Virtual particle
Encyclopedia
In physics
, a virtual particle is a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle
. The degree of uncertainty of each is inversely proportional to time duration (for energy
) or to position span (for momentum
).
Virtual particles exhibit some of the phenomena that real 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 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
or magnetic field
, or the components of any field that do not carry information from place to place at the speed of light (information radiated by means of a field must be composed of real particles). Virtual photons are also a major component of antenna near field
phenomena and induction fields, which have shorter-range effects, and do not radiate through space with the same range-properties as do electromagnetic wave photon
s. For example, the energy carried from one winding of a transformer to another, or to and from a patient in an MRI scanner, in quantum terms is carried by virtual photons, not real photons.
The virtual particle forms of massless particles, such as photons, do have mass (which may be either positive or negative) and are said to be off mass shell. They are allowed to have mass (which consists of "borrowed energy") because they exist for only a temporary time, which in turn gives them a limited "range". This is in accordance with the uncertainty principle
, which allows existence of such particles of borrowed energy, so long as their energy, multiplied by the time they exist, is a fraction of Planck's constant. Possession of mass also allows single virtual photons to be more easily created and emitted from single charged elementary particles, something that cannot happen for massless photons, without violating conservation of momentum and energy (single real photons are always created and emitted from systems of two or more particles). For particles that do have a rest mass, their virtual forms still violate the energy-momentum relation
of special relativity, in having a mass more or less than predicted by the relation:
The concept of virtual particles is closely related to the idea of quantum fluctuations. Virtual particles can be thought of as coming into existence as quantities, such as the electric field, which fluctuate around their expectation values
as required by quantum mechanics.
of quantum field theory
, an approximation scheme in which interactions (in essence, forces) between real particles are calculated in terms of exchanges of virtual particles. Any process involving virtual particles admits a schematic representation known as a Feynman diagram
, which facilitates the understanding of calculations.
A virtual particle is one that does not precisely obey the relationship for a short time. In other words, its kinetic energy may not have the usual relationship to velocity–indeed, it can be negative. The probability amplitude for it to exist tends to be canceled out by destructive interference over longer distances and times. A virtual particle 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 artifact of perturbation theory
, and do not appear in a non-perturbative treatment.
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 cause the effect, or that the effect occurs because of the existence of virtual particles.
zone of coils and antennas.
Some field interactions which may be seen in terms of virtual particles are:
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 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
in and.
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 electrons, and antiparticles to hole
s. A variety of interesting phenomena can be attributed to this structure.
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". In mathematical terms, they correspond to the propagator
s appearing in the diagram.
In the image to the right, the solid lines correspond to real particles (of momentum p1 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.
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, because, in mathematical terms, they are the same objects and it is only our definition of "reality" that 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 must 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.
a†a, where a is the particle annihilation operator and a† the particle creation operator (sometimes collectively called ladder operator
s). In many cases, the particle number operator does not commute
with the 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 time-energy uncertainty principle in a vacuum.
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 dielectric
s.
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 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 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 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.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, a virtual particle is a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle
Uncertainty principle
In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...
. The degree of uncertainty of each is inversely proportional to time duration (for energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
) or to position span (for momentum
Momentum operator
In quantum mechanics, momentum is defined as an operator on the wave function. The Heisenberg uncertainty principle defines limits on how accurately the momentum and position of a single observable system can be known at once...
).
Virtual particles exhibit some of the phenomena that real particle
Elementary particle
In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s do, such as obedience to the conservation law
Conservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
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 quanta
Quantum
In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...
that describe fields of the basic force interactions, which cannot be described in terms of real particles. Examples of these are static force fields
Static forces and virtual-particle exchange
Static force fields are fields, such as a simple electric, magnetic or gravitational fields, that exist without excitations. The most common approximation method that physicists use for scattering calculations can be interpreted as static forces arising from the interactions between two bodies...
, such as a simple electric
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
or magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
, or the components of any field that do not carry information from place to place at the speed of light (information radiated by means of a field must be composed of real particles). Virtual photons are also a major component of antenna near field
Near and far field
The near field and far field and the transition zone are regions of the electromagnetic radiation field that emanates from a transmitting antenna, or as a result of radiation scattering off an object...
phenomena and induction fields, which have shorter-range effects, and do not radiate through space with the same range-properties as do electromagnetic wave photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s. For example, the energy carried from one winding of a transformer to another, or to and from a patient in an MRI scanner, in quantum terms is carried by virtual photons, not real photons.
