Bruker:Nghtwlkr/Sandkasse3

Partikkelfysikk
Teorier
Standardmodellen
Kvantemekanikk
Kvantefeltteori (QFT)
Kvanteelektrodynamikk (QED)
Kvantekromodynamikk (QCD)
Den spesielle relativitetsteorien
Vekselvirkning
Sterk kjernekraft
Elektromagnetisme
Svak kjernekraft
Gravitasjon
Fargekraft
Elementærpartikler
Fermioner
Kvarker
Oppkvark
Nedkvark
Særkvark
Sjarmkvark
Bunnkvark
Toppkvark
Leptoner
Elektron
Positron
Nøytrino
Myon
Tau
Bosoner
Gauge-bosoner
Foton
W- og Z-bosoner
Gluon
Graviton
Higgs-boson
Sammensatte partikler
Hadroner
Mesoner
Pion
Baryoner
Proton
Nøytron
Atomkjerner
Atomer
Molekyler
Egenskaper
Energi
Bevegelsesmengde
Elektrisk ladning
Spinn
Paritet
Isospinn
Svakt isospinn
Fargeladning
Kjernefysikk Atom

I fysikk er fotonet en elementærpartikkel. Det er den grunnleggende «enheten» av lys og alle andre former for elektromagnetisk stråling. Det er også bærer av den elektromagnetiske kraften. Effekten av denne kraften kan lett observeres på både mikroskopisk og makroskopisk nivå siden fotonet ikke har noen hvilemasse. Dette tillater vekselvirkning over store avstander. Som alle elementærpartikler er fotonet styrt av kvantemekanikken og fremviser både partikkel- og bølgeegenskaper, en bølge-partikkel-dualitet. For eksempel, et foton kan både interferere med seg selv (bølgeegenskap) og samtidig ha en bestemt posisjon i rommet (partikkegenskap).

Det moderne konseptet for fotonet ble gradvis skapt av Albert Einstein for å forklare eksperimentelle observasjoner som ikke passet den klassiske bølgemodellen for lys. Fotonmodellen kunne forklare frekvensavhengigheten til lysets energi og hvordan materie og stråling kan være i termisk likevekt. Den redegjør også for avvikende observasjoner, som egenskapene til stråling fra «sorte legemer», som andre fysikere, deriblandt Max Planck, hadde prøvd å forklare ved semiklassiske modeller der lyset fortsatt blir beskrevet av Maxwells ligninger men der matrialene er kvantisert. Selvom disse semiklassiske modellene bidro til utviklingen av kvantemekanikken beviste senere eksperimenter Einsteins hypotese om at lyset i seg selv er kvantisert. Lyskvant er fotoner.

I den moderne stadardmodellen i partikkelfysikk blir fotonene beskrevet som en nødvendig konsekvens av at de fysiske lovene har en viss symmetri ved hvert punkt i romtiden. De indre egenskapene til fotoner, som ladning, masse og spinn, blir bestemt av denne gauge-symmetrien.

Fotonkonseptet har ført til enorme fremskritt innen eksperimentell og teoretisk fysikk, som lasere, Bose-Einstein-kondensater, kvantefeltteori og sannsynlighetstolkning i kvantemekanikk. Det har blitt anvendt i fotokjemi, høyoppløsningsmikroskopi og måling av molekylære avstander. Nylig har fotoner blitt studert som element i kvantedatamaskiner og for sofistikerte anvendelser innen optisk kommunikasjon som kvantekryptografi.

Nomenklatur

I 1900 jobbet Max Planck med sort-legeme-stråling og foreslo at energien i de elektromagnetiske bølgene bare kunne frigis i «energipakker», han kalte disse kvant. Senere, i 1905, gikk Albert Einstein videre ved å foreslå at EM-bølgene bare kunne eksistere i diskret bølgepakker. Han kalte slike bølgepakker for lyskvant (Tysk: das Lichtquant). Navnet foton avledes fra det greske ordet for lys, φως (omskrevet phôs), og ble skapt i 1926 av den fysikeren og kjemikeren Gilbert N. Lewis, som publiserte en spekulativ teori der fotoner var umulig å skape og umulig å ødelegge. Selvom Lewis' teori aldri ble akseptert og motbevist i mange eksperiment ble hans nye nanv, foton, raskt plukket opp av de flestse fysikere. Isaac Asimov kreditterer Arthur Compton i å definere energikvant som fotoner i 1927.

