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The definition of non-locality
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08-09-2020 6:29pm#1I had always understood quantum non-locality to mean the instantaneous influence a measurement at location A has in location B. This is usually invoked as a possible explanation for the observed correlations in quantum experiments, correlations that violate Bell's inequality. The reason this influence is termed "non-local" is to contrast it with the idea of Einsteinian locality, where influences can only propagate at a maximum velocity, c. In this instance, "non-locality" unambiguously refers to the explanation of the phenomenon of violations of Bell's inequality.
In a recent discussion however, it was claimed that "Non-locality" is an ordinary language term and does not have a single well-defined technical meaning, but rather a number of well-defined technical meanings. One such "well-defined" meaning that was touted was that "non-locality" means "violates the Bell inequalities".
To me the latter appears to be completely redundant and, at best, a simple misapplication of the term or, at worst, a deliberate bait and switch.
There is a clear and obvious connection between the two and it is conceivable that both would be used interchangeably in certain contexts - where precision is not critical to the point. While both of the examples above refer to violations of Bell's inequality, the former uses non-locality to refer to the process which gives rise to the phenomenon while the latter simply rebrands the phenomenon as "non-locality" and offers nothing further by way of explanation - which to me makes it redundant and serves only to obfuscate the issue.
A few questions:
1) Does anyone know which use of the term preceded the other?
2) Is the latter use of the term in widespread use?
3) Are there other definitions of non-locality?0
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latter simply rebrands the phenomenon as "non-locality" and offers nothing further by way of explanation
We can observe correlations in sequences of spacelike-separated measurement outcomes that violate Bell inequalities.
If we proceed with a quantum theory applied only to the system being measured, the correlations are fully explained by the prepared ensemble and choice of experiments. The applied quantum theory can be one where experimental outcomes at A do not influence spacelike-separated outcomes at B and vice versa.
If we instead proceed with a classical theory applied only to the system being measured, the correlations are fully explained by the prepared ensemble and choice of experiments only if the applied classical theory is one where experimental outcomes at A influence spacelike-separated outcomes at B and vice versa.
tl;dr Nonlocality in the latter sense is observed fact. Nonlocality in the former sense is one possible explanation of the latter, but not one we are compelled to adopt.0 -
Thanks Morbert.We can observe correlations in sequences of spacelike-separated measurement outcomes that violate Bell inequalities.
If we proceed with a quantum theory applied only to the system being measured, the correlations are fully explained by the prepared ensemble and choice of experiments. The applied quantum theory can be one where experimental outcomes at A do not influence spacelike-separated outcomes at B and vice versa.
If we instead proceed with a classical theory applied only to the system being measured, the correlations are fully explained by the prepared ensemble and choice of experiments only if the applied classical theory is one where experimental outcomes at A influence spacelike-separated outcomes at B and vice versa.
tl;dr Nonlocality in the latter sense is observed fact. Nonlocality in the former sense is one possible explanation of the latter, but not one we are compelled to adopt.
That reads to me as though, in both cases, non-locality is referring to a specific explanation of the correlations with the idea that experimental outcomes at A influence spacelike-separated outcomes at B and vice versa.
Granted, in the case of the former we might not be compelled to accept that explanation, but it is still appears as though the term non-local refers to that specific type of explanation; as opposed to, simply, the observed correlations themselves being referred to as non-local.
Using the term non-local to refer, simply, to the observed correlations appears to me to be redundant and misleading - but I might still be missing something.0 -
Thanks Morbert.
That reads to me as though, in both cases, non-locality is referring to a specific explanation of the correlations with the idea that experimental outcomes at A influence spacelike-separated outcomes at B and vice versa.
Granted, in the case of the former we might not be compelled to accept that explanation, but it is still appears as though the term non-local refers to that specific type of explanation; as opposed to, simply, the observed correlations themselves being referred to as non-local.
I'm not sure I follow. In the former case, nonlocality refers to Bell inequality violations, as opposed to spacelike-separated events influencing each other. Or are you saying it is clearer to stipulate nonlocality as only referring to this influence, and not the strong correlations themselves.0 -
Apologies, maybe I misinterpreted your post.I'm not sure I follow. In the former case, nonlocality refers to Bell inequality violations, as opposed to spacelike-separated events influencing each other. Or are you saying it is clearer to stipulate nonlocality as only referring to this influence, and not the strong correlations themselves.
