Photon

For other uses, see Photon (disambiguation).

Photon
Classification
Elementary particle Boson Gauge boson Electromagnetic interaction
Properties
Symbol: $\gamma \ \mathrm {or} \ h\nu$ Mass: 0 Electric Charge: 0 Spin: 1

In modern physics, the photon is the elementary particle responsible for electromagnetic interactions and light. The photon is massless, has no electric charge and does not decay spontaneously in empty space. A photon can have two different helicities (polarization states) and has three continuous parameters, the components of its wave vector. Photons are emitted in many natural processes, e.g., when a charge is accelerated, when an atom or a nucleus jumps from a higher to lower energy level, or when a particle and its antiparticle are annihilated. Photons are absorbed in the time-reversed processes, e.g., in the production of particle–antiparticle pairs or in an atomic or nuclear transition to a higher energy level. Throughout this article, the term light refers to all forms of electromagnetic radiation, not just to light visible to the human eye.

Nomenclature

The concept of the photon was developed gradually (1905–1917) by Albert Einstein, who called it a "light quantum" [Lichtquantum]. The name "photon" derives from the Greek word φῶς, "phōs" (meaning light) and was coined by the distinguished physical chemist Gilbert N. Lewis, who published a speculative theory in which photons were "uncreatable and indestructible" (Lewis 1926). Although Lewis' theory was never accepted (being contradicted by many experiments), his new name, photon, was adopted immediately by most physicists.

In physics, a photon is usually denoted by the symbol γ, the Greek letter gamma. In chemistry and optical engineering, photons are usually symbolized by hν, the amount of energy of each photon.

Energy, momentum, angular momentum and mass

Main article: Special relativity

The prevailing Standard Model of physics predicts that the photon is massless, which is consistent with experiment. Hence, the photon moves at $c\!$ (the speed of light in empty space), and its energy $E\!$ and momentum $\mathbf {p}$ are related by $E=c\,p\!$, where $p\!$ is the magnitude of the momentum. For comparison, the corresponding equation for particles with an invariant mass $m\!$ would be $E^{2}=c^{2}p^{2}+m^{2}c^{4}\!$, as shown in special relativity.

As an illustration of photon momentum, the classical pressure of electromagnetic radiation on an object derives from the transfer of photon momentum per unit time and unit area to that object, since pressure is force per unit area and force is the change in momentum per unit time.

The energy and momentum of a photon depend only on its frequency $\nu \!$ or, equivalently, its wavelength $\lambda \!$

$E=\hbar \omega =h\nu \!$

$\mathbf {p} =\hbar \mathbf {k}$

and consequently the magnitude of the momentum is

$p=\hbar k={\frac {h}{\lambda }}={\frac {h\nu }{c}}$

where $h\!$ is Planck's constant; $\hbar$ is Planck's reduced constant, $h/2\pi \!$; $\mathbf {k}$ is the wave vector; $k\!$ is its magnitude, the wave number, $2\pi /\lambda \!$; and $\omega \!$ is the angular frequency, $2\pi \nu \!$. Notice that $\mathbf {k}$ points in the direction of the photon's propagation. The photon also carries a fixed amount $\pm \hbar$ of spin angular momentum that does not depend on its frequency.

For illustration, these formulae show that the annihilation of a particle with its antiparticle must result in at least two photons, not one. In the center of mass frame, the colliding antiparticles have no net momentum, whereas a single photon always has momentum. Hence, conservation of momentum requires that at least two photons are created, with zero net momentum. The energy of the two photons (and, hence, their frequency) may be determined from conservation of four-momentum. The reverse process, pair production, is the dominant mechanism by which high-energy photons (such as gamma rays) lose energy while passing through matter.

Historical development

Main article: Light

Thomas Young's two-slit experiment in 1805 showed that light could act as a wave, helping to defeat early particle theories of light.

