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Here is a thread on Bell's theorem with easy explanations: Bell's Theorem - Easy explained
For nonlocality I recommend reading this post on the Backreaction blog: Nonlocal correlations between the Canary Islands
It assumes though that you know about Minkowski diagrams and light cones.
Once you have understood the concept of a light cone consider the following situation (see attachment, but rightclick on it and open it in a new tab):
You have two detectors A and B and each of them measures a particle of the entangled pair.
M(A) and M(B) denote the measurements at A and B.
When a measurement takes place we suppose a signal of the outcome is emitted. For example if you measure spin-up at detector A a signal is emitted at M(A) (see forward light cone).
This signal could reach the other particle flying to B and influence it, i.e. it tells the second particle to have spin-down, provided that M(B) lies in the forward light cone of M(A).
To prevent this we put M(B) outside
of M(A)'s light cone, i.e. the measurement M(B) takes place before the signal can reach the particle flying to B. So, there is no way M(A) can have an influence on M(B).
However, let's assume that the light cone is time-symmetric, i.e. the light cone also moves backward in time. We call this the backward light cone (see attachment). This backward light cone reaches the source at t=0 which means that it could have influenced the particle flying to B and told it to have spin-down. This is known as backward causation
. (I have read about it in the paper Bell's inequality and 'ghost-like action-at-a-distance' in quantum mechanics
by Richard D Mattuck.)
You can read about it here:
1. Backward Causation
Read the section that starts with "Costa de Beauregard".
2. Action at a Distance in Quantum Mechanics
See Figure 3.
The idea of a backward light cone looks good in the drawing but it has a problem. It means that a future event can influence the past.