Physical constant
A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, 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 in vacuum c, the gravitational constant G, the Planck constant h, the electric constant ε0, and the elementary charge e. Physical constants can take many dimensional forms: the speed of light signifies a maximum speed for any object and its dimension is length divided by time; while the proton-to-electron mass ratio, is dimensionless.
The term "fundamental physical constant" is sometimes used to refer to universal-but-dimensioned physical constants such as those mentioned above.[1] Increasingly, however, physicists reserve the expression for the narrower case of dimensionless universal physical constants, such as the fine-structure constant α, which characterizes the strength of the electromagnetic interaction.
Physical constant, as discussed here, should not be confused with empirical constants, which are coefficients or parameters assumed to be constant in a given context without being fundamental.[2] Examples include the characteristic time, characteristic length, or characteristic number (dimensionless) of a given system, or material constants (e.g., Madelung constant, electrical resistivity, and heat capacity) of a particular material or substance.
Characteristics[edit]
Physical constants are parameters in a physical theory that cannot be explained by that theory. This may be due to the apparent fundamental nature of the constant or due to limitations in the theory. Consequently, physical constants must be measured experimentally.[3]: 9
The set of parameters considered physical constants change as physical models change and how fundamental they appear can change. For example, the speed of light was originally considered a property of light, a specific system. The discovery and verification of Maxwell's equations connect the same quantity an entire system, electromagnetism. When the theory of special relativity emerged, the quantity came to be understood as the basis of causality.[3] The speed of light is so fundamental it now defines the international unit of length.
Relationship to units[edit]
Numerical values[edit]
Whereas the physical quantity 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 is defined as having the numerical value of 299792458 when expressed in the SI unit metres per second, and as having the numerical value of 1 when expressed in the natural units 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.
The number of fundamental physical constants depends on the physical theory accepted as "fundamental".
Currently, this is the theory of general relativity 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[3] lists 22 "fundamental constants of our standard model" as follows:
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).[3]
The discovery of variability in any of these constants would be equivalent to the discovery of "new physics".[3]
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 Lévy-Leblond 1977, not all physical constants are of the same importance, with some having a deeper role than others.
Lévy-Leblond 1977 proposed a classification schemes of three types of 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, which was a class A constant (characteristic of light) when it was first measured, but became a class B constant (characteristic of electromagnetic phenomena) with the development of classical electromagnetism, and finally a class C constant with the discovery of special relativity.[5]
Dimensionless physical constants[edit]
Any ratio between physical constants of the same dimensions results in a dimensionless physical constant, for example, the proton-to-electron mass ratio. The fine-structure constant α is the best known dimensionless fundamental physical constant. It is the value of the elementary charge 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, its value and uncertainty as determined at the time was consistent with 1/137. This motivated Arthur Eddington (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.[15] 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.[16]