With a few notable exceptions, most theories up to the eighteenth century hypothesized that light was composed of particles, although such models could not easily account for the refraction, diffraction and birefringence of light, all of which were observed in the seventeenth century. Several wave theories of light were proposed by René Descartes (1637), Robert Hooke (~1665), and Christian Huygens (1678), but particle models remained the dominant theory, owing mainly to the influence of Isaac Newton. In the early nineteenth century, wave models were developed by Thomas Young and August Fresnel, with improved experiments showing the interference and diffraction of light. Ray and particle models adapted to explain these effects, but by mid-century the wave approach became dominant because of its ability to explain polarization effects. James Clerk Maxwell's prediction (1873) that light was an electromagnetic wave — which was confirmed experimentally by Heinrich Hertz's detection of radio waves (1888) — seemed to be the final blow to particle models of light.

In 1900, Maxwell's theoretical model of light as oscillating electric and magnetic fields seemed complete. However, several observations could not be explained by any wave model, leading to the idea that light-energy was packaged into quanta described by E=hν. Later experiments showed that these light-quanta also carry momentum and, thus, could be considered particles: the photon concept was born, leading to a deeper understanding of the electric and magnetic fields themselves.

The Maxwell wave theory, however, does not account for all properties of light. The Maxwell theory predicts that the energy of a light wave depends only on its intensity, not on its frequency; nevertheless, several independent types of experiments show that the energy imparted by light to atoms depends only on the light's frequency, not on its intensity. For example, some chemical reactions can be provoked only by light of frequency higher than a certain threshold; light of lower frequency, no matter how intense, is incapable of exciting the reaction. Similarly, electrons can be ejected from a metal plate by shining light of sufficiently high frequency on it (the photoelectric effect); the energy of the ejected electron is related only to the light's frequency, not to its intensity.

At the same time, careful investigations of blackbody radiation carried out over four decades (1860–1900) by various researchers culminated in Max Planck's hypothesis that the energy of any system that absorbs or emits electromagnetic radiation of frequency $\nu \!$ must be an integer multiple of a frequency-dependent energy quantum $E=h\nu \!$. A theory that does not adopt this energy quantization cannot account for the fact that matter and radiation can be in a state of thermal equilibrium, as shown by Albert Einstein in 1905.

Since the Maxwell theory of light allows for all possible energies of electromagnetic radiation, most physicists assumed initially that the energy quantization resulted from some unknown constraint on the matter that absorbs or emits the radiation. Einstein was the first to propose that the energy quantization was a property of electromagnetic radiation itself. In his 1905 paper A Heuristic Model of the Creation and Transformation of Light, Einstein accepts provisionally the validity of Maxwell's wave theory, but points out that the energy of a light wave may be localized into points that move independently of one another, even if the wave itself is spread continuously over space. In his 1909 work The Development of Our Views on the Composition and Essence of Radiation and two later works (1916b and 1917 references below), Einstein goes further and shows that, if Planck's law of black-body radiation is accepted, the energy quanta must also carry momentum, making them full-fledged particles. This photon momentum was observed experimentally by Arthur Compton in 1922, for which he received the Nobel Prize in 1927. The pivotal question was then: how to unify Maxwell's wave theory of light with its experimentally observed particle nature? The answer to this question occupied Albert Einstein for the rest of his life, and was solved in quantum electrodynamics and its successor, the Standard Model.

Early objections to the photon hypothesis

Up to 1922, most physicists were reluctant to accept that electromagnetic radiation was quantized. Instead, they tried to account for photon behavior by quantizing matter, as in the Bohr model of the atom (shown here). Although all such semiclassical models have been disproven by experiment, these early atomic models led to the birth of quantum mechanics.

Einstein's 1905 predictions were verified experimentally in several ways within the first two decades of the 20th century, as recounted in Robert Millikan's Nobel lecture (see References). However, before Compton's famous experiment in 1922, most physicists were very reluctant to believe that electromagnetic radiation itself might be particulate. (See, for example, the Nobel lectures of Wien, Planck and Millikan in the References below.) This reluctance is understandable, given the success and plausibility of Maxwell's electromagnetic wave model of light. Therefore, most physicists assumed rather that energy quantization resulted from some unknown constraint on the matter that absorbs or emits radiation. Niels Bohr, Arnold Sommerfeld and others tried to produce atomic models with discrete energy levels that might account for the sharp spectral lines and energy quantization observed in the emission and absorption of light by atoms. It was only the Compton scattering of a photon by a free electron (which can have no energy levels, since it has no internal structure) that convinced most physicists that light itself was quantized, since classical electrodynamics predicts that a free charge cannot change the frequency of the light with which it interacts.

