Photon
A photon is an elementary particle, the quantum
of light and all other forms of electromagnetic
radiation, and the force carrier for the electromagnetic
force, even when static via virtual photons.
The effects of this force are easily observable
at both the microscopic and macroscopic level,
because the photon has zero rest mass; this
allows long distance interactions. Like all
elementary particles, photons are currently
best explained by quantum mechanics and exhibit
wave–particle duality, exhibiting properties
of both waves and particles. For example,
a single photon may be refracted by a lens
or exhibit wave interference with itself,
but also act as a particle giving a definite
result when its position is measured.
The modern photon concept was developed gradually
by Albert Einstein to explain experimental
observations that did not fit the classical
wave model of light. In particular, the photon
model accounted for the frequency dependence
of light's energy, and explained the ability
of matter and radiation to be in thermal equilibrium.
It also accounted for anomalous observations,
including the properties of black-body radiation,
that other physicists, most notably Max Planck,
had sought to explain using semiclassical
models, in which light is still described
by Maxwell's equations, but the material objects
that emit and absorb light do so in amounts
of energy that are quantized (i.e., they change
energy only by certain particular discrete
amounts and cannot change energy in any arbitrary
way). Although these semiclassical models
contributed to the development of quantum
mechanics, many further experiments starting
with Compton scattering of single photons
by electrons, first observed in 1923, validated
Einstein's hypothesis that light itself is
quantized. In 1926 the optical physicist Frithiof
Wolfers and the chemist Gilbert N. Lewis coined
the name photon for these particles, and after
1927, when Arthur H. Compton won the Nobel
Prize for his scattering studies, most scientists
accepted the validity that quanta of light
have an independent existence, and the term
photon for light quanta was accepted.
In the Standard Model of particle physics,
photons are described as a necessary consequence
of physical laws having a certain symmetry
at every point in spacetime. The intrinsic
properties of photons, such as charge, mass
and spin, are determined by the properties
of this gauge symmetry. The photon concept
has led to momentous advances in experimental
and theoretical physics, such as lasers, Bose–Einstein
condensation, quantum field theory, and the
probabilistic interpretation of quantum mechanics.
It has been applied to photochemistry, high-resolution
microscopy, and measurements of molecular
distances. Recently, photons have been studied
as elements of quantum computers and for sophisticated
applications in optical communication such
as quantum cryptography.
Nomenclature
In 1900, Max Planck was working on black-body
radiation and suggested that the energy in
electromagnetic waves could only be released
in "packets" of energy. In his 1901 article
in Annalen der Physik he called these packets
"energy elements". The word quanta (singular
quantum) was used even before 1900 to mean
particles or amounts of different quantities,
including electricity. Later, in 1905, Albert
Einstein went further by suggesting that electromagnetic
waves could only exist in these discrete wave-packets.
He called such a wave-packet the light quantum
(German: das Lichtquant). The name photon
derives from the Greek word for light, φῶς
(transliterated phôs). Arthur Compton used
photon in 1928, referring to Gilbert N. Lewis
The same name was used earlier, by the American
physicist and psychologist Leonard T. Troland,
who coined the word in 1916, in 1921 by the
Irish physicist John Joly and in 1926 by the
French physiologist René Wurmser (1890-1993)
and by the French physicist Frithiof Wolfers
(ca. 1890-1971). Although the name was suggested
initially as a unit related to the illumination
of the eye and the resulting sensation of
light and lateron in a physiological context,
although Wolfers's and Lewis's theories were
never accepted as they were contradicted by
many experiments, the new name was adopted
quite immediately by most physicists after
Compton used it.
In physics, a photon is usually denoted by
the symbol γ (the Greek letter gamma). This
symbol for the photon probably derives from
gamma rays, which were discovered in 1900
by Paul Villard, named by Ernest Rutherford
in 1903, and shown to be a form of electromagnetic
radiation in 1914 by Rutherford and Edward
Andrade. In chemistry and optical engineering,
photons are usually symbolized by hν, the
energy of a photon, where h is Planck's constant
and the Greek letter ν (nu) is the photon's
frequency. Much less commonly, the photon
can be symbolized by hf, where its frequency
is denoted by f.
