Why rare events happen: a quantum interpreter ✛
An interpreter in a courtroom is distracted by every rustle: the creak of a chair, a cough, the rustle of papers. By the end of the day, they are not translating what the witness said, but what they heard through the noise. Rare translation errors are not the result of one loud shout, but the accumulation of many small noises.
In the quantum world, rare events arise in a similar way: a particle can end up far from its expected position not because of one giant leap, but because of many coordinated small steps. Scientists have found a way to compute the probability of such events. It turns out that one must take into account not only the usual measure of difference between distributions, but also how exactly we measure the system. It is as if the interpreter also loses information by choosing words from a limited vocabulary.
This method was applied to the early Universe, where rare fluctuations could generate black holes. It turned out that previous calculations might have underestimated the frequency of such events. Now, like an interpreter who knows their weaknesses, we can more accurately predict when to expect errors.
In a classical random walk, the probability that all N steps go in the same direction is exponentially small, but it is precisely such collective fluctuations, not a single giant jump, that are usually responsible for rare events. In the quantum case, the situation is analogous: the distribution tail may be determined not by quantum tunneling but by the coordinated behavior of many small quantum steps.