The virtual particle forms of massless particles, such as photons, do have mass (which may be either positive or negative) and are said to be off mass shell. They are allowed to have mass (which consists of "borrowed energy") because they exist for only a temporary time, which in turn gives them a limited "range". This is in accordance with the uncertainty principle
Uncertainty principle
In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...
, which allows existence of such particles of borrowed energy, so long as their energy, multiplied by the time they exist, is a fraction of Planck's constant. Possession of mass also allows single virtual photons to be more easily created and emitted from single charged elementary particles, something that cannot happen for massless photons, without violating conservation of momentum and energy (single real photons are always created and emitted from systems of two or more particles). For particles that do have a rest mass, their virtual forms still violate the energy-momentum relation
Energy-momentum relation
In special relativity, the energy-momentum relation is a relation between the energy, momentum and the mass of a body: E^2 = m^2 c^4 + p^2 c^2 , \;where c is the speed of light, E \; is total energy, m \; is invariant mass, and p = |\vec p|\; is momentum....
of special relativity, in having a mass more or less than predicted by the relation:
- E2 − p2 = m2
The concept of virtual particles is closely related to the idea of quantum fluctuations. Virtual particles can be thought of as coming into existence as quantities, such as the electric field, which fluctuate around their expectation values
Expectation value (quantum mechanics)
In quantum mechanics, the expectation value is the predicted mean value of the result of an experiment. Despite the name, it is not the most probable value of a measurement...
as required by quantum mechanics.
Properties
The concept of virtual particles arises in the perturbation theoryPerturbation theory (quantum mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an...
of quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
, an approximation scheme in which interactions (in essence, forces) between real particles are calculated in terms of exchanges of virtual particles. Any process involving virtual particles admits a schematic representation known as a Feynman diagram
Feynman diagram
Feynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prize-winning American physicist Richard Feynman, and first introduced in 1948...
, which facilitates the understanding of calculations.
A virtual particle is one that does not precisely obey the relationship for a short time. In other words, its kinetic energy may not have the usual relationship to velocity–indeed, it can be negative. The probability amplitude for it to exist tends to be canceled out by destructive interference over longer distances and times. A virtual particle can be considered a manifestation of quantum tunnelling
Quantum tunnelling
Quantum tunnelling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the sun, and has important...
. 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 artifact of perturbation theory
Perturbation theory (quantum mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an...
, and do not appear in a non-perturbative treatment.
There are two principal ways in which the notion of virtual particles appears in modern physics. They appear as intermediate terms in Feynman diagram
Feynman diagram
Feynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prize-winning American physicist Richard Feynman, and first introduced in 1948...
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.
Manifestations
There are many observable physical phenomena resulting from interactions involving virtual particles. For bosonic particles that exhibit rest mass when they are free and "real," virtual interactions are characterized by the relatively short range of the force interaction produced by particle exchange. 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 fieldNear and far field
The near field and far field and the transition zone are regions of the electromagnetic radiation field that emanates from a transmitting antenna, or as a result of radiation scattering off an object...
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 photonPhotonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
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 fieldMagnetic fieldA magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
between magnetic dipoleDipoleIn physics, there are several kinds of dipoles:*An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some distance. A permanent electric dipole is called an electret.*A...
s. It is caused by the exchange of virtual photonPhotonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s. In symmetric 3-dimensional space this exchange results in the inverse square law for magnetic force. Since the photon has no mass, the magnetic potential has an infinite range. - Much of the so-called near-fieldNear and far fieldThe near field and far field and the transition zone are regions of the electromagnetic radiation field that emanates from a transmitting antenna, or as a result of radiation scattering off an object...
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 are important contributors to the total EM field, but both of which effect decay with increasing distance from the antenna much more quickly than do the influence of "conventional" electromagnetic waves "far" from the source ("far" in terms of terms of ratio of antenna length or diamter, to wavelength). These far-field waves, for which E is (in the limit of long distance) equal to cB, are composed of real photons. It should be noted that real and virtual photons are mixed near an antenna, with the virtual photons responsible only for the "extra" magnetic-inductive and static-electric effects, which cause any imbalance between E and cB. As distance from the antenna grows, the near-field effects die out more quickly, and only the "radiative" effects that are due to real photons remain as important effects. That is, virtual effects extend to infinity, but they drop off in field strength as 1/r2 rather than the field of of EM waves composed of real photons, which drop 1/r (the powers, respectively, decrease as 1/r4 and 1/r2). See near and far fieldNear and far fieldThe near field and far field and the transition zone are regions of the electromagnetic radiation field that emanates from a transmitting antenna, or as a result of radiation scattering off an object...
