Dimensionless physical constant
Encyclopedia
In physics
, a dimensionless physical constant (sometimes fundamental physical constant) is a universal physical constant
that is dimensionless
- having no unit attached, so its numerical value is the same under all possible systems of units. The best known example is the fine structure constant α, with the approximate value 1/137.036.
However, the term fundamental physical constant has also been used (as by NIST) to refer to universal but dimensional physical constant
s such as the speed of light
c, vacuum permittivity ε0, Planck's constant h, or the gravitational constant
G.
the numerical values of a selected basis set of dimensional physical constants can be normalized to 1 by a choice of units. The basis set consists of time
, length
, mass
, charge
, and temperature
, or an equivalent set. A choice of units is called a system of units. The SI, the international system of units, is such a system of units. As another example, one system of units appears when the numerical values of the speed of light
in a vacuum, the universal gravitational constant, and the constants of Planck, Coulomb, and Boltzmann, are all set to 1; this system of units is called the system of natural units or Planck units
.
In contrast, the numerical values of dimensionless physical constants are independent on the units used. Such constants include:
At the present time, the values of the dimensionless physical constants cannot be calculated; they are determined only by physical measurement
. This is one of the unsolved problems of physics
.
The best known of the dimensionless constants is the fine structure constant:
where e is the elementary charge
, ħ is the reduced Planck's constant, c is the speed of light
in a vacuum, and ε0 is the permittivity of free space. The fine structure constant determines the strength of the electromagnetic force. Note that at low energies, α ≈ 1/137, whereas at the scale of the Z boson, about 90 GeV
, one measures α ≈ 1/127. There is no accepted theory explaining the value of α.
The analog of the fine structure constant for gravitation
is the gravitational coupling constant
. This constant requires the arbitrary choice of a pair of objects having mass. The electron and proton are natural choices because they are stable, and their properties are well measured and well understood. If αG is calculated from two protons, its value is ≈10−38.
The list of dimensionless physical constants increases in length whenever experiments measure new relationships between physical phenomena. The list of fundamental dimensionless constants, however, decreases when advances in physics
show how some previously known constant can be computed in terms of others. The reduction of chemistry to physics was a big step in this direction, since the properties of atoms and molecules can now be calculated from the Standard Model
. A long-sought goal of theoretical physics is to find first principles from which all of the fundamental dimensionless constants can be calculated and compared to the measured values. A successful "Theory of Everything
" would allow such a calculation, but so far, this goal has remained elusive.
of particle physics
from the 1970s contained 19 fundamental dimensionless constants describing the mass
es of the particles and the strengths of the electroweak and strong forces. In the 1990s, neutrino
s were discovered to have nonzero mass, and a quantity called the theta angle was found to be indistinguishable from zero.
The complete standard model
requires 25 fundamental dimensionless constants (Baez, 2002). Their numerical values are, at present, not understood. These 25 constants are:
One constant is required for cosmology
:
Thus, currently there are 26 known fundamental dimensionless physical constants. However, this number may not be the final one. First, one of the mentioned constants, the Higgs boson mass, is unknown, as the Higgs boson has not yet been discovered. Secondly, if neutrinos turn out to be Majorana fermion
s, the Maki-Nakagawa-Sakata matrix has two additional parameters. Finally, if dark matter
is discovered, or if the description of dark energy
requires more than the cosmological constant
, further fundamental constants will be needed.
, cosmology
, quantum physics, teleology
, and the anthropic principle
in the fine structure constant, the proton-to-electron mass ratio
(which they, along with Barrow (2002), call β), and the coupling constant
s for the strong force and gravitation
.
, in his book Just Six Numbers, mulls over the following six dimensionless constants, whose values he deems fundamental to present-day physical theory and the known structure of the universe:
N and ε govern the fundamental interaction
s of physics. The other constants (D excepted) govern the size, age
, and expansion of the universe. These five constants must be estimated empirically. D, on the other hand, is necessarily a nonzero natural number and cannot be measured. Hence most physicists would not deem it a dimensionless physical constant of the sort discussed in this entry. There are also compelling physical and mathematical reasons why D = 3.
Any plausible fundamental physical theory must be consistent with these six constants, and must either derive their values from the mathematics of the theory, or accept their values as empirical.
The mathematician Simon Plouffe
has made an extensive search of computer databases of mathematical formulae, seeking formulae for the mass ratios of the fundamental particles. However, such studies of fundamental constants often drift into numerology
.
One well-known example of numerology is by the astrophysicist Arthur Eddington. He set out alleged mathematical reasons why the reciprocal of the fine structure constant had to be exactly 136. When its value was discovered to be closer to 137, he changed his argument to match that value. Experiments have since shown that Eddington was wrong; to six significant digits, the reciprocal of the fine-structure constant is 137.036.
