Thanks for pointing that you. My goal was to point out an empirical observation that can't be explained by a local hidden variables theory. You're right that I

Thanks for pointing that you. My goal was to point out an empirical observation that can't be explained by a local hidden variables theory. You're right that I didn't explain how quantum mechanics predicts the same result, because that's tricky to do in the scope of such an article. Here's a little more on that: One way you could do this experiment is to create 2 entangled electrons. Measuring the spin of an electron in the x, y,or z direction corresponds to the 3 doors on the box. Spin in a given direction is a binary variable for an electron (up or down) so that corresponds to the color of the light in each door (red or green). Since the electrons are entangled, if you measure the spin of one of them in the x direction (say), then this also constitutes a measurement of the spin of the other particle in the x direction. And you can show using quantum mechanics that if you measure the spin of an electron in the x direction, the spin in the y or the z direction will be up with probability 50% and down with probability 50%. I left this as an empirical fact because I don't know how to explain it with actually resorting to doing quantum mechanics.