Here is my understanding of the idea that information can't be passed using entanglement - based on two entangled electrons with opposite spin.

Suppose I closed my eyes and dropped one shoe of a pair in one box and the other into another, and then mailed one box off to a friend in the next town, or in Andromeda without looking at the contents. When I came to open my box, and found a left shoe (say), I would instantly know what was in my friend's box - a right shoe -, but there would be nothing magical or quantum about that! Also there would be no information transfer.

Now suppose I did the same with an entangled pair of electrons. The crucial difference is that both of us could measure our electron's spin about 3 different possible axes - X, Y, or Z. Suppose I measured in the Z direction, if my friend also measures in the Z direction, the result is analogous to the shoes above, but if he measures the spin about Y or Z he should get a spin which is plus or minus one half with equal probabilities. If this is repeated a lot of times, and all the data is collected, it will be obvious that whenever we both chose the same measurement direction (long after the particles separated) we came up with opposite spin values.

Keep in mind that even if you measure the spin about a different axis, QM requires that the answer is either +1/2 or -1/2.

This means that in some strange way, every time I made a measurement, I transmitted the direction of measurement to my friend.

The reason this doesn't count as information transfer, is that my friend has the choice of measuring the spin about 3 possible axes, and he will get random 50/50 answers on all through axes! He doesn't learn anything from the experiment until all the data is brought together - because he doesn't learn which spin value I actually measured!

That is (I hope) standard QM, but I can't help wondering if there is more to quantum probabilities than is usually assumed. For example, if people can preferentially select quantum states, this might not show up in normal physics experiments - only experiments like Dean Radin's - where he does report such an effect!

David