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A physical constant, sometimes fundamental physical constant or universal constant, is a
physical quantity A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For examp ...
that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a
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 ...
, which has a fixed numerical value, but does not directly involve any physical measurement. There are many physical constants in science, some of the most widely recognized being 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 a vacuum ''c'', the gravitational constant ''G'', 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 ...
''h'', the electric constant ''ε''0, and 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 ...
''e''. Physical constants can take many dimensional forms: the speed of light signifies a maximum
speed In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quanti ...
for any object and its
dimension In physics and mathematics, the dimension of a mathematical 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 (1D) because only one coordin ...
is
length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the In ...
divided by
time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, t ...
; while the
fine-structure constant In physics, 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 between ele ...
''α'', which characterizes 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 ...
, is dimensionless. The term ''fundamental physical constant'' is sometimes used to refer to universal-but-dimensioned physical constants such as those mentioned above. Increasingly, however, physicists only use ''fundamental physical constant'' for dimensionless physical constants, such as the fine-structure constant ''α''. Physical constant, as discussed here, should not be confused with other quantities called "constants", which are assumed to be constant in a given context without being fundamental, such as the " time constant" characteristic of a given system, or material constants (e.g., Madelung constant,
electrical resistivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allow ...
, and
heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capaci ...
). Since May 2019, all of the
SI base unit The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which al ...
s have been defined in terms of physical constants. As a result, five constants:
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 f ...
in vacuum, ''c''; 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 ...
, ''h''; 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 ...
, ''e''; the
Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining c ...
, ''N''A; and the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas cons ...
, ''k''B, have known exact numerical values when expressed in SI units. The first three of these constants are fundamental constants, whereas ''N''A and ''k''B are of a technical nature only: they do not describe any property of the universe, but instead only give a proportionality factor for defining the units used with large numbers of atomic-scale entities.

# Choice of units

Whereas the
physical quantity A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For examp ...
indicated by a physical constant does not depend on the unit system used to express the quantity, the numerical values of dimensional physical constants do depend on choice of unit system. The term "physical constant" refers to the physical quantity, and not to the numerical value within any given system of units. For example, 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 defined as having the numerical value of when expressed in the
SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
metres per second, and as having the numerical value of 1 when expressed in the
natural units In physics, natural units are physical units of measurement in which only universal physical constants are used as defining constants, such that each of these constants acts as a coherent unit of a quantity. For example, the elementary charge ...
Planck length per Planck time. While its numerical value can be defined at will by the choice of units, the speed of light itself is a single physical constant. Any
ratio In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
between physical constants of the same dimensions results in a dimensionless physical constant, for example, the
proton-to-electron mass ratio In physics, the proton-to-electron mass ratio, ''μ'' or ''β'', is the rest mass of the proton (a baryon found in atoms) divided by that of the electron (a lepton found in atoms), a dimensionless quantity, namely: :''μ'' = The number in paren ...
. Any relation between physical quantities can be expressed as a relation between dimensionless ratios via a process known as
nondimensionalisation Nondimensionalization is the partial or full removal of physical dimensions from an equation involving physical quantities by a suitable substitution of variables. This technique can simplify and parameterize problems where measured units are ...
. The term of "fundamental physical constant" is reserved for physical quantities which, according to the current state of knowledge, are regarded as immutable and as non-derivable from more fundamental principles. Notable examples are the speed of light ''c'', and the gravitational constant ''G''. The
fine-structure constant In physics, 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 between ele ...
''α'' is the best known dimensionless fundamental physical constant. It is the value 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 ...
squared expressed in Planck units. This value has become a standard example when discussing the derivability or non-derivability of physical constants. Introduced 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 ...
, its value as determined at the time was consistent with 1/137. This motivated
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 ...
(1929) to construct an argument why its value might be 1/137 precisely, which related to the Eddington number, his estimate of the number of protons in the Universe. By the 1940s, it became clear that the value of the fine-structure constant deviates significantly from the precise value of 1/137, refuting Eddington's argument. With the development of
quantum chemistry Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contribution ...
in the 20th century, however, a vast number of previously inexplicable dimensionless physical constants ''were'' successfully computed from theory. In light of that, some theoretical physicists still hope for continued progress in explaining the values of other dimensionless physical constants. It is known that the Universe would be very different if these constants took values significantly different from those we observe. For example, a few percent change in the value of the fine structure constant would be enough to eliminate stars like our Sun. This has prompted attempts at anthropic explanations of the values of some of the dimensionless fundamental physical constants.