Physical properties
A photon is massless, has no electric charge,
and is stable. A photon has two possible polarization
states. In the momentum representation, which
is preferred in quantum field theory, a photon
is described by its wave vector, which determines
its wavelength λ and its direction of propagation.
A photon's wave vector may not be zero and
can be represented either as a spatial 3-vector
or as a (relativistic) four-vector; in the
latter case it belongs to the light cone (pictured).
Different signs of the four-vector denote
different circular polarizations, but in the
3-vector representation one should account
for the polarization state separately; it
actually is a spin quantum number. In both
cases the space of possible wave vectors is
three-dimensional.
The photon is the gauge boson for electromagnetism,
and therefore all other quantum numbers of
the photon (such as lepton number, baryon
number, and flavour quantum numbers) are zero.
Photons are emitted in many natural processes.
For example, when a charge is accelerated
it emits synchrotron radiation. During a molecular,
atomic or nuclear transition to a lower energy
level, photons of various energy will be emitted,
from radio waves to gamma rays. A photon can
also be emitted when a particle and its corresponding
antiparticle are annihilated (for example,
electron–positron annihilation).
In empty space, the photon moves at c (the
speed of light) and its energy and momentum
are related by E = pc, where p is the magnitude
of the momentum vector p. This derives from
the following relativistic relation, with
m = 0:
The energy and momentum of a photon depend
only on its frequency (ν) or inversely, its
wavelength (λ):
where k is the wave vector (where the wave
number k = |k| = 2π/λ), ω = 2πν is the
angular frequency, and ħ = h/2π is the reduced
Planck constant.
Since p points in the direction of the photon's
propagation, the magnitude of the momentum
is
The photon also carries spin angular momentum
that does not depend on its frequency. The
magnitude of its spin is and the component
measured along its direction of motion, its
helicity, must be ±ħ. These two possible
helicities, called right-handed and left-handed,
correspond to the two possible circular polarization
states of the photon.
To illustrate the significance of these formulae,
the annihilation of a particle with its antiparticle
in free space must result in the creation
of at least two photons for the following
reason. In the center of mass frame, the colliding
antiparticles have no net momentum, whereas
a single photon always has momentum (since
it is determined, as we have seen, only by
the photon's frequency or wavelength—which
cannot be zero). Hence, conservation of momentum
(or equivalently, translational invariance)
requires that at least two photons are created,
with zero net momentum. (However, it is possible
if the system interacts with another particle
or field for annihilation to produce one photon,
as when a positron annihilates with a bound
atomic electron, it is possible for only one
photon to be emitted, as the nuclear Coulomb
field breaks translational symmetry.) The
energy of the two photons, or, equivalently,
their frequency, may be determined from conservation
of four-momentum. Seen another way, the photon
can be considered as its own antiparticle.
The reverse process, pair production, is the
dominant mechanism by which high-energy photons
such as gamma rays lose energy while passing
through matter. That process is the reverse
of "annihilation to one photon" allowed in
the electric field of an atomic nucleus.
The classical formulae for the energy and
momentum of electromagnetic radiation can
be re-expressed in terms of photon events.
For example, the 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.
Experimental checks on photon mass
The photon is currently understood to be strictly
massless, but this is an experimental question.
If the photon is not a strictly massless particle,
it would not move at the exact speed of light
in vacuum, c. Its speed would be lower and
depend on its frequency. Relativity would
be unaffected by this; the so-called speed
of light, c, would then not be the actual
speed at which light moves, but a constant
of nature which is the maximum speed that
any object could theoretically attain in space-time.
Thus, it would still be the speed of space-time
ripples (gravitational waves and gravitons),
but it would not be the speed of photons.
