I Issues on notation and concept of entanglement

[AndreiB]

It really means the following. Suppose that two quantum observables, A and B, commute. Furthermore, suppose that Alice measured A, that Bob knows that Alice measured it, but that he does not know the result of her measurement. Then, from this knowledge, Bob cannot conclude anything new about the probabilities of measurement outcomes of B.

This seems compatible with A causing B, right?

 

[vanhees71]

No, it's not necessarily compatible with A causing B. An event at B can be causally influenced by A only if the event at B is in some future lightcome of an event at A. This holds for all special-relativistic dynamical models including standard local relativistic QFT.

 

[AndreiB]

An event at B can be causally influenced by A only if the event at B is in some future lightcome of an event at A.

How does this follow from what Weinberg says? There is no talk there about lightcones.

 

[Demystifier]

This seems compatible with A causing B, right?

It depends on what one means by "causing", but in the sense you mean it I would agree. Of course, adherents of orthodox QM by "causing" mean something else.

 

[Demystifier]

But you also need nonexistant things.

Which ones? I don't need mediator.

 

[AndreiB]

It depends on what one means by "causing", but in the sense you mean it I would agree. Of course, adherents of orthodox QM by "causing" mean something else.

By causing I mean that the spin at B is instantly forced to take the opposite value of A.

 

[Demystifier]

By causing I mean that the spin at B is instantly forced to take the opposite value of A.

Yes, in that sense I agree.

 

[vanhees71]

Even if you agree with that, the cause is not a faster-than-light interaction, at least not within a local relativistic QFT, but it's due to the correlation described by entanglement.

 

[martinbn]

Which ones? I don't need mediator.

And CI doesn't need values for observables that have not been measured. It is exactly the same. You also need something (the action) that is there, but no way you can tell even in principle, it is like it isn't there.

 

[Demystifier]

You also need something (the action) that is there

Define "action"!

 

[Demystifier]

Even if you agree with that, the cause is not a faster-than-light interaction, at least not within a local relativistic QFT, but it's due to the correlation described by entanglement.

The cause I have in mind is of course a faster-than-light interaction, which of course is incompatible with orthodox relativistic QFT, which of course is why I have in mind an unorthodox relativistic QFT. The unorthodox relativistic QFT uses all the equations of orthodox QFT and makes the same measurable predictions, but the narrative is slightly different.

 

[vanhees71]

Well, but then you contradict the mathematical formulations. How can an interpretation make sense if it contradicts the mathematical foundations, and if all measurable predictions are the same what sense does it make to invent inconsistencies between interpretation on the one hand as well as the mathematical description and empirical facts?

 

[Demystifier]

Well, but then you contradict the mathematical formulations. How can an interpretation make sense if it contradicts the mathematical foundations, and if all measurable predictions are the same what sense does it make to invent inconsistencies between interpretation on the one hand as well as the mathematical description and empirical facts?

There are no inconsistencies. You assume that only one interpretation (the orthodox one) is consistent with the undisputed equations, but that's wrong. There are many interpretations of quantum theory consistent with the equations of quantum theory.

 

[martinbn]

Define "action"!

https://www.physicsforums.com/threa...-concept-of-entanglement.1007463/post-6545856

 

[vanhees71]

There are no inconsistencies. You assume that only one interpretation (the orthodox one) is consistent with the undisputed equations, but that's wrong. There are many interpretations of quantum theory consistent with the equations of quantum theory.

How can an interpretation claiming the existence of ftl interactions be consistent for a theory which excludes them in its mathematical formulation?

 

[martinbn]

How can an interpretation claiming the existence of ftl interactions be consistent for a theory which excludes them in its mathematical formulation?

By using different terminology. Interaction means something else, not what you might have guessed. Just like non-local means something else, not the usual.

 

[Demystifier]

How can an interpretation claiming the existence of ftl interactions be consistent for a theory which excludes them in its mathematical formulation?

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.

 

[vanhees71]

By using different terminology. Interaction means something else, not what you might have guessed. Just like non-local means something else, not the usual.

Yes, and this is what makes this philosophy inclined topic so useless for science. You use the words not in their clear scientific meaning but distort them as long as it has no meaning anymore at all. Within the exact sciences one should say interaction when one means an interaction and correlation when one means correlation and should keep this strictly separated with a well-defined meaning. You save a lot of time for real discussions rather than defining again and again the same words.

 

[vanhees71]

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.

Standard QFT uses physical arguments and doesn't interoduce fictitious enigmatic entities called $\lambda$ in the first place. I guess you mean $\lambda$ as in Bell's original paper on his local deterministic HV models, and this is disproven by experiment. We can move on with new physics for at least 10-20 year now!