I'll try and break it down a bit more and that way my error might be more obvious. I think my issue lies with case #1, so sticking with that for now:
Emphasis is my own.the correlations are fully explained by the prepared ensemble and choice of experiments. The applied quantum theory can be one where experimental outcomes at A do not influence spacelike-separated outcomes at B and vice versa.
I'm reading the above to mean that the correlations, or the violations of Bell's inequality, can be explained without reference to outcomes at A influencing outcomes at B and vice versa. But equally, they can be explained with reference to same. In both explanations (with & without) we have the violations of Bell's inequality.
It's being stated that non-locality simply means "violations of Bell's inequality". So, in both instances we have non-locality.
In the second instance however, we have an explanation for that use of the term "non-locality" which says that experimental outcomes at A influence outcomes at B and vice versa. Incidentally, the term used for this explanation, or these superluminal influences, is also "non-locality" (let's call this non-locality2 for now).
So, we have non-locality2 as an explanation for non-locality1.
We might ask, why do we use the term "non-locality", what does it mean?
"Non-locality2" is the one with which I am most familiar because I have only encountered non-locality used in that manner. We use the term non-locality in this sense because it involves actions at A influencing outcomes at B and vice versa, which violates the notion of Einsteinian locality - which says that influences can only travel at the speed of light (ignoring signalling). These superluminal (or non-local) influences are invoked to explain the violations of Bell's inequality.
If we ask the same question for the other definition: why do we use the term non-locality, what does it mean?
We use the term non-locality to refer to violations of Bell's inequality. Full stop.
In the latter definition of the term, it would seem, to me anyway, that there is some conflation of the cause - actions at A influencing outcomes at B and vice versa - with the effect - violations of Bell's inequality.
Using the term "non-local" to refer, simply, to the violations of Bell's inequality seems redundant because it doesn't add any further level of clarification. Even if it was only the case of simply re-naming something which has self-explanatory name, it would still only seem to add an unnecessary level of obfuscation.
It only serves to further obfuscate things because the term "non-local" is also used to refer to a very particular explanation of Bell's inequality violations, where actions at A influence outcomes at B and vice versa.
The use of the term as per "non-locality2" offers more by way of explanation. It also incorporates that to which the "non-locality1" refers.0 -
I'm reading the above to mean that the correlations, or the violations of Bell's inequality, can be explained without reference to outcomes at A influencing outcomes at B and vice versa. But equally, they can be explained with reference to same. In both explanations (with & without) we have the violations of Bell's inequality.
Re/ my use of the word can: There are theories that are local2 and there are theories that are nonlocal2. This quality of being local2 or nonlocal2 manifests in the dynamics postulated by the theory, and isn't just an interpretational issue.
The structure of quantum theories are such that we can apply a quantum theory that is local2 to the system that will account for the violation of Bell inequalities. (And on a broader note, there are good reasons to favour local2 theories in general)
If we instead consider a classical theory, we cannot apply a local2 classical theory to the system that can account for the violation of Bell inequalities, at least if we want the application to be robust enough to handle our freedom to choose the experiment we carry out.
Re/ how we ought to use words like local: I do think its clearer and more effective to stipulate locality to mean locality2.0 -
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All theories then would be non-local1 wouldn't they, as they would all have to include violations of Bell's inequality?Re/ my use of the word can: There are theories that are local2 and there are theories that are nonlocal2. This quality of being local2 or nonlocal2 manifests in the dynamics postulated by the theory, and isn't just an interpretational issue.
Not to be one of those people who get their knickers in a twist over the use of "theory" instead of "interpretation", but would an example of a theory/interpretation that is non-local2 be Bohmian Mechanics?The structure of quantum theories are such that we can apply a quantum theory that is local2 to the system that will account for the violation of Bell inequalities. (And on a broader note, there are good reasons to favour local2 theories in general)
What would be an example of a theory that is local2?
I'm inclined to agree, obviously. I was under the impression that "non-locality" was only ever used to mean non-locality2 but that may just be because I wasn't picking up on the nuance (or maybe I was just confusing myself :pac:)Re/ how we ought to use words like local: I do think its clearer and more effective to stipulate locality to mean locality2.0 -
All theories then would be non-local1 wouldn't they, as they would all have to include violations of Bell's inequality?
I'd have to think about that more but I think I'd agree. Bell's theorem places a bound on possible correlations that is partially contingent on locality2. Without locality2, that bound is gone.Not to be one of those people who get their knickers in a twist over the use of "theory" instead of "interpretation", but would an example of a theory/interpretation that is non-local2 be Bohmian Mechanics?
