When I tell my students this I often get the feeling that they think I'm pulling their collective leg, but this phenomenon is well-known among physicists. Here's physicist Brian Greene discussing it:
All I can do when I see a video like this is paraphrase Shakespeare in Hamlet: There are more things in heaven and on earth than we could ever dream of. QE certainly lends credence to the view of physicist Sir James Jeans that the world looks more like a grand idea than a grand machine. In fact, it looks very much as though, at bottom, it's an idea in the mind of God. At least that might explain how one particle "knows" what's happening to the other.