 

[Demystifier]

I guess you mean $\lambda$ as in Bell's original paper on his local deterministic HV models, and this is disproven by experiment.

I mean Bell's $\lambda$ which can be either local or nonlocal. The nonlocal Bell's $\lambda$ is of course not disproven.

 

[vanhees71]

Is there any relativistic causal non-local theory for $\lambda$? If not, you can of course speculate a lot without much scientific substance.

 

[Morbert]

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?

 

[Demystifier]

Is there any relativistic causal non-local theory for $\lambda$?

No, but there is nonrelativistic causal nonlocal theory for $\lambda$ which makes the same measurable predictions as relativistic local QFT.

 

[vanhees71]

In nonrelativistic physics causality is not a big issue, because all you need is ordering in absolute time. How such a theory can make the same measurable predictions as relativistic local QFT is an enigma to me. In such a model I indeed could have instantaneous causal changes at far distant places, but according to relativistic local QFT I cannot.

 

[Demystifier]

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?

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.)

 

[Demystifier]

How such a theory can make the same measurable predictions as relativistic local QFT is an enigma to me.

I've tried to make it very simple in http://thphys.irb.hr/wiki/main/images/3/3d/QFound5.pdf

 

[martinbn]

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.

What is the physical counterpart of $\lambda$?

 

[Demystifier]

What is the physical counterpart of $\lambda$?

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]

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.

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]

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.

Did you try to read some other text (not written by me) on Bohmian mechanics? Did you have similar problems?

 

[martinbn]

Did you try to read some other text (not written by me) on Bohmian mechanics? Did you have similar problems?

It's worse. I can ask you, but I cannot ask a text.

 

[vanhees71]

I've tried to make it very simple in http://thphys.irb.hr/wiki/main/images/3/3d/QFound5.pdf

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]

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.

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.

 

[gentzen]

To think there were an "ontology" of the vector potentials in gauge theories must be flawed and lead to wrong conclusions.

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.

But I somehow have the impression that you had something completely different in mind when you wrote "... must be flawed and lead to wrong conclusions."

 

[Demystifier]

It's worse. I can ask you, but I cannot ask a text.

When you ask me, does it actually help?

 

[vanhees71]

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.

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]

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.

What exactly does not make sense if you compute everything in a fixed gauge?

 

[vanhees71]

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.

 

[Demystifier]

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.

How is that relevant from a scientific point of view if that makes correct measurable predictions?

 

[vanhees71]

It obviously doesn't, because what works in the "real world" is Maxwell's theory and not some distortion of it.

 

[Demystifier]

It obviously doesn't, because what works in the "real world" is Maxwell's theory and not some distortion of it.

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]

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.

 

[Demystifier]

because electrodynamics makes only mathematical sense as a gauge theory

Here is what one of your favored books (Schwartz, QFT and the Standard Model) says:

"8.6 Is gauge invariance real?

Gauge invariance is not physical. It is not observable and is not a symmetry of nature.
Global symmetries are physical, since they have physical consequences, namely conservation of charge. That is, we measure the total charge in a region, and if nothing leaves that region, whenever we measure it again the total charge will be exactly the same. There is no such thing that you can actually measure associated with gauge invariance. We introduce gauge invariance to have a local description of massless spin-1 particles. The existence of these particles, with only two polarizations, is physical, but the gauge invariance is merely a redundancy of description we introduce to be able to describe the theory with a local Lagrangian. ...
In summary, although gauge invariance is merely a redundancy of description, it makes
it a lot easier to study field theory. The physical content is what we saw in the previous
section with the Lorentz transformation properties of spin-1 fields: massless spin-1 fields
have two polarizations. If there were a way to compute S-matrix elements without a local
Lagrangian (and to some extent there is, for example, using recursion relations, as we will
see in Chapter 27), we might be able to do without this redundancy altogether."

 

[Demystifier]

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.

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]

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).

 

[Demystifier]

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).

That's not what Schwartz is saying in the quote above.

 

[vanhees71]

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.

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.

 

[vanhees71]

That's not what Schwartz is saying in the quote above.

But that's what's behind what he is saying!

 

[Demystifier]

Also Bohmian mechanics doesn't make much sense to me.

I am fine with that, but then I can't understand why do you often praise the book on Bohmian mechanics by Durr.

 

[vanhees71]

It's the only book, where I thought to understand what's behind Bohmian mechanics. I can appreciate a good treatment of a theory even if I don't think that the theory is of much additional value in comparison to the standard theories.