does not specify the beables of the theory it only speaks about observables. Therefore one cannot say if the theory is local or not.
BM, as it is usually understood is non-local because events in a region 1 can have a causal influence on events in a region 2 where 1 and 2 are spacelike separated. For example, the velocity of a particle in region 1 might be influenced by the particle configuration in region 2.

My point here is that one is not forced to interpret the BM formalism in this way. One can propose that the particle in region 1 did not receive a ftl signal from 2, communicating the particle configuration there, but it made use of past information, arrived at c to "calculate" this configuration. The velocity of particle in 1 remains related to the particle configuration in 2 by the same formula, but no causal connection exists between 1 and 2. Therefore, in this interpretation, BM is local.

In the same way you can calculate where Pluto, or Mars, or Alpha Centaury is "now" from the information you have (light arrived at c). There is no need to establish a non-local communication to those objects.

BUT none of these provide a complete explanation of how those results are achieved, including BM which seems to be described as some kind of combination of the Bohm Interpretation & Consistent Histories Interpretation. All contain an unexplained probabilistic element that must be accepted as a real active function without provable explanation.

I'm not sure I understand you here. I agree that BM contains an "unexplained element", the wave function, which has beable status although it cannot be mapped to our 4d-space-time, but there is nothing probabilistic about that.

[As to using Pluto for an example, add one more planet and refer to the orbital three body problem]

The fact that a 3+ body problem cannot be solved exactly is irrelevant. The system remains perfectly deterministic, although chaotic.

None of these versions of “local” is what is intended by most people when they say “Local”. They mean LOCAL as Einstein intended in EPR and what the Bell theorem tests for. Meaning a “Local” solution that can be described in classical understandable terms sometimes also referred to as “Local & Realistic” and the possibility of Classically describable HV, not some abstract function declared a ‘HV’. Anyone can “open their mind” in a metaphysical way to visualize a “Non-local” that does not make that interpretation “Bell-Local”. They are variations of the “Born probabilistic interpretation”.

So far I’ve only seen how the interpretation of BM can visualize a solution to no better level of understanding than any other QM like “Born probabilistic interpretation”.

Therefore, in the sense that most understand the term local; “BM local” should be considered Non-Local (i.e. not Bell Local).

Please explain why my interpretation of BM, where the instantaneous correlations between events in region 1 and 2 are NOT causally related is non-local.

 

[RandallB]

Nice post, but I do not understand this particular sentence. What would be the unexplained PROBABILISTIC element for BM?

To simplify the issue as much as possible we have in an EPR-Bell polarization test we have four elements to deal with, two Photons A & B created from a single point and two detectors DA & DB.
From the perspective of a Detector making a measurement to be compared with the other Detector it has three “probabilistic” issues to consider against its own fixed setting. The random setting of the other detector, and the variables associated with Each of the Photons. The issue is how these various random events coordinate across time and distance to successfully violate Bell Inequities.

As mentioned before: “Bohm Interpretation” uses a pilotwave / guidewave to synchronize these probabilities. And Consistent Histories Interpretation uses particle histories that somehow conspire to achieve the same synchronization.

I’m no expert on BM or the ueit version of it - but it seems to be a mixture of these two replacing the pilotwave with a “universal wavefunction” including a wave history backwards and forwards though history (to the Big Bang if needed) to link in a synchronized way the two detectors and two photons in some synchronization to again to successfully violate Bell Inequities. Like the “Consistent Histories Interpretation” I suppose these results can be considered “predetermined” by a “deterministic” past and future, instead of probabilistic. As in we are only experiencing observations and events that have already been set place, only waiting for the photons and us to follow a deterministic timelines we cannot change. That is a philosophy that does not belong in this forum. In the view of “Einstein Local” Consistent Histories Interpretation. Sometimes this is also referred to a the events as their correlations being part of a “conspiracy” which the theory does not explain why determinism would go to the trouble of creating such a unrealistic “conspiracy” of results. Which runs it afoul of the other half “Einstein Local” that requires both “Local and Realistic”

None of these things can be convincing described to a Local & Realist in the way local is expected by EPR. There the positioning of the detectors must remain random and not part of defining a solution by finding any form of coordination between them. Only defining variables set into the two independent photons at their creation (no entanglement) can be allowed in a “Local & Realistic” solution.

Unfortunately the misuse of the terms “local” and “hidden variable” by Non-Local theories is so prevalent an badly understood that now assume anyone using “HV” or “local” most likely do not know what they are saying or will be misunderstood. I’ve taken to always referring to them as “Einstein HV” or “Bell Local” and why I now always spell them out that way and expect only those meanings to be used in the “Finding Einstein’s Hidden Variable” thread.

RB

 

[RandallB]

Please explain why my interpretation of BM, where the instantaneous correlations between events in region 1 and 2 are NOT causally related is non-local.

Because your version of BM-Local is “unrealistic” in terms of the “Local and Realistic understanding of Bell-Local by Bell.

You cannot expect everyone to just shove in your version of BM-Local as “local” when the expectation of for the word “local” is the EPR meaning of “Bell Local” or “Einstein Local” that would expect a Einstein Hidden Variable to be defined in classical terms.

You said before you draw your version of a BM-local HV in a two dimensional diagram, if you want be convincing just produce the drawing! But when you say it may be “ugly”, that cannot include any imaginary or probabilistic function somehow incorporated into the drawing. It needs to solve a EPR-Bell problem strictly from a Classical Commonsense application of what is in the drawing.

Otherwise your definition of local is simply something different that the “Local” as defined by “Einstein Local” everyone else assumes by the word local.