In quantum physics, a quantum fluctuation is the temporary change in the amount of energy in a point in space, as prescribed by Werner Heisenberg's uncertainty principle. This allows the creation of particle-antiparticle pairs of virtual particles. Although the particles are not directly detectable, the cumulative effects of these particles are measurable; for example, the effective charge of the electron is different from its "naked" charge. Quantum fluctuations may have been necessary for the origin of the structure of the universe: According to the model of expansive inflation, the fluctuations that existed when inflation began were amplified and formed the seeds of all currently observed large-scale structure. Vacuum energy may also be responsible for the current accelerating expansion of the universe. According to the formula of the uncertainty principle derived by Mandelshtam & Tamm, the uncertainty in energy and time can be related by the relation where ≈ Js.
Field fluctuations
A quantum fluctuation is the temporary appearance of energetic particles out of empty space, as allowed by the uncertainty principle. The uncertainty principle states that for a pair of conjugate variables such as position/momentum or energy/time, it is impossible to have a precisely determined value of each member of the pair at the same time. For example, a particle pair can pop out of the vacuum during a very short time interval. An extension is applicable to the "uncertainty in time" and "uncertainty in energy". An illustration of this distinction can be seen by considering quantum and classical Klein-Gordon fields: For the quantized Klein–Gordon field in the vacuum state, we can calculate the probability density that we would observe a configuration at a time in terms of its Fourier transform to be In contrast, for the classical Klein–Gordon field at non-zero temperature, the Gibbs probability density that we would observe a configuration at a time is These probability distributions illustrate that every possible configuration of the field is possible, with the amplitude of quantum fluctuations controlled by Planck's constant, just as the amplitude of thermal fluctuations is controlled by, where is Boltzmann's constant. Note that the following three points are closely related:
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. Quantum effects that are consequences only of quantum fluctuations, not of subtleties of measurement incompatibility, can alternatively be models of classical continuous random fields.
Interpretations
The success of quantum fluctuation theories have given way to metaphysical interpretations on the nature of reality and their potential role in the origin and structure of the universe:
The fluctuations are a manifestation of the innate uncertainty on the quantum level
A fundamental particle arising out of its quantum field is always inescapably subject to this reality and is thus describable by an associated wave function.
The wave function of a quantum particle represents the reality of the innate quantum fluctuations at the core of the universe and bestows the particle its counter-intuitive quantum behavior. In the double slit experiment each particle makes an unpredictable choice between alternative possibilities. Cumulatively, those choices are consistent with an interference pattern with the inherent fluctuations of the underlying quantum field. Such an underlying immutable quantum field by which quantum fluctuations are correlated in a universal scale may explain the non-locality of quantum entanglement as a natural process. As has been recently demonstrated, charged extended particles can experience self-oscillatory dynamics as a result of classical electrodynamic self-interactions. This trembling motion has a frequency that is closely related to the zitterbewegung frequency appearing in Dirac's equation. The mechanism producing these fluctuations arises because some parts of an accelerated charged composite particle emit perturbing electromagnetic fields that can affect other parts of the particle, producing self-forces. Using the Liénard-Wiechert potential as solutions to Maxwell's equations with sources, it can be shown that these forces can be described in terms of differential equations with state-dependent delay, which display limit cycle behavior. Therefore, the principle of inertia, as appearing in Newton's first law, would only hold in an average sense, since uniform motion is unstable. Consequently, pilot waves would be necessary attached to any electromagnetically interacting body.
