[boyce]

The difference is that the same experiment in quantum terms would have you look at the ball through a colour filter and determine the probability of a range of possibilities (and therefore the other ball wherever it is) but then seeing the statistics show the particular filter you choose changes the probability of what colour ball you have and therefore the distant ball also

[jobigoud]

Ah, thanks for your comment. I also thought the measurement was just revealing an underlying property. But now if I understand correctly the method of measurement is biasing the results, and the other particle will still be correlated with the biased result. So the way we measure the first particle has an impact on the value of the second one.

[boyce]

Precisely! This has been pretty extensively tested - https://en.wikipedia.org/wiki/Bell_test_experiments - and is true even at distances and within timescales where a photon couldn't travel between the two entangled particles (i.e. to send that information)