Assumptions of the Bell theorem

[Lynch101]

There are no FTL causal influences within local relativistic QFT. The experimentally confirmed violations of Bell's inequality, consistent with the predictions of local relativistic QFT (usually QED since most experiments are done with entangled photons) are thus still consistent with locality.

I wasn't suggesting that there were. I was simply stating, if we can say that a system is spatially extended and
we can say that measurement on the part of the system in one laboratory has an immediate causal influence on the part of the system in the spatially separated laboratory, then there are, necessarily, FTL causal influences.

This might not apply to realativistic QFT

 

[vanhees71]

No, that's the common mistake to confuse causal influences with statistical correlations. The point is that any phenomenon which can be described with relativistic local QFT is consistent with locality, because QFT is a local description.

It's also a mistake to conclude from the 100% correlations between the outcomes of measurments or certain observables on parts of an entangled quantum system to conclude that the measured values must have been predetermined before measurement, because QT is a description where this is not the case and still in full agreement with the observed statistical facts.

It was Bell's great merit to have found a way to scientifically decide between this assumption ("local deterministic hidden-variable model") and "Q(F)T".

 

[Lynch101]

@Demystifier is 3D space an assumption of the Bell Theorem?

 

[Demystifier]

@Demystifier is 3D space an assumption of the Bell Theorem?

I would say no, but it may depend on what do you mean by "space" which can have a different number of dimensions. If you mean "space" in the sense in which space in string theory is 9-dimensional, then the number of dimensions doesn't matter.

 

[Lynch101]

I would say no, but it may depend on what do you mean by "space" which can have a different number of dimensions. If you mean "space" in the sense in which space in string theory is 9-dimensional, then the number of dimensions doesn't matter.

Without ascribing any ontological properties to 'space' I simply mean that the experimental set-up is assumed to be modeled using 3 dimensions, as represented graphically using XYZ axes, and that it is/should be possible to represent everything from the experimental set-up with respect to these axes.

 

[Demystifier]

Without ascribing any ontological properties to 'space' I simply mean that the experimental set-up is assumed to be modeled using 3 dimensions, as represented graphically using XYZ axes, and that it is/should be possible to represent everything from the experimental set-up with respect to these axes.

Yes, that's an assumption of the Bell theorem. Why do you ask, do you see a way out of this assumption?

 

[Lynch101]

Yes, that's an assumption of the Bell theorem. Why do you ask, do you see a way out of this assumption?

I thought there might be, but based on the replies in another thread I am reconsidering.

 

[Lynch101]

No, that's the common mistake to confuse causal influences with statistical correlations. The point is that any phenomenon which can be described with relativistic local QFT is consistent with locality, because QFT is a local description.

It's also a mistake to conclude from the 100% correlations between the outcomes of measurments or certain observables on parts of an entangled quantum system to conclude that the measured values must have been predetermined before measurement, because QT is a description where this is not the case and still in full agreement with the observed statistical facts.

It was Bell's great merit to have found a way to scientifically decide between this assumption ("local deterministic hidden-variable model") and "Q(F)T".

@Demystifier Do these statement all apply to Bohmian Mechanics?

 

[Demystifier]

@Demystifier Do these statement all apply to Bohmian Mechanics?

I cannot tell because the question is too vague. How exactly would you restate his claims by using the expression "Bohmian mechanics" (BM)?

Note also that "local" in the standard QFT context does not have the same meaning as "local" in the Bohmian context. In the former sense, BM is local as much as standard QFT. BM is nonlocal in the latter sense, but the latter sense is a non-sense from the standard QFT point of view.

 

[Lynch101]

I cannot tell because the question is too vague. How exactly would you restate his claims by using the expression "Bohmian mechanics"?

Do particles not have predetermined values in Bohmian Mechanics and does it not rely on FTL causal influences?

 

[Demystifier]

Do particles not have predetermined values in Bohmian Mechanics and does it not rely on FTL causal influences?

Values immediately after measurement may differ from values immediately before measurement, in that sense they are not predetermined. But values after measurement are determined by values (of all variables of the universe) before measurement, in that sense they are predetermined and involve FTL causal influences.

 

[Lynch101]

Values immediately after measurement may differ from values immediately before measurement, in that sense they are not predetermined. But values after measurement are determined by values (of all variables of the universe) before measurement, in that sense they are predetermined and involve FTL causal influences.

Thank you, I was just trying to make sense of Vanhees's comment above about it being a 'common mistake to confuse causal influences with statistical correlations' with regard to the use of the term 'non-local'.

 

[Demystifier]

'common mistake to confuse causal influences with statistical correlations'

It's not a mistake, according to Reichenbach common cause principle.
https://plato.stanford.edu/entries/physics-Rpcc/

Almost all science assumes Reichenbach common cause principle. Standard interpretation of QM is the only exception.