## Natural units

It is possible to combine dimensional universal physical constants to define fixed quantities of any desired dimension, and this property has been used to construct various systems of natural units of measurement. Depending on the choice and arrangement of constants used, the resulting natural units may be convenient to an area of study. For example, Planck units, constructed from ''c'', ''G'', ''ħ'', and ''k''B give conveniently sized measurement units for use in studies of
quantum gravity Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the ...
, and Hartree atomic units, constructed from ''ħ'', ''m''e, ''e'' and 4''πε''0 give convenient units in
atomic physics Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...
. The choice of constants used leads to widely varying quantities.

# Number of fundamental constants

The number of fundamental physical constants depends on the physical theory accepted as "fundamental". Currently, this is the theory of
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physic ...
for gravitation and the Standard Model for electromagnetic, weak and strong nuclear interactions and the matter fields. Between them, these theories account for a total of 19 independent fundamental constants. There is, however, no single "correct" way of enumerating them, as it is a matter of arbitrary choice which quantities are considered "fundamental" and which as "derived". Uzan (2011) lists 22 "unknown constants" in the fundamental theories, which give rise to 19 "unknown dimensionless parameters", as follows: *the gravitational constant ''G'', *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 ...
''c'', *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 ...
''h'', *the 9 Yukawa couplings for the quarks and leptons (equivalent to specifying the rest mass of these elementary particles), *2 parameters of the Higgs field potential, *4 parameters for the quark mixing matrix, *3 coupling constants for the
gauge group In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie grou ...
s SU(3) × SU(2) × U(1) (or equivalently, two coupling constants and the Weinberg angle), *a phase for the
QCD vacuum 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 typ ...
. The number of 19 independent fundamental physical constants is subject to change under possible extensions of the Standard Model, notably by the introduction of neutrino mass (equivalent to seven additional constants, i.e. 3 Yukawa couplings and 4 lepton mixing parameters). The discovery of variability in any of these constants would be equivalent to the discovery of " new physics". The question as to which constants are "fundamental" is neither straightforward nor meaningless, but a question of interpretation of the physical theory regarded as fundamental; as pointed out by , not all physical constants are of the same importance, with some having a deeper role than others. proposed a classification schemes of three types of constants: *A: physical properties of particular objects *B: characteristic of a class of physical phenomena *C: universal constants The same physical constant may move from one category to another as the understanding of its role deepens; this has notably happened 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 ...
, which was a class A constant (characteristic of
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 t ...
) when it was first measured, but became a class B constant (characteristic of electromagnetic phenomena) with the development of
classical electromagnetism Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model; It is, therefore, a classical ...
, and finally a class C constant with the discovery of
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The law ...
.

