Physical constant

A physical constant is a quantity with a value that is generally believed to be universal and unchanging. In physics, constants appear in mathematical formulations of natural laws, such as Newton's law of gravitation (G) and Maxwell's equations (c, ε₀, μ₀). They are distinguished from mathematical constants like π, which have no physical dimensions.

Constants are essential for defining units and for testing theories. For example, the fine-structure constant α = e²/(4πε₀ħc) is dimensionless and its precise value is crucial in quantum electrodynamics.¹

Physical constants can be classified into two categories: fundamental constants, which are believed to be properties of nature itself (e.g., c, G, ħ), and derived constants, which are combinations of fundamental ones (e.g., the Rydberg constant). Some constants, like the speed of light, are now defined exactly in the SI system, fixing their values by definition.²

There are also constants that are specific to particular systems, such as the standard acceleration due to gravity (g₀ = 9.80665 m/s²), which is a defined value for metrology, not a fundamental constant.

The values of constants are determined through high-precision experiments. The CODATA (Committee on Data for Science and Technology) regularly publishes recommended values based on worldwide measurements. For instance, the Planck constant was measured using Kibble balances and X-ray crystal density methods, leading to its exact definition in 2019.³

Some constants, like the gravitational constant G, are notoriously difficult to measure accurately; its relative uncertainty is about 2.2×10⁻⁵, much larger than for other constants.⁴

In the 2019 revision of the International System of Units (SI), seven defining constants were assigned exact values, including the speed of light c, the Planck constant h, the elementary charge e, and the Boltzmann constant k. This redefinition tied the base units to fundamental constants, making them independent of physical artifacts.²

This change improved the stability and universality of measurements, but it also means that some constants are no longer measured but defined, shifting the focus to the realization of units.

Whether constants are truly constant is a subject of active research. Some theories, such as string theory, suggest that constants may vary over cosmic time or in different regions of the universe. Observations of quasar absorption spectra have placed stringent limits on the variation of the fine-structure constant, showing it changes by less than 10⁻⁵ over the last 10 billion years.⁵

The anthropic principle posits that the values of constants are such that they allow the existence of observers, which has been used to explain the fine-tuning of the universe for life.

Among the lesser-known constants is the von Klitzing constant R_K = h/e², which appears in the quantum Hall effect and is now used to define the ohm. Another is the Josephson constant K_J = 2e/h, which relates frequency to voltage in superconductors and defines the volt.³

The concept of a constant has also been applied to cosmology, such as the cosmological constant Λ, which is associated with dark energy. Its measured value is about 10⁻¹²² in Planck units, an extreme fine-tuning problem known as the cosmological constant problem.

Historically, the idea of constants emerged in the 19th century with the work of scientists like Maxwell, who identified c as a fundamental constant. The term "physical constant" was popularized by Arthur Eddington, who speculated on their numerical relationships.

CODATA

Committee on Data for Science and Technology; provides internationally recommended values for physical constants.

Fine-structure constant

Dimensionless constant α ≈ 1/137 that characterizes the strength of electromagnetic interaction.

Kibble balance

An electromechanical instrument used to measure the Planck constant by comparing electrical and mechanical power.

Anthropic principle

The idea that the universe's observed properties are constrained by the requirement that observers exist.