 

[Lynch101]

No, that's the common mistake to confuse causal influences with statistical correlations. The point is that any phenomenon which can be described with relativistic local QFT is consistent with locality, because QFT is a local description.

But some physicists are referring to FTL causal influences, when they use the term 'non-local', would you agree?

It's also a mistake to conclude from the 100% correlations between the outcomes of measurments or certain observables on parts of an entangled quantum system to conclude that the measured values must have been predetermined before measurement, because QT is a description where this is not the case and still in full agreement with the observed statistical facts.

Are there interpretations which do conclude this? Demystifier has clarified that the values prior to measurement could be different but they would still be single, well-defined values. Are you saying that this is a 'common mistake'?

It was Bell's great merit to have found a way to scientifically decide between this assumption ("local deterministic hidden-variable model") and "Q(F)T".

Violations of Bell's inequality don't decide in favour of QFT though, does it? The various interpretations which do rely on FTL causal influences and pre-determined particle positons are not ruled out by Bell's Theorem but would, according to your position, be incompatible with QFT given their employment of FTL causality.

Or would you say that because that FTL causality cannot be used for signaling that it doesn't contradict QFT?

 

[vanhees71]

I use the words "local" and "non-local" only in one proper mathematical meaning, i.e., that local observables in relativistic QFTs commute with the Hamilton density when their space-time arguments are space-like separated, i.e., $[\hat{O}(x),\hat{\mathcal{H}}(y)]=0$ for $(x-y) \cdot (x-y)<0$ (west-coast convention, i.e., $\eta_{\mu \nu}=\mathrm{diag}(1,-1,-1,-1)$. Thus there cannot be any causal connections between space-like separated events.

For me an observable in Q(F)T has a predetermined value if and only if the system is prepared in a state such that the probability for measuring one of the possible values with 100% probability. Otherwise the value is indetermined before measurement and the state preparation only implies a certain probability for finding each of its possible values and nothing else. In which state the system is after the measurement depends on the construction of the measurement device, i.e., the specific interaction between the measured system and the measurement device. Since these interactions are just usual interactions described by local relativistic QFT there's no faster-than-light causal effect by a local measurement at one place and another space-like separated local measurement at another place. If the two space-like separated local measurements refer to entangled parts of a quantum system, then the observed correlations are not mutually caused by the local measurements but are due to the preparation of the system in the entangled state before any of the two measurements where done. By construction there is no contradiction between relativistic spacetime causality constraints and local relativistic QFT.

To confuse long-ranged correlations and inseparability of entangled systems with causal interactions at a distance is only misleading and contradicts the very foundational construction of local relativistic QFT.

 

[AndreiB]

I use the words "local" and "non-local" only in one proper mathematical meaning, i.e., that local observables in relativistic QFTs commute with the Hamilton density when their space-time arguments are space-like separated, i.e., $[\hat{O}(x),\hat{\mathcal{H}}(y)]=0$ for $(x-y) \cdot (x-y)<0$ (west-coast convention, i.e., $\eta_{\mu \nu}=\mathrm{diag}(1,-1,-1,-1)$. Thus there cannot be any causal connections between space-like separated events.

Why is it not possible for the A measurement to cause the result at B if "local observables in relativistic QFTs commute with the Hamilton density when their space-time arguments are space-like separated"? How is this proven?

 

[Lynch101]

I use the words "local" and "non-local" only in one proper mathematical meaning, i.e., that local observables in relativistic QFTs commute with the Hamilton density when their space-time arguments are space-like separated, i.e., $[\hat{O}(x),\hat{\mathcal{H}}(y)]=0$ for $(x-y) \cdot (x-y)<0$ (west-coast convention, i.e., $\eta_{\mu \nu}=\mathrm{diag}(1,-1,-1,-1)$. Thus there cannot be any causal connections between space-like separated events.

For me an observable in Q(F)T has a predetermined value if and only if the system is prepared in a state such that the probability for measuring one of the possible values with 100% probability. Otherwise the value is indetermined before measurement and the state preparation only implies a certain probability for finding each of its possible values and nothing else. In which state the system is after the measurement depends on the construction of the measurement device, i.e., the specific interaction between the measured system and the measurement device. Since these interactions are just usual interactions described by local relativistic QFT there's no faster-than-light causal effect by a local measurement at one place and another space-like separated local measurement at another place. If the two space-like separated local measurements refer to entangled parts of a quantum system, then the observed correlations are not mutually caused by the local measurements but are due to the preparation of the system in the entangled state before any of the two measurements where done. By construction there is no contradiction between relativistic spacetime causality constraints and local relativistic QFT.

