Virtual particle
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In [[physics]], a '''virtual particle''' is a particle that exists for a limited time and space, introducing uncertainty in their energy and momentum due to the [[Heisenberg Uncertainty Principle]]. (Indeed, because energy and momentum in quantum mechanics are time and space derivative [[operator]]s, then due to [[Fourier transform]]s their spans are inversely proportional to time duration and position spans, respectively).
Virtual particles exhibit some of the phenomena that real [[Elementary particle|particle]]s do, such as obedience to the [[conservation law]]s. If a single particle is detected, then the consequences of its existence are prolonged to such a degree that it cannot be virtual. Virtual particles are viewed as the [[quantum|quanta]] that describe fields of the basic force interactions, which cannot be described in terms of real particles. Examples of these are static force fields, such as a simple [[electric field|electric]] or [[magnetic field]]s, or any field that exists without excitations that result in its carrying information from place to place.
==Properties==
The concept of virtual particles necessarily arises in the [[perturbation theory]] of quantum field theory, where interactions (essentially, forces) between real particles are described in terms of exchanges of virtual particles. Any process involving virtual particles admits a schematic representation known as a [[Feynman diagram]] which facilitates understanding of calculations.
A virtual particle is one that does not precisely obey the <math>m^2c^4 = E^2 - p^2c^2</math> relationship for a short time. In other words, their kinetic energy may not have the usual relationship to velocity — indeed, it can be negative. The probability amplitude for them to exist tends to be canceled out by [[destructive interference]] over longer distances and times. They can be considered a manifestation of [[quantum tunnelling]]. The range of forces carried by virtual particles is limited by the uncertainty principle, which regards energy and time as conjugate variables; thus virtual particles of larger mass have more limited range.
There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields. As such, virtual particles are also excitations of the underlying fields, but are detectable only as forces but not particles. They are "temporary" in the sense that they appear in calculations, but are not detected as single particles. Thus, in mathematical terms, they never appear as indices to the [[scattering matrix]], which is to say, they never appear as the observable inputs and outputs of the physical process being modelled. In this sense, virtual particles are an artefact of [[perturbation theory (quantum mechanics)| perturbation theory]], and do not appear in a [[nonperturbative]] treatment. As such, their objective existence as "particles" is questionable;{{Fact|date=February 2008}} however, the term is useful in informal, casual conversation, or in rendering concepts into layman's terms.{{Fact|date=February 2008}}
There are two principal ways in which the notion of virtual particles appear in modern physics. They appear as intermediate terms in [[Feynman diagram]]s; that is, as terms in a perturbative calculation. They also appear as an infinite set of states to be summed or integrated over in the calculation of a semi-non-perturbative effect. In the latter case, it is sometimes said that virtual particles cause the effect, or that the effect occurs because of the existence of virtual particles.{{Fact|date=February 2008}}
==Manifestations==
There are many observable physical phenomena resulting from interactions involving virtual particles. All tend to be characterized by the relatively short range of the force interaction producing them. Some of them are:
* The Coulomb force between electric charges. It is caused by exchange of virtual [[photon]]s. In symmetric 3-dimensional space this exchange results in [[inverse square law]] for force.
* The so-called [[near field]] of radio antennas, where the magnetic effects of the current in the antenna wire and the charge effects of the wire's capacitive charge are detectable, but both of which effects disappear with increasing distance from the antenna much more quickly than do the influence of conventional [[electromagnetic waves]], for which E is always equal to cB, and which are composed of real photons.
* The [[strong nuclear force]] between [[quark]]s - it is the result of interaction of virtual [[gluon]]s. The residual of this force outside of quark triplets (neutron and proton) holds neutrons and protons together in nuclei, and is due to virtual mesons such as the [[pi meson]] and [[rho meson]].
* The [[weak nuclear force]] - it is the result of exchange by virtual [[W boson]]s.
* The [[spontaneous emission]] of a [[photon]] during the decay of an excited atom or excited nucleus; such a decay is prohibited by ordinary quantum mechanics and requires the quantization of the electromagnetic field for its explanation.
* The [[Casimir effect]], where the [[ground state]] of the quantized electromagnetic field causes attraction between a pair of electrically neutral metal plates.