I fysikk er fotonet vanligvis betegnet med symbolet γ (den greske bokstaven gamma). Dette symbolet stammer mest sannsynlig fra gammastråler, som ble oppdaget og navngitt i 1900 av Paul Ulrich Villard og ble påvist å være en form for elektromagnetisk stråling i 1914 av Ernest Rutherford og Edward Andrade. I kjemi og optikk blir vanligvis fotoner symbolisert ved hν, energien til et foton, der h er Plancks konstant og den greske bokstaven ν (ny) er fotonets frekvens. Mindre brukt er hf, der f er frekvensen.

Fysiske egenskaper

Se også: spesiell relativitet

Et Feynmandiagram over utvekslingen av et virtuelt foton (symbolisert av en oscillerende linjen merket γ (gamma) mellom et elektron og et positron.

Fotonet er masseløst, har ingen ladning, og henfaller ikke spontant i tomt rom. Et foton har to mulige polarisasjonstilstander og er beskrevet av presist tre kontinuerlige parametre: komponentene i dets bølgevektor, som bestemmer dets bølgelengde λ og dets forplantningsretning. Fotonet er gaugebosonet for elektromagnetisme, og derfor er alle andre kvantetall, som leptonnummer og baryontall, null. I tillegg er ikke fotonet bygd opp av kvarker.

Fotoner blir emittert i mange naturlige prosesser. For eksempel, når en ladning er akselerert emitterer det synkrotronstråling. I løpet av molekylær, atomær eller nukleær overgang til et lavere energinivå, vil fotoner av forskjellig energi bli emittert, fra infrarød stråling til gammastråling. Et foton kan også bli emmitert når en partikkel og dets korresponderende antipartikkel annihilerer, for eksempel elektron-positron annihilasjon.

I tomt rom beveger fotonet seg med lysets hastighet, c, og dets energi og impuls er knyttet sammen som E = pc, der p er størrelsen av impulsvektoren p. Til sammenligning er den tilsvarende ligningen for partikler med masse m:

$\ E^{2}=c^{2}p^{2} m^{2}c^{4}.$

Energien og impulsen til et foton avhenger kun av dets frekvens (ν) eller tilsvarende, dets bølgelengde (λ):

$\ E=\hbar \omega =h\nu ={\frac {hc}{\lambda }}$

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

der k er bølgevektoren (der absoluttverdien er bølgetallet k = 2π/λ og retningen angir retningen til energiforplantningen), ω = 2πν er vinkelfrekvensen og ħ = h/2π er Plancks reduserte konstant.

Siden p peker i fotonets forplantningsretning er størrelsen av impulsen

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

Fotonet har også et spinn som ikke avhenger av frekvensen. Størrelsen på spinnet er $\scriptstyle {{\sqrt {2}}\hbar }$ og komponenten målt langs forplantningsretningen, dets helisitet, må være ±ħ. Disse to mulige helisitetene, kalt høyrehendt ( ħ) og venstrehendt (-ħ), korresponderer til de to mulige sirkulære polarisasjonstilstandene til fotonet.

For å illustrere betydningen av disse formlene kan vi se på annihileringen av en partikkel med dets antipartikkel. Denne hendelsen må resultere i minst to fotoner. Grunnen til dette er at i massesentersystemet har ikke de kolliderende partiklene noen netto impuls, men et enkelt foton har alltid en impuls siden impulsen til et foton er bestemt av dets frekvens eller bølgelengde som aldri kan være null. Så, på grunn av impulsbevarelse krever dette at minst to foton blir skapt med null netto impuls. Energien til de to fononene kan bli bestemt fra impulsbevarelse. Sett på en annen måte, fotonet kan sees på som sin egen antipartikkel. Den motsatte prosessen, par-produksjon, er den dominante mekanismen bak energitapet til høy-energetiske fotoner, som gamma-stråler, når de passerer gjennom materie.