Do the fundamental constants vary?
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...
, a dimensionless physical constant (sometimes fundamental physical constant) is a universal physical constant
Physical constant
A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.There are many physical constants in...
that is dimensionless
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...
- having no unit attached, so its numerical value is the same under all possible systems of units. The best known example is the fine structure constant α, with the approximate value 1/137.036.
However, the term fundamental physical constant has also been used (as by NIST) to refer to universal but dimensional physical constant
Physical constant
A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.There are many physical constants in...
s such as 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...
c, vacuum permittivity ε0, Planck's constant h, or the gravitational constant
Gravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
G.
Introduction
The numerical values of dimensional physical constants depends on the units used. The reason is thatthe numerical values of a selected basis set of dimensional physical constants can be normalized to 1 by a choice of units. The basis set consists of time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
, length
Length
In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...
, mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
, 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...
, and temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
, or an equivalent set. A choice of units is called a system of units. The SI, the international system of units, is such a system of units. As another example, one system of units appears when the numerical values of 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 a vacuum, the universal gravitational constant, and the constants of Planck, Coulomb, and Boltzmann, are all set to 1; this system of units is called the system of natural units or Planck units
Planck units
In physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units elegantly simplify...
.
In contrast, the numerical values of dimensionless physical constants are independent on the units used. Such constants include:
- α, the fine structure constant, the coupling constantCoupling constantIn 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...
for the electromagnetic interaction (≈1/137.036); - μ or β, the proton-to-electron mass ratioProton-to-electron mass ratioIn physics, the proton-to-electron mass ratio, μ or β, is simply the rest mass of the proton divided by that of the electron...
, the rest mass of the protonProtonThe proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
divided by that of the electronElectronThe 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...
(≈1836.15). More generally, the rest masses of all elementary particles relative to that of the electronElectronThe 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...
; - αs, the coupling constantCoupling constantIn 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...
for the strong force (≈1); - αG, the gravitational coupling constantGravitational coupling constantIn physics, the gravitational coupling constant, αG, is the coupling constant characterizing the gravitational attraction between two charged elementary particles having nonzero mass...
.
At the present time, the values of the dimensionless physical constants cannot be calculated; they are determined only by physical measurement
Metrology
Metrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...
. This is one of the unsolved problems of physics
Unsolved problems in physics
This is a list of some of the major unsolved problems in physics. Some of these problems are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result...
.
The best known of the dimensionless constants is the fine structure constant:
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 is the reduced Planck's constant, c is 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 a vacuum, and ε0 is the permittivity of free space. The fine structure constant determines the strength of the electromagnetic force. Note that at low energies, α ≈ 1/137, whereas at the scale of the Z boson, about 90 GeV
GEV
GEV or GeV may stand for:*GeV or gigaelectronvolt, a unit of energy equal to billion electron volts*GEV or Grid Enabled Vehicle that is fully or partially powered by the electric grid, see plug-in electric vehicle...
, one measures α ≈ 1/127. There is no accepted theory explaining the value of α.
The analog of the fine structure constant for gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
is the 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...
. This constant requires the arbitrary choice of a pair of objects having mass. The electron and proton are natural choices because they are stable, and their properties are well measured and well understood. If αG is calculated from two protons, its value is ≈10−38.
The list of dimensionless physical constants increases in length whenever experiments measure new relationships between physical phenomena. The list of fundamental dimensionless constants, however, decreases when advances 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...
show how some previously known constant can be computed in terms of others. The reduction of chemistry to physics was a big step in this direction, since the properties of atoms and molecules can now be calculated from 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...
. A long-sought goal of theoretical physics is to find first principles from which all of the fundamental dimensionless constants can be calculated and compared to the measured values. A successful "Theory of Everything
Theory of everything
A theory of everything is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle....
" would allow such a calculation, but so far, this goal has remained elusive.
Constants in the standard model and in cosmology
The original standard modelStandard 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
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...
from the 1970s contained 19 fundamental dimensionless constants describing the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
es of the particles and the strengths of the electroweak and strong forces. In the 1990s, neutrino
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...
s were discovered to have nonzero mass, and a quantity called the theta angle was found to be indistinguishable from zero.
The complete 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...
requires 25 fundamental dimensionless constants (Baez, 2002). Their numerical values are, at present, not understood. These 25 constants are:
- the fine structure constant;
- the strong coupling constantCoupling constantIn 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...
; - the massMassMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
es of the fundamental particles (relative to the Planck mass), namely the six quarkQuarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s, the six leptonLeptonA lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
s, the Higgs bosonHiggs bosonThe Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
, the W boson, and the Z boson; - four parameters of the CKM matrix, describing how quarkQuarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s oscillate between different forms; - four parameters of the Maki-Nakagawa-Sakata matrix, which does the same thing for neutrinoNeutrinoA neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...
s.