Even after Compton's experiment, Bohr, Hendrik Kramers and John Slater made one last attempt to preserve the Maxwell's continuous electromagnetic field model of light, the so-called BKS model of 1924. To account for the then-available data, two drastic hypotheses had to be made:

• Energy and momentum are conserved only on the average in interactions between matter and radiation, not in elementary processes such as absorption and emission. This allows one to reconcile the discontinuously changing energy of the atom (jump between energy states) with the continuously release of energy into radiation.

• Causality is abandoned. For example, spontaneous emissions are merely emissions induced by a "virtual" electromagnetic field.

However, refined Compton experiments showed that energy-momentum is conserved extraordinarily well in elementary processes; and also that the jolting of the electron and the generation of a new photon in Compton scattering obey causality to within 10 ps. Accordingly, Bohr and his co-workers gave their model "as honorable a funeral as possible". Nevertheless, the BKS model inspired Werner Heisenberg in his development of quantum mechanics.

A few physicists persisted in developing semiclassical models in which electromagnetic radiation is not quantized, but matter obeys the laws of quantum mechanics (reviewed in Mandel 1976). Despite the overwhelming evidence for photons from chemical and physical experiments, this evidence cannot considered as absolutely definitive, since the experiments involve the interaction of light with matter; a sufficiently complicated theory of matter could in principle account for the observations. Nevertheless, all semiclassical theories were refuted definitively in the 1970's and 1980's by elegant photon-correlation experiments. Hence, Einstein's hypothesis that quantization is a property of electromagnetic radiation itself is considered to be proven.

Wave–particle duality

Main articles: Wave–particle duality and Squeezed coherent state

The dual wave–particle nature of photons is difficult to visualize, and warrants further discussion. On the one hand, the photon displays diffraction and interference (wave phenomena) on the length scale of its wavelength. For example, a single photon passing through a double-slit experiment would land on the screen with a probability distribution given by its interference pattern determined by Maxwell's equations. However, experiments confirm that the photon is not just a short pulse of electromagnetic radiation; it does not spread out as it propagates, nor does it divide in two when it encounters a beam splitter. Rather, the photon seems like a point-like particle, since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (≈10^–15 m across) or even the point-like electron. Nevertheless, the photon is not a point-like particle whose trajectory is shaped probabilistically by the electromagnetic field, as conceived by Einstein and others; that hypothesis was also refuted by the photon-correlation experiments cited above . According to quantum electrodynamics (see below), the photon is a quantum of an electromagnetic mode that stretches over all space, a quantum that is responsible for the electromagnetic field in the first place.

The quantum mechanics of material particles features an uncertainty principle that forbids the simultaneous measurement of the position and momentum of a particle in the same direction. An analogous principle for photons forbids the simultaneous measurement of the number of photons (see Fock state and below) in an electromagnetic wave and the phase of that wave (see coherent state and squeezed coherent state).

Bose–Einstein model of a photon gas

Main article: Bose–Einstein statistics

In 1924, Satyendra Nath Bose derived Planck's law of black-body radiation without using any electromagnetism at all, but rather a modification of coarse-grained counting of phase space. In 1924–1925, Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious non-local interaction", now understood as the requirement for a symmetric quantum mechanical wave function. This work led to the concept of coherent states and the development of the laser. In the same papers, Einstein extended Bose's formalism to material particles (bosons) and predicted that they would condense into their lowest quantum state at low enough temperatures (Bose–Einstein condensation). In 1926, Paul Dirac showed that the number of photons is not conserved.

