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,[1] as prescribed by Werner Heisenberg's uncertainty principle. They are minute random fluctuations in the values of the fields which represent elementary particles, such as electric and magnetic fields which represent the electromagnetic force carried by photons, W and Z fields which carry the weak force, and gluon fields which carry the strong force.[2]
The uncertainty principle states the uncertainty in energy and time can be related by[3]
\DeltaE\Deltat\geq\tfrac{1}{2}\hbar~
\DeltaE
\Deltat
Another consequence is the Casimir effect. 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.[4] [5] [6]
In quantum field theory, fields undergo quantum fluctuations. A reasonably clear distinction can be made between quantum fluctuations and thermal fluctuations of a quantum field (at least for a free field; for interacting fields, renormalization substantially complicates matters). An illustration of this distinction can be seen by considering quantum and classical Klein–Gordon fields:[7] For the quantized Klein–Gordon field in the vacuum state, we can calculate the probability density that we would observe a configuration
\varphit(x)
\tilde\varphit(k)
\rho0[\varphit]=\exp{\left[-
| 1 | \int | |
| \hbar |
| d3k | |
| (2\pi)3 |
| *(k)\sqrt{|k| | |
| \tilde\varphi | |
| t |
2+m
| 2}\tilde\varphi | |
| t(k)\right]}. |
In contrast, for the classical Klein–Gordon field at non-zero temperature, the Gibbs probability density that we would observe a configuration
\varphit(x)
t
\rhoE[\varphit]=\exp[-H[\varphit]/kBT]=\exp{\left[-
| 1 | \int | |
| kBT |
| d3k | |
| (2\pi)3 |
| *(k) | |
| \tilde\varphi | |
| t |
| 1 | |
| 2 |
\left(|k|2+
| 2\right)\tilde\varphi | |
| m | |
| t(k)\right]}. |
\hbar
kBT
\sqrt{|k|2+m2}
\tfrac{1}{2}(|k|2+m2)
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).