# Non-locality versus Action-at-a-distance

I thought this was an interesting paper as it argues that while some type of non-locality is likely a necessary feature of QM, it might not necessitate action-at-a-distance (even within an ontological interpretation). The basic argument appears to rest on a some distinction between locality versus local causality:
One way to violate the Bell locality condition-and this is the way that any deterministic theory must do it-is via straightforward action at a distance. However, we should also consider the possibility of a stochastic theory with probabilistic laws that involve irreducible correlations. The sort of non-locality inherent in such a theory involves relations between events that are significantly different from causal relations as usually conceived. Perhaps surprisingly, such a theory, unlike its deterministic cousins, need not invoke a distinguished relation of distant simultaneity.
Lessons of Bell's Theorem: Nonlocality, yes; Action at a distance, not

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## Answers and Replies

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

I'm not sure about the validity of Myrvold's argument. He holds that the setting parameters are variables that can be the target of an intervention so they can therefore change the probabilities of events at a distance implying a clear case of action-at-a-distance; however, this isn't the case with outcome variables:
The outcome variables are not the sorts of things that can be a target of an intervention-there's no process that can set them to particular values-and so they don't fall within the paradigm cases of causal relations....unlike the instrument settings, the outcome can't be set by any other process, external to the system, whether controlled by an agent or not.
So Myrvold holds that while PI (Parameter Independence) necessitates local causality, this isn't the case with OI (Outcome Independence). With outcome variables there's no causal link between outcome variables, as neither variable can be the target of an intervention as is the case with setting parameters. This leads Myrvold to conclude that violation of OI does not necessarily imply action-at-a-distance (i.e. violation of local causality) although it implies some type of non-locality. If I'm understanding Myrvold, he appears to be arguing that violating OI is compatible with local causality in a way that violating PI is not. He and Norsen have been debating this issue on the response section of his paper.

I'm not sure about the validity of Myrvold's argument. He holds that the setting parameters are variables that can be the target of an intervention so they can therefore change the probabilities of events at a distance implying a clear case of action-at-a-distance; however, this isn't the case with outcome variables:

So Myrvold holds that while PI (Parameter Independence) necessitates local causality, this isn't the case with OI (Outcome Independence). With outcome variables there's no causal link between outcome variables, as neither variable can be the target of an intervention as is the case with setting parameters. This leads Myrvold to conclude that violation of OI does not necessarily imply action-at-a-distance (i.e. violation of local causality) although it implies some type of non-locality. If I'm understanding Myrvold, he appears to be arguing that violating OI is compatible with local causality in a way that violating PI is not. He and Norsen have been debating this issue on the response section of his paper.
This is an interesting argument. I think parameter independence can be assumed with proper randomization and lack of conspiracy. However outcome independence can be violated in two ways:

1. If the inequalities use independent outcomes but for some reason the experiments generate outcomes that are not independent.
2. If the inequalities use outcomes which are not independent but the outcomes in the experiments are independent.

Only (1) implies violation of local causality. (2) would requires a re-evaluation whether the terms in the inequality actually do have the same degrees of freedom as in the experiment.

morrobay
Gold Member
On page 3 of the paper they state that for any value for a factor Z the probability of Y depends on X
and that the realization of Y occurs at a later time than setting of X.
I equate factor Z as a a hidden variable in a casual stochastic hidden variable ( outcome independent ) theory that can account for inequality violations.
In relation to #1. above the analogy for the Z value is equivalent to a spatial/temporal setting for events that are independent .But when taken together their combined effect exhibit a wave like pattern faster than c where there is no propagation of information

morrobay
Gold Member
I thought this was an interesting paper as it argues that while some type of non-locality is likely a necessary feature of QM, it might not necessitate action-at-a-distance (even within an ontological interpretation). The basic argument appears to rest on a some distinction between locality versus local causality:

Lessons of Bell's Theorem: Nonlocality, yes; Action at a distance, not
So this non locality is local relativistic casual : that no object or signal can travel faster than light.
But it does not rule out an information free superluminal effect.
Can this type of effect, local relativistic casual , allow for the outcome of one system to depend on the measurement of the other and violate the inequality ? While still maintaining locality assumption based on past variable λ , p(ab|xy,λ) = p(a|x,λ)(p|b,yλ) In summery can this inequality
(AB) + (AB') + (A'B) - (A'B') ≤ 2 A,A' BB' = ± 1 with above locality assumption be violated with local relativistic causality ?

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So this non locality is local relativistic casual : that no object or signal can travel faster than light.
But it does not rule out an information free superluminal effect.
What I don't understand is that even if there is no possibility of superluminal signalling ((involving violation of joint assumptions of locality and causality), how can superluminal information transfer (supposedly involving just violation of locality) still be compatible with special relativity? Doesn't the possibility of superluminal information transfer (even if "hidden" or not involving an "agent" or some type of information transfer when nature is left to herself) at least, within any ontological interpretation, necessarily compromise special relativity?

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