for a more detailed discussion. See near field communicationNear Field CommunicationNear field communication, or NFC, allows for simplified transactions, data exchange, and wireless connections between two devices in proximity to each other, usually by no more than a few centimeters. It is expected to become a widely used system for making payments by smartphone in the United States...
for practical communications applications of near fields. - Electromagnetic inductionElectromagnetic inductionElectromagnetic induction is the production of an electric current across a conductor moving through a magnetic field. It underlies the operation of generators, transformers, induction motors, electric motors, synchronous motors, and solenoids....
. This phenomenon transferring energy to and from a magnetic coil via a changing (electro)magnetic field can be viewed as a near-field effect. It is the basis for power transfer in transformers and electric generators and motors, and also signal transfer in metal detectors, magnetic and magnetoacustic anti theft electronic tagsElectronic article surveillanceElectronic article surveillance is a technological method for preventing shoplifting from retail stores or pilferage of books from libraries. Special tags are fixed to merchandise or books. These tags are removed or deactivated by the clerks when the item is properly bought or checked out...
, and even signals between patient and machine in an MRI scanner. Some confusion about the use of "radio waves" results when these devices are used at conventional RF frequencies, as they are in an MRI scanner. See resonant inductive couplingResonant inductive couplingResonant inductive coupling or electrodynamic induction is the near field wireless transmission of electrical energy between two coils that are highly resonant at the same frequency. The equipment to do this is sometimes called a resonant or resonance transformer. While many...
and wireless energy transferWireless energy transferWireless energy transfer or wireless power is the transmission of electrical energy from a power source to an electrical load without artificial interconnecting conductors. Wireless transmission is useful in cases where interconnecting wires are inconvenient, hazardous, or impossible...
for other practical examples. - The strong nuclear force between quarkQuarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s is the result of interaction of virtual gluonGluonGluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....
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 mesonRho mesonIn particle physics, a rho meson is a short-lived hadronic particle that is an isospin triplet whose three states are denoted as , and . After the pions and kaons, the rho mesons are the lightest strongly interacting particle with a mass of roughly for all three states...
. - The weak nuclear force - it is the result of exchange by virtual W and Z bosonsW and Z bosonsThe W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...
. - The spontaneous emissionSpontaneous emissionSpontaneous emission is the process by which a light source such as an atom, molecule, nanocrystal or nucleus in an excited state undergoes a transition to a state with a lower energy, e.g., the ground state and emits a photon...
of a photonPhotonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
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 effectCasimir effectIn quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, like capacitors placed a few micrometers apart, without any external electromagnetic field...
, where the ground stateGround stateThe ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...
of the quantized electromagnetic field causes attraction between a pair of electrically neutral metal plates. - The van der Waals forceVan der Waals forceIn physical chemistry, the van der Waals force , named after Dutch scientist Johannes Diderik van der Waals, is the sum of the attractive or repulsive forces between molecules other than those due to covalent bonds or to the electrostatic interaction of ions with one another or with neutral...
, which is partly due to the Casimir effect between two atoms. - Vacuum polarizationVacuum polarizationIn quantum field theory, and specifically quantum electrodynamics, vacuum polarization describes a process in which a background electromagnetic field produces virtual electron–positron pairs that change the distribution of charges and currents that generated the original electromagnetic...
, which involves pair productionPair productionPair production refers to the creation of an elementary particle and its antiparticle, usually from a photon . For example an electron and its antiparticle, the positron, may be created...
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 radiationHawking radiationHawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...
, 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
Solid-state physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from...
; indeed, one can often gain a better intuitive understanding by examining these cases. In semiconductor
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
s, the roles of electrons, positrons and photons in field theory are replaced by electrons in the conduction band
Conduction band
In the solid-state physics field of semiconductors and insulators, the conduction band is the range of electron energies, higher than that of the valence band, sufficient to free an electron from binding with its individual atom and allow it to move freely within the atomic lattice of the material...
, holes in the valence band
Valence band
In solids, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature....
