photon

Photon (ɣ)

classification
Elementary particle
boson
gauge boson
properties
electric charge neutral
Dimensions kg
Spin parity 1 -
Interactions electromagnetic
gravitation

The photon (from Greek φῶς phōs , genitive φωτός phōtos " light ") is the interaction particle of the electromagnetic interaction . Clearly speaking, photons are what electromagnetic radiation consists of. This is why the term light quantum or light particle is sometimes used. In quantum electrodynamics , the photon, as a mediator of the electromagnetic interaction, belongs to the gauge bosons and is therefore an elementary particle .

The photon is an elementary particle with no mass , but with energy and momentum , both of which are proportional to its frequency , as well as angular momentum . If its stay is restricted to a resting system with finite volume, it makes a contribution to the mass of the system proportional to its energy.

Research history

Since ancient times there have been various, sometimes contradicting, ideas about the nature of light. Until the beginning of the 19th century , wave and particle theories competed with each other (see the history section in the light article ) . Then the wave nature of light seemed to be proven by many phenomena (e.g. interference and polarization phenomena ) and understood as an electromagnetic wave by Maxwell's equations drawn up in 1867 . There was also evidence of a particle character. A historically important experiment in this regard was the observation of the photoelectric effect by Heinrich Hertz and Wilhelm Hallwachs in 1887 .

The discovery of the quantization of electromagnetic radiation was based on Planck's law of radiation , which describes the thermal radiation of a black body . In order to explain this law theoretically, Max Planck had to assume that the surface of the black body can only exchange discrete amounts of energy proportional to the frequency with the electromagnetic field at any frequency . However, Planck himself only imagined the energy exchange quantized, not the electromagnetic radiation per se.

Albert Einstein then set up the light quantum hypothesis in his publication on the photoelectric effect in 1905 . According to her, light is a stream of "energy quanta localized in spatial points, which move without dividing and can only be absorbed and generated as a whole". Due to widespread doubts about these views, this work was not awarded the Nobel Prize until 1919 (Planck) and 1922 (Einstein) .

In many cases, however, the particle character of electromagnetic radiation was still doubted until Arthur Compton was able to prove in the years 1923–1925 that X-rays act on individual electrons in exactly the same way as bombardment with individual particles, whose energies and pulses correspond to those of high-energy light quanta. For the discovery and interpretation of the Compton effect named after him, he received the Nobel Prize in Physics in 1927 (as one of two awardees).

The formal quantum theory of light was developed starting in 1925 with the work of Max Born , Pascual Jordan and Werner Heisenberg . The theory of electromagnetic radiation that is valid today is quantum electrodynamics (QED); it also describes the light quanta. Its beginnings go back to a work by Paul Dirac in 1927, in which the interaction of quantized electromagnetic radiation with an atom is analyzed. The QED was developed in the 1940s and honored in 1965 with the award of the Nobel Prize in Physics to Richard Feynman , Julian Schwinger and Shin'ichirō Tomonaga . In QED, the electromagnetic field itself is quantized and the photon its elementary excitation.

Albert Einstein wrote in a letter to his friend Michele Besso in 1951 :

“The whole 50 years of conscious brooding did not bring me closer to the answer to the question 'What are light quanta?' Today every scoundrel thinks he knows, but he is wrong ... "

Name and symbol

The word photon is derived from the Greek word for light, φῶς ( phôs ). The name had been introduced by various authors since 1916 for a small amount of energy that can trigger a photochemical or photoelectric effect, but was hardly taken into account. Max Planck z. B. spoke in his Nobel Prize speech in 1920 about "light quanta". The name was finally made known by Arthur Compton , who referred to a publication by the chemist Gilbert Newton Lewis in 1926. Lewis used the term in the context of a model he proposed for the interaction of atoms with light. Among other things, this model falsely provided for a conservation of the number of photons and was generally not recognized.

The symbol ( gamma ) is generally used for the photon . In high-energy physics this symbol, however, is reserved for the high-energy photons of gamma radiation (gamma quanta), and also relevant in this branch of physics X-ray photon often get the symbol X (of X-rays and English: X-ray ). ${\ displaystyle \ \ gamma}$

Very often a photon is also represented by the energy it contains : ${\ displaystyle E}$

• ${\ displaystyle E _ {\ text {photon}} = h \, \ nu = {\ frac {hc} {\ lambda}}}$
with Planck's quantum of action , the (light) frequency , the wavelength and the speed of light${\ displaystyle \, h}$ ${\ displaystyle \, \ nu}$ ${\ displaystyle \, \ lambda}$ ${\ displaystyle \, c}$

or.

