Physical constant

A physical constant, sometimes called a 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 has dimension of 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. 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 constants, 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. 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

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.

As a result of the new definitions, an SI unit like the kilogram can be written in terms of fundamental constants and one experimentally measured constant, ΔνCs:

The discovery of variability in any of these constants would be equivalent to the discovery of "new physics".

Tests on time-independence

By definition, fundamental physical constants are subject to measurement, so that their being constant (independent on both the time and position of the performance of the measurement) is necessarily an experimental result and subject to verification.

Paul Dirac in 1937 speculated that physical constants such as the gravitational constant or the fine-structure constant might be subject to change over time in proportion of the age of the universe. Experiments can in principle only put an upper bound on the relative change per year. For the fine-structure constant, this upper bound is comparatively low, at roughly 10−17 per year (as of 2008).

The gravitational constant is much more difficult to measure with precision, and conflicting measurements in the 2000s have inspired the controversial suggestions of a periodic variation of its value in a 2015 paper. However, while its value is not known to great precision, the possibility of observing type Ia supernovae which happened in the universe's remote past, paired with the assumption that the physics involved in these events is universal, allows for an upper bound of less than 10−10 per year for the gravitational constant over the last nine billion years.

Similarly, an upper bound of the change in the proton-to-electron mass ratio has been placed at 10−7 over a period of 7 billion years (or 10−16 per year) in a 2012 study based on the observation of methanol in a distant galaxy.

It is problematic to discuss the proposed rate of change (or lack thereof) of a single dimensional physical constant in isolation. The reason for this is that the choice of units is arbitrary, making the question of whether a constant is undergoing change an artefact of the choice (and definition) of the units.

For example, in SI units, the speed of light was given a defined value in 1983. Thus, it was meaningful to experimentally measure the speed of light in SI units prior to 1983, but it is not so now. Similarly, with effect from May 2019, the Planck constant has a defined value, such that all SI base units are now defined in terms of fundamental physical constants. With this change, the international prototype of the kilogram is being retired as the last physical object used in the definition of any SI unit.

Tests on the immutability of physical constants look at dimensionless quantities, i.e. ratios between quantities of like dimensions, in order to escape this problem. Changes in physical constants are not meaningful if they result in an observationally indistinguishable universe. For example, a "change" in the speed of light c would be meaningless if accompanied by a corresponding change in the elementary charge e so that the expression e2/(4πε0ħc) (the fine-structure constant) remained unchanged.

Dimensionless physical constants

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, introduced by Arnold Sommerfeld, 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.

Fine-tuned universe

Some physicists have explored the notion that if the dimensionless physical constants had sufficiently different values, our Universe would be so radically different that intelligent life would probably not have emerged, and that our Universe therefore seems to be fine-tuned for intelligent life. The anthropic principle states a logical truism: the fact of our existence as intelligent beings who can measure physical constants requires those constants to be such that beings like us can exist. There are a variety of interpretations of the constants' values, including that of a divine creator (the apparent fine-tuning is actual and intentional), or that the universe is one universe of many in a multiverse (e.g. the many-worlds interpretation of quantum mechanics), or even that, if information is an innate property of the universe and logically inseparable from consciousness, a universe without the capacity for conscious beings cannot exist.

Table of physical constants

The table below lists some frequently used constants and their CODATA recommended values. For an extended list, refer to List of physical constants.

{| class="wikitable sortable"

! Quantity

! Symbol

! Value

! Relativestandarduncertainty

| elementary charge

| <math>e</math>

| Newtonian constant of gravitation

| <math>G</math>

| Planck constant

| <math>h</math>

| speed of light in vacuum

| <math>c</math>

| vacuum electric permittivity

| <math> \varepsilon_0</math>

| vacuum magnetic permeability

| <math> \mu_0 </math>

| electron mass

| <math>m_{\mathrm{e </math>

| fine-structure constant

| <math>\alpha = e^2 / 2 \varepsilon_0 h c </math>

| Josephson constant

| <math>K_{\mathrm{J = 2 e / h </math>

| Rydberg constant

| <math>R_\infin = \alpha^2 m_{\mathrm{e c / 2 h </math>

| von Klitzing constant

| <math>R_{\mathrm{K = h / e^2 </math>

References

External links

Sixty Symbols, University of Nottingham
IUPAC – Gold Book