Stimulated and spontaneous emission

Main article: Stimulated emission

The concept of stimulated emission was predicted by Einstein in his kinetic derivation of E=hν, and led to the development of the laser. His derivation also provoked further developments in the quantum treatment of light, the semiclassical model and quantum electrodynamics (see below).

In 1916, Einstein showed that Planck's quantum hypothesis $E=h\nu$ could be derived from a kinetic rate equation. Given a cavity filled with electromagnetic radiation and systems that can emit and absorb that radiation, Einstein assumed that emission/absorption of radiation of frequency $\nu$ causes a well-defined change in a system's energy and further hypothesized that the transition rate $R_{ij}$ from energy $E_{i}$ to energy $E_{j}$ is given by

$R_{ij}=N_{i}A_{ij}+N_{i}B_{ij}\rho (\nu )\!$

where $N_{i}$ represents the number of molecules of energy $E_{i}$ and $\rho (\nu )$ is the density of radiation at frequency $\nu$ within the cavity. $A_{ij}$ and $B_{ij}$ are rate constants; $A_{ij}$ is the rate constant for emitting radiation spontaneously, whereas $B_{ij}$ is the rate constant for absorbing radiation from the cavity (if $E_{i}<E_{j}$) or emitting it in response to the ambient radiation (if $E_{i}>E_{j}$, induced or stimulated emission). Planck's energy quantization $E=h\nu$ is a necessary consequence of this hypothesized rate equation and the basic requirements that the ambient radiation be in thermal equilibrium with the emitting/absorbing systems and independent of their material composition.

Einstein was also able to show that $B_{ij}=B_{ji}$ and, perhaps even more remarkably,

$A_{ij}={\frac {8\pi h\nu ^{3}}{c^{3}}}B_{ij}$

Einstein noted that the rate constants $A_{ij}$ and $B_{ij}$ should be derivable from a "mechanics and electrodynamics modified to accommodate the quantum hypothesis". This prediction was borne out in quantum mechanics and quantum electrodynamics respectively; both are required to derive Einstein's rate constants from first principles (see Dirac 1927 references below).

Einstein was troubled by the fact that his theory seemed incomplete, since it did not determine the direction of a spontaneously emitted photon. A probabilistic nature of light-particle motion was first considered by Newton in his treatment of birefringence and, more generally, of the splitting of light beams at interfaces into a transmitted beam and a reflected beam. Newton hypothesized that hidden variables in the light particle determined which path it would follow. Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation from quantum mechanics. Ironically, Max Born's probabilitistic interpretation of the wave function was inspired by Einstein's later work searching for a more complete theory (his "ghost-field" approach).

Semiclassical approach to radiation

Main article: Perturbation theory (quantum mechanics)

As shown by Dirac in 1926, Einstein's coefficients $B_{ij}$ for induced transitions can be computed semiclassically, i.e., by treating the electromagnetic radiation classically and the material system quantum mechanically. The incoming radiation is treated as a sinusoidal electric field applied to the material system, with an small (perturbative) interaction energy $H=-2\mathbf {d} \cdot \mathbf {{\mathcal {E}}_{0}} \cos \omega t$, where $\mathbf {d}$ is the material system's electric dipole moment and where $\mathbf {{\mathcal {E}}_{0}}$ and $\omega$ represent the electric field and angular frequency of the incoming radiation, respectively. The probability per unit time $w_{ji}$ of the radiation inducing a transition between discrete energy levels $E_{i}$ and $E_{j}$ may be computed using time-dependent perturbation theory

$w_{ji}={\frac {2\pi }{\hbar ^{2}}}\left|\langle \phi _{j}|\mathbf {d} \cdot \mathbf {{\mathcal {E}}_{0}} |\phi _{i}\rangle \right|^{2}\delta (\omega _{ij}-\omega )$

where $\omega _{ij}$ is defined by $\omega _{ij}\equiv \left(E_{i}-E_{j}\right)/\hbar$, and where $\phi _{i}$ and $\phi _{j}$ represent the unperturbed eigenstates of energy $E_{i}$ and $E_{j}$, respectively. Assuming that the polarization vector $\mathbf {{\mathcal {E}}_{0}}$ of the incoming radiation is oriented randomly relative to the dipole moment $\mathbf {d}$ of the material system, the corresponding $B_{ij}$ rate constants can be computed