Den klassiske formelen for energi og impuls for elektromagnetisk stråling kan uttrykkes ved fotonvekselvirkninger. For eksempel, strålingstrykket fra elektromagnetisk stråling på et objekt kommer fra overføring av fotonenes impuls per tids- og arealenhet på objektet, siden trykk er kraft per arealenhet og kraft er endring i impuls per tidsenhet.

Historisk utvikling

Utdypende artikkel: Lys

Thomas Youngs dobbel-spalte eksperiment i 1805 viste at lys kan opptre som en bølge, og hjalp til å motbevise tidlige teorier om at lys var partikler.

I de fleste teorier frem til 1700-tallet ble lys sett på som partikler. En av de tidligste partikkelteoriene ble beskrevet i the Book of Optics (1021, oversatt til latin på begynnelsen 1200-tallet) av Alhazen, som hevdet at lysstråler var strømmer av svært små partikler som «manglet alle sanselige kvaliteter bortsett fra energi.» Siden partikkelmodellen vanskelig kan forklare refraksjon, diffraksjon og dobbeltbrytning av lys, ble bølgeteorier foreslått i stedet av René Descartes (1637), Robert Hooke (1665), og Christian Huygens (1678); likevel, partikkelmodeller forble dominante, hovedsaklig på grunn av Isaac Newtons innflytelse. Tidlig på 1800-tallet demonstrerte Thomas Young og Augustin Fresnel interferens og diffraksjon av lys og innen 1850 var bølgemodeller akseptert i alminnelighet. James Clerk Maxwells forutsigelse i 1865 om at lys var en elektronmagnetisk bølge — noe som ble bekreftet eksperimentellt i 1888 av Heinrich Hertz' oppdagelse av radiobølger — virket som den siste spikeren i kista for partikkelmodellen for lys.

I 1900, Maxwells teoretiske modell for lys som oscillerende elektriske og magnetiske felt virket tilsynelatende komplett. Likevel, flere observasjoner kunne ikke forklares av noen bølgemodell for elektromagnetisk stråling, noe som ledet til ideen om at lysenergien var pakket i kvant beskrevet av E=hν. Senere eksperiment viste at disse lyskvantene også hadde en impuls og kunne derfor betraktes som partikler: foton-konseptet var født, noe som førte til en dypere forståelse av det elektriske og magnetiske feltet i seg selv.

Maxwells bølgeteori klarer ikke å redegjøre for alle egenskapene til lys. Maxwells teori forutsier at energien til en lysbølge kun avhenger av dets intensitet, ikke av dets frekvens; ikke desto mindre, flere uavhengige typer eksperiment viser at den overførte energien fra lys til atom kun avhenger av lysets frekvens, ikke dets intensitet. For eksempel, enkelte kjemiske reaksjoner fremkalles av lys med en frekvens høyere enn en viss terskelfrekvens; lys med en lavere frekvens enn terskelfrekvensen, uansett intensitet, vil ikke sette igang reaksjonen. På samme måte kan elektroner kastes ut fra en metallplate ved å lyse på den med en tilstrekkelig høy frekvens (fotoelektrisk effekt); energien til elektronet som ble kastet ut avhenger kun av lysets frekvens, ikke til dets intensitet.

På samme tid ledet undersøkelser av sort-legeme stråling, utført gjennom fire tiår (1860-1900) av forskjellige forskere, til Max Plancks hypotese om at energien til ethvert system som absorberer eller emitterer elektromagnetisk stråling med frekvens $\nu$ er et heltallsmultiplum av energikvant $E=h\nu$. Som vist av Albert Einstein må det antas en eller annen form for kvantisering for å kunne forklare den termmiske likevekten som observeres mellom materie og elektromagnetisk stråling; for denne forklaringen av den fotoelektriske effekten fikk Einstein Nobelprisen i fysikk i 1921.

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. In 1905, Einstein was the first to propose that energy quantization was a property of electromagnetic radiation itself. Although he accepted the validity of Maxwell's theory, Einstein pointed out that many anomalous experiments could be explained if the energy of a Maxwellian light wave were localized into point-like quanta that move independently of one another, even if the wave itself is spread continuously over space. In 1909 and 1916, Einstein showed that, if Planck's law of black-body radiation is accepted, the energy quanta must also carry momentum $p=h/\lambda$, making them full-fledged particles. This photon momentum was observed experimentally by Arthur Compton, 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 (see Second quantization and The photon as a gauge boson, below).

