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Concept
Dimensionless physical constant
Summary
In physics, a dimensionless physical constant is a physical constant that is dimensionless, i.e. a pure number having no units attached and having a numerical value that is independent of whatever system of units may be used.
In aerodynamics for example, if one considers one particular airfoil, the Reynolds number value of the laminar–turbulent transition is one relevant dimensionless physical constant of the problem. However, it is strictly related to the particular problem: for example, it is related to the airfoil being considered and also to the type of fluid in which it moves.
The term fundamental physical constant is used to refer to some dimensionless constants. Perhaps the best-known example is the fine-structure constant, α, which has an approximate value of .
It has been argued the term fundamental physical constant should be restricted to the dimensionless universal physical constants that currently cannot be derived from any other source; this stricter definition is followed here.
However, the term fundamental physical constant has also been used occasionally to refer to certain universal dimensioned physical constants, such as the speed of light c, vacuum permittivity ε0, Planck constant h, and the gravitational constant G, that appear in the most basic theories of physics. NIST and CODATA sometimes used the term in this less strict manner.
There is no exhaustive list of such constants but it does make sense to ask about the minimal number of fundamental constants necessary to determine a given physical theory. Thus, the Standard Model requires 25 physical constants, about half of them are the masses of fundamental particles (which become "dimensionless" when expressed relative to the Planck mass or, alternatively, as coupling strength with the Higgs field along with the gravitational constant).
Fundamental physical constants cannot be derived and have to be measured.
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