A Quantum Roll of the Dice

In A Philosophical Essay on Probabilities, published in 1814, Pierre-Simon Laplace introduced a notorious hypothetical creature: a “vast intelligence” that knew the complete physical state of the present universe. For such an entity, dubbed “Laplace’s demon” by subsequent commentators, there would be no mystery about what had happened in the past or what would happen at any time in the future. According to the clockwork universe described by Isaac Newton, the past and future are exactly determined by the present.

Laplace’s demon was never supposed to be a practical thought experiment; the imagined intelligence would have to be essentially as vast as the universe itself. And in practice, chaotic dynamics can amplify tiny imperfections in the initial knowledge of the system into complete uncertainty later on. But in principle, Newtonian mechanics is deterministic.

A century later, quantum mechanics changed everything. Ordinary physical theories tell you what a system is and how it evolves over time. Quantum mechanics does this as well, but it also comes with an entirely new set of rules, governing what happens when systems are observed or measured. Most notably, measurement outcomes cannot be predicted with perfect confidence, even in principle. The best we can do is to calculate the probability of obtaining each possible outcome, according to what’s called the Born rule: The wave function assigns an “amplitude” to each measurement outcome, and the probability of getting that result is equal to the amplitude squared. This feature is what led Albert Einstein to complain about God playing dice with the universe.

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