To confuse long-ranged correlations and inseparability of entangled systems with causal interactions at a distance is only misleading and contradicts the very foundational construction of local relativistic QFT.

But do you accept that some physicists use the term 'non-local' to refer to FTL causal influences?

 

[vanhees71]

I can't force people to use an understandable and consistent terminology, but if they use the term non-local in this sense, they don't talk about standard local relativistic QFT or they falsely name phenomena non-local when they talk about correlations of far-distant local observations.

 

[Lynch101]

I can't force people to use an understandable and consistent terminology, but if they use the term non-local in this sense, they don't talk about standard local relativistic QFT or they falsely name phenomena non-local when they talk about correlations of far-distant local observations.

So, just going back to the original point, whether the term 'non-local' or 'inseparability' is (mis)used, the (or an) issue of contention is whether or not there are FTL causal influences in nature which explain the observed correlations in quantum experiments.

Edit: again, it seems to come back to the question of completeness.

While quantum theory might not necessarily be FTL 'non-local' there are those who would say that nature must employ FTL causation to explain the outcomes of individual experiments.

 

[vanhees71]

Again:

Locality: There are no FTL causal influcences according to local relativistic QFT (by construction)

Completeness: There's not one reproducible observation that contradicts the prediction of QFT. In this sense it's complete as a natural sciences.

Whether it's complete in a philosophical or religious sense, is subject to personal opinion, and this cannot be answered by the scientific method and as such not subject for discussion in a science forum.

 

[Lynch101]

Again:

Locality: There are no FTL causal influcences according to local relativistic QFT (by construction)

There are according to Bohemian Mechanics

Completeness: There's not one reproducible observation that contradicts the prediction of QFT. In this sense it's complete as a natural sciences.

Whether it's complete in a philosophical or religious sense, is subject to personal opinion, and this cannot be answered by the scientific method and as such not subject for discussion in a science forum.

So, interpretations of quantum theory which contradict the notion of 'no FTL causal influences' are not subject for discussion in a science forum?

 

[vanhees71]

There is no convincing Bohmian reinterpretation of relativistic local QFT. So I don't know, what you are referring to.

Of course you can discuss models that contradict the so far observed facts and their descriptions by local relativistic QFT. Such models are per se "scientific" if they make clear predictions about observables which contradict the established theories and thus make them testable to decide whether they are better descriptions of the phenomena or the established theories.

Bell's inequality is a prime example for this: Making some assumptions, leading to observable predictions contradicting the established quantum theory (Bell's inequalities) makes it possible to test them and quantum theory against each other. The unanimous decision favors quantum theory by an amazing level of significance.

 

[physika]

If two 'ends' are spatially separated and an action performed one one end instantaneously affects the other end, then, by my reasoning, this would imply an FTL causal influence. Is there any alternative?

predefined values.

 

[vanhees71]

or correlations due to entanglement with maximally (!) undetermined values as described by Q(F)T.

 

[Demystifier]

There is no convincing Bohmian reinterpretation of relativistic local QFT.

How do you know that? Did you actually read some of the existing Bohmian reinterpretations of relativistic QFT?

 

[Demystifier]

Locality: There are no FTL causal influcences according to local relativistic QFT (by construction)

Nonlocality: There are FTL causal influences according to Bohmian relativistic QFT (by construction)

Completeness: There's not one reproducible observation that contradicts the prediction of QFT. In this sense it's complete as a natural sciences.

Completeness: There's not one reproducible observation that contradicts the prediction of Bohmian QFT. In this sense it's complete as a natural sciences.

Whether it's complete in a philosophical or religious sense, is subject to personal opinion, and this cannot be answered by the scientific method and as such not subject for discussion in a science forum.

Whether Bohmian QFT is convincing in a philosophical or religious sense, is subject to personal opinion, and this cannot be answered by the scientific method and as such not subject for discussion in a science forum.

 

[physika]

There is no convincing Bohmian reinterpretation of relativistic local QFT. So I don't know, what you are referring to.

Of course you can discuss models that contradict the so far observed facts and their descriptions by local relativistic QFT. Such models are per se "scientific" if they make clear predictions about observables which contradict the established theories and thus make them testable to decide whether they are better descriptions of the phenomena or the established theories.

Bell's inequality is a prime example for this: Making some assumptions, leading to observable predictions contradicting the established quantum theory (Bell's inequalities) makes it possible to test them and quantum theory against each other. The unanimous decision favors quantum theory by an amazing level of significance.

Tumulka

 

[Demystifier]

Tumulka

Tumulka what?

 

[physika]

Tumulka what?

Bohmian relativistic...

 

[Demystifier]

Bohmian relativistic...

No, collapse relativistic. https://arxiv.org/abs/quant-ph/0602208