Fundamental Physical ConstantsEdit

Fundamental physical constants are the numerical values that appear in the laws of physics and connect different physical quantities across scales—from the tiniest subatomic processes to the dynamics of stars and galaxies. They serve as the fixed scaffolding upon which theories are built and predictions are tested. While some constants are tied to the units we use to measure quantities, others are dimensionless and carry a sense of universality that transcends human conventions. The study of these constants spans metrology, theory, and experimentation, and it underpins technologies ranging from spectroscopy to GPS.

In modern physics, constants fall into two broad classes. Dimensional constants, such as the speed of light in vacuum or Planck’s constant, acquire numerical values only when expressed in a chosen system of units. Dimensionless constants, such as the fine-structure constant, have no units and retain the same numerical value across unit systems. Dimensionless constants are often viewed as truly "fundamental" in the sense that their values are intrinsic to the laws of nature rather than to human measurement conventions.

The values and even the existence of certain constants are topics of ongoing investigation and debate. While the overwhelming majority of physicists treat the constants as fixed, some lines of inquiry explore whether their values might vary over cosmological timescales or in different regions of space. Experimental and observational efforts—ranging from precision spectroscopy of distant quasars to atomic clock comparisons—have placed stringent bounds on any such variation. In parallel, the precise measurement and codification of constants guide the ongoing refinement of the international system of units, ensuring that the constants reflect the most stable and reproducible reference points available.

Dimensional versus dimensionless constants

Most equations in physics involve a mix of quantities with units and pure numbers. The numerical value of a dimensional constant depends on the unit system used. For example, the speed of light in vacuum, often denoted c, is a dimensional constant with units of meters per second in the common metric system. Since 1983, the meter has been defined in terms of the speed of light: one meter is the distance light travels in vacuum in 1/299,792,458 of a second, effectively making c an exact and defined quantity SI base units and Speed of light.

In contrast, a dimensionless constant has no units and expresses a pure ratio or fundamental proportion. The fine-structure constant α ≈ 1/137.035999... is a quintessential example; it characterizes the strength of electromagnetic interactions independent of any measurement system. Because α is dimensionless, its numerical value is a property of the theory itself rather than of how we choose to measure length, time, or mass Fine-structure constant.

Notable constants

A representative sample of constants that appear across physical theories and experimental practice includes both dimensional and dimensionless items. Values below reflect the consensus codified in the latest CODATA recommendations, which are periodically updated as measurements improve. Where relevant, the values have been fixed or defined by recent updates to the International System of Units (SI).

Speed of light in vacuum, c: exactly 299,792,458 meters per second. The meter is defined by this constant, making c an exact quantity in SI. See Speed of light and SI base units.
Planck constant, h: approximately 6.62607015×10^-34 joule seconds. In the current SI, h is fixed by definition, tying mass, energy, and frequency together in quantum relations; the reduced Planck constant ħ = h/(2π) ≈ 1.0545718×10^-34 J·s Planck constant.
Elementary charge, e: exactly 1.602176634×10^-19 coulomb. The elementary charge is fixed in the SI redefinition, linking electrical current to fundamental charge. See Elementary charge.
Boltzmann constant, k_B: exactly 1.380649×10^-23 joules per kelvin. This fixes the relationship between temperature and energy, and it is central to statistical mechanics and thermodynamics. See Boltzmann constant and Kelvin.
Avogadro constant, N_A: exactly 6.02214076×10^23 per mole. This fixes the number of constituent particles per mole and underpins the mole as a unit of amount of substance. See Avogadro constant and SI base units.
Fine-structure constant, α: approximately 1/137.035999... This dimensionless quantity controls the strength of electromagnetic interactions and features prominently in quantum electrodynamics. See Fine-structure constant.
Gravitational constant, G: approximately 6.67430×10^-11 m^3 kg^-1 s^-2. G sets the strength of gravity in Newton’s law and general relativity, though it is known with relatively larger experimental uncertainty compared with many other constants. See Gravitational constant.
Electron mass, m_e: about 9.10938356×10^-31 kilograms. Electron and proton masses set the scale for atomic and molecular structure; these are measured quantities that feed into many theoretical predictions. See Electron mass.
Proton mass, m_p: about 1.67262192369×10^-27 kilograms. The proton mass sets the scale of atomic nuclei alongside the neutron mass. See Proton mass.
Rydberg constant, R∞: approximately 10,973,731.568160 cm^-1. This combination of fundamental constants governs the wavelengths of spectral lines in hydrogen-like systems; it is central to precision spectroscopy. See Rydberg constant.
Planck units: a system of natural units built from G, c, and ħ, defining scales for length, mass, time, etc., in terms of fundamental constants. See Planck units.
SI base units: the seven base units (meter, kilogram, second, ampere, kelvin, mole, candela) whose definitions are increasingly tied to fixed numerical values of fundamental constants. See SI base units.

