The term physical constant expresses the notion of a physical quantity subject to experimental measurement which is independent of the time or location of the experiment. The constancy (immutability) of any "physical constant" is thus subject to experimental verification.

- Dimensionality
- Fine-structure constant
- Speed of light
- Gravitational constant
- Proton-to-electron mass ratio
- Cosmological constant
- See also
- References

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.^{ [1] } Experiments conducted since then have put upper bounds on their time-dependence. This concerns the fine-structure constant, the gravitational constant and the proton-to-electron mass ratio specifically, for all of which there are ongoing efforts to improve tests on their time-dependence.^{ [2] }

The immutability of these fundamental constants is an important cornerstone of the laws of physics as currently known; the postulate of the time-independence of physical laws is tied to that of the conservation of energy (Noether's theorem), so that the discovery of any variation would imply the discovery of a previously unknown law of force.^{ [3] }

In a more philosophical context, the conclusion that these quantities are constant raises the question of why they have the specific value they do in what appears to be a "fine-tuned universe", while their being variable would mean that their known values are merely an accident of the current time at which we happen to measure them.^{ [4] }

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 a system of units may arbitrarily select any physical constant as its basis, making the question of which constant is undergoing change an artefact of the choice of units.^{ [5] }^{ [6] }^{ [7] }

For example, in SI units, the speed of light has been 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. 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 ratio *e*^{2}:*c* (the fine-structure constant) remained unchanged.^{ [8] }

Natural units are systems of units entirely based in fundamental constants. In such systems, it is meaningful to measure any specific quantity which is *not* used in the definition of units. For example, in Stoney units, the elementary charge is set to *e* = 1 while the reduced Planck constant is subject to measurement, *ħ* ≈ 137.03, and in Planck units, the reduced Planck constant is set to *ħ* = 1, while the elementary charge is subject to measurement, *e* ≈ (137.03)^{1/2}. The 2019 redefinition of SI base units expresses all SI base units in terms of fundamental physical constants, effectively transforming the SI system into a system of natural units.

In 1999, evidence for time variability of the fine-structure constant based on observation of quasars was announced^{ [9] } but a much more precise study based on CH molecules did not find any variation.^{ [10] }^{ [11] } An upper bound of 10^{−17} per year for the time variation, based on laboratory measurements, was published in 2008.^{ [12] } Observations of a quasar of the universe at only 0.8 billion years old with AI analysis method employed on the Very Large Telescope (VLT) found a spatial variation preferred over a no-variation model at the level.^{ [13] }

The time-variation of fine-structure constant is equivalent to the time-variation of one or more of: speed of light, Planck constant, vacuum permittivity, and elementary charge, since .

The gravitational constant *G* is 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.^{ [14] } 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 over the last nine billion years.^{ [15] } The quantity is simply the change in time of the gravitational constant, denoted by , divided by *G*.

As a dimensional quantity, the value of the gravitational constant and its possible variation will depend on the choice of units; in Planck units, for example, its value is fixed at *G* = 1 by definition. A meaningful test on the time-variation of *G* would require comparison with a non-gravitational force to obtain a dimensionless quantity, e.g. through the ratio of the gravitational force to the electrostatic force between two electrons, which in turn is related to the dimensionless fine-structure constant.

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.^{ [16] }^{ [17] }

The cosmological constant is a measure of the energy density of the vacuum. It was first measured, and found to have a positive value, in the 1990s. It is currently (as of 2015) estimated at 10^{−122} in Planck units.^{ [18] } Possible variations of the cosmological constant over time or space are not amenable to observation, but it has been noted that, in Planck units, its measured value is suggestively close to the reciprocal of the age of the universe squared, Λ ≈ *T*^{−2}. Barrow and Shaw proposed a modified theory in which Λ is a field evolving in such a way that its value remains Λ ~ *T*^{−2} throughout the history of the universe.^{ [19] }

A **physical constant**, sometimes **fundamental physical constant** or **universal constant**, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is distinct from a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement.

The **gravitational constant**, denoted by the capital letter *G*, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity.

In cosmology, the **cosmological constant**, alternatively called **Einstein's cosmological constant**, is the constant coefficient of a term that Albert Einstein temporarily added to his field equations of general relativity. He later removed it. Much later it was revived and reinterpreted as the energy density of space, or vacuum energy, that arises in quantum mechanics. It is closely associated with the concept of dark energy.

**Hubble's law**, also known as the **Hubble–Lemaître law**, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving away from Earth. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit toward the red end of the visible spectrum.

In physics, the **fine-structure constant**, also known as the **Sommerfeld constant**, commonly denoted by α, is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles.

A **dimensionless quantity** is a quantity to which no physical dimension is assigned. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time.

A **base unit of measurement** is a unit of measurement adopted for a *base quantity*. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others. The SI base units, or *Systeme International d'unites*, consists of the metre, kilogram, second, ampere, kelvin, mole and candela.

A **geometrized unit system**, **geometric unit system** or **geometrodynamic unit system** is a system of natural units in which the base physical units are chosen so that the speed of light in vacuum, *c*, and the gravitational constant, *G*, are set equal to unity.

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.