Early objections

Up to 1923, most physicists were reluctant to accept that light itself was quantized. Instead, they tried to explain photon behavior by quantizing only matter, as in the Bohr model of the hydrogen atom (shown here). Even though these semiclassical models were only a first approximation, they were accurate for simple systems and they led to quantum mechanics.

Einstein's 1905 predictions were verified experimentally in several ways in the first two decades of the 20th century, as recounted in Robert Millikan's Nobel lecture. However, before Compton's experiment showing that photons carried momentum proportional to their frequency (1922), most physicists were reluctant to believe that electromagnetic radiation itself might be particulate. (See, for example, the Nobel lectures of Wien, Planck and Millikan.). Instead, there was a widespread belief that energy quantization resulted from some unknown constraint on the matter that absorbs or emits radiation. Attitudes changed over gradually. In part, the change can be traced to experiments such as Compton scattering, where it was much more difficult not to ascribe quantization to light itself to explain the observed results.

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

1. 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 continuous release of energy into radiation.
2. 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 failures of the BKS model inspired Werner Heisenberg in his development of matrix mechanics.

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

Wave–particle duality and uncertainty principles

Se også: Wave–particle duality, Squeezed coherent state og Uncertainty principle

Photons, like all quantum objects, exhibit both wave-like and particle-like properties. Their dual wave–particle nature can be difficult to visualize. The photon displays clearly wave-like phenomena such as diffraction and interference on the length scale of its wavelength. For example, a single photon passing through a double-slit experiment lands 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 a short pulse of electromagnetic radiation; it does not spread out as it propagates, nor does it divide when it encounters a beam splitter.^{[trenger referanse]} Rather, the photon seems to be 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 our present understanding, the electromagnetic field itself is produced by photons, which in turn result from a local gauge symmetry and the laws of quantum field theory (see the Second quantization and Gauge boson sections below).

Heisenberg's thought experiment for locating an electron (shown in blue) with a high-resolution gamma-ray microscope. The incoming gamma ray (shown in green) is scattered by the electron up into the microscope's aperture angle θ. The scattered gamma ray is shown in red. Classical optics shows that the electron position can be resolved only up to an uncertainty Δx that depends on θ and the wavelength λ of the incoming light.

A key element of quantum mechanics is Heisenberg's uncertainty principle, which forbids the simultaneous measurement of the position and momentum of a particle along the same direction. Remarkably, the uncertainty principle for charged, material particles requires the quantization of light into photons, and even the frequency dependence of the photon's energy and momentum. An elegant illustration is Heisenberg's thought experiment for locating an electron with an ideal microscope. The position of the electron can be determined to within the resolving power of the microscope, which is given by a formula from classical optics

$\Delta x\sim {\frac {\lambda }{\sin \theta }}$

where $\theta$ is the aperture angle of the microscope. Thus, the position uncertainty $\Delta x$ can be made arbitrarily small by reducing the wavelength $\lambda$. The momentum of the electron is uncertain, since it received a "kick" $\Delta p$ from the light scattering from it into the microscope. If light were not quantized into photons, the uncertainty $\Delta p$ could be made arbitrarily small by reducing the light's intensity. In that case, since the wavelength and intensity of light can be varied independently, one could simultaneously determine the position and momentum to arbitrarily high accuracy, violating the uncertainty principle. By contrast, Einstein's formula for photon momentum preserves the uncertainty principle; since the photon is scattered anywhere within the aperture, the uncertainty of momentum transferred equals

$\Delta p\sim p_{\mathrm {photon} }\sin \theta ={\frac {h}{\lambda }}\sin \theta$

giving the product $\Delta x\Delta p\,\sim \,h$, which is Heisenberg's uncertainty principle. Thus, the entire world is quantized; both matter and fields must obey a consistent set of quantum laws, if either one is to be quantized.

