How is locality preserved in quantum mechanics? I was reading this post:
http://motls.blogspot.com/2015/06/locality-nonlocality-and-anti-quantum.html
Specifically here: "There is no nonlocality. There is no action at a distance. There is no doubt about this statement."
I am puzzled how locality is preserved. Suppose we do the standard experiment with two correlated particles. We measure one particles spin along a particularly axis. The other particle has opposite spin along the same axis.
If the particle does not have a spin before it is measured, and if you measure the spin of one, the other has definite opposite spin... how is there not some kind of action at a distance?
EDIT:
Here's a video with Murray Gell-Mann where he says the same thing. But it still doesn't clear up anything for me:
https://www.youtube.com/watch?v=AlIlkn3OxMI
 A: In general terms - 
Locality is preserved in one of the two ways - 


*

*The two entangled particles start with a complex/capable enough wave function that generates the correlation even when independently (without need of any mysterious link) working on two particles. - This is mainstream, most accepted quantum explanation. I guess this is referred to as superposition principle, multiple particle joint amplitude .. If someone has learnt the QM math well enough, then there are high chances that this will be the best solution in his/her opinion.

*Many people still seem to think that all possible classical explanations of correlation have not been exhausted, and there can be some explanation that still needs to be discovered.
The correlation means following behavior - 
a) anti correlation in every direction, always
b) statistically 50/50 in any one direction for each particle independently
c) statistically Sq(sin(A/2)) correlation at relative angle of A.
d) Please comment if any additions/correction are needed to the above three.
Local variables/plans (i.e. fully pre-determined plans) are not sufficient to exhibit the correlations and this has been mathematically proved by Bell's inequality. 
Bell's inequality disproved the ability of "local" "static" "variables" to describe the correlation. It did not disprove same for "local" "functions" like superposition etc.
A: A quantum system is described by a set of operators called observables. Those observables represent all of the possible outcomes of a particular measurement. When you measure an entangled system, all of the possible outcomes happen. The correlation is only established after the measurement results are 'compared', that is, after information about one result interacts with information about the other, see
http://arxiv.org/abs/quant-ph/9906007
http://arxiv.org/abs/1109.6223,
for more detail.
