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Encyclopedia > Physical constant

A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement. In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. ... A physical quantity is either a quantity within physics that can be measured (e. ... A mathematical constant is a quantity, usually a real number or a complex number, that arises naturally in mathematics and does not change. ...

There are many physical constants in science, some of the most widely recognized being the rationalized Planck's constant h, the gravitational constant G, the speed of light in the vacuum c, the electric constant ε0, and the elementary charge e. Physical constants can take many dimensional forms: the speed of light signifies a maximum speed limit of the universe and is expressed dimensionally as length divided by time; while the fine-structure constant α, which characterizes the strength of the electromagnetic interaction, is dimensionless. A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum. ... The electric constant () is the permittivity of vacuum, a physical constant, defined by: where: - magnetic constant - speed of light In SI units, the value is exactly expressed by: = 2. ... The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ... 2-dimensional renderings (ie. ... This article does not cite any references or sources. ... For other uses, see Universe (disambiguation). ... For other uses of this word, see Length (disambiguation). ... This article is about the concept of time. ... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement...

## Dimensionful and dimensionless physical constants GA_googleFillSlot("encyclopedia_square");

Whereas the values of physical constants do not depend on the unit system used, the numerical values of dimensionful physical constants do depend on the unit used. Therefore, these numerical values (such as 299,792,458 for the constant speed of light c expressed in units of meters per second) are not values that a theory of physics can be expected to predict. The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum. ...

Ratios of like-dimensioned physical constants do not depend on unit systems in this way (the units cancel), so they are pure (dimensionless) numbers whose values a future theory of physics could conceivably hope to predict. Additionally, all equations describing laws of physics can be expressed without dimensional physical constants via a process known as nondimensionalization, but the dimensionless constants will remain. Thus, theoretical physicists tend to regard these dimensionless quantities as fundamental physical constants. For a list of set rules, see Laws of science. ... Nondimensionalization refers to the partial or full removal of units from a mathematical equation by a suitable substitution of variables. ... In physics, fundamental physical constants are, in the strictest sense, physical constants that are independent of systems of units and hence are dimensionless numbers. ...

However, the phrase fundamental physical constant is also used in other ways. For example, the National Institute of Standards and Technology [1] uses it to refer to any universal physical quantity believed to be constant, such as the speed of light, c, and the gravitational constant G. As a non-regulatory agency of the United States Department of Commerce’s Technology Administration, the National Institute of Standards (NIST) develops and promotes measurement, standards, and technology to enhance productivity, facilitate trade, and improve the quality of life. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...

The fine-structure constant α is probably the best known dimensionless fundamental physical constant. Many attempts have been made to derive its value (currently measured at about 1/137.035999) from theory, but so far none have succeeded. The same holds for the dimensionless ratios of masses of fundamental particles (the most apparent is mp/me, approximately 1836.152673). With the development of quantum chemistry in the 20th century, however, a vast number of previously inexplicable dimensionless physical constants were successfully computed from theory. As such, some theoretical physicists still hope for continued progress in explaining the values of dimensionless physical constants. The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement... ...

It is known that the universe would be very different if these constants took values significantly different from those we observe. For example, a few percent change in the value of the fine structure constant would be enough to eliminate stars like our Sun. This has prompted attempts at anthropic explanations of the dimensionless physical constants. In physics and cosmology, the anthropic principle states that we should take into account the constraints that our existence as observers imposes on the sort of universe that we could observe. ...

## How constant are the physical constants?

Beginning with Paul Dirac in 1937, some scientists have speculated that physical constants may actually decrease in proportion to the age of the universe. Scientific experiments have not yet pinpointed any definite evidence that this is the case, although they have placed upper bounds on the maximum possible relative change per year at very small amounts (roughly 10−5 per year for the fine structure constant α and 10−11 for the gravitational constant G). Paul Adrien Maurice Dirac, OM, FRS (IPA: [dÉªrÃ¦k]) (August 8, 1902 â€“ October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... Year 1937 (MCMXXXVII) was a common year starting on Friday (link will display the full calendar) of the Gregorian calendar. ...

It is currently disputed [2] [3] that any changes in dimensionful physical constants such as G, c, ħ, or ε0 are operationally meaningful;[1] however, a sufficient change in a dimensionless constant such as α is generally agreed to be something that would definitely be noticed. If a measurement indicated that a dimensionful physical constant had changed, this would be the result or interpretation of a more fundamental dimensionless constant changing, which is the salient metric. From John D. Barrow 2002: John David Barrow FRS (born November 29, 1952, London) is an English cosmologist, theoretical physicist, and mathematician. ...

