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Jayson_Virissimo comments on Open Thread, January 15-31, 2012 - Less Wrong Discussion
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What dbaupp said. But in particular you square first and then add because arriving at a different time makes the possibilities distinguishable, and so there is no interference (you don't add the complex amplitudes).
Ah good. This is a good explanation and I had been wondering how the different timing would affect it. Thanks to you and dbaupp.