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Quantum nonlocality is often misunderstood - even by physicists.
In order to help explain some of its features to a complete non-physicist,
I wrote the following logic puzzle. Once you are convinced that a complete
solution to the puzzle is "logically impossible", you'll understand some of the
intuitive problems physicists face.
The puzzle is whimsically based around James Randi's million
dollar challenge - Randi offers $1 million to anyone who
can demonstrate paranormal phenomena under controlled conditions - you
can find out more from www.randi.org.
To me quantum phenomena are as close to magical as this universe will allow:
THE PUZZLE:
A group of three self-proclaimed psychics is captured and imprisoned by the infamous underground group PSI (Protectors of Scientific Integrity). The leader of the kidnappers, a certain Rames Jandi ("Rah-mez Yan-dee"), makes the generous offer that their lives will be spared if they can demonstrate psychic ability in ANY test of their own choosing (subject to the kidnappers' agreement that it does demonstrate psychic ability of course!).
The psychics propose the following test:
1. The three psychics will be taken to separate locations and locked in completely sealed rooms. (If you're picky you can add the restriction that the rooms are separated by many light years in order to avoid the "Peter Popoff effect" so to speak.)
2. Each psychic will be asked a question by a captor - the question will be either "WHAT IS X" or "WHAT IS Y".
3. The captors agree that either:
(A) All three psychics will be asked the "X" question; or
(B) One psychic will be asked the "X" question while the other two will be asked the "Y" question.
The captors will secretly choose uniformly at random from the four possibilities on each trial.
4. To the (meaningless) question the psychics must reply either "+1" or "-1" as they wish (utilizing whatever telepathic powers they deem necessary).
5. The psychics are deemed to have "won" if the product of their answers is -1 when case (A) of step 3 has occurred, but +1 when case (B) occurred.
6. Steps 2-5 are repeated 1000 times, and the psychics will be released if they win every single time.
Rames Jandi is a pretty good mathematician, and after a little thought he decides that they cannot possibly win more than 75% of the time without using some form of psychic ability [a copy of his proof is given below]. He therefore makes the generous offer that they need only win on more than 900 of the trials, and that if they do he will not only release them but he will give up his nefarious ways and become a naturopath for energy unbalanced alien visitors.
Unfortunately for Jandi the psychics DO pass the test - and in fact they win every single one of the 1000 trials.
How did they do it?
[Aside:
Jandi's proof that they cannot win 100% of the time:
Label the psychics A,B,C.
Let X(A) be the value (+1 or -1) that psychic A will answer if she is asked the X question, Y(A) is what she answers if asked the Y question. Similarly define X(B), Y(B), X(C), Y(C).
To win 100% of the time would require:
X(A)*X(B)*X(C) = -1
X(A)*Y(B)*Y(C) = +1
Y(A)*X(B)*Y(C) = +1
Y(A)*Y(B)*X(C) = +1
Multiplying the 4 equations together gives:
X(A)^2 * Y(A)^2 * X(B)^2 * Y(B)^2 * X(C)^2 * Y(C)^2 = -1
Since every factor on the left is the square of +1 or -1, the left hand side must be +1, which contradicts the right hand side. Thus all four equations cannot have simultaneous solutions. It is simple to find a set of values satisfying 3 of the 4 equations however.]
Solution to the puzzle
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