YesWhat would be an example of a theory that is local2?
A local2 theory is e.g. one with a Lagrangian that only depends on the coordinates of the system. Quantum mechanics, quantum electrodynamics etc are examples of local2 theories.0 -
I'd have to think about that more but I think I'd agree. Bell's theorem places a bound on possible correlations that is partially contingent on locality2. Without locality2, that bound is gone.
Yes
A local2 theory is e.g. one with a Lagrangian that only depends on the coordinates of the system. Quantum mechanics, quantum electrodynamics etc are examples of local2 theories.
Thanks Morbert.0 -
Hi. I hope this isn't considered a necro-post, as it is less than 3 months,
and I am quite interested in this topic,
and I may have some information which is helpful.
I haven't heard of the terms "locality1" or "locality2". In most discussions I see only a single "principle of locality", which is described here: ...wiki/Principle_of_locality
However, scientists don't really seem to discuss the "principle of locality" much these days but instead discuss the "principle of local realism", which is defined as follows: "The world is made up of real stuff, existing in space and changing only through local interactions "
(www dot nature dot com/articles/nature15631)
Now, going beyond the definition itself, just in 2015 something shocking was proven, because "local realism" was experimentally shown to be disproven to a high degree of confidence by Quantum Entanglement. Before that time, there were some "loopholes" available, but by the end of 2015, there were no loopholes left except for "almost metaphysical" ones (for example Superdeterminism)
So most scientists today are (effectively) stumped by how Entanglement can do the instantaneous and it-definitely-happens action at a distance, and I'm working on a solution myself.0 -
Quantum Theory says there isn't action-at-a-distance. What's happening in entanglement is that we have correlations too strong to support the conjunction of:So most scientists today are (effectively) stumped by how Entanglement can do the instantaneous and it-definitely-happens action at a distance, and I'm working on a solution myself.
(a) Local interactions
(b) Quantum systems possess values for observables prior to measurement
Since the experiments show entanglement to be correct, one of these is false. Quantum Theory says (b) is false. Interactions are local but the values we measure didn't pre-exist before the measurement, nor do they follow from any property which existed before the measurement.0 -
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Much appreciated.Hi. I hope this isn't considered a necro-post, as it is less than 3 months,
and I am quite interested in this topic,
and I may have some information which is helpful.
non-Locality 1 & 2 were just terms I was using in this thread to differentiate between two interpretations of non-locality that I had encountered. The one I was familiar with was the idea of action at a distance or FLT causal influences.I haven't heard of the terms "locality1" or "locality2". In most discussions I see only a single "principle of locality", which is described here: ...wiki/Principle_of_locality
The key difference between the two, as I understood them, was that one was simply being used to refer to the observed phenomenon, the observed correlations in entanglement experiments i.e. statistical violations of Bell's inequality, while the other refers to an attempted explanation of the observed phenomenon i.e. the mechanism which explains the observed correlations.
The former is deemed non-local bcos if nature were local in the sense EPR had envisaged, then Bell's inequality would have been obeyed. Since nature violates Bell's inequality, the observed correlations could not be caused by an EPR local process and so the observed correlations are deemed "non-local".
At least, that is how I interpret the information I have encountered. To my mind, I think it is a bit redundant and potentially misleadig to call the observed correlations "non-local" when the term seems to have been intended to describe "spooky action-at-a-distance".
Sabine Hossenfelder outlines it pretty clearly in this video:
That's cool Goosius, that you are working on a solution! I'd be interested in your insights - although, I would definitely need the ELI5* version.However, scientists don't really seem to discuss the "principle of locality" much these days but instead discuss the "principle of local realism", which is defined as follows: "The world is made up of real stuff, existing in space and changing only through local interactions "
(www dot nature dot com/articles/nature15631)
Now, going beyond the definition itself, just in 2015 something shocking was proven, because "local realism" was experimentally shown to be disproven to a high degree of confidence by Quantum Entanglement. Before that time, there were some "loopholes" available, but by the end of 2015, there were no loopholes left except for "almost metaphysical" ones (for example Superdeterminism)
So most scientists today are (effectively) stumped by how Entanglement can do the instantaneous and it-definitely-happens action at a distance, and I'm working on a solution myself.
