Assumptions of the Bell theorem

[Demystifier]

Much later a new job forced me to really learn and understand QM.

May I ask what's your job? It sounds as if it is not an academic job, so I'm curious what kind of non-academic job requires good understanding of QM.

 

[Lynch101]

not necessarily.

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?

 

[vanhees71]

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.

 

[gentzen]

May I ask what's your job? It sounds as if it is not an academic job, so I'm curious what kind of non-academic job requires good understanding of QM.

If you work in the semiconductor industry, then you have a good chance to encounter tasks where a good understanding of physics is helpful. This physics can also reach into the domain of QM, sometimes more, sometimes less. Let me elaborate on what I wrote in the New Members Introductions Forum:

I am an applied mathematician working in semiconductor manufacturing. This means stuff like optical lithography, ebeam lithography, resist development processes, etching processes, optical metrology, scanning electron beam metrology, and other related physical or chemical processes.

My QM tasks are about the interaction of electron beams with matter. At the beginning (February 2013) it was about the energy range 10 keV - 100 keV, i.e. the simulation of electron beam lithography. An understanding of QM was still unimportant here, it was enough to use databases with (differential) scattering cross-sections (for atoms) provided by others, and there were also existing simulators against which I could verify our simulator. (The simulator already existed, only it provided significantly different results than existing simulators. It was my job to find the causes and fix them.)

From the beginning it was clear that we also wanted to be able to simulate scanning electron microscopy (SEM). Internal prototypes, external simulators and code "licensed" from research institutes existed for this as well. But that was a tragedy because each simulator calculated totally different results and there was no chance of differentiating right from wrong. Well, for some simulators you could explain why they were definitely wrong. But it wasn't bad either, because after "directed self assembly" (DSA) went out of fashion again, the end customers' need for the simulation of the SEM also decreased. (And there were and are many other tasks for me.) With DSA, defects can arise under the surface, and the task of the SEM simulation would have been to determine from what depth on which defects (size, material) can still be seen, what the signal-to-noise ratio is, and which SEM settings (energy of the electrons, which type of detectors, ...) would be helpful.

Then a student did his master's thesis with us extending the simulator with charging effects and doing clean room SEM measurements to somewhat verify the stuff. He was really enthusiastic, and then also finished a PhD thesis on related topics later. ... And customers for the simulator also emerged: the manufacturers of the SEM machines.

 

[Lynch101]

Well yes. The problem is that the disagreement is about philosophy and not about physics. The indication for that is that obviously we still have not a clear agreement on the meaning of the words, particularly locality. For me locality is simply microcausality. For you obviously it has a different meaning. The same holds for "reality", which is even harder to define. For me reality is objective, reproducible observability, i.e., what can be tested by experiments.

With words like 'reality', there is a danger of descending into a philosophical rabbit hole in trying to define the terms with impossible precision. It is possible, however, to avoid such tangents by defining it in contrast to other well defined terms.

For example, with regard to 'the physical reality' referred to in the EPR paper (which Bell took as the basis for his own paper), 'the physical reality' can be defined in contrast to 'the mathematical model' of the physical experimental set-up. So, 'the physical reality' simply refers to the what is happening in the lab.

Sure, in "bread-and-butter physics" dealing with the description of observable phenomena, there's only one meaning of "locality", namely the impossibility to transmit information with any "faster-than-light signal" within any theory which is consistent with any theory within the (special-)relativistic (!) spacetime model.

Is there not also the possibility to interpret it as the impossibility of causal influences propagating FTL? But, as long as FTL causal influences cannot be used for signaling they would not violate relativity. Some might say that it violates the 'spirit' of relativity, but that is a separate matter. (I'm not arguing that it does violate relativity, just that there is another possible interpretation of 'locality'.)

What's often confusingly called "non-locality" in the more quantum-foundations inclined community refers to long-ranged correlations between "entangled parts" of a quantum system. It would help tremendously to call this "inseparability" as Einstein did.

At this stage, you are probably right. The term 'inseparability' might be better because too much time seems to go into discussing the meaning of the word 'non-local'.

From my reading of the literature and from discussions on here about the literature, my reasoning leads me to conclude that there are those who us the term 'non-locality' not simply to refer to the observed correlations, rather about the possible mechanisms which could explain the observed correlations. They seem to be talking about causal influences propagating FTL or, more accurately, instantaneously.

There seems to be others then who use the term 'non-local' to simply refer to the observed correlations themselves.

But, if we do choose to use the term 'inseparability' - where we talk about a single system - we can ask if the system is spatially separated, given that it is measured in spatially separated laboratories. We can then ask if measurement on one 'end' has an instantaneous (or FTL) causal influence on the other, spatially separated 'end'.

By my reasoning, the underlying issue is whether or not there are FTL causal influences, regardless of whether we use the terms 'non-locality' or 'inseparability'.

 

[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