"[An] important lesson we learn from the way that pure numbers like α define the world is what it really means for worlds to be different. The pure number we call the fine structure constant and denote by α is a combination of the electron charge, e, the speed of light, c, and Planck's constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h, and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our world. The only thing that counts in the definition of worlds are the values of the dimensionless constants of Nature. If all masses were doubled in value you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged."

## Anthropic principle

Some physicists have explored the notion that if the (dimensionless) fundamental 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 Strong anthropic principle states that it must be because these fundamental constants acquired their respective values that there was sufficient order in the Universe and richness in elemental diversity for life to have formed, which subsequently evolved the necessary intelligence toward observing that these constants have taken on the values they have, which then allowed for our privileged perspective from the Weak anthropic principle standpoint. In physics, fundamental physical constants are physical constants that are independent of systems of units and are in general dimensionless numbers. ... The deepest visible-light image of the cosmos. ... In philosophy, the anthropic principle in its most basic form states that any valid theory of the universe must be consistent with our existence as carbon-based human beings at this particular time and place in the universe. ... In physics and cosmology, the anthropic principle is an umbrella term for various dissimilar attempts to explain the structure of the universe by way of coincidentally balanced features that are necessary and relevant to the existence on Earth of biochemistry, carbon-based life, and eventually human beings to observe such...

## Table of universal constants

Quantity Symbol Value Relative Standard Uncertainty
speed of light in vacuum $c ,$ 299 792 458 m·s−1 defined
Newtonian constant of gravitation $G ,$ 6.67428(67) × 10−11m³·kg−1·s−2 1.0 × 10−4
Planck's constant $h ,$ 6.626 068 96(33) × 10−34 J·s 5.0 × 10−8
Dirac's constant $hbar = h / (2 pi)$ 1.054 571 628(53) × 10−34 J·s 5.0 × 10−8

â€œLightspeedâ€ redirects here. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... Plancks constant, denoted h, is a physical constant that is used to describe the sizes of quanta. ...

## Table of electromagnetic constants

Quantity Symbol Value[2] (SI units) Relative Standard Uncertainty
magnetic constant (vacuum permeability) $mu_0 ,$ 4π × 10−7 N·A−2 = 1.256 637 061... × 10−6 N·A−2 defined
electric constant (vacuum permittivity) $epsilon_0 = 1/(mu_0 c^2) ,$ 8.854 187 817... × 10−12F·m−1 defined
characteristic impedance of vacuum $Z_0 = mu_0 c ,$ 376.730 313 461... Ω defined
Coulomb's constant $kappa = 1 / 4piepsilon_0 ,$ 8.987 551 787 4 × 109 N·m²C−2 defined
elementary charge $e ,$ 1.602 176 487(40) × 10−19 C 2.5 × 10−8
Bohr magneton $mu_B = e hbar / 2 m_e$ 927.400 915(23) × 10−26 J·T−1 2.5 × 10−8
conductance quantum $G_0 = 2 e^2 / h ,$ 7.748 091 7004(53) × 10−5 S 6.8 × 10−10
inverse conductance quantum $G_0^{-1} = h / 2 e^2 ,$ 12 906.403 7787(88) Ω 6.8 × 10−10
Josephson constant $K_J = 2 e / h ,$ 483 597.891(12) × 109 Hz·V−1 2.5 × 10−8
magnetic flux quantum $phi_0 = h / 2 e ,$ 2.067 833 667(52) × 10−15 Wb 2.5 × 10−8
nuclear magneton $mu_N = e hbar / 2 m_p$ 5.050 783 43(43) × 1027 J·T−1 8.6 × 10−8
von Klitzing constant $R_K = h / e^2 ,$ 25 812.807 557(18) Ω 6.8 × 10−10