The analogous uncertainty principle for photons forbids the simultaneous measurement of the number $n$ of photons (see Fock state and the Second quantization section below) in an electromagnetic wave and the phase $\phi$ of that wave

$\Delta n\Delta \phi >1$

See coherent state and squeezed coherent state for more details.

Both photons and material particles such as electrons create analogous interference patterns when passing through a double-slit experiment. For photons, this corresponds to the interference of a Maxwell light wave whereas, for material particles, this corresponds to the interference of the Schrödinger wave equation. Although this similarity might suggest that Maxwell's equations are simply Schrödinger's equation for photons, most physicists do not agree. For one thing, they are mathematically different; most obviously, Schrödinger's one equation solves for a complex field, whereas Maxwell's four equations solve for real fields. More generally, the normal concept of a Schrödinger probability wave function cannot be applied to photons. Being massless, they cannot be localized without being destroyed; technically, photons cannot have a position eigenstate $|\mathbf {r} \rangle$, and, thus, the normal Heisenberg uncertainty principle $\Delta x\Delta p>h/2$ does not pertain to photons. A few substitute wave functions have been suggested for the photon, but they have not come into general use. Instead, physicists generally accept the second-quantized theory of photons described below, quantum electrodynamics, in which photons are quantized excitations of electromagnetic modes.

Bose–Einstein model of a photon gas

Utdypende artikler: Bose gas, Bose–Einstein statistics og Spin-statistics theorem

In 1924, Satyendra Nath Bose derived Planck's law of black-body radiation without using any electromagnetism, but rather a modification of coarse-grained counting of phase space. 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 state. 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; this Bose–Einstein condensation was observed experimentally in 1995.

The modern view on this is that photons are, by virtue of their integer spin, bosons (as opposed to fermions with half-integer spin). By the spin-statistics theorem, all bosons obey Bose–Einstein statistics (whereas all fermions obey Fermi-Dirac statistics).

Stimulated and spontaneous emission

Utdypende artikler: Stimulated emission og Laser

Stimulated emission (in which photons "clone" themselves) was predicted by Einstein in his kinetic analysis, and led to the development of the laser. Einstein's derivation inspired further developments in the quantum treatment of light, which led to the statistical interpretation of quantum mechanics.

In 1916, Einstein showed that Planck's radiation law could be derived from a semi-classical, statistical treatment of photons and atoms, which implies a relation between the rates at which atoms emit and absorb photons. The condition follows from the assumption that light is emitted and absorbed by atoms independently, and that the thermal equilibrium is preserved by interaction with atoms. Consider a cavity in thermal equilibrium and filled with electromagnetic radiation and atoms that can emit and absorb that radiation. Thermal equilibrium requires that the energy density $\rho (\nu )$ of photons with frequency $\nu$ (which is proportional to their number density) is, on average, constant in time; hence, the rate at which photons of any particular frequency are emitted must equal the rate of absorbing them.

Einstein began by postulating simple proportionality relations for the different reaction rates involved. In his model, the rate $R_{ji}$ for a system to absorb a photon of frequency $\nu$ and transition from a lower energy $E_{j}$ to a higher energy $E_{i}$ is proportional to the number $N_{j}$ of atoms with energy $E_{j}$ and to the energy density $\rho (\nu )$ of ambient photons with that frequency,

$R_{ji}=N_{j}B_{ji}\rho (\nu )\!$

where $B_{ji}$ is the rate constant for absorption. For the reverse process, there are two possibilities: spontaneous emission of a photon, and a return to the lower-energy state that is initiated by the interaction with a passing photon. Following Einstein's approach, the corresponding rate $R_{ij}$ for the emission of photons of frequency $\nu$ and transition from a higher energy $E_{i}$ to a lower energy $E_{j}$ is

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

where $A_{ij}$ is the rate constant for emitting a photon spontaneously, and $B_{ij}$ is the rate constant for emitting it in response to ambient photons (induced or stimulated emission). In thermodynamic equilibrium, the number of atoms in state i and that of atoms in state j must, on average, be constant; hence, the rates $R_{ji}$ and $R_{ij}$ must be equal. Also, by arguments analogous to the derivation of Boltzmann statistics, the ratio of $N_{i}$ and $N_{j}$ is $g_{i}/g_{j}\exp {(E_{j}-E_{i})/kT)},$ where $g_{i,j}$ are the degeneracy of the state i and that of j, respectively, $E_{i,j}$ their energies, k the Boltzmann constant and T the system's temperature. From this, it is readily derived that $g_{i}B_{ij}=g_{j}B_{ji}$ and

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

The A and Bs are collectively known as the Einstein coefficients.

