Schizophrenic Playing Card

An ideal playing card stands perfectly balanced on its edge. According to the rules of quantum mechanics, this card will fall in both directions at once! That is, the final state of the card is the superposition of the two alternative falling directions, with ψ₁ for left and ψ₂ for right. The card’s wave function changes smoothly and continuously from the balanced state to the mysterious final state Ψ = ψ₁ + ψ₂ with two alternatives that seem to have the card in two places at once. Why haven’t we seen this happen in the everyday world around us?

Answer

According to the rules of QM, the final state should be the superposition of the two alternative falling directions, with equal amplitudes ψ₁ for left and ψ₂ for right. But we never see a card fall both ways simultaneously. Any air molecule colliding with the card is equivalent to an observation, a measurement process, so QM rule 3 applies and the outcome reduces to the classical one, with equal probabilities P₁ to fall to the left side and P₂ to fall to the right side.

The term describing this reduction of the wave function to the classical probabilities that have no QM interference is often called decoherence. The Schrodinger equation, which is deterministic, controls the entire process.