, and phonon
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...
s or vibrations of the crystal lattice. A virtual particle is in a virtual state
Two-photon absorption
Two-photon absorption is the simultaneous absorption of two photons of identical or different frequencies in order to excite a molecule from one state to a higher energy electronic state. The energy difference between the involved lower and upper states of the molecule is equal to the sum of the...
where the probability amplitude
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number whose modulus squared represents a probability or probability density.For example, if the probability amplitude of a quantum state is \alpha, the probability of measuring that state is |\alpha|^2...
is not conserved. Examples of macroscopic virtual phonons, photons, and electrons in the case of the tunneling process were presented by Günter Nimtz
Günter Nimtz
Günter Nimtz is a German physicist, working at the 2nd Physics Institute at the University of Cologne in Germany. He has investigated narrow-gap semiconductors and liquid crystals and was engaged in several interdisciplinary studies on the effect of non-ionizing electromagnetic radiation in...
in and.
History
Paul DiracPaul Dirac
Paul Adrien Maurice Dirac, OM, FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...
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
Dirac sea
The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by the Dirac equation for relativistic electrons...
. The Dirac sea has a direct analog to the electronic band structure
Electronic band structure
In solid-state physics, the electronic band structure of a solid describes those ranges of energy an electron is "forbidden" or "allowed" to have. Band structure derives from the diffraction of the quantum mechanical electron waves in a periodic crystal lattice with a specific crystal system and...
in crystalline solids as described in solid state physics. Here, particles correspond to conduction electrons, and antiparticles to hole
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...
s. A variety of interesting phenomena can be attributed to this structure.
Virtual particles in Feynman diagrams
Scattering amplitude
In quantum physics, the scattering amplitude is the amplitude of the outgoing spherical wave relative to the incoming plane wave in the stationary-state scattering process...
s in theoretical particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
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
Feynman diagram
Feynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prize-winning American physicist Richard Feynman, and first introduced in 1948...
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". In mathematical terms, they correspond to the propagator
Propagator
In quantum mechanics and quantum field theory, the propagator gives the probability amplitude for a particle to travel from one place to another in a given time, or to travel with a certain energy and momentum. Propagators are used to represent the contribution of virtual particles on the internal...
s appearing in the diagram.
In the image to the right, the solid lines correspond to real particles (of momentum p1 and so on), while the dotted line corresponds to a virtual particle carrying momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
k. For example, if the solid lines were to correspond to electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s interacting by means of the electromagnetic interaction, the dotted line would correspond to the exchange of a virtual photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
. In the case of interacting nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...
s, the dotted line would be a virtual pion
Pion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
. In the case of quark
Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s interacting by means of the strong force, the dotted line would be a virtual gluon
Gluon
Gluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....
, and so on.
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
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
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
), and then is absorbed somewhere else (say a photoreceptor cell in the eyeball
Human eye
The human eye is an organ which reacts to light for several purposes. As a conscious sense organ, the eye allows vision. Rod and cone cells in the retina allow conscious light perception and vision including color differentiation and the perception of depth...
). 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, because, in mathematical terms, they are the same objects and it is only our definition of "reality" that is weak here. In practice, a clear distinction can be made: real photons are detected as individual particles in particle detector
Particle detector
In experimental and applied particle physics, nuclear physics, and nuclear engineering, a particle detector, also known as a radiation detector, is a device used to detect, track, and/or identify high-energy particles, such as those produced by nuclear decay, cosmic radiation, or reactions in a...
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 must be meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s or vector boson
Vector boson
In particle physics, a vector boson is a boson with the spin quantum number equal to 1.The vector bosons considered to be elementary particles in the Standard Model are the gauge bosons or, the force carriers of fundamental interactions: the photon of electromagnetism, the W and Z bosons of the...
s, as in the example above; they may also be fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
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 vacuums
In formal terms, a particle is considered to be an eigenstate of the particle number operatorParticle number operator
In quantum mechanics, for systems where the total number of particles may not be preserved, the number operator is the observable that counts the number of particles.The number operator acts on Fock space...
a†a, where a is the particle annihilation operator and a† the particle creation operator (sometimes collectively called ladder operator
Ladder operator
In linear algebra , a raising or lowering operator is an operator that increases or decreases the eigenvalue of another operator. In quantum mechanics, the raising operator is sometimes called the creation operator, and the lowering operator the annihilation operator...
s). In many cases, the particle number operator does not commute
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:...
with the Hamiltonian
Hamiltonian (quantum mechanics)
In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...
