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Is there any relativistic causal non-local theory for ##\lambda##? If not, you can of course speculate a lot without much scientific substance.
No, but there is nonrelativistic causal nonlocal theory for ##\lambda## which makes the same measurable predictions as relativistic local QFT.vanhees71 said:Is there any relativistic causal non-local theory for ##\lambda##?
So far nobody found computational advantages of Bohmian fields (BTW, there are examples of computational advantages of Bohmian particles), but it helps a lot to sharpen intuitions. In addition to offering a solution of the measurement problem, Bohmian fields offer a very simple solution of the problem of time in quantum gravity. (There is also a claim that it helps to solve the Boltzmann brain problem is cosmology, but I don't find it convincing.)Morbert said:Stepping away from the philosophy for a moment: Are there quantities Bohmian field theories can more readily compute? Or processes? I don't think a nonlocal skeleton ##\lambda## is automatically a bad idea, but does it sharpen any ambiguities or render some intuitions or computations more available?
I've tried to make it very simple in http://thphys.irb.hr/wiki/main/images/3/3d/QFound5.pdfvanhees71 said:How such a theory can make the same measurable predictions as relativistic local QFT is an enigma to me.
What is the physical counterpart of ##\lambda##?Demystifier said:By extending the set of interacting objects. Relativistic QFT excludes ftl interactions in a law for evolution of the state in the Hilbert space ##\psi##. But minimal relativistic QFT says nothing about other possible interacting objects ##\lambda## that are not given by ##\psi##. Bohmian interpretation is an extension of minimal relativistic QFT. It does not change the evolution of ##\psi##, but it makes a concrete proposal for ##\lambda## and postulates a nonlocal law for evolution of ##\lambda##. Since minimal and Bohmian QFT agree on equations for ##\psi##, and since minimal QFT says nothing mathematical about the evolution of ##\lambda##, there is no any mathematical contradiction between minimal and Bohmian QFT. The contradiction is only philosophical, because minimal QFT uses some philosophical arguments to argue that there is no ##\lambda## to begin with.
Or schematically:
Minimal QFT: ##\psi## local, period.
Bohmian QFT: ##\psi## local, ##\lambda## nonlocal.
In Bohmian mechanics it's a local beable such as particle positions or a field configuration. Note that local beables (ontic things with values at well defined points in space) have nonlocal interactions.martinbn said:What is the physical counterpart of ##\lambda##?
You need to write a dictionary. You said "By extending the set of interacting objects.", but particle positions are not physical object and cannot interact! Particles are objects that can interact. It seems that you uses phrases that should be used for the territory, but you use them for the map all the time. I know that you think I have a problem with nonlocality, but if everything was local I would have the same problem. It is just very hard to keep track of what is what.Demystifier said:In Bohmian mechanics it's a local beable such as particle positions or a field configuration. Note that local beables (ontic things with values at well defined points in space) have nonlocal interactions.
Did you try to read some other text (not written by me) on Bohmian mechanics? Did you have similar problems?martinbn said:You need to write a dictionary. You said "By extending the set of interacting objects.", but particle positions are not physical object and cannot interact! Particles are objects that can interact. It seems that you uses phrases that should be used for the territory, but you use them for the map all the time. I know that you think I have a problem with nonlocality, but if everything was local I would have the same problem. It is just very hard to keep track of what is what.
It's worse. I can ask you, but I cannot ask a text.Demystifier said:Did you try to read some other text (not written by me) on Bohmian mechanics? Did you have similar problems?
This is obviously a basic misinterpretation of the gauge-vector fields. These are of course not observables, because they don't fulfill the microcausality principle. Only gauge-independent quantities can be observables. To think there were an "ontology" of the vector potentials in gauge theories must be flawed and lead to wrong conclusions. Particularly it's clear that also the observable phase shifts in the Aharonov-Bohm effect are gauge invariant, because the magnetic flux entering them is gauge invariant and can be expressed with gauge-invariant fields, obeying the microcausality principle.Demystifier said:I've tried to make it very simple in http://thphys.irb.hr/wiki/main/images/3/3d/QFound5.pdf
You missed the point. Suppose that some hypothetical civilization only discovered electrodynamics in the Coulomb gauge and never discovered the gauge invariance. I claim that they would never observe any contradiction between theory and experiment. If you agree with that statement (and I don't see any reason why shouldn't you), then it should be obvious they would have a Lorentz and gauge non-noninvariant theory that agrees with experiments.vanhees71 said:This is obviously a basic misinterpretation of the gauge-vector fields. These are of course not observables, because they don't fulfill the microcausality principle. Only gauge-independent quantities can be observables. To think there were an "ontology" of the vector potentials in gauge theories must be flawed and lead to wrong conclusions. Particularly it's clear that also the observable phase shifts in the Aharonov-Bohm effect are gauge invariant, because the magnetic flux entering them is gauge invariant and can be expressed with gauge-invariant fields, obeying the microcausality principle.