* The [[van der Waals force]], which is partly due to the Casimir effect between two atoms,
* [[Vacuum polarization]], which involves [[pair production]] or the [[decay of the vacuum]], which is the spontaneous production of particle-antiparticle pairs (such as electron-positron).
* [[Lamb shift]] of positions of atomic levels.
* [[Hawking radiation]], where the gravitational field is so strong that it causes the spontaneous production of photon pairs (with black body energy distribution) and even of particle pairs.
Most of these have analogous effects in [[solid-state physics]]; indeed, one can often gain a better intuitive understanding by examining these cases. In [[semiconductor]]s, the roles of electrons, positrons and photons in field theory are replaced by electrons in the [[conduction band]], holes in the [[valence band]], and [[phonon]]s or vibrations of the crystal lattice. A [[Virtual_particle]] is in a [[Two-photon absorption|virtual state]] where the [[probability amplitude]] is not conserved.
[[Antiparticle]]s have been proven to exist and should not be confused with virtual particles or virtual antiparticles.
==History==
[[Paul Dirac]] was the first to propose that empty space (a vacuum) can be visualized as consisting of a sea of virtual electron-positron pairs, known as the [[Dirac sea]]. The Dirac sea has a direct analog to the [[electronic band structure]] in [[crystalline]] solids as described in [[solid state physics]]. Here, particles correspond to [[conduction electron]]s, and antiparticles to [[electron hole|hole]]s. A variety of interesting phenomena can be attributed to this structure.
==Virtual particles in Feynman diagrams==
[[Image:1pxchg.svg|thumb|right|One particle exchange scattering diagram]]
The calculation of [[scattering amplitude]]s in theoretical [[particle physics]] requires the use of some rather large and complicated integrals over a large number of variables. These integrals do, however, have a regular structure, and may be represented as [[Feynman diagram]]s. The appeal of the Feynman diagrams is strong, as it allows for a simple visual presentation of what would otherwise be a rather arcane and abstract formula. In particular, part of the appeal is that the outgoing legs of a Feynman diagram can be associated with real, [[on-shell]] particles. Thus, it is natural to associate the other lines in the diagram with particles as well, called the "virtual particles". Mathematically, they correspond to the [[propagator]]s appearing in the diagram.
In the image above and to the right, the solid lines correspond to real particles (of momentum <math>p_1</math> and so on), while the dotted line corresponds to a virtual particle carrying [[momentum]] ''k''. For example, if the solid lines were to correspond to [[electron]]s interacting by means of the [[electromagnetic interaction]], the dotted line would correspond to the exchange of a virtual [[photon]]. In the case of interacting [[nucleon]]s, the dotted line would be a virtual [[pion]]. In the case of [[quark]]s interacting by means of the [[strong force]], the dotted line would be a virtual [[gluon]], and so on.
[[Image:Vacuum polarization.svg|thumb|right|One-loop diagram with fermion propagator]]
It is sometimes said that all [[photon]]s are virtual photons. This is because the world-lines of photons always resemble the dotted line in the above Feynman diagram: the photon was emitted somewhere (say, a distant [[star]]), and then is absorbed somewhere else (say a [[photoreceptor cell]] in the [[eyeball]]). Furthermore, in a vacuum, a photon experiences no passage of (proper) time between emission and absorption. This statement illustrates the difficulty of trying to distinguish between "real" and "virtual" particles as mathematically they are the same objects and it is only our definition of "reality" which is weak here. In practice, a clear distinction can be made: real photons are detected as individual particles in [[particle detector]]s, whereas virtual photons are not directly detected; only their average or side-effects may be noticed, in the form of ''forces'' or (in modern language) ''interactions'' between particles.
Virtual particles need not be [[meson]]s or [[boson]]s, as in the example above; they may also be [[fermion]]s. However, in order to preserve quantum numbers, most simple diagrams involving fermion exchange are prohibited. The image to the right shows an allowed diagram, a [[one-loop diagram]]. The solid lines correspond to a fermion propagator, the wavy lines to bosons.
