Trying to think of classical models to explain the EPR paradox kinda misses the point of the EPR paradox, because the point of the EPR paradox is to assume that there is indeed nothing linking the two particles until you look to then show you that this leads to a contradiction with Einstein’s definition of locality.† You can indeed trivially think of classical explanations to explain the EPR paradox and how the +1 and -1 particles might be linked and predetermined, but that’s not the point of the EPR paper which is to explore what happens if we don’t make this assumption.
The paper that instead explores what happens if we do assume they are predetermined is Bell’s theorem, and Bell’s theorem is more complicated than just assuming that the particles are entangled and opposites such that one will be measured to be +1 and the other to be -1. Bell’s theorem shows that the behavior of the individual particle can be dependent upon the configuration of a collection of measurement devices, even if the particle only ever interacts with one measurement device in the collection. That not only violates Einstein’s definition of locality, but if you try to make it deterministic, it ends up violating special relativity as well.
The simplest demonstration of this is with three particles in the GHZ experiment. The point is, again, not merely that the particles have correlated values but that (1) those values are statistically dependent upon the configuration of the measurement device and (2) the values for an individual particle can be statistically dependent upon the configuration of a collection of measurement devices even if it never interacts with most of the devices in the collection.
† “Locality” is used in two different senses in the literature. One is relativistic locality which means nothing can travel faster than light. The other is what I like to call coordinate locality which is what Einstein had in mind with the EPR paper, which is the idea that things have to locally interact to become dependent upon one another. The EPR paper is a proof by contradiction that quantum mechanics without hidden variables violates coordinate locality specifically.
Trying to think of classical models to explain the EPR paradox kinda misses the point of the EPR paradox, because the point of the EPR paradox is to assume that there is indeed nothing linking the two particles until you look to then show you that this leads to a contradiction with Einstein’s definition of locality.† You can indeed trivially think of classical explanations to explain the EPR paradox and how the +1 and -1 particles might be linked and predetermined, but that’s not the point of the EPR paper which is to explore what happens if we don’t make this assumption.
The paper that instead explores what happens if we do assume they are predetermined is Bell’s theorem, and Bell’s theorem is more complicated than just assuming that the particles are entangled and opposites such that one will be measured to be +1 and the other to be -1. Bell’s theorem shows that the behavior of the individual particle can be dependent upon the configuration of a collection of measurement devices, even if the particle only ever interacts with one measurement device in the collection. That not only violates Einstein’s definition of locality, but if you try to make it deterministic, it ends up violating special relativity as well.
The simplest demonstration of this is with three particles in the GHZ experiment. The point is, again, not merely that the particles have correlated values but that (1) those values are statistically dependent upon the configuration of the measurement device and (2) the values for an individual particle can be statistically dependent upon the configuration of a collection of measurement devices even if it never interacts with most of the devices in the collection.
† “Locality” is used in two different senses in the literature. One is relativistic locality which means nothing can travel faster than light. The other is what I like to call coordinate locality which is what Einstein had in mind with the EPR paper, which is the idea that things have to locally interact to become dependent upon one another. The EPR paper is a proof by contradiction that quantum mechanics without hidden variables violates coordinate locality specifically.