An "ontology" is just a (mathematical) model in a certain sense, there is no need to draw premature conclusions. Using the vector potentials as model can indeed be dangerous, but the reasons are related to topology, not to the violation of Lorentz invariance. Gauge fixing always lead to valid local models, but topological obstructions often prevent getting a valid global model from such local models.vanhees71 said:To think there were an "ontology" of the vector potentials in gauge theories must be flawed and lead to wrong conclusions.
When you ask me, does it actually help?martinbn said:It's worse. I can ask you, but I cannot ask a text.
If they discovered (classical or quantum) electrodynamics they'd also have discovered gauge invariance, because electrodynamics makes only mathematical sense as a gauge theory, let alone its success in describing all electromagnetic phenomena.Demystifier said:You missed the point. Suppose that some hypothetical civilization only discovered electrodynamics in the Coulomb gauge and never discovered the gauge invariance. I claim that they would never observe any contradiction between theory and experiment. If you agree with that statement (and I don't see any reason why shouldn't you), then it should be obvious they would have a Lorentz and gauge non-noninvariant theory that agrees with experiments.
What exactly does not make sense if you compute everything in a fixed gauge?vanhees71 said:If they discovered (classical or quantum) electrodynamics they'd also have discovered gauge invariance, because electrodynamics makes only mathematical sense as a gauge theory, let alone its success in describing all electromagnetic phenomena.
How is that relevant from a scientific point of view if that makes correct measurable predictions?vanhees71 said:Your (mis)interpretation of the Coulomb-gauge-fixed equations is a typical example. You claim there were actions at a distance, because you claim that the potentials were physical fields.
But the Maxwell theory and its distortion differ only in philosophy. So what really disturbs you are some philosophical quibbles that have nothing to do with science.vanhees71 said:It obviously doesn't, because what works in the "real world" is Maxwell's theory and not some distortion of it.
Here is what one of your favored books (Schwartz, QFT and the Standard Model) says:vanhees71 said:because electrodynamics makes only mathematical sense as a gauge theory
I did not say that potentials are physical. I said they could be ontic, but ontic is definitely not the same as observable. I can accept that you don't understand what ontic means, but then you don't understand even the Bohmian interpretation of nonrelativistic QM, in which case you have absolutely no chance to understand Bohmian interpretation of relativistic QFT.vanhees71 said:How can this be: If you claim the potentials were physical fields you must necessarily have observables differing from Maxwell's observables, because in Maxwell's theory only the field ##(\vec{E},\vec{B})## is observable. If this is not the case, then your claim that the potentials were physical fields is unsubstantiated and you are back at Maxwell's theory which is a gauge theory.
That's not what Schwartz is saying in the quote above.vanhees71 said:Yes indeed, it underlines the importance of gauge invariance. Without gauge invariance you have unphysical degrees of freedom which make trouble (acausality and in the quantum case non-unitarity of the S-matrix).
Ok, if ontic doesn't mean physical aka observable, it doesn't make sense to me. Also Bohmian mechanics doesn't make much sense to me. I think it's just a curious attempt to reintroduce a kind of determinism through the backdoor but without any consequences for the physics.Demystifier said:I did not say that potentials are physical. I said they could be ontic, but ontic is definitely not the same as observable. I can accept that you don't understand what ontic means, but then you don't understand even the Bohmian interpretation of nonrelativistic QM, in which case you have absolutely no chance to understand Bohmian interpretation of relativistic QFT.
But that's what's behind what he is saying!Demystifier said:That's not what Schwartz is saying in the quote above.
I am fine with that, but then I can't understand why do you often praise the book on Bohmian mechanics by Durr.vanhees71 said:Also Bohmian mechanics doesn't make much sense to me.
The way I see it, you deeply disagree with Schwartz. He seems to be saying that gauge invariance is just a convenient mathematical trick which makes some calculations easier, while you seem to saying that gauge invariance is a deep truth without which it is absolutely impossible to get correct physical results.vanhees71 said:But that's what's behind what he is saying!
In another book by Durr, the title of the very first section in the very first chapter is "Ontology".vanhees71 said:Ok, if ontic doesn't mean physical aka observable, it doesn't make sense to me.
The book (Verständliche Quantenmechanik: Drei mögliche Weltbilder der Quantenphysik) is not just on Bohmian mechanics. But it is indeed well written, easy to read, and clears up quite some confusion.Demystifier said:I am fine with that, but then I can't understand why do you often praise the book on Bohmian mechanics by Durr.
Yes, but in this case I can understand @vanhees71 because this theory is a Bohmian interpretation of relativistic QM, not of relativistic QFT, while @vanhees71 thinks that relativistic QM is wrong even in an orthodox form.gentzen said:But I also share your confusion, because that book also talks about relativistic Bohm-Dirac theory, but vanhees71 seemed pretty sure that there is no such thing.
Well, it may well depend on a reader's opinion which meaning he reads into the words of an author.Demystifier said:The way I see it, you deeply disagree with Schwartz. He seems to be saying that gauge invariance is just a convenient mathematical trick which makes some calculations easier, while you seem to saying that gauge invariance is a deep truth without which it is absolutely impossible to get correct physical results.