What causes it and how does it occur? If you do post some mathematics, please explain what each term means too please.
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Quantum fluctuations are a popular buzzword for the statistical triviality that the variance of a random variable A with zero mean is typically not zero - except that A is now an operator. Some people therefore think that this deserves a much more mysterious name.
Taken from the section ''Does the vacuum fluctuate?'' in Chapter A8: Virtual particles and vacuum fluctuations of A theoretical physics FAQ