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In
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which re ...
, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the
electromagnetic interaction In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
between elementary charged particles. It is a dimensionless quantity, independent of the
system of units A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Systems of measuremen ...
used, which is related to the strength of the coupling of an
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fund ...
''e'' with the
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classica ...
, by the formula . Its numerical value is approximately , with a relative uncertainty of The constant was named by
Arnold Sommerfeld Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretical ...
, who introduced it in 1916 Equation 12a, ''"rund 7·" (about ...)'' when extending the
Bohr model In atomic physics, the Bohr model or Rutherford–Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar Syst ...
of the atom. quantified the gap in the fine structure of the spectral lines of the hydrogen atom, which had been measured precisely by
Michelson Michelson may refer to: * Michelson (name), Michelson (surname), people with the given name or surname * 27758 Michelson discovered in 1991 * Michelson (crater) on the moon * Michelson-Gale-Pearson experiment, science * Michelson interferometer, mo ...
and
Morley Morley may refer to: Places England * Morley, Norfolk, a civil parish * Morley, Derbyshire, a civil parish * Morley, Cheshire, a village * Morley, County Durham, a village * Morley, West Yorkshire, a suburban town of Leeds and civil parish ...
in 1887.


Definition

In terms of other fundamental physical constants, may be defined as: \alpha = \frac = \frac , where * is the
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fund ...
(); * is the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
(); * is the reduced Planck constant, * is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
(); * is the electric constant (). Since the
2019 redefinition of the SI base units In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144t ...
, the only quantity in this list that does not have an exact value in SI units is the electric constant.


Alternative systems of units

The electrostatic cgs system sets the
Coulomb constant The Coulomb constant, the electric force constant, or the electrostatic constant (denoted , or ) is a proportionality constant in electrostatics equations. In SI base units it is equal to .Derived from ''k''e = 1/(4''πε''0) – It was named ...
, as commonly found in older physics literature, where the expression of the fine-structure constant becomes \alpha = \frac . A nondimensionalised system commonly used in high energy physics sets \ \varepsilon_0 = c = \hbar = 1\ , where the expressions for the fine-structure constant becomes \alpha = \frac . As such, the fine-structure constant is just a quantity determining (or determined by) the
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fund ...
: in terms of such a natural unit of charge. In the system of Hartree atomic units, which sets , the expression for the fine-structure constant becomes \alpha = \frac .


Measurement

The 2018 CODATA recommended value of is : = . This has a relative standard uncertainty of This value for gives , 3.6 standard deviations away from its old defined value, but with the mean differing from the old value by only 0.54 
parts per billion In science and engineering, the parts-per notation is a set of pseudo-units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they ...
. Historically the value of the reciprocal of the fine-structure constant is often given. The 2018 CODATA recommended value is : = . While the value of can be determined from estimates of the constants that appear in any of its definitions, the theory of
quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
(QED) provides a way to measure directly using the
quantum Hall effect The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance ex ...
or the anomalous magnetic moment of the
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
. Other methods include the A.C. Josephson effect and photon recoil in atom interferometry. There is general agreement for the value of , as measured by these different methods. The preferred methods in 2019 are measurements of electron anomalous magnetic moments and of photon recoil in atom interferometry. The theory of QED predicts a relationship between the dimensionless magnetic moment of the
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
and the fine-structure constant (the magnetic moment of the electron is also referred to as the electron -factor ). The most precise value of obtained experimentally (as of 2012) is based on a measurement of using a one-electron so-called "quantum cyclotron" apparatus, together with a calculation via the theory of QED that involved tenth-order Feynman diagrams: : = . This measurement of has a relative standard uncertainty of . This value and uncertainty are about the same as the latest experimental results. Further refinement of the experimental value was published by the end of 2020, giving the value : = , with a relative accuracy of , which has a significant discrepancy from the previous experimental value.


