Inquantum field theory, thequantum vacuum state (also called thequantum vacuum orvacuum state) is thequantum state with the lowest possibleenergy. Generally, it contains no physical particles. However, the quantum vacuum is not a simple empty space,[1][2] but instead contains fleetingelectromagnetic waves andparticles that pop into and out of the quantum field.[3][4][5]
TheQED vacuum ofquantum electrodynamics (or QED) was the first vacuum ofquantum field theory to be developed. QED originated in the 1930s, and in the late 1940s and early 1950s, it was reformulated byFeynman,Tomonaga, andSchwinger, who jointly received the Nobel prize for this work in 1965.[6] Today, theelectromagnetic interactions and theweak interactions are unified (at very high energies only) in the theory of theelectroweak interaction.
TheStandard Model is a generalization of the QED work to include all the knownelementary particles and their interactions (except gravity).Quantum chromodynamics (or QCD) is the portion of the Standard Model that deals withstrong interactions, and theQCD vacuum is the vacuum of quantum chromodynamics. It is the object of study in theLarge Hadron Collider and theRelativistic Heavy Ion Collider, and is related to the so-called vacuum structure ofstrong interactions.[7]
If the quantum field theory can be accurately described throughperturbation theory, then the properties of the vacuum are analogous to the properties of theground state of a quantum mechanicalharmonic oscillator, or more accurately, theground state of ameasurement problem. In this case, thevacuum expectation value of anyfield operator vanishes. For quantum field theories in which perturbation theory breaks down at low energies (for example,Quantum chromodynamics or theBCS theory ofsuperconductivity), field operators may obtain non-vanishingvacuum expectation values byspontaneous symmetry breaking. In the Standard Model, the Higgs field acquires a non-zero expectation value when the electroweak symmetry is broken, and this explains part of the masses of other particles.
The vacuum state is associated with azero-point energy, and this zero-point energy (equivalent to the lowest possible energy state) has measurable effects. It may be detected as theCasimir effect in the laboratory. Inphysical cosmology, the energy of the cosmological vacuum appears as thecosmological constant. The energy of a cubic centimeter of empty space has been calculated figuratively to be one trillionth of anerg (or 0.6 eV).[8] An outstanding requirement imposed on a potentialTheory of Everything is that the energy of the quantum vacuum state must explain the physically observed cosmological constant.
For arelativistic field theory, the vacuum isPoincaré invariant, which follows fromWightman axioms but can also be proved directly without these axioms.[9] Poincaré invariance implies that onlyscalar combinations of field operators have non-vanishingvacuum expectation values. The vacuum may break some of theinternal symmetries of theLagrangian of the field theory. In this case, the vacuum has less symmetry than the theory allows, and one says thatspontaneous symmetry breaking has occurred.
Quantum corrections to Maxwell's equations are expected to result in a tiny nonlinear electric polarization term in the vacuum, resulting in a field-dependent electrical permittivity ε deviating from the nominal value ε0 ofvacuum permittivity.[10] These theoretical developments are described, for example, in Dittrich and Gies.[5] The theory ofquantum electrodynamics predicts that theQED vacuum should exhibit a slightnonlinearity so that in the presence of a very strong electric field, the permittivity is increased by a tiny amount with respect to ε0. Subject to ongoing experimental efforts[11] is the possibility that a strong electric field would modify the effectivepermeability of free space, becominganisotropic with a value slightly belowμ0 in the direction of the electric field and slightly exceedingμ0 in the perpendicular direction. The quantum vacuum exposed to an electric field exhibitsbirefringence for an electromagnetic wave traveling in a direction other than the electric field. The effect is similar to theKerr effect but without matter being present.[12] This tiny nonlinearity can be interpreted in terms of virtualpair production.[13] A characteristic electric field strength for which the nonlinearities become sizable is predicted to be enormous, aboutV/m, known as theSchwinger limit; the equivalentKerr constant has been estimated, being about 1020 times smaller than the Kerr constant of water. Explanations fordichroism from particle physics, outside quantum electrodynamics, also have been proposed.[14] Experimentally measuring such an effect is challenging,[15] and has not yet been successful.
