The QED vacuum or quantum electrodynamic vacuum is the field-theoretic vacuum of

quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the Theory of relativity, relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quant ...

. It is the lowest energy state (the ground state) of the electromagnetic field when the fields are quantized. When the

Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

is hypothetically allowed to approach zero, QED vacuum is converted to classical vacuum, which is to say, the vacuum of classical electromagnetism. Another field-theoretic vacuum is the QCD vacuum of the

Standard Model The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...

Fluctuations

The QED vacuum is subject to fluctuations about a dormant zero average-field condition; Here is a description of the quantum vacuum:

Virtual particles

It is sometimes attempted to provide an intuitive picture of virtual particles based upon the Heisenberg energy-time uncertainty principle:

\Delta E \Delta t \ge \frac \, ,

(where and are

energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...

and

time Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...

variations, and the

divided by 2) arguing along the lines that the short lifetime of virtual particles allows the "borrowing" of large energies from the vacuum and thus permits particle generation for short times. 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 determines a "budget" for borrowing energy . Another issue is the meaning of "time" in this relation, because energy and time (unlike position and momentum , for example) do not satisfy a canonical commutation relation (such as ). Various schemes have been advanced to construct an observable that has some kind of time interpretation, and yet does satisfy 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

The

Heisenberg uncertainty principle The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position a ...

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 Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly Quantum fluctuation, fluctuate in their lowest energy state as described by the Heisen ...

. 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 and a ''scalar'' potential to represent the basic electromagnetic electric field and magnetic field using the relations:

\begin
\mathbf B &= \mathbf \,, \\ 
\mathbf E &= -\frac \mathbf - \mathbfV \, . 
\end

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'' , given by:

\mathbf \Pi = \varepsilon_0 \frac \mathbf A \, ,

where is the electric constant of the

SI units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official st ...

. Quantization is achieved by insisting that the momentum field and the vector potential do not commute. That is, the equal-time commutator is:

= -i\hbar \delta_\delta (\mathbf-\mathbf')\, ,

where , are spatial locations, is the

reduced Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

, is the

Kronecker delta In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: \delta_ = \begin 0 &\text i \neq j, \\ 1 &\ ...

and is the

Dirac delta function In mathematical analysis, the Dirac delta function (or distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line ...

. The notation denotes the

commutator In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. Group theory The commutator of two elements, ...

. :Quantization can be achieved without introducing the vector potential, in terms of the underlying fields themselves:

= -\epsilon_\frac \frac \delta (\boldsymbol) \, ,

where the

circumflex The circumflex () is a diacritic in the Latin and Greek scripts that is also used in the written forms of many languages and in various romanization and transcription schemes. It received its English name from "bent around"a translation of ...

denotes a Schrödinger time-independent field operator, and 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. The electromagnetic field has therefore a zero-point energy, and 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 Spontaneous emission is the process in which a Quantum mechanics, quantum mechanical system (such as a molecule, an atom or a subatomic particle) transits from an excited state, excited energy state to a lower energy state (e.g., its ground state ...

, the transition of an excited atom to a state of lower energy by emission of a

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can ...

even when no external perturbation of the atom is present.

Electromagnetic properties

The polarisation of light emitted by a neutron star

As a result of quantization, the quantum electrodynamic vacuum can be considered as a material medium. It 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 of the classical vacuum. Likewise, its permeability can be calculated and differs slightly from . This medium is a dielectric with relative dielectric constant > 1, and is diamagnetic, with relative magnetic permeability < 1. Under some extreme circumstances in which the field exceeds the

Schwinger limit In quantum electrodynamics (QED), the Schwinger limit is a scale above which the electromagnetic field is expected to become Nonlinear system, nonlinear. The limit was first derived in one of QED's earliest theoretical successes by Fritz Sauter ...

(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. Many of electromagnetic effects of the vacuum are small, and only recently have experiments been designed to enable the observation of nonlinear effects. PVLAS and other teams are working towards the needed sensitivity to detect QED effects.

Attainability

A perfect vacuum is itself only attainable in principle. It is an idealization, like

absolute zero Absolute zero is the lowest possible temperature, a state at which a system's internal energy, and in ideal cases entropy, reach their minimum values. The absolute zero is defined as 0 K on the Kelvin scale, equivalent to −273.15 ° ...

for temperature, that can be approached, but never actually realized: 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

, the

Casimir effect In quantum field theory, the Casimir effect (or Casimir force) is a physical force (physics), force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of a field (physics), field. The term Casim ...

and the

Lamb shift In physics, the Lamb shift, named after Willis Lamb, is an anomalous difference in energy between two electron orbitals in a hydrogen atom. The difference was not predicted by theory and it cannot be derived from the Dirac equation, which pre ...

have been experimentally verified, suggesting QED vacuum is a good model for a high quality 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 Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the v ...

treats gravitational effects not included in the Standard Model. It remains an open question whether further refinements in experimental technique ultimately will support another model for realizable vacuum.

References