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
Observable
In physics, particularly in quantum physics, a system observable is a property of the system state that can be determined by some sequence of physical operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value off...
s, is represented by a probability distribution
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
. Since these particles do not have a permanent existence, they are called virtual particles or vacuum fluctuations of vacuum energy
Vacuum energy
Vacuum energy is an underlying background energy that exists in space even when the space is devoid of matter . The concept of vacuum energy has been deduced from the concept of virtual particles, which is itself derived from the energy-time uncertainty principle...
. In a certain sense, they can be understood to be a manifestation of the time-energy uncertainty principle in a vacuum.
An important example of the "presence" of virtual particles in a vacuum is the Casimir effect
Casimir effect
In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, like capacitors placed a few micrometers apart, without any external electromagnetic field...
. 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
Zero-point energy
Zero-point energy is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state. All quantum mechanical systems undergo fluctuations even in their ground state and have an associated zero-point energy, a consequence of their wave-like nature...
results in forces acting on suitably arranged metal plates or dielectric
Dielectric
A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...
s.
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 orderNormal order
In quantum field theory a product of quantum fields, or equivalently their creation and annihilation operators, is usually said to be normal ordered when all creation operators are to the left of all annihilation operators in the product. The process of putting a product into normal order is...
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 particle
Elementary particle
In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
and antiparticle
Antiparticle
Corresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.The...
, 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
Frame of reference
A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...
, the virtual particles may appear to be real to the accelerating observer; this is known as the Unruh effect
Unruh effect
The Unruh effect , was first described by Stephen Fulling in 1973, Paul Davies in 1975 and Bill Unruh in 1976. It is the prediction that an accelerating observer will observe black-body radiation where an inertial observer would observe none...
. In short, the vacuum of a stationary frame appears, to the accelerated observer, to be a warm gas
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...
of real particles in thermodynamic equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...
. The Unruh effect is a toy model for understanding Hawking radiation
Hawking radiation
Hawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...
, the process by which black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
s evaporate.
Another example is pair production
Pair production
Pair production refers to the creation of an elementary particle and its antiparticle, usually from a photon . For example an electron and its antiparticle, the positron, may be created...
in very strong electric fields, sometimes called vacuum decay. If, for example, a pair of atomic nuclei
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
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
Dirac sea
The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by the Dirac equation for relativistic electrons...
, with the electron attracted to the nucleus to annihilate the positive charge. This pair-creation amplitude was first calculated by Julian Schwinger
Julian Schwinger
Julian Seymour Schwinger was an American theoretical physicist. He is best known for his work on the theory of quantum electrodynamics, in particular for developing a relativistically invariant perturbation theory, and for renormalizing QED to one loop order.Schwinger is recognized as one of the...
in 1951.
The restriction to particle–antiparticle pairs is actually only necessary if the particles in question carry a conserved
Conservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
quantity, such as electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
, which is not present in the initial or final state. Otherwise, other situations can arise. For instance, the beta decay
Beta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...
of a neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
can happen through the emission of a single virtual, negatively charged W particle that almost immediately decays into a real electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
and antineutrino; the neutron turns into a proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
when it emits the W particle. The evaporation of a black hole is a process dominated by photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s, which are their own antiparticles and are uncharged.
See also
- Virtual StateVirtual state (physics)The term virtual state is commonly used to refer to two different types of states in physical systems. It may refer to a very short-lived, unobservable quantum state or a real, but unstable, state...
- Static forces and virtual-particle exchangeStatic forces and virtual-particle exchangeStatic force fields are fields, such as a simple electric, magnetic or gravitational fields, that exist without excitations. The most common approximation method that physicists use for scattering calculations can be interpreted as static forces arising from the interactions between two bodies...
- Vacuum stateVacuum stateIn quantum field theory, the vacuum state is the quantum state with the lowest possible energy. Generally, it contains no physical particles...
- Vacuum Rabi oscillationVacuum Rabi oscillationA vacuum Rabi oscillation is a damped oscillation of an initially excited atom coupled to an electromagnetic resonator or cavity in which the atom alternately emits photon into a single-mode electromagnetic cavity and reabsorbs them. The atom interacts with a single-mode field confined to a limited...
- Force carrierForce carrierIn particle physics, quantum field theories such as the Standard Model describe nature in terms of fields. Each field has a complementary description as the set of particles of a particular type...
- QCD vacuumQCD vacuumThe QCD vacuum is the vacuum state of quantum chromodynamics . It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate...
External links
- 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.