Fine-structure constant

# Fine-structure constant

Discussion

Encyclopedia
In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, the fine-structure constant (usually denoted α, the Greek letter alpha
Alpha
Alpha is the first letter of the Greek alphabet. Alpha or ALPHA may also refer to:-Science:*Alpha , the highest ranking individuals in a community of social animals...

) is a fundamental physical constant, namely the coupling constant
Coupling constant
In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. Usually the Lagrangian or the Hamiltonian of a system can be separated into a kinetic part and an interaction part...

characterizing the strength of the electromagnetic interaction. Being a dimensionless quantity
Dimensionless quantity
In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a "pure" number, and as such always has a dimension of 1. Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and...

, it has constant numerical value in all systems of units. Arnold Sommerfeld
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics...

introduced the fine-structure constant in 1916.

The current recommended value of α is

## Definition

Three equivalent definitions of α in terms of other fundamental physical constants are:

where:
• e is the elementary charge
Elementary charge
The elementary charge, usually denoted as e, is the electric charge carried by a single proton, or equivalently, the absolute value of the electric charge carried by a single electron. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called...

;
• ħ = h/2π is the reduced Planck constant
Planck constant
The Planck constant , also called Planck's constant, is a physical constant reflecting the sizes of energy quanta in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory, who discovered it in 1899...

;
• c is the speed of light in vacuum;
• ε0 is the electric constant
Electric constant
The physical constant ε0, commonly called the vacuum permittivity, permittivity of free space or electric constant is an ideal, physical constant, which is the value of the absolute dielectric permittivity of classical vacuum...

or permittivity of free space;
• or µ0 is the magnetic constant or permeability of free space;
• or ke is the Coulomb constant.

In electrostatic cgs units, the unit of electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

, the statcoulomb
Statcoulomb
The statcoulomb or franklin or electrostatic unit of charge is the physical unit for electrical charge used in the centimetre-gram-second system of units and Gaussian units. It is a derived unit given by...

, is defined so that the Coulomb constant, ke, or the permittivity factor
Electric constant
The physical constant ε0, commonly called the vacuum permittivity, permittivity of free space or electric constant is an ideal, physical constant, which is the value of the absolute dielectric permittivity of classical vacuum...

, 4πε0, is 1 and dimensionless. Then the expression of the fine-structure constant becomes the abbreviated

an expression commonly appearing in physics literature.

## Measurement

The 2010 CODATA recommended value of α is
This has a relative standard uncertainty of 0.32 parts per billion

While the value of α can be estimated from the values of the constants appearing in any of its definitions, the theory of quantum electrodynamics
Quantum electrodynamics
Quantum electrodynamics 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 special relativity is achieved...

(QED) provides a way to measure α directly using the quantum Hall effect or the anomalous magnetic moment of the electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

. The theory of QED predicts a relationship between the dimensionless magnetic moment of the electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

(or the "Lande g-factor
Landé g-factor
In physics, the Landé g-factor is a particular example of a g-factor, namely for an electron with both spin and orbital angular momenta. It is named after Alfred Landé, who first described it in 1921....

", g) and the fine structure constant α. The most precise value of α obtained experimentally through the present is based on a new measurement of g using a one-electron so-called "quantum cyclotron" apparatus, together with a calculation via the theory of QED that involved 891 four-loop Feynman diagrams:

This measurement of α has a precision of 0.37 parts per billion. This value and uncertainty are about the same as the latest experimental results.

## Erroneous 2006 recommended value

According to 2006 CODATA, the recommended value for α was 7.2973525376(50) x 10−3 = 1/137.035999679(94). However, after the 2006 CODATA adjustment was completed, an error was discovered in one of the main data inputs. Nevertheless, the 2006 CODATA recommended value was republished in 2008. A revised standard value, taking recent research and adjustments to SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

units into account, was published in June 2011.

