Quantum fluctuation

We can construct a classical continuous random field that has the same probability density as the quantum vacuum state, so that the principal difference from quantum field theory is the measurement theory (measurement in quantum theory is different from measurement for a classical continuous random field, in that classical measurements are always mutually compatible – in quantum mechanical terms they always commute). Quantum effects that are consequences only of quantum fluctuations, not of subtleties of measurement incompatibility, can alternatively be models of classical continuous random fields.