I Why are terms like "deterministic" rarely used in Bell context

[greypilgrim]

Hi.

In the context of Bell-like inequalities, the words to use seem to be "realism", "locality", "contextuality", "definiteness" and of course their negations. I have rarely seen those terms in classical physics (except maybe locality) before the Bell context.
In classical physics (and philosophy), one of the big questions has been if the world is deterministic or not.

Usually when "determinism" is used in the context with quantum foundations, it's in popular articles where they don't want to explain realism and locality.

So my question is: Does the violation of Bell-like inequalities of QM say anything about determinism, and what? Or is it unsuited to make statements about determinism?

 

[Nugatory]

So my question is: Does the violation of Bell-like inequalities of QM say anything about determinism?

No.
Bell’s theorem says that any theory that meets certain conditions (stated in his paper, of course) must obey the inequality. Determinism is not one of those conditions.

 

[greypilgrim]

Does realism follow from determinism, if all the initial conditions are known?

 

[atyy]

Bell's theorem does say something about determinism. All the terms used are defined differently by different authors, but here are some interesting papers.

https://arxiv.org/abs/1503.06413
Causarum Investigatio and the Two Bell's Theorems of John Bell
Howard M. Wiseman, Eric G. Cavalcanti

https://arxiv.org/abs/1708.00265
Certified randomness in quantum physics
Antonio Acín, Lluis Masanes

https://arxiv.org/abs/1210.6514
Full randomness from arbitrarily deterministic events
Rodrigo Gallego, Lluis Masanes, Gonzalo de la Torre, Chirag Dhara, Leandro Aolita, Antonio Acin

 

[Demystifier]

Some versions of Bell theorem assume determinism, but modern refined versions of the Bell theorem usually don't assume it. So I would say that the modern view of the Bell theorem is that it says nothing about determinism. Instead of determinism, modern versions talk about realism. But what exactly this "realism" is, it's not easy to tell. In theorems it's represented with clear math, but it's hard to say precisely what is "realism" on the conceptual level. It's more or less the same as "ontic" stuff, but it's hard to make a precise definition of "ontic". Some physicists find this concept intuitive without a need for a precise definition, others are completely baffled with it.
https://www.physicsforums.com/threads/ontology.1007637/
https://www.physicsforums.com/threads/learning-the-word-ontic.1008388/

 

[martinbn]

Some versions of Bell theorem assume determinism, but modern refined versions of the Bell theorem usually don't assume it. So I would say that the modern view of the Bell theorem is that it says nothing about determinism. Instead of determinism, modern versions talk about realism. But what exactly this "realism" is, it's not easy to tell. In theorems it's represented with clear math, but it's hard to say precisely what is "realism" on the conceptual level. It's more or less the same as "ontic" stuff, but it's hard to make a precise definition of "ontic". Some physicists find this concept intuitive without a need for a precise definition, others are completely baffled with it.
https://www.physicsforums.com/threads/ontology.1007637/
https://www.physicsforums.com/threads/learning-the-word-ontic.1008388/

Actually what is the clear math that represents "realism/ontic"?

 

[Demystifier]

Actually what is the clear math that represents "realism/ontic"?

It's $\lambda$, the mathematical meaning of which is always clear in theorems.

 

[martinbn]

It's $\lambda$,

I thought that $\lambda$ is whatever remaining paramters there might be, that are not explicitely used. And that there is no requirement that it has to be real.

the mathematical meaning of which is always clear in theorems.

I am not sure about that. In what I have seen, it was never even mentioned what it might be. A real number, a function, a vector, ...

 

[Demystifier]

I am not sure about that. In what I have seen, it was never even mentioned what it might be. A real number, a function, a vector, ...

I think it's red herring from your side. In professional objections on Bell theorem, nobody ever complained about that.

 

[martinbn]

I think it's red herring from your side. In professional objections on Bell theorem, nobody ever complained about that.

I know, that this doesn't change anything about the theorem. But it would be nice to be a bit precise. Just giving a notation and then manipulating it is very unsettling for me. It is done quite often in physics, it is not specific to Bell's theorem.

 

[Demystifier]

I know, that this doesn't change anything about the theorem. But it would be nice to be a bit precise. Just giving a notation and then manipulating it is very unsettling for me. It is done quite often in physics, it is not specific to Bell's theorem.

Yes, for instance we physicists often like to not distinguish integral from sum.

 

[DrChinese]

Actually what is the clear math that represents "realism/ontic"?

My take is different than Demystifier's.

The key novel element of Bell is the assumption of realism, which is shown in Bell circa (14): "It follows that c is another unit vector [in addition to a and b]..." (which exactly answers your question).

This assumption is a mathematical restatement of the EPR assumption that there are "elements of reality" (i.e. vectors a, b, c, etc), a deduction they deemed "reasonable" since the outcomes of various measurements could be predicted with 100% certainty. In their view, such outcomes must actually be predetermined. There is your chain from "realism/Bell realism" to the "determinism" referenced in the title of this thread.

Since different authors use the terms "realism", "determinism", "objective" differently, it is easy for us to get lost in semantics. It is like this within the generally accepted science: Bell stood on the intended arguments of EPR, and showed that the EPR reasoning was in conflict with the predictions of QM. If you have other definitions/arguments about the subject, then you may or may not come to the same conclusion.

Is determinism the same as realism? Probably not. Does that change the Bell result? I don't think so. If realism falls per Bell, then I would say determinism falls too (although the reverse is probably not true).

 

[Killtech]

Actually what is the clear math that represents "realism/ontic"?

It's λ, the mathematical meaning of which is always clear in theorems.

Looking at the formulation of the assumptions and the theorem, i don't think it makes more sense to view Bell as being about Einstein-locality of all the information bearing variables relevant for predictions of the model (Bell factorization condition on the random variables). While the "information bearing" is meant as an idea of realism, the word itself is too loosely defined and invites for pointless arguing - there is just no consensus about it's exact general mathematical formulation.