$B_{ji}={\frac {8\pi ^{2}}{3\hbar ^{2}}}\left|\langle \phi _{j}|\mathbf {d} |\phi _{i}\rangle \right|^{2}$

from which $B_{ji}=B_{ij}$. Thus, if the two states $\phi _{i}$ and $\phi _{j}$ do not result in a net dipole moment (i.e., if $\langle \phi _{j}|\mathbf {d} |\phi _{i}\rangle =0$), the absorption and induced emission are said to be "disallowed".

However, this semiclassical approach does not yield the coefficients $A_{ij}$ for spontaneous emission from first principles, although they can be calculated using the correspondence principle and the classical (low-frequency) limit of Planck's law of black body radiation (the Rayleigh-Einstein-Jeans law). Nor does this semiclassical approach require the introduction of photons per se, although their energy law $E=\hbar \omega$ is used. A true derivation from first principles was developed by Dirac that required the quantization of the electromagnetic field itself; in this approach, photons are the quanta of the field. This approach is called second quantization or quantum field theory; the earlier quantum mechanics (the quantization of material particles moving in a potential) represents the "first quantization".

Second quantization

Main article: Quantum field theory

Different electromagnetic modes (such as those depicted here) can be treated as independent simple harmonic oscillators. A photon corresponds to a unit of energy E=hν in its electromagentic mode.

In 1910, Peter Debye derived Planck's law of black-body radiation from a relatively simple assumption. He correctly decomposed the electromagnetic field in a cavity into its Fourier modes, and assumed that the energy in any mode was an integer multiple of $h\nu \!$, where $\nu \!$ is the frequency of the electromagnetic mode. Planck's law of black-body radiation follows immediately as a geometric sum. However, Debye's approach failed to give the correct formula for the energy fluctuations of blackbody radiation, derived by Einstein in 1909.

In 1925, Born, Heisenberg and Jordan reinterpreted Debye's concept in a key way. The electromagnetic Fourier modes (defined by their wave vector $\mathbf {k}$ and polarization state) are equivalent to a set of uncoupled simple harmonic oscillators, as may be shown classically. Treated quantum mechanically, the energy levels of such oscillators are known to be $E=nh\nu \!$, where $\nu \!$ is the oscillator frequency. The key new step was to identify an electromagnetic mode with energy $E=nh\nu \!$ as a state with $n\!$ photons, each of energy $h\nu \!$. This approach gives the correct energy fluctuation formula.

In quantum field theory, probabilities of events are computed by summing over all possible ways in which they can happen, as in the Feynman diagram shown here.

In 1927, Dirac took this one step further. He treated the interaction between a charge and an electromagnetic field as a small perturbation that induces transitions in the photon states, changing the numbers of photons in the modes, while conserving energy and momentum overall. Dirac was able to derive Einstein's $A_{ij}\!$ and $B_{ij}\!$ coefficients from first principles, and showed that photons automatically obey Bose–Einstein statistics. The second-order perturbation theory can involve virtual photons, transient intermediate states of the electromagnetic field; the static electric and magnetic interactions are mediated by such virtual photons. In such quantum field theories, the probability of observable events is calculated by summing over all possible intermediate steps, even ones that are unphysical; hence, virtual photons are not constrained to satisfy $E=p\,c\!$, and can exist in three polarization states (instead of the two states observed physically). Although these transient virtual photons can never be observed, they contribute measurably to the probabilities of observable events. Indeed, such second-order and higher-order perturbation calculations can make infinite contributions, a problem that was overcome in quantum electrodynamics by using renormalization.