Physical interpretations

The fine-structure constant, , has several physical interpretations. is: = \frac . , The ratio of the velocity of the electron in the first circular orbit of the Bohr model of the atom, which is , to the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
in vacuum, . This is Sommerfeld's original physical interpretation. Then the square of is the ratio between the Hartree energy ( approximately twice its ionization energy) and the
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
rest energy (511 keV). , \alpha^2 is the ratio of the potential energy of the electron in the first circular orbit of the Bohr model of the atom and the energy m_\mathrm c^2 equivalent to the mass of an electron. Using the Virial theorem in the Bohr model of the atom U_ = 2 U_ which means that U_ = m_\mathrm v_\mathrm^2 = m_\mathrm (\alpha c)^2 = \alpha^2 (m_\mathrm c^2). Essentially this ratio follows from the electron's velocity being v_\mathrm = \alpha c. , The two ratios of three characteristic lengths: the
classical electron radius The classical electron radius is a combination of fundamental physical quantities that define a length scale for problems involving an electron interacting with electromagnetic radiation. It links the classical electrostatic self-interaction energ ...
, the
Compton wavelength The Compton wavelength is a quantum mechanical property of a particle. The Compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the rest energy of that particle (see mass–energy equivalence). It ...
of the electron , and the
Bohr radius The Bohr radius (''a''0) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of a ...
: r_\text = \frac = \alpha^2 a_0 , In
quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
, is directly related to the
coupling constant In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between tw ...
determining the strength of the interaction between
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
s and
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are Massless particle, massless ...
s. The theory does not predict its value. Therefore, must be determined experimentally. In fact, is one of the empirical parameters in the Standard Model of
particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, whose value is not determined within the Standard Model. , In the
electroweak theory In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very diffe ...
unifying the
weak interaction In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interactio ...
with
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
, is absorbed into two other
coupling constant In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between tw ...
s associated with the electroweak gauge fields. In this theory, the
electromagnetic interaction In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
is treated as a mixture of interactions associated with the electroweak fields. The strength of the
electromagnetic interaction In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
varies with the strength of the
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of h ...
field. , In the fields of electrical engineering and solid-state physics, the fine-structure constant is one fourth the product of the characteristic impedance of free space, ~ Z_0 = \mu_0 c = \sqrt , and the
conductance quantum The conductance quantum, denoted by the symbol , is the quantized unit of electrical conductance. It is defined by the elementary charge ''e'' and Planck constant ''h'' as: :G_0 = \frac = It appears when measuring the conductance of a quantum p ...
, G_0 = \frac: \alpha = \tfrac Z_0 G_0\ . The optical conductivity of
graphene Graphene () is an allotrope of carbon consisting of a Single-layer materials, single layer of atoms arranged in a hexagonal lattice nanostructure.
for visible frequencies is theoretically given by  , and as a result its light absorption and transmission properties can be expressed in terms of the fine-structure constant alone. The absorption value for normal-incident light on graphene in vacuum would then be given by or 2.24%, and the transmission by } or 97.75% (experimentally observed to be between 97.6% and 97.8%). The reflection would then be given by }. , The fine-structure constant gives the maximum positive charge of an atomic nucleus that will allow a stable electron-orbit around it within the Bohr model (element feynmanium). For an electron orbiting an atomic nucleus with atomic number the relation is . The Heisenberg uncertainty principle momentum/position uncertainty relationship of such an electron is just . The relativistic limiting value for is , and so the limiting value for is the reciprocal of the fine-structure constant, 137. , The magnetic moment of the electron indicates that the charge is circulating at a radius } with the velocity of light. It generates the radiation energy and has an angular momentum . The field energy of the stationary Coulomb field is } and defines the classical electron radius . These values inserted into the definition of alpha yields . It compares the dynamic structure of the electron with the classical static assumption. , Alpha is related to the probability that an electron will emit or absorb a photon. , Given two hypothetical point particles each of Planck mass and elementary charge, separated by any distance, is the ratio of their electrostatic repulsive force to their gravitational attractive force. , The square of the ratio of the
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fund ...
to the Planck charge \alpha = \left( \frac \right)^2 ~. When perturbation theory is applied to
quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
, the resulting perturbative expansions for physical results are expressed as sets of power series in . Because is much less than one, higher powers of are soon unimportant, making the perturbation theory practical in this case. On the other hand, the large value of the corresponding factors in
quantum chromodynamics In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a ty ...
makes calculations involving the
strong nuclear force The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called t ...
extremely difficult.