• ${\ displaystyle E _ {\ text {photon}} = \ hbar \, \ omega}$
with the reduced Planckian quantum of action and the (light) angular frequency .${\ displaystyle \ hbar = {\ frac {h} {2 \ pi}}}$ ${\ displaystyle \, \ omega = 2 \ pi \, \ nu}$

properties

All electromagnetic radiation, from radio waves to gamma radiation , is quantized into photons . This means that the smallest possible amount of energy in electromagnetic radiation of a certain frequency is a photon. Photons have an infinite natural lifespan, but can be created or destroyed in a variety of physical processes. A photon has no mass . It follows from this that it always moves with the speed of light in a vacuum , provided it is in a state with a well-defined momentum, i.e. it can be represented by a single plane wave . Otherwise it moves with the group speed of the plane waves involved. A photon in the superposition of pulses of several directions moves slower than the speed of light even in a vacuum (see Bessel ray ) . In optical media with a refractive index , the group velocity is reduced by the factor due to the interaction of the photons with the matter . ${\ displaystyle c}$ ${\ displaystyle n> 1}$${\ displaystyle n}$

Generation and detection

Photons can be generated in many ways, in particular through transitions ("quantum leaps") of electrons between different states (e.g. different atomic or molecular orbitals or energy bands in a solid ). Photons can also in nuclear transitions, particle antiparticle -Vernichtungsreaktionen ( annihilation ), or by any fluctuations are generated in an electromagnetic field.

Photomultipliers , photoconductors or photodiodes , among other things , can be used to detect photons . CCDs , vidicons , PSDs , quadrant diodes or photo plates and films are used for the spatially resolving detection of photons. In the IR range also are bolometers used. Photons in the gamma ray range can be detected individually by Geiger counters . Photomultipliers and avalanche photodiodes can also be used for single photon detection in the optical range, whereby photomultipliers generally have the lower dark counting rate, but avalanche photodiodes can still be used with lower photon energies up to the IR range.

Dimensions

The photon is an elementary particle with mass . In addition to experimental measurements that prove this fact very well (see below), this is theoretically justified by the fact that a mass term of the photon would violate the gauge invariance of the Lagrangian within the framework of quantum electrodynamics. In contrast to other particles, the photon does not experience a change in mass due to interaction with vacuum fluctuations . ${\ displaystyle m = 0}$

A physical system at rest experiences an increase in mass because of the equivalence of mass and energy when it picks up a photon of energy . ${\ displaystyle \ Delta m = E / c ^ {2}}$${\ displaystyle E}$

Theoretical formulation

In the context of quantum electrodynamics, the photons are the transmitters of electromagnetic interaction ; the equation of motion of the photons must therefore correspond to the classical Maxwell equations

${\ displaystyle \ partial _ {\ mu} F ^ {\ mu \ nu} = 0}$

obey (in this section only the behavior in a vacuum is considered). The Lagrange density , which leads to the Maxwell equations via the Lagrange formalism , is

${\ displaystyle {\ mathcal {L}} = - {\ frac {1} {4}} F ^ {\ mu \ nu} F _ {\ mu \ nu}}$

without a mass term of the photon of the shape . Such a term is forbidden because it violates the invariance of the Lagrange density under the classical gauge transformations of the electromagnetic field . Even in higher orders of quantum electrodynamic perturbation theory, the mass of the photon remains protected by the gauge symmetry. ${\ displaystyle A _ {\ mu} m _ {\ gamma} ^ {2} A ^ {\ mu}}$

Since the Higgs particle has no electrical charge, the photon does not receive any mass through the Higgs mechanism - in contrast to the other calibration bosons of the electroweak interaction .

