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Simple example would be the double spit experiment, the interference pattern that is observed does not make sense in a model where each photon has a direction when it is emitted by the source. You remember when you were first introduced to the quadratic equation in algebra class or wherever and how it can spit out two results and at first you had to figure out which was the "real" result (x must be 2 apples because Sally can't have -3 apples) but later you'd accept any answers that the equation spit out as real (maybe Sally owes somebody three apples, maybe we're taking about less tangible things and it's spitting out imaginary numbers). It's kind of the sam.

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