The presence of virtual particles can be rigorously based upon thenon-commutation of thequantized electromagnetic fields. Non-commutation means that although theaverage values of the fields vanish in a quantum vacuum, theirvariances do not.[16] The term "vacuum fluctuations" refers to the variance of the field strength in the minimal energy state,[17] and is described picturesquely as evidence of "virtual particles".[18] It is sometimes attempted to provide an intuitive picture of virtual particles, or variances, based upon the Heisenbergenergy-time uncertainty principle:(with ΔE and Δt being theenergy andtime variations respectively; ΔE is the accuracy in the measurement of energy and Δt is the time taken in the measurement, andħ is theReduced Planck constant) 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.[19] Although the phenomenon of virtual particles is accepted, this interpretation of the energy-time uncertainty relation is not universal.[20][21] One issue is the use of an uncertainty relation limiting measurement accuracy as though a time uncertainty Δt determines a "budget" for borrowing energy ΔE. Another issue is the meaning of "time" in this relation because energy and time (unlike positionq and momentump, for example) do not satisfy acanonical commutation relation (such as[q,p] = i ħ).[22] 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.[23][24] Many approaches to the energy-time uncertainty principle are a long and continuing subject.[24]
According toAstrid Lambrecht (2002): "When one empties out a space of all matter and lowers the temperature to absolute zero, one produces in aGedankenexperiment [thought experiment] the quantum vacuum state."[1] According toFowler &Guggenheim (1939/1965), thethird law of thermodynamics may be precisely enunciated as follows:
It is impossible by any procedure, no matter how idealized, to reduce any assembly to the absolute zero in a finite number of operations.[25] (See also.[26][27][28])
Photon-photon interaction can occur only through interaction with the vacuum state of some other field, such as the Dirac electron-positron vacuum field; this is associated with the concept ofvacuum polarization.[29] According toMilonni (1994): "... all quantum fields have zero-point energies and vacuum fluctuations."[30] This means that there is a component of the quantum vacuum respectively for each component field (considered in the conceptual absence of the other fields), such as the electromagnetic field, the Dirac electron-positron field, and so on. According to Milonni (1994), some of the effects attributed to thevacuum electromagnetic field can have several physical interpretations, some more conventional than others. TheCasimir attraction between uncharged conductive plates is often proposed as an example of an effect of the vacuum electromagnetic field. Schwinger, DeRaad, and Milton (1978) are cited by Milonni (1994) as validly, though unconventionally, explaining the Casimir effect with a model in which "the vacuum is regarded as truly a state with all physical properties equal to zero."[31][32] In this model, the observed phenomena are explained as the effects of the electron motions on the electromagnetic field, called the source field effect. Milonni writes:
The basic idea here will be that the Casimir force may be derived from the source fields alone even in completely conventional QED, ... Milonni provides detailed argument that the measurable physical effects usually attributed to the vacuum electromagnetic field cannot be explained by that field alone, but require in addition a contribution from the self-energy of the electrons, or their radiation reaction. He writes: "The radiation reaction and the vacuum fields are two aspects of the same thing when it comes to physical interpretations of various QED processes including theLamb shift,van der Waals forces, and Casimir effects."[33]
This point of view is also stated by Jaffe (2005): "The Casimir force can be calculated without reference to vacuum fluctuations, and like all other observable effects in QED, it vanishes as the fine structure constant,α, goes to zero."[34]
For all field states that have classical analog the field quadraturevariances are also greater than or equal to this commutator.
The spontaneous, temporary emergence of particles from vacuum is called a "vacuum fluctuation".
The interaction will last for a certain durationΔt. This implies that the amplitude for the total energy involved in the interaction is spread over a range of energiesΔE.
