An Experiment That Changed How We Think About Reality
wired.com
wired.com
"To some researchers, the experiments suggest that quantum objects are as definite as droplets, and that they too are guided by pilot waves — in this case, fluid-like undulations in space and time. These arguments have injected new life into a deterministic (as opposed to probabilistic) theory of the microscopic world first proposed, and rejected, at the birth of quantum mechanics."
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.
With the quantum as stated above you still won't get 50% on random "doors", because there is a chance that you open the same "door" on both particles increasing the probability of getting a match beyond 50%?
To avoid having 55% on random doors, you'd need < 50% on the non equal "doors", which implies something other than even chances.
(Quantum is beyond me I suspect!)
I think it's "The Fabric of the Cosmos" http://www.amazon.com/Fabric-Cosmos-Texture-Reality-Penguin-...
The problem is that quantum mechanics predicts (and experiments show) that the distribution you actually get is 50%, which is lower than what you would expect no matter what stamp configuration you get.
On the other hand, it's possible that the way you choose which door to open is not distributed randomly. One of the ways to reconcile Bell's theorem is that there's a passport stamp that mind-controls you into picking doors with a 50% distribution. It's not a very popular theory, but it exists. [2]
[1] Assuming RGG without loss of generality
1-R 1-R = Match
1-R 2-G = Miss
1-R 3-G = Miss
2-G 1-R = Miss
2-G 2-G = Match
2-G 3-G = Match
3-G 1-R = Miss
3-G 2-G = Match
3-G 3-G = Match
Five matches to four misses.