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{{Short description|Transient quantum fluctuation (physics)}}
{{distinguish|Antiparticle}}
{{For|related articles|Quantum vacuum (disambiguation)}}
{{Use American English|date = February 2019}}
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A '''virtual particle''' is a theoretical transient [[particle]] that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the [[uncertainty principle]], which allows the virtual particles to spontaneously emerge from vacuum at short time and space ranges.<ref>{{cite book |author=Griffiths, D.J. |title=[[Introduction to Elementary Particles (book)|Introduction to Elementary Particles]]|publisher=[[John Wiley & Sons]] |year=2008 |isbn=978-3-527-40601-2 |edition=2nd |page=65 |author-link=David J. Griffiths}}</ref> The concept of virtual particles arises in the [[perturbation theory (quantum mechanics)|perturbation theory]] of [[quantum field theory]] (QFT) where interactions between ordinary particles are described in terms of exchanges of virtual particles. A process involving virtual particles can be described by a schematic representation known as a [[Feynman diagram]], in which virtual particles are represented by internal lines.<ref>Peskin, M.E., Schroeder, D.V. (1995). ''An Introduction to Quantum Field Theory'', Westview Press, {{ISBN|0-201-50397-2}}, p. 80.</ref><ref>Mandl, F., Shaw, G. (1984/2002). ''Quantum Field Theory'', John Wiley & Sons, Chichester UK, revised edition, {{ISBN|0-471-94186-7}}, pp. 56, 176.</ref>

Virtual particles do not necessarily carry the same [[mass]] as the corresponding ordinary particle, although they always conserve [[energy]] and [[momentum]]. The closer its characteristics come to those of ordinary particles, the longer the virtual particle exists.  They are important in the physics of many processes, including particle scattering and [[Casimir force]]s.   In quantum field theory, forces—such as the [[electromagnetic repulsion]] or attraction between two charges—can be thought of as resulting from the exchange of [[virtual photon]]s between the charges. Virtual photons are the [[exchange particle]]s for the [[Electromagnetism|electromagnetic interaction]].

The term is somewhat loose and vaguely defined,<ref>{{Cite journal |last=Martinez |first=Jean-Philippe |date=2024-06-01 |title=Virtuality in Modern Physics in the 1920s and 1930s: Meaning(s) of an Emerging Notion |url=https://direct.mit.edu/posc/article-abstract/32/3/350/116521/Virtuality-in-Modern-Physics-in-the-1920s-and?redirectedFrom=fulltext |journal=Perspectives on Science |volume=32 |issue=3 |pages=350–371 |doi=10.1162/posc_a_00610 |issn=1063-6145}}</ref> in that it refers to the view that the world is made up of "real particles". "Real particles" are better understood to be excitations of the underlying quantum fields. Virtual particles are also excitations of the underlying fields, but are "temporary" in the sense that they appear in calculations of interactions, but never as asymptotic states or indices to the [[scattering matrix]]. The accuracy and use of virtual particles in calculations is firmly established, but as they cannot be detected in experiments, deciding how to precisely describe them is a topic of debate.<ref>{{cite journal|last1=Jaeger|first1=Gregg|title=Are virtual particles less real?|journal=Entropy |volume=21 |issue=2|page=141|date=2019|doi=10.3390/e21020141|pmid=33266857 |pmc=7514619|bibcode=2019Entrp..21..141J|url=http://philsci-archive.pitt.edu/15858/1/Jaeger%20Are%20Virtual%20Particles%20Less%20Real_%20entropy-21-00141-v3.pdf|doi-access=free}}</ref> Although widely used, they are by no means a necessary feature of QFT, but rather are mathematical conveniences — as demonstrated by [[lattice field theory]], which avoids using the concept altogether.{{cn|date=May 2025}}

== Properties ==
The concept of virtual particles arises in the [[Perturbation theory (quantum mechanics)|perturbation theory]] of [[quantum field theory]], an approximation scheme in which interactions (in essence, forces) between actual particles are calculated in terms of exchanges of virtual particles. Such calculations are often performed using schematic representations known as  [[Feynman diagram]]s, in which virtual particles appear as internal lines. By expressing the interaction in terms of the exchange of a virtual particle with [[four-momentum]] {{mvar|q}}, where {{mvar|q}} is given by the difference between the four-momenta of the particles entering and leaving the interaction vertex, ''both momentum and energy are conserved at the interaction vertices'' of the Feynman diagram.<ref name=Thomson>{{cite book|last1=Thomson|first1=Mark|title=Modern particle physics|date=2013|publisher=Cambridge University Press|location=Cambridge|isbn=978-1107034266}}</ref>{{rp|119}}