One constant is required for 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...
:
- the cosmological constantCosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
(in terms of Planck unitsPlanck unitsIn physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units elegantly simplify...
) of Einstein's equations for general relativityGeneral relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
.
Thus, currently there are 26 known fundamental dimensionless physical constants. However, this number may not be the final one. First, one of the mentioned constants, the Higgs boson mass, is unknown, as the Higgs boson has not yet been discovered. Secondly, if neutrinos turn out to be Majorana fermion
Majorana fermion
In physics, a Majorana fermion is a fermion which is its own anti-particle. The term is used in opposition to Dirac fermion, which describes particles that differ from their antiparticles...
s, the Maki-Nakagawa-Sakata matrix has two additional parameters. Finally, if dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
is discovered, or if the description of 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...
requires more than the cosmological constant
Cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
, further fundamental constants will be needed.
Barrow and Tipler
Barrow and Tipler (1986) anchor their broad-ranging discussion of astrophysicsAstrophysics
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...
, 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...
, quantum physics, teleology
Teleology
A teleology is any philosophical account which holds that final causes exist in nature, meaning that design and purpose analogous to that found in human actions are inherent also in the rest of nature. The word comes from the Greek τέλος, telos; root: τελε-, "end, purpose...
, and 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...
in the fine structure constant, the proton-to-electron mass ratio
Proton-to-electron mass ratio
In physics, the proton-to-electron mass ratio, μ or β, is simply the rest mass of the proton divided by that of the electron...
(which they, along with Barrow (2002), call β), and 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...
s for the strong force and gravitation
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...
.
Martin Rees's Six Numbers
Martin ReesMartin Rees, Baron Rees of Ludlow
Martin John Rees, Baron Rees of Ludlow, OM, FRS is a British cosmologist and astrophysicist. He has been Astronomer Royal since 1995 and Master of Trinity College, Cambridge since 2004...
, in his book Just Six Numbers, mulls over the following six dimensionless constants, whose values he deems fundamental to present-day physical theory and the known structure of the universe:
- N≈1036: the ratio of the fine structure constant (the dimensionless coupling constantCoupling constantIn 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...
for electromagnetismElectromagnetismElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
) to the gravitational coupling constantGravitational coupling constantIn physics, the gravitational coupling constant, αG, is the coupling constant characterizing the gravitational attraction between two charged elementary particles having nonzero mass...
, the latter defined using two protonProtonThe proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
s. In Barrow and Tipler (1986) and elsewhere in Wikipedia, this ratio is denoted α/αG. N governs the relative importance of gravity and electrostatic attraction/repulsion in explaining the properties of baryonic matter; - ε≈0.007: The fraction of the mass of four protonProtonThe proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
s that is released as energy when fusedNuclear fusionNuclear 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...
into a heliumHeliumHelium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...
nucleus. ε governs the energy output of stars, and is determined by the coupling constantCoupling constantIn 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...
for the strong force; - Ω ≈ 0.3: the ratio of the actual density of the universe to the critical (minimum) density required for the universeUniverseThe Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
to eventually collapse under its gravity. Ω determines the ultimate fate of the universeUltimate fate of the universeThe ultimate fate of the universe is a topic in physical cosmology. Many possible fates are predicted by rival scientific theories, including futures of both finite and infinite duration....
. If Ω>1, the universe will experience a Big CrunchBig CrunchIn physical cosmology, the Big Crunch is one possible scenario for the ultimate fate of the universe, in which the metric expansion of space eventually reverses and the universe recollapses, ultimately ending as a black hole singularity.- Overview :...
. If Ω<1, the universe will expand forever; - λ ≈ 0.7: The ratio of the energy density of the universe, due to the cosmological constantCosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
, to the critical density of the universe. Others denote this ratio by
; - Q ≈ 10– 5: The energy required to break up and disperse an instance of the largest known structures in the universe, namely a galactic cluster or superclusterSuperclusterSuperclusters are large groups of smaller galaxy groups and clusters and are among the largest known structures of the cosmos. They are so large that they are not gravitationally bound and, consequently, partake in the Hubble expansion.-Existence:...
, expressed as a fraction of the energy equivalent to the rest mass m of that structure, namely mc2; - D = 3: the number of macroscopic spatial dimensionDimensionIn physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
s.
N and ε govern the fundamental interaction
Fundamental interaction
In particle physics, fundamental interactions are the ways that elementary particles interact with one another...
s of physics. The other constants (D excepted) govern the size, age
Age of the universe
The age of the universe is the time elapsed since the Big Bang posited by the most widely accepted scientific model of cosmology. The best current estimate of the age of the universe is 13.75 ± 0.13 billion years within the Lambda-CDM concordance model...
