QED vacuum

The QED vacuum or quantum electrodynamic vacuum is the field-theoretic vacuum of quantum electrodynamics. It is the lowest energy state (i.e., the ground state) of the electromagnetic field when the fields are quantized. When the Planck constant is hypothetically allowed to approach zero, QED vacuum is converted to classical vacuum; that is, the vacuum of classical electromagnetism.

Another field-theoretic vacuum is the QCD vacuum of the Standard Model.

A Feynman diagram (box diagram) for photon-photon scattering, where one photon scatters from the transient vacuum charge fluctuations of the other.

Fluctuations

The QED vacuum is subject to fluctuations about a dormant zero average-field condition:

File:Vacuum fluctuations revealed through spontaneous parametric down-conversion.ogv

A description of the quantum vacuum is given by Joseph Silk in On the Shores of the Unknown (pg. 62): Template:Quote

Virtual particles

Template:Main An intuitive picture of virtual particles can be attempted based upon the Heisenberg energy-time uncertainty principle $$\mathrm{\Delta }E\mathrm{\Delta }t\ge \frac{\hslash }{2},$$ where Template:Math and Template:Math are the uncertainties in energy and time, respectively, with Template:Mvar the Planck constant divided by 2Template:Pi. Using this starting point, it could be argued that the short lifetime of virtual particles allows the "borrowing" of large energies from the vacuum, thus permitting particle generation over short time intervals.

This interpretation of the energy-time uncertainty relation is not universally accepted, however. One issue is the use of an uncertainty relation limiting measurement accuracy as though a time uncertainty Template:Math determines a "budget" for borrowing energy Template:Math. Another issue is the meaning of "time" in this relation, because energy and time (unlike position Template:Mvar and momentum Template:Mvar, for example) do not satisfy a canonical commutation relation (such as Template:Math). Various schemes have been advanced to construct an observable that has some kind of time interpretation while also satisfying a canonical commutation relation with energy. The many approaches to the energy-time uncertainty principle are a continuing subject of study.

Quantization of the fields

Template:Main The Heisenberg uncertainty principle does not allow a particle to exist in a state in which the particle is simultaneously at a fixed location and has also zero momentum. Instead, the particle has a range of momenta, the distribution of which is attributable to quantum fluctuations; if confined, it has a zero-point energy.

An uncertainty principle applies to all quantum mechanical operators that do not commute. In particular, it applies also to the electromagnetic field; in order to understand this, it is necessary to elucidate the role of commutators for this field.

The standard approach to the quantization of the electromagnetic field begins by introducing a vector potential Template:Math and a scalar potential Template:Mvar to represent the electric field Template:Math and magnetic field Template:Math using the relations $$\begin{array}{cc}𝐁& =𝜵\mathbf{\times }𝐀;\\ 𝐄& =-\frac{\partial }{\partial t}𝐀-𝜵V.\end{array}$$ The vector potential is not completely determined by these relations, leaving open a so-called gauge freedom. Resolving this ambiguity using the Coulomb gauge leads to a description of the electromagnetic fields in the absence of charges in terms of the vector potential and the momentum field Template:Math, given by $$𝜫={\epsilon }_0\frac{\partial }{\partial t}𝐀,$$ where Template:Math is the electric constant in SI units. Quantization is achieved by insisting that the momentum field and the vector potential do not commute. That is, the equal-time commutator is $$[{\mathrm{\Pi }}_i(𝐫,t),A_j({𝐫}^{\prime },t)]=-i\hslash {\delta }_{ij}\delta (𝐫-{𝐫}^{\prime }),$$ where Template:Math, Template:Math are spatial locations, Template:Mvar is the reduced Planck constant, Template:Mvar is the Kronecker delta, and Template:Math is the Dirac delta function. The notation Template:Math represents the commutator.

Quantization can be achieved without introducing the vector potential in terms of the underlying fields themselves: $$[{\hat{E}}_k(𝒓),{\hat{B}}_{k^{\prime }}({𝒓}^{\prime })]=-{\epsilon }_{k{k}^{\prime }m}\frac{i\hslash }{{\epsilon }_0}\frac{\partial }{\partial x_m}\delta (𝒓\mathit{-}{𝒓}^{\prime }),$$ where the circumflex denotes a Schrödinger time-independent field operator, and Template:Mvar is the antisymmetric Levi-Civita tensor.

Because of the non-commutation of field variables, the variances of the fields cannot be zero, although their averages are zero. So, the electromagnetic field has a zero-point energy, and therefore a lowest quantum state. The interaction of an excited atom with this lowest quantum state of the electromagnetic field is what leads to spontaneous emission: The transition of an excited atom to a state of lower energy by emission of a photon even when no external perturbation of the atom is present.

Electromagnetic properties

The polarization of observed light in an extremely strong magnetic field suggests that the empty space around the neutron star RX J1856.5−3754 is subject to vacuum birefringence.

As a result of quantization, the quantum electrodynamic vacuum can be considered a material medium. It is capable of vacuum polarization. In particular, the force law between charged particles is affected. The electrical permittivity of the quantum electrodynamic vacuum can be calculated, and it differs slightly from the simple Template:Math of the classical vacuum. (Likewise, its permeability can also be calculated and differs slightly from Template:Math.) This medium is a dielectric with relative dielectric constant greater than 1, and is diamagnetic, with relative magnetic permeability less than 1. In extreme conditions in which the field exceeds the Schwinger limit (e.g., in the exterior regions of pulsars), the quantum electrodynamic vacuum is thought to exhibit nonlinearity in the fields. Calculations also indicate birefringence and dichroism in the presence of strong fields. Many electromagnetic effects of the vacuum are difficult to detect, and only recently have experiments been designed to enable the observation of nonlinear effects. To this end, PVLAS and other teams are working towards the needed sensitivity to detect quantum electrodynamic nonlinearity.

Attainability

A perfect vacuum is itself only attainable in principle. It is an idealization, similar to absolute zero for temperature, that can be approached, but never actually realized. This idea is summarized by Luciano Boi in Creating the physical world ex nihilo? (pg. 55):

Virtual particles make a perfect vacuum unrealizable, but leave open the question of attainability of a quantum electrodynamic vacuum, or QED vacuum. Predictions of QED vacuum such as spontaneous emission, the Casimir effect, and the Lamb shift have been experimentally verified, suggesting QED vacuum is a good model for a near-perfect realizable vacuum. There are competing theoretical models for vacuum, however. For example, quantum chromodynamic vacuum includes many virtual particles not treated in quantum electrodynamics. The vacuum of quantum gravity treats gravitational effects not included in the Standard Model. It remains an open question whether further refinements in experimental technique will ultimately support another model for a realizable vacuum.

See also

• Feynman diagram
• History of quantum field theory
• Precision tests of QED