A virtual particle does not precisely obey the [[energy–momentum relation]] {{math|''m''<sup>2</sup>''c''<sup>4</sup> {{=}} ''E''<sup>2</sup> − ''p''<sup>2</sup>''c''<sup>2</sup>}}. Its kinetic energy may not have the usual relationship to [[velocity]]. It can be negative.<ref>{{cite book|last1=Hawking|first1=Stephen|title=A brief history of time|date=1998|publisher=Bantam Books|location=New York|isbn=9780553896923|edition=Updated and expanded tenth anniversary}}</ref>{{rp|110}} This is expressed by the phrase ''[[On shell and off shell|off mass shell]]''.<ref name=Thomson/>{{rp|119}} The probability amplitude for a virtual particle to exist tends to be canceled out by [[destructive interference]] over longer distances and times. As a consequence, a real photon is massless and thus has only two polarization states, whereas a virtual one, being effectively massive, has three polarization states.

[[Quantum tunnelling]] may be considered a manifestation of virtual particle exchanges.<ref>{{cite book|last1=Walters|first1=Tony Hey; Patrick|title=The new quantum universe|date=2004|publisher=Cambridge Univ. Press|location=Cambridge [u.a.]|isbn=9780521564571|edition=Reprint.|bibcode=2003nqu..book.....H}}</ref>{{rp|235}} 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.<ref name=Calle>{{cite book|last1=Calle|first1=Carlos I.|title=Superstrings and other things : a guide to physics|date=2010|publisher=CRC Press/Taylor & Francis|location=Boca Raton|isbn=9781439810743|edition=2nd |pages=443&ndash;444}}</ref>

Written in the usual mathematical notations, in the equations of physics, there is no mark of the distinction between virtual and actual particles. The amplitudes of processes with a virtual particle interfere with the amplitudes of processes without it, whereas for an actual 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, actual particles are viewed as being detectable excitations of underlying quantum fields. Virtual particles are also viewed as excitations of the underlying fields, but appear only as forces, not as detectable particles. They are "temporary" in the sense that they appear in some 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.

There are two principal ways in which the notion of virtual particles appears 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 contribute to a mechanism that mediates the effect, or that the effect occurs through the virtual particles.<ref name=Thomson/>{{rp|118}}

== Manifestations ==
There are many observable physical phenomena that arise in interactions involving virtual particles. For bosonic particles that exhibit [[rest mass]] when they are free and actual, virtual interactions are characterized by the relatively short range of the force interaction produced by particle exchange. [[Color confinement|Confinement]] can lead to a short range, too. Examples of such short-range interactions are the strong and weak forces, and their associated field bosons.

For the gravitational and electromagnetic forces, the zero rest-mass of the associated boson particle permits long-range forces to be mediated by virtual particles. However, in the case of photons, power and information transfer by virtual particles is a relatively short-range phenomenon (existing only within a few wavelengths of the field-disturbance, which carries information or transferred power), as for example seen in the characteristically short range of inductive and capacitative effects in the [[Near and far field|near field]] zone of coils and antennas.

