This is very confusing. "But according to quantum mechanics, the answer is 50%". How is this so? The article doesn't mention how quantum mechanics explains what is going on, just that "classical physics" doesn't.
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.
Classical physics ALSO says that the other two directions have a 50% probability of being red/green regardless of the value in the x "door".
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.
How does this relate to Wired's other article on the pilot wave explanation of quantum mechanics?[1]
"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."
It's explained in the footnote of the article. Bell's experiment rules out local hidden variable theories but it's still possible to formulate non-local hidden variable theories that work.
In Brian Greene's book "Fabrics of the Universe" he also mentioned some other experiments that completely shattered our understanding of reality. One such was the quantum eraser and especially delayed choice quantum eraser, which COULD mean causality can be violated.
Why do the 3-color passport stamps have to be distributed normally? If some patterns were more common than others, than couldn't it explain the 55.55%?
That wouldn't matter (at least as I understand the article explanation). There's 2^3 = 8 different stamp configurations, two of which (RRR/GGG) trivially have 100% match likelyhood. The other six are all equivalent, and they all predict the same thing. There's (3 choices of doors) * (3 choices of doors) = 9 ways to expose the stamp configuration, and in any of the six equivalent stamps there's five ways to match colors to four ways to differ, 5/9 = 55.55%, the expected distribution. [1]
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
Is it possible that the 3-door box is not doing the same thing as the 1-door box? By this I mean that the 1-door box is measuring some hidden variable that the 3-door box is not measuring?