Einstein could not fully justify his rate equations, but claimed that it should be possible to calculate the coefficients $A_{ij}$, $B_{ji}$ and $B_{ij}$ once physicists had obtained "mechanics and electrodynamics modified to accommodate the quantum hypothesis". In fact, in 1926, Paul Dirac derived the $B_{ij}$ rate constants in using a semiclassical approach, and, in 1927, succeeded in deriving all the rate constants from first principles within the framework of quantum theory. Dirac's work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also called second quantization or quantum field theory; earlier quantum mechanical treatments only treat material particles as quantum mechanical, not the electromagnetic field.

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 probabilistic interpretation of the wave function was inspired by Einstein's later work searching for a more complete theory.

Second quantization

Utdypende artikkel: 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 electromagnetic 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, which were derived by Einstein in 1909.

In 1925, Born, Heisenberg and Jordan reinterpreted Debye's concept in a key way. As may be shown classically, the Fourier modes of the electromagnetic field—a complete set of electromagnetic plane waves indexed by their wave vector k and polarization state—are equivalent to a set of uncoupled simple harmonic oscillators. 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, the probability of an event is computed by summing the probability amplitude (a complex number) for all possible ways in which the event can occur, as in the Feynman diagram shown here; the probability equals the square of the modulus of the total amplitude.

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 the Bose–Einstein statistics of photons is a natural consequence of quantizing the electromagnetic field correctly (Bose's reasoning went in the opposite direction; he derived Planck's law of black body radiation by assuming BE statistics). In Dirac's time, it was not yet known that all bosons, including photons, must obey BE statistics.

Dirac's 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 amplitude 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 $E=pc$, and may have extra polarization states; depending on the gauge used, virtual photons may have three or four polarization states, instead of the two states of real photons. 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 give apparently infinite contributions to the sum. Such unphysical results are corrected for using the technique of renormalization. Other virtual particles may contribute to the summation as well; for example, two photons may interact indirectly through virtual electron-positron pairs. In fact, such photon-photon scattering, as well as electron-photon scattering, is meant to be one of the modes of operations of the planned particle accelerator, the International Linear Collider.

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

Utdypende artikkel: Gauge theory

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

The quanta of an Abelian gauge field must be massless, uncharged bosons, as long as the symmetry is not broken; hence, the photon is predicted to be massless, and to have zero electric charge and integer spin. The particular form of the electromagnetic interaction specifies that the photon must have spin ±1; thus, its helicity must be $\pm \hbar$. These two spin 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 in the electroweak interaction was accomplished by Sheldon Glashow, Abdus Salam and Steven Weinberg, for which they were awarded the 1979 Nobel Prize in physics. Physicists continue to hypothesize grand unified theories that connect these four gauge bosons with the eight gluon gauge bosons of quantum chromodynamics; however, key predictions of these theories, such as proton decay, have not been observed experimentally.

Photon structure

Utdypende artikkel: Quantum chromodynamics

According to quantum chromodynamics, a photon can interact both as a point-like particle, or as a collection of quarks and gluons, i.e., like a hadron. The structure of the photon is determined not by the traditional valence quark distributions as in a proton, but by fluctuations of the point-like photon into a collection of partons.

Contributions to the mass of a system

Se også: Mass in special relativity og General relativity

The energy of a system that emits a photon is decreased by the energy $E$ of the photon as measured in the rest frame of the emitting system, which may result in a reduction in mass in the amount ${E}/{c^{2}}$. Similarly, the mass of a system that absorbs a photon is increased by a corresponding amount. As an application, the energy balance of nuclear reactions involving photons is commonly written in terms of the masses of the nuclei involved, and terms of the form ${E}/{c^{2}}$ for the gamma photons (and for other relevant energies, such as the recoil energy of nuclei).