The characterization of the universe as **finely tuned** suggests that the occurrence of life in the universe is very sensitive to the values of certain fundamental physical constants and that values different from the observed ones are more probable. If the values of any of certain free parameters in contemporary physical theories had differed only slightly from those observed, the evolution of the universe would have proceeded very differently, and "life as we know it" might not have been possible.

In theoretical physics, the **hierarchy problem** is the problem concerning the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on why, for example, the weak force is 10^{24} times stronger than gravity.

The **Lambda-CDM**, **Lambda cold dark matter** or **ΛCDM** model is a mathematical model of the Big Bang theory with three major components:

- a cosmological constant denoted by lambda (Λ) associated with dark energy,
- the postulated cold dark matter, and
- ordinary matter.

A **variable speed of light** (**VSL**) is a feature of a family of hypotheses stating that the speed of light may in some way not be constant, for example, that it varies in space or time, or depending on frequency. Accepted classical theories of physics, and in particular general relativity, predict a constant speed of light in any local frame of reference and in some situations these predict apparent variations of the speed of light depending on frame of reference, but this article does not refer to this as a variable speed of light. Various alternative theories of gravitation and cosmology, many of them non-mainstream, incorporate variations in the local speed of light.

The **Dirac large numbers hypothesis** (**LNH**) is an observation made by Paul Dirac in 1937 relating ratios of size scales in the Universe to that of force scales. The ratios constitute very large, dimensionless numbers: some 40 orders of magnitude in the present cosmological epoch. According to Dirac's hypothesis, the apparent similarity of these ratios might not be a mere coincidence but instead could imply a cosmology with these unusual features:

In physical cosmology and astronomy, **dark energy** is an unknown form of energy that affects the universe on the largest scales. Its primary effect is to drive the accelerating expansion of the universe. Assuming that the lambda-CDM model of cosmology is correct, dark energy is the dominant component of the universe, contributing 68% of the total energy in the present-day observable universe while dark matter and ordinary (baryonic) matter contribute 26% and 5%, respectively, and other components such as neutrinos and photons are nearly negligible. Dark energy's density is very low: 6×10^{−10} J/m^{3}, much less than the density of ordinary matter or dark matter within galaxies. However, it dominates the universe's mass–energy content because it is uniform across space.

In mathematical physics, **de Sitter invariant special relativity** is the speculative idea that the fundamental symmetry group of spacetime is the indefinite orthogonal group SO(4,1), that of de Sitter space. In the standard theory of general relativity, de Sitter space is a highly symmetrical special vacuum solution, which requires a cosmological constant or the stress–energy of a constant scalar field to sustain.

In physics the **Stoney units** form a system of units named after the Irish physicist George Johnstone Stoney, who first proposed them in 1881. They are the earliest example of natural units, i.e., a coherent set of units of measurement designed so that chosen physical constants fully define and are included in the set.

In particle physics and physical cosmology, **Planck units** are a system of units of measurement defined exclusively in terms of four universal physical constants: *c*, *G*, *ħ*, and *k*_{B}. Expressing one of these physical constants in terms of Planck units yields a numerical value of 1. They are a system of natural units, defined using fundamental properties of nature rather than properties of a chosen prototype object. Originally proposed in 1899 by German physicist Max Planck, they are relevant in research on unified theories such as quantum gravity.

In physics, **natural units** are physical units of measurement in which only universal physical constants are used as defining constants, such that each of these constants acts as a coherent unit of a quantity. For example, the elementary charge *e* may be used as a natural unit of electric charge, and the speed of light *c* may be used as a natural unit of speed. A purely natural system of units has all of its units defined such that each of these can be expressed as a product of powers of defining physical constants.

**Jean-Philippe Uzan** is a French cosmologist and *directeur de recherche* employed by the Centre national de la recherche scientifique (CNRS).

- ↑ P.A.M. Dirac (1938). "A New Basis for Cosmology".
*Proceedings of the Royal Society A*.**165**(921): 199–208. Bibcode:1938RSPSA.165..199D. doi:10.1098/rspa.1938.0053. - ↑ CODATA Recommended Values of the Fundamental Physical Constants: 2010" (March 15, 2012): "Although the possible time variation of the constants continues to be an active field of both experimental and theoretical research, there is no observed variation relevant to the data on which the 2010 recommended values are based; see, for example, the recent reviews by Uzan (2011) and Chiba (2011). Other references may be found in the FCDC bibliographic database at physics.nist.gov/constantsbib using, for example, the keywords 'time variation' or 'constants.'".
- ↑ "Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free fall. Thus, it is of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy." Uzan (2011)
- ↑ Uzan (2011), chapter 7: "Why Are The Constants Just So?": "The numerical values of the fundamental constants are not determined by the laws of nature in which they appear. One can wonder why they have the values we observe. In particular, as pointed out by many authors (see below), the constants of nature seem to be fine-tuned [Leslie (1989)]. Many physicists take this fine-tuning to be an explanandum that cries for an explanans, hence following Hoyle [(1965)] who wrote that 'one must at least have a modicum of curiosity about the strange dimensionless numbers that appear in physics.'"
- ↑ Duff, M. J. (2014). "How fundamental are fundamental constants?".
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