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{{Short description|Lowest energy state in quantum electrodynamics}}{{For|articles related to the QED vacuum|Quantum vacuum (disambiguation)}}The QED vacuum or quantum electrodynamic vacuum is the field-theoretic vacuum of quantum electrodynamics. It is the lowest energy state (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, which is to say, the vacuum of classical electromagnetism.Another field-theoretic vacuum is the QCD vacuum of the Standard Model.File:Photon-photon scattering.svg|thumb|A Feynman diagram (box diagram) for photon-photon scattering, one photon scatters from the transient vacuum charge fluctuations of the other]]

Fluctuations

File:Vacuum fluctuations revealed through spontaneous parametric down-conversion.ogv|thumb|right|150px| The video of an experiment showing vacuum fluctuations (in the red ring) amplified by spontaneous parametric down-conversionspontaneous parametric down-conversionThe 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{hbar}{2} , , (where {{math|ΔE}} and {{math|Δt}} are energy and time variations, and {{mvar|ħ}} the Planck constant divided by 2{{pi}}) 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 {{math|Δt}} determines a “budget” for borrowing energy {{math|ΔE}}. Another issue is the meaning of “time” in this relation, because energy and time (unlike position {{mvar|q}} and momentum {{mvar|p}}, for example) do not satisfy a canonical commutation relation (such as {{math|1=[q, p] = iħ}}). 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 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. mathbf B &= mathbf {nabla times A},, mathbf E &= -frac{partial}{partial t} mathbf{A} - mathbf{nabla}V , . end{align} 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 {{math|Π}}, given by: mathbf Pi = varepsilon_0 frac{ partial }{partial t} mathbf A , , where {{math|ε0}} is the electric constant of the 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: bigl[Pi_i(mathbf{r}, t), A_j(mathbf{r}’, t)bigr] = -ihbar delta_{ij}delta (mathbf{r}-mathbf{r}’), , where {{math|r}}, {{math|r′}} are spatial locations, {{mvar|ħ}} is the reduced Planck constant, {{mvar|δij}} is the Kronecker delta and {{math|δ(r − r′)}} is the Dirac delta function. The notation {{math|[ , ]}} denotes the commutator. 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, 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

{{See also|Lamb shift|Casimir effect|Spontaneous emission}}File:The polarisation of light emitted by a neutron star.jpg|thumb|The polarization of the observed light in the extremely strong magnetic field suggests that the empty space around the neutron star RX J1856.5−3754RX J1856.5−3754As 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 {{math|ε0}} of the classical vacuum. Likewise, its permeability can be calculated and differs slightly from {{math|μ0}}. 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 (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 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 spontaneous emission, the Casimir effect and the Lamb shift 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 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.

See also

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

References

{{reflist|refs=This commutation relation is oversimplified, and a correct version replaces the {{mvar|δ}} product on the right by the transverse {{mvar|δ}}-tensor: where {{math|û}} is the unit vector of {{math|k}}, {{math|û {{=}} {{sfrac|k|k}}}}. For a discussion see, BOOK, Atom-Field Interactions and Dressed Atoms, Cambridge Studies in Modern Optics, vol. 17, G., Compagno, R., Passante, F., Persico,books.google.com/books?id=R2GUQlBEeekC&pg=PA31, §2.1 Canonical quantization in the Coulomb gauge, 31, 2005, Cambridge University Press, 978-0-521-01972-9, BOOK, Conceptual Foundations of Quantum Field Theory, Tian Yu, Cao,books.google.com/books?id=d0wS0EJHZ3MC&pg=PA179, 179, For each stationary classical background field there is a ground state of the associated quantized field. This is the vacuum for that background., 978-0-521-60272-3, Cambridge University Press, 2004, Classical vacuum is not a material medium, but a reference state used to define the SI units. Its permittivity is the electric constant and its permeability is the magnetic constant, both of which are exactly known by definition, and are not measured properties. See Mackay & Lakhtakia, p. 20, footnote 6.BOOK, Tom G., Mackay, Akhlesh, Lakhtakia, Electromagnetic Anisotropy and Bianisotropy: A Field Guide,books.google.com/books?id=AcMyp7wxWpsC&pg=PA201, 201, 978-981-4289-61-0, World Scientific, 2010, A vaguer description is provided by BOOK, Quarks, Leptons and the Big Bang, Jonathan, Allday,books.google.com/books?id=kgsBbv3-9xwC&pg=PA224, 224, The interaction will last for a certain duration {{math, Δt, . This implies that the amplitude for the total energy involved in the interaction is spread over a range of energies {{math|ΔE}}. |isbn=978-0-7503-0806-9 |edition=2nd |publisher=CRC Press |year=2002}}QCD vacuum is paramagnetic, while QED vacuum is diamagnetic. 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