Precisely! This has been pretty extensively tested - https://en.wikipedia.org/wiki/Bell_test_experiments https://en.wikipedia.org/wiki/Bell_test_experiments - a

Precisely! This has been pretty extensively tested - https://en.wikipedia.org/wiki/Bell_test_experiments 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)