Experimental Findings

If the mass of the photon were different from zero, then it would make itself noticeable through different sequences. None of them have yet been observed. The accuracy of the experiments allows the statement that a possible photon mass must in any case be below , that is the most part of the mass of the hydrogen atom. ${\ displaystyle 10 ^ {- 18} \, \ mathrm {eV} \! / \! c ^ {2}}$${\ displaystyle 10 ^ {27}}$

If photons had mass,

• then a Yukawa potential would result for the electrostatic field of a point charge instead of the Coulomb potential , i.e. an additional exponential attenuation factor. The fact that this was not observed in laboratory experiments suggests that a possible mass of the photon cannot be greater than .${\ displaystyle 1 {,} 5 \ cdot 10 ^ {- 9} \, \ mathrm {eV \! / c ^ {2}}}$
• then the field of a magnetic dipole would have a component anti-parallel to the dipole, which is spatially constant in a first approximation and proportional to the assumed mass of the photon. By measuring the earth's magnetic field, the existence of such a contribution can be excluded to such an extent that the possible mass of the photon cannot be higher .${\ displaystyle 2 {,} 3 \ cdot 10 ^ {- 15} \, \ mathrm {eV \! / c ^ {2}}}$
• then changes would result for the magnetic field of a rotating dipole, which in the case of the sun would affect the solar wind up to the distance from Pluto . Such deviations have not yet been proven, which results in the currently (as of 2014) lowest experimental upper limit for a possible photon mass.${\ displaystyle 10 ^ {- 18} \, \ mathrm {eV} \! / \! c ^ {2}}$

The photon with the highest energy to date, more than 100 TeV, was reported by Chinese scientists from a detector field in Tibet in 2019. It probably came from the Crab Nebula.

Gravity field

Photons are also influenced by the gravitational field , which is only correctly described by the general theory of relativity . When flying past a heavy body, they are deflected from their path twice as much as would be expected according to classical physics for a particle moving at the speed of light (see also gravitational time dilation and tests of general relativity ). According to the relativistic description of gravity , the photons, like all bodies not influenced by other forces, follow a geodesic of curved spacetime. Photons themselves belong to the sources of gravitation, as they influence the curvature of space-time with their energy density (see energy-momentum tensor in general relativity ).

Spin

According to Maxwell's equations, circularly polarized EM waves with energy and angular frequency have an angular momentum of the size , i.e. exactly the amount of angular momentum per photon . Photons are spin- 1 particles and therefore bosons . Any number of photons can occupy the same quantum mechanical state, which is implemented in a laser , for example . ${\ displaystyle E}$${\ displaystyle \ omega}$${\ displaystyle E / \ omega}$${\ displaystyle E = \ hbar \ omega}$${\ displaystyle \ hbar}$

While the electron spin is parallel or antiparallel to any given direction, the photon spin can only be oriented parallel or antiparallel to the flight direction , i.e. to its momentum, due to the lack of mass . The helicity of the photons of a circularly polarized wave is therefore a characteristic quantity. If the direction of propagation is reversed by a mirror, or the direction of rotation is reversed, for example by a λ / 2 plate , the helicity changes its sign.

Linearly polarized electromagnetic waves consist of the superposition of right and left polarized photons. A single photon can also be linearly polarized by superimposing two oppositely circularly polarized states . The expected value of the angular momentum along the direction of flight is then zero, but a left or right circularly polarized photon can be found in a linearly polarized photon with a 50% probability each.

Photons in a vacuum

Photons in a state of well-defined momentum move at the speed of light . The dispersion relation , i.e. H. the dependence of the angular frequency of a photon on its circular wave number is linear in a vacuum, because the quantum mechanical relationships apply ${\ displaystyle c = 299 \, 792 \, 458 \; \ mathrm {m / s}}$ ${\ displaystyle \ omega}$ ${\ displaystyle k}$

${\ displaystyle E = \ hbar \ omega}$

and

${\ displaystyle p = \ hbar k}$

as well as the energy-momentum relation

${\ displaystyle E = pc}$.

Numerical values, as they typically occur in optical spectra, can be determined as follows:

${\ displaystyle E = \ hbar \ omega = (6 {,} 582 \, 119 \, 569 \ ldots \, \ cdot \, 10 ^ {- 16} \, {\ rm {{eVs}) \ cdot \ omega }}}$ ,   E in eV ( electron volts ), ω in s −1 ( angular frequency ), 1 eV corresponds approximately to ω of 1.520 · 10 15  s −1
${\ displaystyle E = h \ cdot \ nu = h \ cdot c / \ lambda = \ left (1 {,} 239 \, 841 \, 984 \ \ mathrm {eV \ mu m} \ right) / \ lambda}$ ,    E in eV (electron volt ), λ in μm ( wavelength ), 1 eV corresponds to about 1.240 μm = 1240 nm

Example: Red light with a wavelength of 620 nm has a photon energy of approximately 2 eV.