A massive photon would have other effects
as well. Coulomb's law would be modified and
the electromagnetic field would have an extra
physical degree of freedom. These effects
yield more sensitive experimental probes of
the photon mass than the frequency dependence
of the speed of light. If Coulomb's law is
not exactly valid, then that would cause the
presence of an electric field inside a hollow
conductor when it is subjected to an external
electric field. This thus allows one to test
Coulomb's law to very high precision. A null
result of such an experiment has set a limit
of m ≲ 10−14 eV/c2.
Sharper upper limits have been obtained in
experiments designed to detect effects caused
by the galactic vector potential. Although
the galactic vector potential is very large
because the galactic magnetic field exists
on very long length scales, only the magnetic
field is observable if the photon is massless.
In case of a massive photon, the mass term
would affect the galactic plasma. The fact
that no such effects are seen implies an upper
bound on the photon mass of m less than 3×10−27 eV/c2.
The galactic vector potential can also be
probed directly by measuring the torque exerted
on a magnetized ring. Such methods were used
to obtain the sharper upper limit of 10−18eV/c2
(the equivalent of 1.07×10−27 atomic mass
units) given by the Particle Data Group.
These sharp limits from the non-observation
of the effects caused by the galactic vector
potential have been shown to be model dependent.
If the photon mass is generated via the Higgs
mechanism then the upper limit of m≲10−14 eV/c2
from the test of Coulomb's law is valid.
Photons inside superconductors do develop
a nonzero effective rest mass; as a result,
electromagnetic forces become short-range
inside superconductors.
Historical development
In most theories up to the eighteenth century,
light was pictured as being made up of particles.
Since particle models cannot easily account
for the refraction, diffraction and birefringence
of light, wave theories of light were proposed
by René Descartes (1637), Robert Hooke (1665),
and Christiaan Huygens (1678); however, particle
models remained dominant, chiefly due to the
influence of Isaac Newton. In the early nineteenth
century, Thomas Young and August Fresnel clearly
demonstrated the interference and diffraction
of light and by 1850 wave models were generally
accepted. In 1865, James Clerk Maxwell's prediction
that light was an electromagnetic wave—which
was confirmed experimentally in 1888 by Heinrich
Hertz's detection of radio waves—seemed
to be the final blow to particle models of
light.
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 are provoked
only by light of frequency higher than a certain
threshold; light of frequency lower than the
threshold, no matter how intense, does not
initiate 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, 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 ν is an integer multiple of
an energy quantum E = hν. As shown by Albert
Einstein, some form of energy quantization
must be assumed to account for the thermal
equilibrium observed between matter and electromagnetic
radiation; for this explanation of the photoelectric
effect, Einstein received the 1921 Nobel Prize
in physics.
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/λ,
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
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 wave
number (or 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 time. 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, Niels 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 data
then available, 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 continuous 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
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
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
exhibiting interference phenomena but only
if no measure was made on the actual slit
being run across. To account for the particle
interpretation that phenomenon is called probability
distribution but behaves according to 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. 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).
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
where is the aperture angle of the microscope.
Thus, the position uncertainty can be made
arbitrarily small by reducing the wavelength
λ. The momentum of the electron is uncertain,
since it received a "kick" from the light
scattering from it into the microscope. If
light were not quantized into photons, the
uncertainty 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
giving the product, 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 of photons (see Fock state and the
Second quantization section below) in an electromagnetic
wave and the phase of that wave
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,
and, thus, the normal Heisenberg uncertainty
principle 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.
Another interpretation, that avoids duality,
is the De Broglie–Bohm theory: knowned also
as the pilot-wave model, the photon in this
theory is both, wave and particle. "This idea
seems to me so natural and simple, to resolve
the wave-particle dilemma in such a clear
and ordinary way, that it is a great mystery
to me that it was so generally ignored", J.S.Bell.
Bose–Einstein model of a photon gas
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. It was later used
by Lene Hau to slow, and then completely stop,
light in 1999 and 2001.