In addition to these, many theories include other constants such as particle masses, coupling constants of the weak and strong interactions, mixing angles, and more. The values of these quantities are cataloged in CODATA’s recommended constants, which provide the most precise and widely accepted figures for scientific work. See CODATA.

SI redefinition and the role of measurement

A major development in the modern era is the redefinition of SI base units in terms of fixed numerical values of fundamental constants. In 2019, the international system shifted to defining several base units by fixing h, e, k_B, and N_A, among others. As a result, many constants become exact by definition rather than measured quantities; their numerical values are set by convention to ensure consistency and reproducibility across laboratories worldwide. This shift reflects a broader trend in metrology: anchoring units to invariant properties of nature rather than relying solely on physical artifacts or artifact-based methods. See SI base units and Planck constant.

Such changes have practical consequences. For instance, basing the meter on c and the second ensures that timekeeping and length measurements are tied to the most fundamental temporal and spatial scales. The impact extends to technologies that demand precise timing and dimensioning, such as satellite navigation, spectroscopy, semiconductor fabrication, and fundamental tests of physics. See Speed of light and Atomic clock.

Variation and debates

A topic of ongoing discussion concerns whether any fundamental constants might vary over time or space. The prevailing view is that, within current observational limits, the constants are constant to a very high degree of precision. Nonetheless, some theoretical frameworks beyond the Standard Model of particle physics allow, in principle, slow drifts or environmental dependencies of certain dimensionless constants. The most scrutinized candidate is the fine-structure constant α, with observational programs examining whether α has different values in distant parts of the cosmos. Results from quasar spectroscopy, microwave background studies, and other probes have yielded tight constraints but not conclusive proof of variation; the interpretation often hinges on systematic uncertainties and model assumptions. See Fine-structure constant and Oklo for historical and empirical context.

Laboratory tests using atomic clocks and precision spectroscopy have placed increasingly stringent limits on temporal drift in α and other dimensionless combinations. In this sense, the constants appear remarkably stable, which in turn supports the idea that the laws of physics possess a deep and robust universality. See Atomic clock and Oklo.

The debate is not about whether constants exist in equations, but about whether their numerical values could shift in regimes not yet explored. Critics sometimes argue that searching for tiny drifts risks overinterpreting noise or systematic effects; supporters contend that even small drifts would herald new physics and necessitate revisions to our understanding of cosmology and fundamental interactions. In science, such debates are productive and grounded in measurement, theory, and the continual refinement of models. See CODATA and Planck units.

Theoretical role and empirical reach

Fundamental constants tie together seemingly disparate domains. They appear in quantum mechanics, electromagnetism, thermodynamics, and gravity, serving as the bridge between theoretical formulations and experimental observables. The value of α, for example, influences spectral lines, atomic structure, and quantum electrodynamics predictions, while c links relativity to measurement of time and space. The relationship between h and energy quanta underpins the entire field of quantum mechanics, and G governs the curvature of spacetime in general relativity, informing our understanding of planetary motion and cosmology. See Quantum electrodynamics and General relativity.

Practically, constants enable precision science. They allow physicists to predict spectra, calibrate instruments, interpret cosmological data, and design technologies with predictable behavior. The CODATA values provide a common reference point for researchers around the world, ensuring that measurements conducted in different laboratories can be meaningfully compared. See CODATA and Rydberg constant.