Variation with energy scale

In
quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
, the more thorough quantum field theory underlying the electromagnetic coupling, the renormalization group dictates how the strength of the electromagnetic interaction grows
logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 o ...
ically as the relevant energy scale increases. The value of the fine-structure constant is linked to the observed value of this coupling associated with the energy scale of the electron mass: the electron is a lower bound for this energy scale, because it (and the
positron The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. It has an electric charge of +1 '' e'', a spin of 1/2 (the same as the electron), and the same mass as an electron. When a positron collid ...
) is the lightest charged object whose quantum loops can contribute to the running. Therefore, is the asymptotic value of the fine-structure constant at zero energy. At higher energies, such as the scale of the
Z boson In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are , , an ...
, about 90 
GeV GEV may refer to: * ''G.E.V.'' (board game), a tabletop game by Steve Jackson Games * Ashe County Airport, in North Carolina, United States * Gällivare Lapland Airport, in Sweden * Generalized extreme value distribution In probability theory ...
, one instead measures an ''effective'' ≈ 1/127. As the energy scale increases, the strength of the electromagnetic interaction in the Standard Model approaches that of the other two
fundamental interaction In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electr ...
s, a feature important for grand unification theories. If quantum electrodynamics were an exact theory, the fine-structure constant would actually diverge at an energy known as the Landau pole – this fact undermines the consistency of quantum electrodynamics beyond perturbative expansions.


History

Based on the precise measurement of the hydrogen atom spectrum by
Michelson Michelson may refer to: * Michelson (name), Michelson (surname), people with the given name or surname * 27758 Michelson discovered in 1991 * Michelson (crater) on the moon * Michelson-Gale-Pearson experiment, science * Michelson interferometer, mo ...
and
Morley Morley may refer to: Places England * Morley, Norfolk, a civil parish * Morley, Derbyshire, a civil parish * Morley, Cheshire, a village * Morley, County Durham, a village * Morley, West Yorkshire, a suburban town of Leeds and civil parish ...
in 1887, Sommerfeld extended the
Bohr model In atomic physics, the Bohr model or Rutherford–Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar Syst ...
to include elliptical orbits and relativistic dependence of mass on velocity. He introduced a term for the fine-structure constant in 1916. The first physical interpretation of the fine-structure constant was as the ratio of the velocity of the electron in the first circular orbit of the relativistic Bohr atom to the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
in the vacuum. Equivalently, it was the quotient between the minimum
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed sys ...
allowed by relativity for a closed orbit, and the minimum angular momentum allowed for it by quantum mechanics. It appears naturally in Sommerfeld's analysis, and determines the size of the splitting or fine-structure of the hydrogenic spectral lines. This constant was not seen as significant until Paul Dirac's linear relativistic wave equation in 1928, which gave the exact fine structure formula. With the development of
quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
(QED) the significance of has broadened from a spectroscopic phenomenon to a general coupling constant for the electromagnetic field, determining the strength of the interaction between electrons and photons. The term is engraved on the tombstone of one of the pioneers of QED,
Julian Schwinger Julian Seymour Schwinger (; February 12, 1918 – July 16, 1994) was a Nobel Prize winning American theoretical physicist. He is best known for his work on quantum electrodynamics (QED), in particular for developing a relativistically invariant ...
, referring to his calculation of the anomalous magnetic dipole moment.


History of measurements

: The CODATA values in the above table are computed by averaging other measurements; they are not independent experiments.


Potential time-variation

Physicists have pondered whether the fine-structure constant is in fact constant, or whether its value differs by location and over time. A varying has been proposed as a way of solving problems in
cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
and
astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the ...
.
String theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and inte ...
and other proposals for going beyond the Standard Model of particle physics have led to theoretical interest in whether the accepted physical constants (not just ) actually vary. In the experiments below, represents the change in over time, which can be computed by prevnow . If the fine-structure constant really is a constant, then any experiment should show that :\frac ~~ \overset ~~ \frac ~~=~~ 0 ~, or as close to zero as experiment can measure. Any value far away from zero would indicate that does change over time. So far, most experimental data is consistent with being constant.