In modern physics notation, the quantum state of the electromagnetic field is written as a Fock state, a tensor product of the states for each electromagnetic mode

$|n_{k_{0}}\rangle \otimes |n_{k_{1}}\rangle \otimes \dots \otimes |n_{k_{n}}\rangle \dots$

where $|n_{k_{i}}\rangle$ represents the state in which $\,n_{k_{i}}$ photons are in the mode $\,k_{i}$. In this notation, the creation of a new photon in mode $\,k_{i}$ (e.g., emitted from an atomic transition) is written as $|n_{k_{i}}\rangle \rightarrow |n_{k_{i}}+1\rangle$. This notation merely expresses the concept of Born, Heisenberg and Jordan described above, and does not add any physics.

The photon as a gauge boson

Main article: Gauge theory

The electromagnetic field can be understood as a gauge theory, i.e., as a field that results from requiring that a symmetry hold independently at every position in spacetime. For the electromagnetic field, this gauge symmetry is the U(1) symmetry of a complex number, i.e., the ability to vary the phase of a complex number without affecting real numbers constructed from it (such as the energy or the Lagrangian).

The quanta of a gauge field must be massless, chargeless bosons, as long as the symmetry is not broken. Hence, the photon is predicted to be massless, chargeless and have integer spin (boson). In particular, the form of the electromagnetic interaction specifies that the photon must have spin ±1, i.e, its spin (not orbital) angular momentum measured along its direction of motion must be $\pm \hbar$. These two components correspond to the classical concepts of right-handed and left-handed circularly polarized light. However, the transient virtual photons of quantum electrodynamics may also adopt unphysical polarization states.

In the prevailing Standard Model of physics, the photon is one of four gauge bosons in the electroweak interaction; the other three are denoted W⁺, W^- and Z⁰ and are responsible for the weak interaction. Unlike the photon, these gauge bosons have invariant mass, owing to a mechanism that breaks their SU(2) gauge symmetry. The unification of the photon with W and Z gauge bosons was accomplished by Sheldon Glashow, Steven Weinberg and Abdus Salam, for which they were awarded the 1979 Nobel Prize in physics.

Experimental limits on mass

Since the photon is a gauge boson, most physicists believe that its intrinsic mass is exactly zero. If the photon has a (tiny) mass then electromagnetism is described by Proca theory instead of the Maxwell equations. This has two important experimental consequences:

• Coulomb's law would be violated which in turn would imply that Gauss's law would be invalid. Electric fields inside a charged hollow conductor would not be zero. A null result from an experiment searching for this effect has yielded a limit on the photon mass of about $10^{-14}\!$ eV.

• The energy density of the electromagnetic field would contain an additional term $m^{2}A_{\mu }A^{\mu }\!$, where m is the mass of the photon and $A_{\mu }\!$ is the Proca vector potential that describes the massive photon. Since the magnetic field is given by $B=\nabla \times A\!$, one would expect large scale magnetic fields to dominate this term; the magnitude of A should be roughly equal to $BR\!$, where B is the "ambient" magnetic field strength and R the range over which it exists. Strong limits on the photon mass have be derived from the potential effects of planetary and galactic vector potentials.

Satellite measurements of planetary magnetic fields were carried out by the Charge Composition Explorer spacecraft and used to derive an upper limit of 6x10^-16 eV (1x10^-51 kg) on the mass of the photon. An improved upper limit of 6x10^-17 eV (1x10^-52 kg) was obtained in 1998 by Roderic Lakes using a Cavendish balance. The same upper limit is given by the Particle Data Group, based on the magnetohydrodynamics of the solar wind.. Studies of galactic magnetic fields suggest an even better upper limit of 3x10^{-27 eV (5x10-63 kg) but the validity of this method has been questioned.}

It has been argued that if the mass of the photon is generated via a Higgs mechanism the limits posed by large scale magnetic fields are invalid.

Although further experiments to tighten the error bars on the photon mass are expected, all data hitherto are consistent with the photon having zero mass.