# Tests on time-independence

By definition, fundamental physical constants are subject to
measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared ...
, so that their being constant (independent on both the time and position of the performance of the measurement) is necessarily an experimental result and subject to verification.
Paul Dirac Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. He was the Lucasian Professor of Mathematics at the Unive ...
in 1937 speculated that physical constants such as the gravitational constant or the
fine-structure constant In physics, 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 between ele ...
might be subject to change over time in proportion of the
age of the universe In physical cosmology, the age of the universe is the time elapsed since the Big Bang. Astronomers have derived two different measurements of the age of the universe: a measurement based on direct observations of an early state of the universe ...
. Experiments can in principle only put an upper bound on the relative change per year. For the fine-structure constant, this upper bound is comparatively low, at roughly 10−17 per year (as of 2008). The gravitational constant is much more difficult to measure with precision, and conflicting measurements in the 2000s have inspired the controversial suggestions of a periodic variation of its value in a 2015 paper. However, while its value is not known to great precision, the possibility of observing type Ia supernovae which happened in the universe's remote past, paired with the assumption that the physics involved in these events is universal, allows for an upper bound of less than 10−10 per year for the gravitational constant over the last nine billion years. Similarly, an upper bound of the change in the
proton-to-electron mass ratio In physics, the proton-to-electron mass ratio, ''μ'' or ''β'', is the rest mass of the proton (a baryon found in atoms) divided by that of the electron (a lepton found in atoms), a dimensionless quantity, namely: :''μ'' = The number in paren ...
has been placed at 10−7 over a period of 7 billion years (or 10−16 per year) in a 2012 study based on the observation of
methanol Methanol (also called methyl alcohol and wood spirit, amongst other names) is an organic chemical and the simplest aliphatic alcohol, with the formula C H3 O H (a methyl group linked to a hydroxyl group, often abbreviated as MeOH). It is ...
in a distant galaxy. It is problematic to discuss the proposed rate of change (or lack thereof) of a single ''dimensional'' physical constant in isolation. The reason for this is that the choice of units is arbitrary, making the question of whether a constant is undergoing change an artefact of the choice (and definition) of the units. For example, in
SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
, the speed of light was given a defined value in 1983. Thus, it was meaningful to experimentally measure the speed of light in SI units prior to 1983, but it is not so now. Similarly, with effect from May 2019, the Planck constant has a defined value, such that all
SI base units The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which al ...
are now defined in terms of fundamental physical constants. With this change, the
international prototype of the kilogram The International Prototype of the Kilogram (referred to by metrologists as the IPK or Le Grand K; sometimes called the '' ur-kilogram,'' or ''urkilogram,'' particularly by German-language authors writing in English) is an object that was used t ...
is being retired as the last physical object used in the definition of any SI unit. Tests on the immutability of physical constants look at ''dimensionless'' quantities, i.e. ratios between quantities of like dimensions, in order to escape this problem. Changes in physical constants are not meaningful if they result in an ''observationally indistinguishable'' universe. For example, a "change" in the speed of light ''c'' would be meaningless if accompanied by a corresponding change in the elementary charge ''e'' so that the ratio (the fine-structure constant) remained unchanged.

# Fine-tuned universe

Some physicists have explored the notion that if the dimensionless physical constants had sufficiently different values, our Universe would be so radically different that intelligent life would probably not have emerged, and that our Universe therefore seems to be fine-tuned for intelligent life. However, the phase space of the possible constants and their values is unknowable, so any conclusions drawn from such arguments are unsupported. The anthropic principle states a logical truism: the fact of our existence as intelligent beings who can measure physical constants requires those constants to be such that beings like us can exist. There are a variety of interpretations of the constants' values, including that of a divine creator (the apparent fine-tuning is actual and intentional), or that ours is one universe of many in 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 ...
(e.g. the
many-worlds interpretation The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wave function collapse. This implies that all possible outcomes of quantum m ...
of
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
), or even that, if information is an innate property of the universe and logically inseparable from consciousness, a universe without the capacity for conscious beings cannot exist. The fundamental constants and quantities of nature have been discovered to be fine-tuned to such an extraordinarily narrow range that if it were not, the origin and evolution of conscious life in the universe would not be permitted.

# Table of physical constants

The table below lists some frequently used constants and their CODATA recommended values. For a more extended list, refer to '' List of physical constants''.

*
List of common physics notations This is a list of common physical constants and variables, and their notations. Note that bold text indicates that the quantity is a vector. Latin characters Greek characters Other characters See also * List of letters used in mathema ...

* * .