## Physical interpretations

The fine structure constant α has several physical interpretations. α is:
• The square of the ratio of the elementary charge
Elementary charge
The elementary charge, usually denoted as e, is the electric charge carried by a single proton, or equivalently, the absolute value of the electric charge carried by a single electron. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called...

to the Planck charge
Planck charge
In physics, the Planck charge , is one of the base units in the system of natural units called Planck units. It is a quantity of electric charge defined in terms of fundamental physical constants.The Planck charge is defined as:...

• The ratio of two energies: (i) the energy needed to overcome the electrostatic repulsion between two electrons a distance of d apart, and (ii) the energy of a single photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

of wavelength (from a modern perspective, of angular wavelength r = d ; see Planck relation):
• The ratio of the velocity of the electron in the Bohr model of the atom to the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

. Hence the square of α is the ratio between the Hartree energy
Hartree energy
The hartree , also known as the Hartree energy, is the atomic unit of energy, named after the British physicist Douglas Hartree. It is defined as...

and the electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

rest mass (511 keV).
• The ratio of three characteristic lengths: the classical electron radius
The classical electron radius, also known as the Lorentz radius or the Thomson scattering length, is based on a classical relativistic model of the electron...

The Bohr radius is a physical constant, approximately equal to the most probable distance between the proton and electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom...

and the Compton wavelength
Compton wavelength
The Compton wavelength is a quantum mechanical property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons...

of the electron :
• In quantum electrodynamics
Quantum electrodynamics
Quantum electrodynamics 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 special relativity is achieved...

, α is the coupling constant
Coupling constant
In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. Usually the Lagrangian or the Hamiltonian of a system can be separated into a kinetic part and an interaction part...

determining the strength of the interaction between electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s and photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s. The theory does not predict its value. Therefore α must be determined experimentally. In fact, α is one of the about 20 empirical parameters in the Standard Model of particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

, whose value is not determined within the Standard Model.
• In the electroweak theory unifying the weak interaction
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...

with electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

, α is absorbed into two other coupling constant
Coupling constant
In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. Usually the Lagrangian or the Hamiltonian of a system can be separated into a kinetic part and an interaction part...

s associated with the electroweak gauge fields
Gauge theory
In physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...

. In this theory, the electromagnetic interaction is treated as a mixture of interactions associated with the electroweak fields. The strength of the electromagnetic interaction varies with the strength of the energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

field.
• Given two hypothetical point particles each of Planck mass and elementary charge, separated by any length, α is the ratio of their electrostatic repulsive force to their gravitational attractive force.
• In the fields of electrical engineering and solid-state physics the ratio of the electromagnetic impedance of free space, 1/(c ε0) = 377 Ω, to the quantum of resistance, h/e2 = 25.8 kΩ, is 2α.

When perturbation theory
Perturbation theory (quantum mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an...

is applied to quantum electrodynamics
Quantum electrodynamics
Quantum electrodynamics 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 special relativity is achieved...

, the resulting perturbative expansions for physical results are expressed as sets of power series in α. Because α is much less than one, higher powers of α are soon unimportant, making the perturbation theory extremely practical in this case. On the other hand, the large value of the corresponding factors in quantum chromodynamics
Quantum chromodynamics
In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...

makes calculations involving the strong nuclear force extremely difficult.

According to the theory of the renormalization group
Renormalization group
In theoretical physics, the renormalization group refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales...

, the value of the fine structure constant (the strength of the electromagnetic interaction) grows logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

ically as the energy scale is increased. The observed value of α is associated with the energy scale of the electron mass; the electron is a lower bound for this energy scale because it (and the positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

) is the lightest charged object whose quantum loops can contribute to the running. Therefore 1/137.036 is the value of the fine structure constant at zero energy. Moreover, as the energy scale increases, the strength of the electromagnetic interaction approaches that of the other two fundamental interaction
Fundamental interaction
In particle physics, fundamental interactions are the ways that elementary particles interact with one another...

s, a fact 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
Landau pole
In physics, the Landau pole is the momentum scale at which the coupling constant of a quantum field theory becomes infinite...