References

1. Goldhaber, Alfred S., and Nieto, Michael Martin, "Terrestrial and Extraterrestrial Limits on The Photon Mass", Rev. Mod. Phys. vol.43 #3 pp.277–296, 1971 [1]
2. E. Fischbach et al., Physical Review Letters, 73, 514–517 25 July 1994.
3. Official particle table http://pdg.lbl.gov/2005/tables/gxxx.pdf
4. L. Davis, A. S. Goldhaber, and M. M. Nieto, Phys. Rev. Lett. 35, 1402 (1975)
5. Roderic Lakes, "Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential", Phys. Rev. Lett. 80, 1826 (1998) [2]
6. J. Luo et al., Phys. Rev. D 59, 042001 (1999)
7. B. E. Schaefer, Phys. Rev. Lett. 82, 4964 (1999)
8. J.Luo et al., Physical Review Letters, (28 February 2003)

Contributions of photons to the invariant mass of a system

Main article: Mass in special relativity

Although the photon is itself massless, it adds to the invariant mass of any system to which it belongs; this is true for every form of energy, as predicted by the special theory of relativity. For example, the invariant mass of a system that emits a photon is decreased by an amount ${E}/{c^{2}}$ upon emission (where $E$ is the energy of the photon in the frame of the emitting system). Similarly, the invariant mass of a system that absorbs a photon is increased by a corresponding amount based on the energy of the photon in the frame of the absorbing system.

This concept is applied in a key prediction of quantum electrodynamics (QED), the quantum theory of electromagnetic interactions begun by Dirac (described above). QED is able to predict the magnetic dipole moment of leptons (such as that of the electron) to extremely high accuracy (16 decimal places); experimental measurements of these magnetic dipole moments have agreed with these predictions perfectly. The predictions, however, require counting the contributions of virtual photons to the invariant mass of the lepton. Another example of such contributions verified experimentally is the QED prediction of the hyperfine structure (the Lamb shift) of bound lepton pairs, such as muonium and positronium.

Photons in matter

Main article: Quantum optics

When photons pass through matter, different frequencies are transmitted at different speeds; this is called dispersion. A similar phenomenon occurs in reflection where surfaces can reflect photons of various frequencies at different angles.

In a material, photons couple to the excitations of the medium and behave differently. These excitations can often be described as quasi-particles (such as phonons and excitons); that is, as quantized wave- or particle-like entities propagating though the matter. "Coupling" means here that photons can transform into these excitations (that is, the photon gets absorbed and medium excited, involving the creation of a quasi-particle) and vice versa (the quasi-particle transforms back into a photon, or the medium relaxes by re-emitting the energy as a photon). However, as these transformations are only possibilities, they are not bound to happen and what actually propagates through the medium is a polariton; that is, a quantum-mechanical superposition of the energy quantum being a photon and of it being one of the quasi-particle matter excitations.

According to the rules of quantum mechanics, a measurement (here: just observing what happens to the polariton) breaks this superposition; that is, the quantum either gets absorbed in the medium and stays there (likely to happen in opaque media) or it re-emerges as photon from the surface into space (likely to happen in transparent media).

Matter excitations have a nonlinear dispersion relation; that is, their momentum is not proportional to their energy. Hence, these particles propagate slower than the vacuum speed of light. (The propagation speed is the derivative of the dispersion relation with respect to momentum.) This is the formal reason why light is slower in media (such as glass) than in vacuum. (The reason for diffraction can be deduced from this by Huygens' principle.) Another way of phrasing it is to say that the photon, by being blended with the matter excitation to form a polariton, acquires a nonzero effective mass, which means that it cannot travel at c, the speed of light in a vacuum.

See also

• Light
• Electromagnetic radiation
• Quantum optics
• Photonics
• Photon polarization
• Particle physics
• List of particles
• Spectroscopy
• Photoelectric effect
• Compton scattering
• Bremsstrahlung
• Cherenkov radiation
• Photokinesis

References

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• Wilhelm Wien Nobel Lecture, delivered 11 December 1911.

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• Clauser JF. (1974) " Experimental distinction between the quantum and classical field-theoretic predictions for the photoelectric effect", Phys. Rev. D, 9, 853–860.

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External links

• The Nature of Light: What Is A Photon? OPN Trends, Oct 2003
• MISN-0-212 Characteristics of Photons (PDF file) by Peter Signell and Ken Gilbert for Project PHYSNET.
• Particle Data Group