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
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 of photons with frequency
(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 for a system
to absorb a photon of frequency and transition
from a lower energy to a higher energy is
proportional to the number of atoms with energy
and to the energy density of ambient photons
with that frequency,
where 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 for the emission of photons of frequency
and transition from a higher energy to a lower
energy is
where is the rate constant for emitting a
photon spontaneously, and 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 and must be
equal. Also, by arguments analogous to the
derivation of Boltzmann statistics, the ratio
of and is where are the degeneracy of the
state i and that of j, respectively, their
energies, k the Boltzmann constant and T the
system's temperature. From this, it is readily
derived that and
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, and once physicists
had obtained "mechanics and electrodynamics
modified to accommodate the quantum hypothesis".
In fact, in 1926, Paul Dirac derived the 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
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, where
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, where
is the oscillator frequency. The key new step
was to identify an electromagnetic mode with
energy as a state with photons, each of energy.
This approach gives the correct energy fluctuation
formula.
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 and 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 B–E
statistics). In Dirac's time, it was not yet
known that all bosons, including photons,
must obey Bose–Einstein 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, 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
where represents the state in which photons
are in the mode. In this notation, the creation
of a new photon in mode (e.g., emitted from
an atomic transition) is written as. This
notation merely expresses the concept of Born,
Heisenberg and Jordan described above, and
does not add any physics.
The hadronic properties of the photon
Measurements of the interaction between energetic
photons and hadrons show that the interaction
is much more intense than expected by the
interaction of merely photons with the hadron's
electric charge. Furthermore, the interaction
of energetic photons with protons is similar
to the interaction of photons with neutrons
in spite of the fact that the electric charge
structures of protons and neutrons are substantially
different.
A theory called Vector Meson Dominance (VMD)
was developed to explain this effect. According
to VMD, the photon is a superposition of the
pure electromagnetic photon (which interacts
only with electric charges) and vector meson.
However, if experimentally probed at very
short distances, the intrinsic structure of
the photon is recognized as a flux of quark
and gluon components, quasi-free according
to asymptotic freedom in QCD and described
by the photon structure function. A comprehensive
comparison of data with theoretical predictions
is presented in a recent review.
The photon as a gauge boson
The electromagnetic field can be understood
as a gauge field, i.e., as a field that results
from requiring that a gauge symmetry holds
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 observables or real valued functions
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. 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 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.
Contributions to the mass of a system
The energy of a system that emits a photon
is decreased by the energy of the photon as
measured in the rest frame of the emitting
system, which may result in a reduction in
mass in the amount. 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 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
Any 'explanation' of how photons travel through
matter has to explain why different arrangements
of matter are transparent or opaque at different
wavelengths (light through carbon as diamond
or not, as graphite) and why individual photons
behave in the same way as large groups. Explanations
that invoke 'absorption' and 're-emission'
have to provide an explanation for the directionality
of the photons (diffraction, reflection) and
further explain how entangled photon pairs
can travel through matter without their quantum
state collapsing.
The simplest explanation is that light that
travels through transparent matter does so
at a lower speed than c, the speed of light
in a vacuum. In addition, light can also undergo
scattering and absorption. There are circumstances
in which heat transfer through a material
is mostly radiative, involving emission and
absorption of photons within it. An example
would be in the core of the Sun. Energy can
take about a million years to reach the surface.
However, this phenomenon is distinct from
scattered radiation passing diffusely through
matter, as it involves local equilibrium between
the radiation and the temperature. Thus, the
time is how long it takes the energy to be
transferred, not the photons themselves. Once
in open space, a photon from the Sun takes
only 8.3 minutes to reach Earth. The factor
by which the speed of light is decreased in
a material 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 excitation
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,
which is responsible for vision, as discovered
in 1958 by Nobel laureate biochemist George
Wald and co-workers. 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.
Analogously, gamma rays can in some circumstances
dissociate atomic nuclei in a process called
photodisintegration.
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 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
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, modulational instability 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.