. This fact makes quantum electrodynamics inconsistent beyond the perturbative expansions.

## History

Arnold Sommerfeld
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics...

introduced the fine-structure constant in 1916, as part of his theory of the relativistic
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

deviations of atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

ic spectral line
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...

s from the predictions of the Bohr model
Bohr model
In atomic physics, the Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing attraction,...

. The first physical interpretation of the fine-structure constant α 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
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

in the vacuum. Equivalently, it was the quotient between the maximum angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

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
Fine structure
In atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to first order relativistic corrections.The gross structure of line spectra is the line spectra predicted by non-relativistic electrons with no spin. For a hydrogenic atom, the gross structure energy...

of the hydrogenic spectral lines
Lyman series
In physics and chemistry, the Lyman series is the series of transitions and resulting ultraviolet emission lines of the hydrogen atom as an electron goes from n ≥ 2 to n = 1...

.

The fine structure constant so intrigued physicist Wolfgang Pauli
Wolfgang Pauli
Wolfgang Ernst Pauli was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after being nominated by Albert Einstein, he received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or...

that he collaborated with psychologist Carl Jung
Carl Jung
Carl Gustav Jung was a Swiss psychiatrist and the founder of Analytical Psychology. Jung is considered the first modern psychiatrist to view the human psyche as "by nature religious" and make it the focus of exploration. Jung is one of the best known researchers in the field of dream analysis and...

in an extraordinary quest to understand its significance.

## Is the fine structure constant actually constant?

Physicists have pondered for many years whether the fine structure constant is in fact constant, i.e., whether or not its value differs by location and over time. Specifically, a varying α has been proposed as a way of solving problems in cosmology
Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...

and astrophysics
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...

. More recently, theoretical interest in varying constants (not just α) has been motivated by string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

and other such proposals for going beyond the Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

of particle physics. The first experimental tests of this question examined the spectral line
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...

s of distant astronomical objects, and the products of radioactive decay
Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles . The emission is spontaneous, in that the atom decays without any physical interaction with another particle from outside the atom...

in the Oklo
Oklo
Oklo is a region near the town of Franceville, in the Haut-Ogooué province of the Central African state of Gabon. Several natural nuclear fission reactors were discovered in the uranium mines in the region in 1972.-History:...

natural nuclear fission reactor
Natural nuclear fission reactor
A natural nuclear fission reactor is a uranium deposit where analysis of isotope ratios has shown that self-sustaining nuclear chain reactions have occurred. The existence of this phenomenon was discovered in 1972 at Oklo in Gabon, Africa, by French physicist Francis Perrin. The conditions under...

. The findings were consistent with no change.

More recently, improved technology has made it possible to probe the value of α 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
University of New South Wales
The University of New South Wales , is a research-focused university based in Kensington, a suburb in Sydney, New South Wales, Australia...

claimed the first detection of a variation in α. Using the Keck telescopes
Keck telescopes
The W. M. Keck Observatory is a two-telescope astronomical observatory at an elevation of near the summit of Mauna Kea in Hawai'i. The primary mirrors of each of the two telescopes are in diameter, making them the second largest optical telescopes in the world, slightly behind the Gran Telescopio...

and a data set of 128 quasars at redshifts 0.5 < z < 3, Webb et al. found that their spectra were consistent with a slight increase in α over the last 10–12 billion years. Specifically, they found that

In 2004, a smaller study of 23 absorption systems by Chand et al., using the Very Large Telescope
Very Large Telescope
The Very Large Telescope is a telescope operated by the European Southern Observatory on Cerro Paranal in the Atacama Desert of northern Chile. The VLT consists of four individual telescopes, each with a primary mirror 8.2m across, which are generally used separately but can be used together to...

, found no measureable variation:

However, in 2007 simple flaws were identified in the analysis method of Chand et al., discrediting those results. Nevertheless, systematic uncertainties are difficult to quantify and so the Webb et al. results still need to be checked by independent analysis, using quasar spectra from different telescopes.

