# Local determinism vs. Local realism vs. Local causality

I found the following definitions for the three different terms. Do you find these definitions exhaustive, or can you suggest more precise formulations?

Einstein's principle of local realism is the combination of the principle of locality (limiting cause-and-effect to the speed of light) with the assumption that a particle must objectively have a pre-existing value (i.e. a real value) for any possible measurement, i.e. a value existing before that measurement is made. However, Fine's theorem shows that, this deterministic assignment of properties is not required to prove Bell's theorem[4]. This is because the set of statistical distributions for measurements on two parties, once locality has been assumed, are independent of whether or not determinism is also assumed. This result demonstrates that one can consider local realism as the statement that real states exist independently of the observer (realism), combined with the assumption that two separated systems each have their own states with local dynamics (locality).

I would say that local determinism needs the probability of obtaining outcome $a$ when measurement $x$ is performed on a local'' system to be $P(a\vert x,\lambda)\in \{0,1\}$, where $\lambda$ are uncontrolled parameters (hidden variables) and $\delta$.

Then, according to [J. Bell, La nouvelle cuisine'' 1990]

A theory will be said to be locally causal if the probabilities attached to values of local beables in a space-time region 1 are unaltered by specification of values of local beables in a space-like separated region 2, when what happens in the backward light cone of 1 is already sufficiently specified, for example by a full specification of local beables in a space- time region 3...

Which one of the above is falsified by a Bell experiment?

Are there even more similar concepts I forgot?

• The historical part of this question might be a good for SE.HistoryOfScienceAndMathematics. – Nat Aug 6 '18 at 9:32
• What are your definitions for these terms? If you are asking about the differences, you need to identify what differences you are asking about. – sammy gerbil Aug 6 '18 at 14:11
• @sammygerbil sure, probably I'm asking consistent definition first. I'll edit the question. – m137 Aug 6 '18 at 15:32
• If you are asking us to provide consistent definitions then explain the differences between them, then I think you are asking a bit too much. Users are expected to demonstrate some research effort. What source(s) are you learning from? What definitions do they give? At the very least you could do an internet search for definitions. – sammy gerbil Aug 6 '18 at 15:43
• @sammygerbil I'm a physicist and I have "rough" definitions for the above concepts. My question was thought for people already familiar with quantum foundations, who might probably already give an answer without much effort. I elaborated and expanded aa bit the question to make it more transparent and accessible. Thanks for the comment. – m137 Aug 7 '18 at 9:13