Some field interactions which may be seen in terms of virtual particles are:
* The [[Coulomb force]] (static electric force) between electric charges. It is caused by the exchange of virtual [[photon]]s. In symmetric 3-dimensional space this exchange results in the [[inverse square law]] for electric force.  Since the photon has no mass, the coulomb potential has an infinite range.
* The [[magnetic field]] between magnetic [[dipole]]s. It is caused by the exchange of virtual [[photon]]s. In symmetric 3-dimensional space, this exchange results in the inverse cube law for magnetic force.  Since the photon has no mass, the magnetic potential has an infinite range. Even though the range is infinite, the time lapse allowed for a virtual photon existence is not infinite.
* [[Electromagnetic induction]]. This phenomenon transfers energy to and from a magnetic coil via a changing (electro)magnetic field.
* The [[strong nuclear force]] between [[quark]]s 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]] is the result of exchange by virtual [[W and Z bosons]].
* 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.
* The [[impedance of free space]], which defines the ratio between the [[electric field strength]] {{math|{{abs|'''E'''}}}} and the [[magnetic field strength]] {{math|{{abs|'''H'''}}}}: {{math|1=''Z''{{sub|0}} = {{abs|'''E'''}} / {{abs|'''H'''}}}}.<ref>{{cite news |url=https://phys.org/news/2013-03-ephemeral-vacuum-particles-speed-of-light-fluctuations.html |title=Ephemeral vacuum particles induce speed-of-light fluctuations |website=Phys.org |access-date=2017-07-24}}</ref>
* Much of the so-called [[Near and far field|near-field]] of radio antennas, where the magnetic and electric effects of the changing current in the antenna wire and the charge effects of the wire's capacitive charge may be (and usually are) important contributors to the total EM field close to the source, but both of which effects are [[dipole]] effects that decay with increasing distance from the antenna much more quickly than do the influence of "conventional" [[electromagnetic waves]] that are "far" from the source.{{efn|"Far" in terms of ratio of antenna length or diameter, to wavelength.}} These far-field waves, for which {{mvar|E}} is (in the limit of long distance) equal to {{mvar|cB}}, are composed of actual photons. Actual and virtual photons are mixed near an antenna, with the virtual photons responsible only for the "extra" magnetic-inductive and transient electric-dipole effects, which cause any imbalance between {{mvar|E}} and {{mvar|cB}}. As distance from the antenna grows, the near-field effects (as dipole fields) die out more quickly, and only the "radiative" effects that are due to actual photons remain as important effects. Although virtual effects extend to infinity, they drop off in field strength as {{math|1/''r''{{sup|2}}}} rather than the field of EM waves composed of actual photons, which drop as {{math|1/''r''}}.{{efn|The electrical power in the fields, respectively, decrease as {{math|1/''r''{{sup|4}}}} and {{math|1/''r''{{sup|2}}}}.}}{{efn|See [[near and far field]] for a more detailed discussion. See [[near-field communication]] for practical communications applications of near fields.}}

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. Examples of macroscopic virtual phonons, photons, and electrons in the case of the tunneling process were presented by [[Günter Nimtz]]<ref name=Nimtz1>{{cite journal |first=G. |last=Nimtz |year=2009 |title=On virtual phonons, photons, and electrons |journal=Found. Phys. |volume=39 |issue=12 |pages=1346–1355|doi=10.1007/s10701-009-9356-z |arxiv=0907.1611 |bibcode=2009FoPh...39.1346N |s2cid=118594121 }}</ref> and Alfons A. Stahlhofen.<ref name=Nimtz2>{{cite journal |first1=A. |last1=Stahlhofen |first2=G. |last2=Nimtz |year=2006 |title=Evanescent modes are virtual photons |journal=Europhys. Lett. |volume=76 |issue=2 |page=198|doi=10.1209/epl/i2006-10271-9 |bibcode=2006EL.....76..189S |s2cid=250758644 }}</ref>

== Feynman diagrams ==
[[File:Momentum exchange.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 actual, [[on-shell]] particles. Thus, it is natural to associate the other lines in the diagram with particles as well, called the "virtual particles".  In mathematical terms, they correspond to the [[propagator]]s appearing in the diagram.

In the adjacent image, the solid lines correspond to actual particles (of momentum p<sub>1</sub> 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.
[[File:Vacuum polarization.svg|thumb|right|One-loop diagram with fermion propagator]]

Virtual particles may be [[meson]]s or [[vector 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.

== Vacuums ==
{{Main article|Quantum fluctuation|QED vacuum|QCD vacuum|Vacuum state}}

In formal terms, a particle is considered to be an [[eigenstate]] of the [[particle number operator]] ''a''<sup>†</sup>''a'', where ''a'' is the particle [[annihilation operator]] and ''a''<sup>†</sup> 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 are not certain to exist, 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#Robertson.E2.80.93Schr.C3.B6dinger uncertainty relations|time-energy uncertainty principle]] in a vacuum.<ref>{{cite book|last1=Raymond|first1=David J.|title=A radically modern approach to introductory physics: volume 2: four forces|date=2012|publisher=New Mexico Tech Press|location=Socorro, NM|isbn=978-0-98303-946-4|pages=252&ndash;254|url=http://kestrel.nmt.edu/~raymond/books/radphys/book2/book2.html#x1-2100014.7}}</ref>