*Explain it like I'm 50 -
Quantum Theory says there isn't action-at-a-distance. What's happening in entanglement is that we have correlations too strong to support the conjunction of:
(a) Local interactions
(b) Quantum systems possess values for observables prior to measurement
Since the experiments show entanglement to be correct, one of these is false. Quantum Theory says (b) is false. Interactions are local but the values we measure didn't pre-exist before the measurement, nor do they follow from any property which existed before the measurement.
I know we've discussed this previously, but the emboldened part is where I still get somewhat confused.
The analogy I have in mind to make sense of that is the question of whether a single molecule of water is actually "wet"?
To my mind "wetness" is not a property of the water molecule, it is the observed property when the water molecule interacts with the measurement device i.e. the measurement device becomes "wet" because it has water on it, but "wetness" is not a property of the water molecule itself.
Does that make sense?0 -
That's a pretty good analogy actually. All the properties we find in experiments with quantum systems are actually just properties of the device/effects the particle has on the device, they're not recordings of genuine properties of the particle.I know we've discussed this previously, but the emboldened part is where I still get somewhat confused.
The analogy I have in mind to make sense of that is the question of whether a single molecule of water is actually "wet"?
To my mind "wetness" is not a property of the water molecule, it is the observed property when the water molecule interacts with the measurement device i.e. the measurement device becomes "wet" because it has water on it, but "wetness" is not a property of the water molecule itself.
Does that make sense?
Of course the confusing thing about quantum theory is that the genuine properties or nature of the particles isn't actually described by the theory at all.0 -
Quantum Theory says there isn't action-at-a-distance. What's happening in entanglement is that we have correlations too strong to support the conjunction of:
(a) Local interactions
(b) Quantum systems possess values for observables prior to measurement
Since the experiments show entanglement to be correct, one of these is false. Quantum Theory says (b) is false. Interactions are local but the values we measure didn't pre-exist before the measurement, nor do they follow from any property which existed before the measurement.
On the above quote, that characterization is incorrect. The Nature paper I quoted earlier explicitly tells us that "Local Realism" is (probably) false, so this can certainly mean that "action at a distance" is possible. The wiki page for "action at a distance" is explicit in telling us that action-at-a-distance is a legitimate and open question ---> QUOTE: " Whether quantum entanglement counts as action-at-a-distance hinges on the nature of the wave function and decoherence, issues over which there is still considerable debate among scientists and philosophers."
Further, the last line of the above quote is misleading. Because one of the most significant loopholes remaining (since 2015) is called "Superdeterminism", and this idea explicitly conjectures that properties DO pre-exist (more accurate we'd better say are 'pre-determined') before the measurement.0 -
Much appreciated.
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That's cool Goosius, that you are working on a solution! I'd be interested in your insights - although, I would definitely need the ELI5* version.
*Explain it like I'm 5
Haha, "Eli5" that's a good one!:D. I'm glad I posted here now, I'm learning new things already.
I have a paper being submitted to some journals right now, so Imma keep quiet about the specifics for the moment, but I can certainly let you know if I get it published.0 -
I wasn't talking about "action at a distance" being impossible. I'm saying that the early results on entanglement showed two ways out:On the above quote, that characterization is incorrect. The Nature paper I quoted earlier explicitly tells us that "Local Realism" is (probably) false, so this can certainly mean that "action at a distance" is possible.
(a) Nonlocality/Action-at-a-distance
(b) Lack of pre-existing properties
And that quantum theory itself takes the latter.
Superdeterminism has been ruled out with the Wood-Spekkens theorem and the Shi-Yang theorem. It's a silly and very misunderstood idea anyway, in my experience most people who mention it don't understand what superdeterminism actually means, but regardless it has been ruled out.Further, the last line of the above quote is misleading. Because one of the most significant loopholes remaining (since 2015) is called "Superdeterminism", and this idea explicitly conjectures that properties DO pre-exist (more accurate we'd better say are 'pre-determined') before the measurement.0 -
That's taken from reddit. There is an entire ELI5 subredditHaha, "Eli5" that's a good one!:D. I'm glad I posted here now, I'm learning new things already.
Oh cool. Fingers crossed for you.I have a paper being submitted to some journals right now, so Imma keep quiet about the specifics for the moment, but I can certainly let you know if I get it published.0 -
Superdeterminism has been ruled out with the Wood-Spekkens theorem and the Shi-Yang theorem. It's a silly and very misunderstood idea anyway, in my experience most people who mention it don't understand what superdeterminism actually means, but regardless it has been ruled out.
We'll disagree on that also. And that's fine. I won't be replying any more about that.0 -
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