==Virtual particles in vacuo==
Formally, a particle is considered to be an [[eigenstate]] of the [[particle number operator]] <math>a^\dagger a</math> where <math>\!a</math> is the particle [[annihilation operator]] and <math>a^\dagger</math> the particle [[creation operator]] (sometimes collectively called [[ladder operator]]s). In many cases, the particle number operator does not [[commutator|commute]] with the [[Hamiltonian (quantum mechanics)|Hamiltonian]] for the system. This implies the number of particles in an area of space is not a well-defined quantity but like other quantum [[observable]]s is represented by a [[probability distribution]]. Since these particles do not have a permanent existence, they are called ''virtual particles'' or '''vacuum fluctuations''' of [[vacuum energy]]. In a certain sense, they can be understood to be a manifestation of the [[uncertainty principle#Energy-time uncertainty principle|time-energy uncertainty principle]] in a vacuum, which bears some similarity to [[Aether theories]].
An important example of the "presence" of virtual particles in a vacuum is the [[Casimir effect]]. Here, the explanation of the effect requires that the total energy of all of the virtual particles in a vacuum can be added together. Thus, although the virtual particles themselves are not directly observable in the laboratory, they do leave an observable effect: their [[zero-point energy]] results in forces acting on suitably arranged metal plates or dielectrics.
==Pair production==
{{main|Pair production}}
In order to conserve the total [[fermion number]] of the universe, a fermion cannot be created without also creating its antiparticle; thus many physical processes lead to [[pair creation]]. The need for the [[normal order]]ing of particle fields in the vacuum can be interpreted by the idea that a pair of virtual particles may briefly "pop into existence", and then annihilate each other a short while later.
Thus, virtual particles are often popularly described as coming in pairs, a [[Elementary particle|particle]] and [[antiparticle]], which can be of any kind. These pairs exist for an extremely short time, and mutually annihilate in short order. In some cases, however, it is possible to boost the pair apart using external energy so that they avoid annihilation and become real particles.
This may occur in one of two ways. In an accelerating [[frame of reference]], the virtual particles may appear to be real to the accelerating observer; this is known as the [[Unruh effect]]. In short, the vacuum of a stationary frame appears, to the accelerated observer, to be a warm [[gas]] of real particles in [[thermodynamic equilibrium]]. The Unruh effect is a toy model for understanding [[Hawking radiation]], the process by which [[black hole]]s evaporate.
Another example is [[pair production]] in very strong electric fields, sometimes called [[vacuum decay]]. If, for example, a pair of [[atomic nucleus|atomic nuclei]] are merged together to very briefly form a nucleus with a charge greater than about 140, (that is, larger than about the inverse of the [[fine structure constant]]), the strength of the electric field will be such that it will be energetically favorable to create positron-electron pairs out of the vacuum or [[Dirac sea]], with the electron attracted to the nucleus to annihilate the positive charge. This pair-creation amplitude was first calculated by [[Julian Schwinger]] in [[1951]].
The restriction to particle-antiparticle pairs is actually only necessary if the particles in question carry a [[conservation law|conserved]] quantity, such as [[electric charge]], which is not present in the initial or final state. Otherwise, other situations can arise. For instance, the [[beta decay]] of a [[neutron]] can happen through the emission of a single virtual, negatively charged [[W particle]] that almost immediately decays into a real [[electron]] and [[antineutrino]]; the neutron turns into a [[proton]] when it emits the W particle. The evaporation of a black hole is a process dominated by [[photon]]s, which are their own antiparticles and are uncharged.
It is sometimes suggested that pair production can be used to explain the origin of matter in the [[universe]]. In models of the [[Big Bang]], it is suggested that vacuum fluctuations, or virtual particles, briefly appear. Then, due to effects such as [[CP-violation]], an imbalance between the number of virtual particles and antiparticles is created, leaving a surfeit of particles, thus accounting for the visible matter in the universe.
== External links ==
* [http://www.sciam.com/askexpert_question.cfm?chanID=sa005&articleID=0004D0F8-772A-1526-B72A83414B7F0000&topicID=13 Are virtual particles really constantly popping in and out of existence?] — Gordon Kane, director of the Michigan Center for Theoretical Physics at the University of Michigan at Ann Arbor, provides an answer at the ''Scientific American'' website.
==References==
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==See also==
*[[Spontaneous emission]]
*[[Vacuum state]]
*[[Vacuum Rabi oscillation]]
*[[Free space]]
*[[QCD vacuum]]
*[[Casimir effect]]
*[[Lamb shift]]
[[Category:Fundamental physics concepts]]
[[Category:Particle physics]]
[[Category:Quantum field theory]]
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