This concept is applied in key predictions of quantum electrodynamics (QED, see above). In that theory, the mass of electrons (or, more generally, leptons) is modified by including the mass contributions of virtual photons, in a technique known as renormalization. Such "radiative corrections" contribute to a number of predictions of QED, such as the magnetic dipole moment of leptons, the Lamb shift, and the hyperfine structure of bound lepton pairs, such as muonium and positronium.

Since photons contribute to the stress-energy tensor, they exert a gravitational attraction on other objects, according to the theory of general relativity. Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warped spacetime, as in gravitational lensing, and their frequencies may be lowered by moving to a higher gravitational potential, as in the Pound-Rebka experiment. However, these effects are not specific to photons; exactly the same effects would be predicted for classical electromagnetic waves.

Photons in matter

Se også: Group velocity og Photochemistry

Light that travels through transparent matter does so at a lower speed than c, the speed of light in a vacuum. For example, photons suffer so many collisions on the way from the core of the sun that radiant energy can take about a million years to reach the surface; however, once in open space, a photon takes only 8.3 minutes to reach Earth. The factor by which the speed of light is decreased is called the refractive index of the material. In a classical wave picture, the slowing can be explained by the light inducing electric polarization in the matter, the polarized matter radiating new light, and the new light interfering with the original light wave to form a delayed wave. In a particle picture, the slowing can instead be described as a blending of the photon with quantum excitations of the matter (quasi-particles such as phonons and excitons) to form a polariton; this polariton has a nonzero effective mass, which means that it cannot travel at c.

Alternatively, photons may be viewed as always traveling at c, even in matter, but they have their phase shifted (delayed or advanced) upon interaction with atomic scatters: this modifies their wavelength and momentum, but not speed. A light wave made up of these photons does travel slower than the speed of light. In this view the photons are "bare", and are scattered and phase shifted, while in the view of the preceding paragraph the photons are "dressed" by their interaction with matter, and move without scattering or phase shifting, but at a lower speed.

Light of different frequencies may travel through matter at different speeds; this is called dispersion. In some cases, it can result in extremely slow speeds of light in matter. The effects of photon interactions with other quasi-particles may be observed directly in Raman scattering and Brillouin scattering.

Photons can also be absorbed by nuclei, atoms or molecules, provoking transitions between their energy levels. A classic example is the molecular transition of retinal (C₂₀H₂₈O, Figure at right), which is responsible for vision, as discovered in 1958 by Nobel laureate biochemist George Wald and co-workers. As shown here, the absorption provokes a cis-trans isomerization that, in combination with other such transitions, is transduced into nerve impulses. The absorption of photons can even break chemical bonds, as in the photodissociation of chlorine; this is the subject of photochemistry.

Technological applications

Photons have many applications in technology. These examples are chosen to illustrate applications of photons per se, rather than general optical devices such as lenses, etc. that could operate under a classical theory of light. The laser is an extremely important application and is discussed above under stimulated emission.

Individual photons can be detected by several methods. The classic photomultiplier tube exploits the photoelectric effect: a photon landing on a metal plate ejects an electron, initiating an ever-amplifying avalanche of electrons. Charge-coupled device chips use a similar effect in semiconductors: an incident photon generates a charge on a microscopic capacitor that can be detected. Other detectors such as Geiger counters use the ability of photons to ionize gas molecules, causing a detectable change in conductivity.

Planck's energy formula $E=h\nu$ is often used by engineers and chemists in design, both to compute the change in energy resulting from a photon absorption and to predict the frequency of the light emitted for a given energy transition. For example, the emission spectrum of a fluorescent light bulb can be designed using gas molecules with different electronic energy levels and adjusting the typical energy with which an electron hits the gas molecules within the bulb.

Under some conditions, an energy transition can be excited by two photons that individually would be insufficient. This allows for higher resolution microscopy, because the sample absorbs energy only in the region where two beams of different colors overlap significantly, which can be made much smaller than the excitation volume of a single beam (see two-photon excitation microscopy). Moreover, these photons cause less damage to the sample, since they are of lower energy.

