{"id":1798,"date":"2008-01-17T19:31:27","date_gmt":"2008-01-18T02:31:27","guid":{"rendered":"http:\/\/dabacon.org\/pontiff\/?p=1798"},"modified":"2008-01-17T19:31:27","modified_gmt":"2008-01-18T02:31:27","slug":"the-contextuality-of-quantum-theory-in-ten-minutes","status":"publish","type":"post","link":"https:\/\/dabacon.org\/pontiff\/2008\/01\/17\/the-contextuality-of-quantum-theory-in-ten-minutes\/","title":{"rendered":"The Contextuality of Quantum Theory in Ten Minutes"},"content":{"rendered":"

Through my computer science “information is king” eyeglasses, there are really only two notions which thoroughly distinguish quantum theory from classical theories of how the world works: the nonlocal nature of quantum correlations as exemplified by Bell’s theorem<\/a> and the much less well known contextual nature of quantum measurements as exemplified by the Bell-Kochen-Specker theorem. While the former is well known (and hence, to paraphrase Gell-Mann, what you’ve heard about it is mostly wrong), the later is less well known. Is that because it is a complicated idea? I don’t think so! Indeed I think you can learn what quantum contextuality means in less than ten minutes. Yep, it’s another edition of “explain quantum theory in ten minutes!”
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\nChristmas where<\/a> I grew up followed strange rules. Every Christmas morning, when I’d come down the stairs to see what Old Saint Nick had left for me, instead of finding my Christmas stocking hanging under the mantel, I would be confronted with a rectangular box (a square cuboid<\/a>) left by Santa. This rectangular box was made of nine cubes pushed together. Here is a top down view of the rectangular box:
\nIn addition to the cubes, on the ends of each of the rows of three cubes there was a button. Similarly on the ends of each column there was a button. These are the little knobby circles in the picture above.
\nBeing confronted by such a contraption on Christmas morning, what would you do? Press one of the buttons, of course! And indeed this is what I have done every Christmas for an enumerable number year. The first time I woke up to this contraption, I pressed the button corresponding to the first row. And what happened? Well the top three boxes open, and out came colored elves (What else did you expect? Presents? You are such a tool of the religion of consumerism!):
\nAfter getting over the shock of there being small elves in the box, I had just enough time to note which box they were in and that two of them were blue and one of them was red. Then the elves disappeared along with the rectangular box.
\nThat was what happened the first Christmas. The second Christmas, I decided that instead of pushing the button corresponding to the first row, I would push the button corresponding to the first column. And then bam, our popped another three elves before disappearing a few seconds later:
\nThis time the elves were in the column of the button I had pushed. “Ah ha,” I remember thinking, “it must be that the button I push reveals the elves in the corresponding row or column! Strange contraption, Santa.” I also remember noting that just like before, the elf in the upper left hand box was colored blue.
\nChristmas number three. I decided that I would pick the row one button again, and see what happened:
\nInteresting! The third Christmas verified that indeed, when I push a button correspond to a row I get that row full of elves. And now something interesting happened. Instead of the upper left hand box containing a blue elf, now it contained a red elf. Okay, so apparently Santa wasn’t giving me a box with the same color elves under each box.
\nNow at about the fourth Christmas, I began to learn about science, and so I decided that I’d better keep track of the colors of all of the elves when I pushed different row and column buttons and see what color elves came out in which boxes. Here for example are the next sixteen Christmas box results:
\nWell by the nineteenth Christmas, it seems that I had collected a lot of data. But science isn’t just about collecting data, it is also about trying to understand this data.
\nSo looking over the data from the nineteen Christmas boxes, I was struck by some regularities. The first was, that while a row or column might yield different blue or red elves, for all of the rows and for all of the columns except the last (farthest to the right) column, the number of elves which were blue was an even number. Go ahead, look at the data. Yep, every row and every column except the last (third) column have an even number of blue elves. And what about that last column? Well in that column it seems that there is always an odd number of blue elves.
\nI have now witnessed many more Christmas boxes. And indeed, at all of those Christmas times, the rules<\/p>\n