An important example of the "presence" of virtual particles in a vacuum is the [[Casimir effect]].<ref>{{cite journal|last1=Choi|first1=Charles Q.|title=A vacuum can yield flashes of light|journal=Nature|date=13 February 2013|doi=10.1038/nature.2013.12430|s2cid=124394711|url=http://www.nature.com/news/a-vacuum-can-yield-flashes-of-light-1.12430|access-date=2 August 2015|doi-access=free}}</ref> 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 [[dielectric]]s.<ref>{{cite journal|last1=Lambrecht|first1=Astrid|title=The Casimir effect: a force from nothing|journal=Physics World|date=September 2002|volume=15|issue=9|pages=29&ndash;32|doi=10.1088/2058-7058/15/9/29}}</ref>  On the other hand, the Casimir effect can be interpreted as the [[Casimir effect#Relativistic van der Waals force|relativistic van der Waals force]].<ref>{{cite journal|last1=Jaffe|first1=R. L.|title=Casimir effect and the quantum vacuum|journal=Physical Review D|date=12 July 2005|volume=72|issue=2|pages=021301|doi=10.1103/PhysRevD.72.021301|arxiv = hep-th/0503158 |bibcode = 2005PhRvD..72b1301J |s2cid=13171179}}</ref>

== Pair production ==
{{Main article|Pair production}}
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 then mutually annihilate, or in some cases, the pair may be boosted apart using external energy so that they avoid annihilation and become actual particles, as described below.

This may occur in one of two ways. In an accelerating [[frame of reference]], the virtual particles may appear to be actual 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 actual particles in [[thermodynamic equilibrium]].

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 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]], which is a [[dimensionless quantity]]), the strength of the electric field will be such that it will be energetically favorable{{explain|reason=In a closed system, energy is conserved, so what is meant by {{''}}energetically favorable{{''}} and why does this lead to positron–electron pair creation?|date=November 2021}} 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.

== Compared to actual particles ==
As a consequence of quantum mechanical [[uncertainty principle|uncertainty]], any object or process that exists for a limited time or in a limited volume cannot have a precisely defined energy or momentum. For this reason, virtual particles &ndash; which exist only temporarily as they are exchanged between ordinary particles &ndash; do not typically obey the [[On shell and off shell|mass-shell relation]]; the longer a virtual particle exists, the more the energy and momentum approach the mass-shell relation.

The lifetime of real particles is typically vastly longer than the lifetime of the virtual particles. Electromagnetic radiation consists of real photons which may travel light years between the emitter and absorber, but (Coulombic) electrostatic attraction and repulsion is a relatively short-range{{Dubious|reason=It is not a short-range force, the range is infinite. E.g., in a system of only two electrons separated by light years, the electrons *will* repel each other|date=June 2023}} force that is a consequence of the exchange of virtual photons {{Citation needed|reason=Need an explicit source for why real particles cannot mediate short-range forces such as Coulombic interactions|date=February 2020}}.

== See also ==
{{div col}}
* [[Anomalous photovoltaic effect]]
* [[False vacuum]]
* [[Force carrier]]
* [[Quasiparticle]]
* [[Static forces and virtual-particle exchange]]
* [[Zero-energy universe]]
* [[Vacuum Rabi oscillation]]
* [[Quantum foam]]
* [[Virtual black hole]]
* [[Added mass]]
{{div col end}}

== Footnotes ==
{{notelist|1}}

== References ==
{{reflist|25em}}

== External links ==
* [https://www.scientificamerican.com/article/are-virtual-particles-rea/ Are virtual particles really constantly popping in and out of existence?]{{nbsp}}– Gordon Kane, director of the Michigan Center for Theoretical Physics at the University of Michigan at Ann Arbor, proposes an answer at the ''Scientific American'' website.
* [http://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/ Virtual Particles: What are they?]
* [http://web.mit.edu/dikaiser/www/FdsAmSci.pdf D Kaiser (2005) ''American Scientist'' '''93''' p. 156  popular article]
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[[Category:Concepts in physics]]
[[Category:Quantum field theory]]