, and expansion of the universe. These five constants must be estimated empirically. D, on the other hand, is necessarily a nonzero natural number and cannot be measured. Hence most physicists would not deem it a dimensionless physical constant of the sort discussed in this entry. There are also compelling physical and mathematical reasons why D = 3.
Any plausible fundamental physical theory must be consistent with these six constants, and must either derive their values from the mathematics of the theory, or accept their values as empirical.
Variation of the constants
The question whether the fundamental dimensionless constants depend on space and time is being extensively researched. Despite several claims, no confirmed variation of the constants has been detected.Calculation attempts
No formulae for the fundamental physical constants are known to this day.The mathematician Simon Plouffe
Simon Plouffe
Simon Plouffe is a Quebec mathematician born on June 11, 1956 in Saint-Jovite, Quebec. He discovered the formula for the BBP algorithm which permits the computation of the nth binary digit of π, in 1995...
has made an extensive search of computer databases of mathematical formulae, seeking formulae for the mass ratios of the fundamental particles. However, such studies of fundamental constants often drift into numerology
Numerology
Numerology is any study of the purported mystical relationship between a count or measurement and life. It has many systems and traditions and beliefs...
.
One well-known example of numerology is by the astrophysicist Arthur Eddington. He set out alleged mathematical reasons why the reciprocal of the fine structure constant had to be exactly 136. When its value was discovered to be closer to 137, he changed his argument to match that value. Experiments have since shown that Eddington was wrong; to six significant digits, the reciprocal of the fine-structure constant is 137.036.
See also
- Cabibbo–Kobayashi–Maskawa matrix (Cabibbo angle)
- coupling constantCoupling constantIn 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...
- Fine-structure constantFine-structure constantIn physics, the fine-structure constant is a fundamental physical constant, namely the coupling constant characterizing the strength of the electromagnetic interaction. Being a dimensionless quantity, it has constant numerical value in all systems of units...
- gravitational coupling constantGravitational coupling constantIn physics, the gravitational coupling constant, αG, is the coupling constant characterizing the gravitational attraction between two charged elementary particles having nonzero mass...
- Neutrino oscillationNeutrino oscillationNeutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvowhereby a neutrino created with a specific lepton flavor can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates...
- Physical cosmologyPhysical cosmologyPhysical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...
- Standard ModelStandard ModelThe 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...
- Weinberg angleWeinberg angleThe Weinberg angle or weak mixing angle is a parameter in the Weinberg–Salam theory of the electroweak interaction, and is usually denoted as θW...
External articles
General- Fundamental Physical Constants from NIST
- Values of fundamental constants. CODATA, 2002.
- John Baez, 2002, "How Many Fundamental Constants Are There?"
- Plouffe. Simon, 2004, "A search for a mathematical expression for mass ratios using a large database."
- K Xiao, Dimensionless Constants and Blackbody Radiation Laws EJTP 8, No. 25 (2011) 379–388
Do the fundamental constants vary?
- John Bahcall, Charles Steinhardt, and David Schlegel, 2004, "Does the fine-structure constant vary with cosmological epoch?" Astrophys. J. 600: 520.
- John D. BarrowJohn D. Barrow-External links:****** The Forum-Publications available on the Internet:************...
and Webb, J. K., "Inconstant Constants - Do the inner workings of nature change with time?" Scientific American (June 2005). - Michael Duff, 2002 "Comment on time-variation of fundamental constants."
- Marion, H., et al. 2003, "A search for variations of fundamental constants using atomic fountain clocks," Phys.Rev.Lett. 90: 150801.
- Martins, J.A.P. et al., 2004, "WMAP constraints on varying α and the promise of reionization," Phys.Lett. B585: 29-34.
- Olive, K.A., et al., 2002, "Constraints on the variations of the fundamental couplings," Phys.Rev. D66: 045022.
- Uzan, J-P, 2003, "The fundamental constants and their variation: observational status and theoretical motivations," Rev.Mod.Phys. 75: 403.
- Webb, J.K. et al., 2001, "Further evidence for cosmological evolution of the fine-structure constant," Phys. Rev. Lett. 87: 091301.
External links
- Murphy, Michael, Web page at the Swinburne University of TechnologySwinburne University of TechnologySwinburne University of Technology is an Australian public dual sector university based in Melbourne, Victoria. The institution was founded by the Honourable George Swinburne in 1908 and achieved university status in June 1992...
, Australia. - Webb, John K., Web page at the University of New South WalesUniversity of New South WalesThe University of New South Wales , is a research-focused university based in Kensington, a suburb in Sydney, New South Wales, Australia...
, Australia.