King et al. have used Markov Chain Monte Carlo
Markov chain Monte Carlo
Markov chain Monte Carlo methods are a class of algorithms for sampling from probability distributions based on constructing a Markov chain that has the desired distribution as its equilibrium distribution. The state of the chain after a large number of steps is then used as a sample of the...

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
Oklo
Oklo is a region near the town of Franceville, in the Haut-Ogooué province of the Central African state of Gabon. Several natural nuclear fission reactors were discovered in the uranium mines in the region in 1972.-History:...

natural nuclear fission reactor
Natural nuclear fission reactor
A natural nuclear fission reactor is a uranium deposit where analysis of isotope ratios has shown that self-sustaining nuclear chain reactions have occurred. The existence of this phenomenon was discovered in 1972 at Oklo in Gabon, Africa, by French physicist Francis Perrin. The conditions under...

in 2004, and concluded that α has changed in the past 2 billion years by 4.5 parts in . 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 radiation
In cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....

. They proposed using this effect to measure the value of α 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 α is strongly dependent upon effective integration time, going as t−1/2. The European LOFAR
LOFAR
LOFAR is the Low Frequency Array for radio astronomy, built by the Netherlands astronomical foundation ASTRON and operated by ASTRON's radio observatory....

A radio telescope is a form of directional radio antenna used in radio astronomy. The same types of antennas are also used in tracking and collecting data from satellites and space probes...

would only be able to constrain Δα/α to about 0.3%. The collecting area required to constrain Δα/α to the current level of quasar constraints is on the order of 100 square kilometers, which is economically impracticable at the present time.

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 variation of α, namely Δα̇/α = 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
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...

-dominated epoch.

In September 2010 researchers from Australia said they had identified a dipole-like structure in the fine structure constant across the observable universe, using data on quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...

s obtained by the Very Large Telescope
Very Large Telescope
The Very Large Telescope is a telescope operated by the European Southern Observatory on Cerro Paranal in the Atacama Desert of northern Chile. The VLT consists of four individual telescopes, each with a primary mirror 8.2m across, which are generally used separately but can be used together to...

, combined with the previous data obtained by Webb at the Keck telescopes
Keck telescopes
The W. M. Keck Observatory is a two-telescope astronomical observatory at an elevation of near the summit of Mauna Kea in Hawai'i. The primary mirrors of each of the two telescopes are in diameter, making them the second largest optical telescopes in the world, slightly behind the Gran Telescopio...

. The fine structure constant appears to have been larger by one part in 100,000 in the direction of the southern hemisphere constellation Ara
Ara (constellation)
Ara is a southern constellation situated between Scorpius and Triangulum Australe. Its name is Latin for "altar". Ara was one of the 48 Greek constellations described by the 2nd century astronomer Ptolemy, and it remains one of the 88 modern constellations defined by the International Astronomical...

, 10 billion years ago. Similarly, the constant appeared to have been smaller by a similar fraction in the northern direction, billions of years ago.

In September and October 2010, after Webb's released research, physicists Chad Orzel
Chad Orzel is an Associate Professor in the Department of Physics and Astronomy at Union College specializing in atomic, molecular, and optical physics. He received his Ph.D. in Chemical Physics from the University of Maryland, College Park, under Nobel Laureate William Daniel Phillips...

and Sean M. Carroll
Sean M. Carroll
Sean Michael Carroll is a senior research associate in the Department of Physics at the California Institute of Technology. He is a theoretical cosmologist specializing in dark energy and general relativity...

suggested different 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 triangles in the plotted graph of the quasars are so well-aligned (triangles, being the 3-omega of the data). On the other hand, 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, as Webb, et al., also concluded in their study.

In October 2011, Webb et al reported
a variation in α dependent on both redshift and spatial direction. They report "the combined data set fits a spatial dipole" with an increase in α with redshift in one direction and a decrease in the other. "[I]ndependent VLT and Keck samples give consistent dipole directions and amplitudes...."