In some cases, two energy transitions can be coupled so that, as one system absorbs a photon, another nearby system "steals" its energy and re-emits a photon of a different frequency. This is the basis of fluorescence resonance energy transfer, a technique that is used in molecular biology to study the interaction of suitable proteins.

Several different kinds of hardware random number generator involve the detection of single photons. In one example, for each bit in the random sequence that is to be produced, a photon is sent to a beam-splitter. In such a situation, there are two possible outcomes of equal probability. The actual outcome is used to determine whether the next bit in the sequence is "0" or "1".

Recent research

Se også: Quantum optics

The fundamental nature of the photon is believed to be understood theoretically; the prevailing Standard Model predicts that the photon is a gauge boson of spin 1, without mass (at rest) and without charge, that results from a local U(1) gauge symmetry and mediates the electromagnetic interaction. However, physicists continue to check for discrepancies between experiment and the Standard Model predictions, in the hope of finding clues to physics beyond the Standard Model. In particular, experimental physicists continue to set ever better upper limits on the charge and mass of the photon; a non-zero value for either parameter would be a serious violation of the Standard Model. However, all experimental data hitherto are consistent with the photon having zero charge and mass. The best universally accepted upper limits on the photon charge and mass are 5×10⁻⁵² C (or 3×10⁻³³ e) and 1.1×10⁻⁵² kg (6×10⁻¹⁷ eV/c², or 1×10⁻²² m_e), respectively.

Much research has been devoted to applications of photons in the field of quantum optics. Photons seem well-suited to be elements of an extremely fast quantum computer, and the quantum entanglement of photons is a focus of research. Nonlinear optical processes are another active research area, with topics such as two-photon absorption, self-phase modulation and optical parametric oscillators. However, such processes generally do not require the assumption of photons per se; they may often be modeled by treating atoms as nonlinear oscillators. The nonlinear process of spontaneous parametric down conversion is often used to produce single-photon states. Finally, photons are essential in some aspects of optical communication, especially for quantum cryptography.

See also

Doppler shift Light Electromagnetic radiation Quantum optics Photonics

Photon polarization Ballistic photon Photography Laser Advanced Photon Source at Argonne National Laboratory

Additional references

By date of publication:

• Clauser, J.F. (1974). «Experimental distinction between the quantum and classical field-theoretic predictions for the photoelectric effect». Physical Review D. 9: 853–860. doi:10.1103/PhysRevD.9.853. 
• Kimble, H.J. (1977). «Photon Anti-bunching in Resonance Fluorescence». Physics Review Letters. 39: 691–695. doi:10.1103/PhysRevLett.39.691.  article web link
• Pais, A. (1982). Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press. 
• Grangier, P. (1986). «Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences». Europhysics Letters. 1: 501–504. doi:10.1209/0295-5075/1/4/004. 
• Lamb, W.E. (1995). «Anti-photon». Applied Physics B. 60: 77–84. doi:10.1007/BF01135846. 
• Special supplemental issue of Optics and Photonics News (vol. 14, October 2003) article web link
  • Roychoudhuri, C. «The nature of light: what is a photon?». Optics and Photonics News. 14: S1 (Supplement). 
  • Zajonc, A. «Light reconsidered». Optics and Photonics News. 14: S2–S5 (Supplement). 
  • Loudon, R. «What is a photon?». Optics and Photonics News. 14: S6–S11 (Supplement). 
  • Finkelstein, D. «What is a photon?». Optics and Photonics News. 14: S12–S17 (Supplement). 
  • Muthukrishnan, A. «The concept of the photon—revisited». Optics and Photonics News. 14: S18–S27 (Supplement). 
  • Mack, H. «A photon viewed from Wigner phase space». Optics and Photonics News. 14: S28–S35 (Supplement). 
• Thorn, J.J. (2004). «Observing the quantum behavior of light in an undergraduate laboratory». American Journal of Physics. 72: 1210–1219. doi:10.1119/1.1737397.  http://people.whitman.edu/~beckmk/QM/grangier/grangier.html
• «Roy Glauber's Nobel Lecture, "100 Years of Light Quanta"».  Delivered 8 December 2005.