Quantum fluctuation

In quantum physics, a quantum fluctuation (also known as a vacuum state fluctuation or vacuum fluctuation) is the temporary random change in the amount of energy in a point in space,[2] as prescribed by Werner Heisenberg's uncertainty principle.

This means that pairs of virtual particles with energy

For example, without quantum fluctuations, the "bare" mass and charge of elementary particles would be infinite; from renormalization theory the shielding effect of the cloud of virtual particles is responsible for the finite mass and charge of elementary particles.

One of the first observations which was evidence for vacuum fluctuations was the Lamb shift in hydrogen.

In July 2020, scientists reported that quantum vacuum fluctuations can influence the motion of macroscopic, human-scale objects by measuring correlations below the standard quantum limit between the position/momentum uncertainty of the mirrors of LIGO and the photon number/phase uncertainty of light that they reflect.

An illustration of this distinction can be seen by considering quantum and classical Klein–Gordon fields:[8] For the quantized Klein–Gordon field in the vacuum state, we can calculate the probability density that we would observe a configuration

to be In contrast, for the classical Klein–Gordon field at non-zero temperature, the Gibbs probability density that we would observe a configuration

is These probability distributions illustrate that every possible configuration of the field is possible, with the amplitude of quantum fluctuations controlled by the Planck constant

Note that the following three points are closely related: A classical continuous random field can be constructed 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).