Vacuum (quantum electrodynamic)

The term quantum electrodynamic vacuum, or QED, refers to the ground state of the electromagnetic field, which is subject to fluctuations about a dormant zero average-field condition. Generally, it contains no physical particles.

According to present-day understanding of what is called the vacuum state or the quantum vacuum, it is "by no means a simple empty space", and again: "it is a mistake to think of any physical vacuum as some absolutely empty void." According to quantum mechanics, the vacuum state is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of existence.

Quantization of the fields

The Heisenberg uncertainty principle does not allow a particle to exist in a state in which the particle is simultaneously at a fixed location, say the origin of coordinates, and has also zero momentum. Instead the particle has a range of momentum and spread in location 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. A digression follows to flesh out the role of commutators for the electromagnetic field.

The standard approach to the quantization of the electromagnetic field begins by introducing a vector potential A and a scalar potential V to represent the basic electromagnetic electric field E and magnetic field B using the relations: ${\begin{aligned}\mathbf {B} &=\mathbf {\nabla \times A} ,\\\mathbf {E} &=-\mathbf {A-\nabla } V\ .\end{aligned}}$ 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 Π, given by: $\mathbf {\Pi } =\varepsilon _{0}{\frac {\partial }{\partial t}}\mathbf {A} \ .$ Quantization is achieved by insisting that the momentum field and the vector potential do not commute.

Because of the non-commutation of field variables, the variances of the fields cannot be zero, although their averages are zero. As a result, the quantum electrodynamic vacuum can be considered as a dielectric medium, and is capable of vacuum polarization. In particular, the force law between charged particles is affected. The electrical permittivity of quantum electrodynamic vacuum can be calculated, and it differs slightly from the simple ε₀ of the classical vacuum. Likewise, its permeability can be calculated and differs slightly from μ₀. This medium is a dielectric with relative dielectric constant > 1, and is diamagnetic, with relative magnetic permeability < 1. Under some extreme circumstances (for example, in the very high fields found in the exterior regions of pulsars ), the quantum electrodynamic vacuum is thought to exhibit nonlinearity in the fields. Calculations also indicate birefringence and dichroism at high fields.

Attainability

A perfect vacuum is itself only realizable in principle. It is an idealization, like absolute zero for temperature, that can be approached, but never actually realized:

“One reason [a vacuum is not empty] is that the walls of a vacuum chamber emit light in the form of black-body radiation...If this soup of photons is in thermodynamic equilibrium with the walls, it can be said to have a particular temperature, as well as a pressure. Another reason that perfect vacuum is impossible is the Heisenberg uncertainty principle which states that no particles can ever have an exact position...More fundamentally, quantum mechanics predicts ... a correction to the energy called the zero-point energy [that] consists of energies of virtual particles that have a brief existence. This is called vacuum fluctuation.” Luciano Boi, "Creating the physical world ex nihilo?" p. 55