To some extent, that is in fact how entanglement works. In fact, if you perform a Bell-style experiment exactly like this (with the two measurements in the two

To some extent, that is in fact how entanglement works. In fact, if you perform a Bell-style experiment exactly like this (with the two measurements in the two galaxies along the same axis), you'll get this same un-interesting result. The problem is that it works like more than this too. Say you have two billiard balls on a very very large table with almost no friction. One ball is stationery, the other is moving towards it and spinning along some axis. When they collide, they'll be sent along some random directions and each with some spin, and their spins are going to add up to the original spin of the moving ball (angular momentum is conserved in frictionless interactions in classical mechanics too). Now, when the ball arrive at a long distance away from each other, two experimenters which can't see the balls measure their spin. They each choose some direction and measure how much their ball spins along that direction. They repeat the experiment lots of times, keeping good track of each individual result. When they later compare notes, they'll measure how much their respective results for each individual experiment were correlated. Since they were measuring along different axis, they didn't both see the exact same result: maybe for the ball that reached one was spinning at one revolution along the 45° axis every two seconds, and the other was spinning at half a revolution along the 1° axis every second. Ultimately, they'll find that the correlation between their experiments was about 75% (each time they measure along unrelated axis, they get no correlation, when they happen to measure along the exact same axis, they get perfect correlation, and when it's in between, it's some subset of that). However, if we repeat the same thing with quantum particles, we actually find a higher correlation, about 85%. This can only happen if (a) measuring one particle changes the other - and we've quickly ruled out that this can happen at slower than light speeds, or (b) the particle pair don't share a definite state to begin with, but assume an appropriate state only when they are measured [or (c) the axis chosen by the experimenters in each measurement somehow depends on the spin of the particle pair].