Physical constant

A physical constant is a fundamental quantity in nature that cannot be explained by any existing theory. Because theories cannot predict these values, scientists must determine them through experimental measurement. These constants are distinct from mathematical constants, which are fixed numerical values that do not involve physical measurement. While a mathematical constant is an abstract concept, a physical constant describes a real property of the universe. They act as the essential parameters that define how physical laws function in our world.

Physical constants can take different dimensional forms depending on what they measure. Some constants are dimensional, meaning they are expressed using units like length, mass, or time. For example, the speed of light, denoted as c, has the dimension of length divided by time. Other constants are dimensionless, meaning they are pure numbers without any units. An example of this is the proton-to-electron mass ratio. Physicists often use the term "fundamental physical constant" to describe universal constants that have dimensions. However, some scientists prefer to reserve that term specifically for dimensionless universal constants, such as the fine-structure constant, which measures the strength of electromagnetic interactions.

Our understanding of these constants often evolves as scientific theories become more advanced. The speed of light provides a perfect example of this shifting perspective. Originally, c was viewed as a simple property of light itself. When Maxwell's equations were discovered and verified, the quantity was linked to the entire system of electromagnetism. Later, the theory of special relativity emerged, and the speed of light became understood as the basis of causality. This progression shows how a constant can move from a specific property to a universal rule. Today, the speed of light is so fundamental that it defines the international unit of length.

In the modern International System of Units (SI), constants are used to define our very measurements. Since a major revision in 2019, all SI units are defined by fixed natural phenomena. This includes three specific fundamental constants: the speed of light (c), the Planck constant (h), and the elementary charge (e). This change means that units like the kilogram are now expressed in terms of these constants. For instance, the kilogram can be written using the Planck constant and an experimentally measured constant called ΔνCs. This shift also means the international prototype of the kilogram is being retired as a physical object.

Scientists can also use these constants to create "natural units" for specific fields of study. By combining different dimensional universal constants, they can build measurement systems that fit a particular area of science. For example, Planck units are constructed using c, the gravitational constant (G), the reduced Planck constant (ħ), and the Boltzmann constant (kB). These are very useful for studying quantum gravity. In atomic physics, researchers use atomic units, which are built from ħ, the electron mass (me), the elementary charge (e), and 4πε0. These systems allow scientists to work with scales that are most convenient for their specific research.

The exact number of fundamental constants depends on which physical theory is considered most fundamental. Currently, scientists rely on general relativity for gravitation and the Standard Model for other interactions. Together, these theories account for 19 independent fundamental constants. However, this number can change depending on how a scientist chooses to categorize them. For example, one list identifies 22 constants for the Standard Model, including the gravitational constant G and various Yukawa couplings. If new physics is discovered, such as the mass of the neutrino, the number of required constants could increase.

Researchers also conduct experiments to test if these constants change over time or space. Paul Dirac speculated in 1937 that constants like G might change as the universe ages. To avoid issues with arbitrary unit systems, scientists focus on testing dimensionless quantities. For the fine-structure constant, researchers have set an upper bound of change at roughly 10⁻¹⁷ per year. For the gravitational constant, observations of type Ia supernovae suggest an upper bound of less than 10⁻¹⁰ per year over the last nine billion years. Studying these values helps scientists determine if the laws of physics are truly universal and unchanging.

Finally, the specific values of these constants lead to profound questions about our existence. Some physicists explore the idea of a "fine-tuned" universe. This concept suggests that if dimensionless constants had different values, intelligent life might never have emerged. This observation is linked to the anthropic principle, which states that our existence as observers requires the constants to be exactly what they are. Some interpret this as evidence of a divine creator, while others suggest we live in a multiverse. In a multiverse, different universes might exist with different constant values, and we simply inhabit one that allows for life.