Past rate of change

The first experimenters to test whether the fine-structure constant might actually vary examined the
spectral line A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to ide ...
s of distant astronomical objects and the products of
radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consid ...
in the Oklo natural nuclear fission reactor. Their findings were consistent with no variation in the fine-structure constant between these two vastly separated locations and times. Improved technology at the dawn of the 21st century made it possible to probe the value of at much larger distances and to a much greater accuracy. In 1999, a team led by John K. Webb of the University of New South Wales claimed the first detection of a variation in . Using the Keck telescopes and a data set of 128 quasars at redshifts , Webb ''et al.'' found that their spectra were consistent with a slight increase in over the last 10–12 billion years. Specifically, they found that :\frac ~~ \overset ~~ \frac ~~=~~ \left(-5.7\pm 1.0 \right) \times 10^ ~. In other words, they measured the value to be somewhere between and . This is a very small value, but the error bars do not actually include zero. This result either indicates that is not constant or that there is experimental error unaccounted for. In 2004, a smaller study of 23 absorption systems by Chand ''et al.'', using the
Very Large Telescope The Very Large Telescope (VLT) is a telescope facility operated by the European Southern Observatory on Cerro Paranal in the Atacama Desert of northern Chile. It consists of four individual telescopes, each with a primary mirror 8.2 m acr ...
, found no measurable variation: : \frac\ =\ \left(-0.6\pm 0.6\right) \times 10^~. However, in 2007 simple flaws were identified in the analysis method of Chand ''et al.'', discrediting those results. King ''et al.'' have used Markov chain Monte Carlo methods to investigate the algorithm used by the UNSW group to determine from the quasar spectra, and have found that the algorithm appears to produce correct uncertainties and maximum likelihood estimates for for particular models. This suggests that the statistical uncertainties and best estimate for stated by Webb ''et al.'' and Murphy ''et al.'' are robust. Lamoreaux and Torgerson analyzed data from the Oklo natural nuclear fission reactor in 2004, and concluded that has changed in the past 2 billion years by 45 parts per billion. They claimed that this finding was "probably accurate to within 20%". Accuracy is dependent on estimates of impurities and temperature in the natural reactor. These conclusions have to be verified. In 2007, Khatri and Wandelt of the University of Illinois at Urbana-Champaign realized that the 21 cm hyperfine transition in neutral hydrogen of the early universe leaves a unique absorption line imprint in the
cosmic microwave background In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spa ...
radiation. They proposed using this effect to measure the value of during the epoch before the formation of the first stars. In principle, this technique provides enough information to measure a variation of 1 part in (4 orders of magnitude better than the current quasar constraints). However, the constraint which can be placed on is strongly dependent upon effective integration time, going as . The European LOFAR radio telescope would only be able to constrain to about 0.3%. The collecting area required to constrain to the current level of quasar constraints is on the order of 100 square kilometers, which is economically impracticable at the present time.


Present rate of change

In 2008, Rosenband ''et al.'' used the frequency ratio of and in single-ion optical atomic clocks to place a very stringent constraint on the present-time temporal variation of , namely = per year. Note that any present day null constraint on the time variation of alpha does not necessarily rule out time variation in the past. Indeed, some theories that predict a variable fine-structure constant also predict that the value of the fine-structure constant should become practically fixed in its value once the universe enters its current
dark energy In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the uni ...
-dominated epoch.


Spatial variation – Australian dipole

In September 2010, researchers from Australia said they had identified a dipole-like structure in the variation of the fine-structure constant across the observable universe. They used data on quasars obtained by the
Very Large Telescope The Very Large Telescope (VLT) is a telescope facility operated by the European Southern Observatory on Cerro Paranal in the Atacama Desert of northern Chile. It consists of four individual telescopes, each with a primary mirror 8.2 m acr ...
, combined with the previous data obtained by Webb at the Keck telescopes. The fine-structure constant appears to have been larger by 1 part in 100,000 in the direction of the southern hemisphere constellation Ara, 10 billion years ago. Similarly, the constant appeared to have been smaller by a similar fraction in the northern direction, 10 billion years ago. In September and October 2010, after Webb ''et al''.'s released research, physicists C. Orzel and S.M. Carroll separately suggested various approaches of how Webb's observations may be wrong. Orzel argues that the study may contain wrong data due to subtle differences in the two telescopes, in which one of the telescopes the data set was slightly high and on the other slightly low, so that they cancel each other out when they overlapped. He finds it suspicious that the sources showing the greatest changes are all observed by one telescope, with the region observed by both telescopes aligning so well with the sources where no effect is observed. Carroll suggested a totally different approach; he looks at the fine-structure constant as a scalar field and claims that if the telescopes are correct and the fine-structure constant varies smoothly over the universe, then the scalar field must have a very small mass. However, previous research has shown that the mass is not likely to be extremely small. Both of these scientists' early criticisms point to the fact that different techniques are needed to confirm or contradict the results, a conclusion Webb, ''et al''., previously stated in their study. In October 2011, Webb ''et al.'' reported a variation in dependent on both redshift and spatial direction. They report "the combined data set fits a spatial dipole" with an increase in with redshift in one direction and a decrease in the other. "Independent VLT and Keck samples give consistent dipole directions and amplitudes ..." As in the earlier article of October 2010 the published map and text (Figure 5) showed calculated dipole axis (−58.0 degrees 17.4 hours) passed through the South Magnetic Pole area with the South Magnetic Pole (−64.4 degrees 15.5 hours) centered in the axis region predicted by Keck observatory data, requiring further analysis as to the cause of observed dipole and location of its axis. In 2020, the team verified their previous results, finding a dipole structure in the strength of the electromagnetic force using the most distant quasar measurements. Observations of the quasar of the universe at only 0.8 billion years old with AI analysis method employed on the Very Large Telescope (VLT) found a spatial variation preferred over a no-variation model at the 3.9\sigma level. Other research disagrees, finding no meaningful variation.