Photons in optical media

In an optical medium, photons interact with the material. A photon can be destroyed by absorption . In doing so, its energy changes into other forms of energy, for example into elementary excitations ( quasiparticles ) of the medium such as phonons or excitons . It is also possible that the photon propagates through a medium. It is hindered by a sequence of scattering processes in which particles of the medium are virtually excited. Photon and reaction of the medium together can be described by a quasiparticle, the polariton . These elementary excitations in matter usually have no linear dispersion relation. Their speed of propagation is slower than the speed of light in a vacuum.

In experiments in quantum optics , the speed of propagation of light in a dilute gas of suitably prepared atoms could be reduced to a few meters per second.

Interaction of photons with matter

Photons that hit matter can trigger different processes depending on the energy range. The energy ranges in which they are relevant for various processes are given below:

Web links

Wiktionary: Photon  - explanations of meanings, word origins, synonyms, translations
Commons : Photon  - collection of images, videos and audio files

On the interaction of photons with photons:

Individual evidence

1. Older literature sometimes still distinguishes the outdated concept of a “moving mass” as opposed to a “rest mass”, see also the special section on this.
2. Albert Einstein: About a heuristic point of view concerning the generation and transformation of light . In: Annals of Physics . tape 322 , no. 6 , 1905, pp. 133 ( online [accessed January 24, 2012]).
3. ↑ In 1918 no Nobel Prize in Physics was awarded. At the end of 1919 Johannes Stark received the 1919 Nobel Prize in Physics and Max Planck the 1918 Nobel Prize in Physics .
4. ^ The 1921 Nobel Prize in Physics was not awarded to Albert Einstein until 1922, although the light quantum hypothesis was left out of the reasoning. At the same time, Niels Bohr received the Nobel Prize in Physics for 1922.
5. ^ Paul Dirac: The Quantum Theory of Emission and Absorption of Radiation. In: Proc. Roy. Soc. A114, 1927. (online) .
6. quoted from Paul. Harry Paul : Photons: Experiments and Their Interpretation . Akademie-Verlag, Berlin 1985, ISBN 3-528-06868-X , limited preview in the Google book search.
7. a b Helge Kragh : Photon: New light on an old name . arXiv, February 28, 2014.
8. ^ Gilbert N. Lewis: The Conservation of Photons. In: Nature. 118, 1926, pp. 874-875. doi: 10.1038 / 118874a0 ( online ).
9. ^ A b Alfred Scharff Goldhaber, Martin Nieto: Photon and graviton mass limits . In: Rev. Mod. Phys. tape 82 , 2010, p. 939 , doi : 10.1103 / RevModPhys.82.939 .
10. a b Particle Data Group, accessed May 18, 2015
11. ^ Alfred S. Goldhaber, Michael Nieto: New Geomagnetic Limit on the Mass of the Photon . In: Physical Review Letters . tape 21 , 1968, p. 567 , doi : 10.1103 / PhysRevLett.21.567 ( online [PDF; accessed on March 6, 2020]).
12. What is the mass of a photon? Retrieved August 10, 2011.
13. Amemori et al.: First detection of photons with energy beyond 100 TeV from an astrophysical source , Phys. Rev. Lett., June 13, 2019
14. See e.g. B. pro-physik.de now also with photons via the spin Hall effect
15. CODATA Recommended Values. National Institute of Standards and Technology, accessed July 30, 2019 . Value for in the unit eVs.${\ displaystyle \ hbar}$
16. CODATA Recommended Values. National Institute of Standards and Technology, accessed July 30, 2019 . Value for h in the unit eVs, inserted into the product hc .
17. CODATA Recommended Values. National Institute of Standards and Technology, accessed July 30, 2019 . Value of the speed of light inserted into the product hc .
18. https://www.nature.com/articles/17561 L. Vestergaard Hau, SE Harris, Z. Dutton, CH Behroozi: Light speed reduction to 17 meters per second in an ultracold atomic gas , in Nature Vol. 397 (1999 ), Pp. 594-598
19. SLAC Experiment 144 Home Page
20. Zeit article on the SLAC experiment