## Anthropic explanation

The anthropic principle
Anthropic principle
In astrophysics and cosmology, the anthropic principle is the philosophical argument that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the argument reason that it explains why the Universe has the age and the fundamental...

is a controversial argument of why the fine-structure constant has the value it does: stable matter, and therefore life and intelligent beings, could not exist if its value were much different. For instance, were α to change by 4%, stellar fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...

would not produce carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

, so that carbon-based life would be impossible. If α were > 0.1, stellar fusion would be impossible and no place in the universe would be warm enough for life as we know it.

## Numerological explanations

As a dimensionless constant which does not seem to be directly related to any mathematical constant
Mathematical constant
A mathematical constant is a special number, usually a real number, that is "significantly interesting in some way". Constants arise in many different areas of mathematics, with constants such as and occurring in such diverse contexts as geometry, number theory and calculus.What it means for a...

, the fine-structure constant has long fascinated physicists. Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...

, one of the originators and early developers of the theory of quantum electrodynamics
Quantum electrodynamics
Quantum electrodynamics 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 special relativity is achieved...

(QED), referred to the fine-structure constant in these terms:
Arthur Eddington argued that the value could be "obtained by pure deduction" and he related it to the Eddington number
Eddington number
In astrophysics, the Eddington number, NEdd, is the number of protons in the observable universe. The name honors the British astrophysicist Arthur Eddington who, in 1938, was the first to propose a calculation of NEdd, and to explain why this number could be important for cosmology and the...

, his estimate of the number of protons in the Universe. This led him in 1929 to conjecture that its reciprocal was precisely the integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

137
137 (number)
137 is the natural number following 136 and preceding 138.-In mathematics :One hundred [and] thirty-seven is the 33rd prime number; the next is 139, with which it comprises a twin prime, and thus 137 is a Chen prime. 137 is an Eisenstein prime with no imaginary part and a real part of the form 3n -...

. Other physicists neither adopted this conjecture nor accepted his arguments but by the 1940s experimental values for 1/α deviated sufficiently from 137 to refute Eddington's argument. Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time. For example, the mathematician James Gilson suggested (earliest archive.org entry dated December 2006 http://web.archive.org/web/20070104030245/http://www.maths.qmul.ac.uk/~jgg/page5.html), that the fine-structure constant has the value:

29 and 137 being the 10th and 33rd prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

s. In 2007, the difference between the CODATA value for α and this theoretical value was about , about 6 times the standard error for the measured value, but as of 2010 CODATA correction the difference became much greater.

## Quotes

• Electric constant
Electric constant
The physical constant ε0, commonly called the vacuum permittivity, permittivity of free space or electric constant is an ideal, physical constant, which is the value of the absolute dielectric permittivity of classical vacuum...

• Gravitational coupling constant
Gravitational coupling constant
In physics, the gravitational coupling constant, αG, is the coupling constant characterizing the gravitational attraction between two charged elementary particles having nonzero mass...

• Planck's constant
• Speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

• Dimensionless Constants and Blackbody Radiation Laws, Electronic Journal of Theoretical Physics, EJTP 8, No. 25(2011)
• "
• "Introduction to the constants for nonexperts," adapted from the Encyclopædia Britannica
Encyclopædia Britannica
The Encyclopædia Britannica , published by Encyclopædia Britannica, Inc., is a general knowledge English-language encyclopaedia that is available in print, as a DVD, and on the Internet. It is written and continuously updated by about 100 full-time editors and more than 4,000 expert...

, 15th ed. Disseminated by the NIST web page.
• CODATA recommended value of α, as of 2006.
• "Fine structure constant," Eric Weisstein's World of Physics website.
• John D. Barrow
John D. Barrow
-External links:****** The Forum-Publications available on the Internet:************...

, and Webb, John K., "Inconstant Constants," Scientific American
Scientific American
Scientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...

, June 2005.