Anthropic explanation

The anthropic principle is an argument about the reason the fine-structure constant has the value it does: stable matter, and therefore life and intelligent beings, could not exist if its value were very different. needs to be between around 1/180 and 1/85 to have proton decay to be slow enough for life to be possible.


Numerological explanations and multiverse theory

As a dimensionless constant which does not seem to be directly related to any
mathematical constant A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Const ...
, the fine-structure constant has long fascinated physicists.
Arthur Eddington Sir Arthur Stanley Eddington (28 December 1882 – 22 November 1944) was an English astronomer, physicist, and mathematician. He was also a philosopher of science and a populariser of science. The Eddington limit, the natural limit to the lumi ...
argued that the value could be "obtained by pure deduction" and he related it to the Eddington number, his estimate of the number of protons in the universe. This led him in 1929 to conjecture that the reciprocal of the fine-structure constant was not approximately but precisely the
integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...
137. By the 1940s experimental values for deviated sufficiently from 137 to refute Eddington's arguments. The fine-structure constant so intrigued physicist Wolfgang Pauli that he collaborated with psychoanalyst
Carl Jung Carl Gustav Jung ( ; ; 26 July 1875 – 6 June 1961) was a Swiss psychiatrist and psychoanalyst who founded analytical psychology. Jung's work has been influential in the fields of psychiatry, anthropology, archaeology, literature, phil ...
in a quest to understand its significance. Similarly, Max Born believed that if the value of differed, the universe would degenerate, and thus that = is a law of nature.
Richard Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfl ...
, one of the originators and early developers of the theory of
quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
(QED), referred to the fine-structure constant in these terms: Conversely, statistician I. J. Good argued that a numerological explanation would only be acceptable if it could be based on a good theory that is not yet known but "exists" in the sense of a
Platonic Ideal The theory of Forms or theory of Ideas is a philosophical theory, fuzzy concept, or world-view, attributed to Plato, that the physical world is not as real or true as timeless, absolute, unchangeable ideas. According to this theory, ideas in th ...
. Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time. However, no numerological explanation has ever been accepted by the physics community. In the early 21st century, multiple physicists, including Stephen Hawking in his book '' A Brief History of Time'', began exploring the idea of a
multiverse The multiverse is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describe them. T ...
, and the fine-structure constant was one of several universal constants that suggested the idea of a fine-tuned universe.


Quotes


See also

* Dimensionless physical constant * Electric constant *
Hyperfine structure In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the n ...
*
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
*
Speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...


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* * (adapted from the ''
Encyclopædia Britannica The ( Latin for "British Encyclopædia") is a general knowledge English-language encyclopaedia. It is published by Encyclopædia Britannica, Inc.; the company has existed since the 18th century, although it has changed ownership various t ...
'', 15th ed. by
NIST The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical s ...
) *
Physicists Nail Down the ‘Magic Number’ That Shapes the Universe
(Natalie Wolchover, ''Quanta magazine,'' December 2, 2020). The value of this constant is given here as 1/137.035999206 (note the difference in the last three digits). It was determined by a team of four physicists led by Saïda Guellati-Khélifa at the Kastler Brossel Laboratory in Paris. * * * * {{cite web , last=Eaves , first=Laurence , author-link=Laurence Eaves , year=2009 , title=The fine structure constant , website=Sixty Symbols , publisher=
Brady Haran Brady John Haran (born 18 June 1976) is an Australian-British independent filmmaker and video journalist who produces educational videos and documentary films for his YouTube channels, the most notable being ''Periodic Videos'' and '' Numbe ...
for the University of Nottingham , url=http://www.sixtysymbols.com/videos/finestructure.htm Dimensionless numbers Electromagnetism Fundamental constants Arnold Sommerfeld