Look up si, Si, SI in Wiktionary, the free dictionary. ... The magnetic constant () is the permeability of vacuum. ... The electric constant () is the permittivity of vacuum, a physical constant, defined by: where: - magnetic constant - speed of light In SI units, the value is exactly expressed by: = 2. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... It has been suggested that this article or section be merged into Electrostatic force. ... The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ... In atomic physics, the Bohr magneton (symbol ) is named after the physicist Niels Bohr. ... The conductance quantum is the quantized unit of conductance. ... The conductance quantum is the quantized unit of conductance. ... Josephson junctions, first postulated by B. D. Josephson and first made by John Rowell and Philip Anderson, are quantum-mechanical circuit elements of superconducting devices. ... The magnetic flux quantum Î¦0 is the quantum of magnetic flux passing through a superconductor. ... The nuclear magneton (symbol ), is a physical constant of magnetic moment, defined by: where: is the elementary charge, is the reduced Plancks constant, is the proton rest mass In the SI system of units its value is approximately: = 5. ... The quantum Hall effect is a quantum mechanical version of the Hall effect, observed in two-dimensional systems of electrons subjected to low temperatures and strong magnetic fields, in which the Hall conductance σ takes on the quantized values where e is the elementary charge and h is Plancks...

## Table of atomic and nuclear constants

Quantity Symbol Value[2] (SI units) Relative Standard Uncertainty
Bohr radius $a_0 = alpha / 4 pi R_infin ,$ 0.529 177 2108(18) × 10−10 m 3.3 × 10−9
classical electron radius $r_e = e^2 / 4piepsilon_0 m_e c^2,$ 2.817 940 2894(58) × 10−15 m 2.1 × 10−9
electron mass $m_e ,$ 9.109 382 15(45) × 10−31 kg 5.0 × 10−8
Fermi coupling constant $G_F / (hbar c)^3$ 1.166 39(1) × 10−5 GeV−2 8.6 × 10−6
fine-structure constant $alpha = mu_0 e^2 c / (2 h) = e^2 / (4 pi epsilon_0 hbar c) ,$ 7.297 352 568(24) × 10−3 3.3 × 10−9
Hartree energy $E_h = 2 R_infin h c ,$ 4.359 744 17(75) × 10−18 J 1.7 × 10−7
proton mass $m_p ,$ 1.672 621 637(83) × 10−27 kg 5.0 × 10−8
quantum of circulation $h / 2 m_e ,$ 3.636 947 550(24) × 10−4 m² s−1 6.7 × 10−9
Rydberg constant $R_infin = alpha^2 m_e c / 2 h ,$ 10 973 731.568 525(73) m−1 6.6 × 10−12
Thomson cross section $(8 pi / 3)r_e^2$ 0.665 245 873(13) × 10−28 2.0 × 10−8
weak mixing angle $sin^2 theta_W = 1 - (m_W / m_Z)^2 ,$ 0.222 15(76) 3.4 × 10−3

Look up si, Si, SI in Wiktionary, the free dictionary. ... In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. ... The classical electron radius, also known as the Compton radius or the Thomson scattering length is based on a classical (i. ... For other uses, see Electron (disambiguation). ... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... A Hartree (symbol Eh) is the atomic unit of energy and is named after physicist Douglas Hartree. ... For other uses, see Proton (disambiguation). ... The Rydberg constant, named after physicist Janne Rydberg, is a physical constant discovered when measuring the spectrum of hydrogen, and building upon results from Anders Jonas Ã…ngstrÃ¶m and Johann Balmer. ... In nuclear and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles. ... The Weinberg angle or weak mixing angle is a parameter in the Abdus-Salam theory of the electroweak force. ...

## Table of physico-chemical constants

Quantity Symbol Value[2] (SI units) Relative Standard Uncertainty
atomic mass unit (unified atomic mass unit) $m_u = 1 u ,$ 1.660 538 86(28) × 10−27 kg 1.7 × 10−7
Avogadro's number $N_A, L ,$ 6.022 1415(10) × 1023 mol−1 1.7 × 10−7
Boltzmann constant $k = R / N_A ,$ 1.380 6505(24) × 10−23 J·K−1 1.8 × 10−6
Faraday constant $F = N_A e ,$ 96 485.3383(83)C·mol−1 8.6 × 10−8
first radiation constant $c_1 = 2 pi h c^2 ,$ 3.741 771 18(19) × 10−16 W·m² 5.0 × 10−8
for spectral radiance $c_{1L} ,$ 1.191 042 82(20) × 10−16 W·m² sr−1 1.7 × 10−7
Loschmidt constant at T=273.15 K and p=101.325 kPa $n_0 = N_A / V_m ,$ 2.686 7773(47) × 1025 m−3 1.8 × 10−6
gas constant $R ,$ 8.314 472(15) J·K−1·mol−1 1.7 × 10−6
molar Planck constant $N_A h ,$ 3.990 312 716(27) × 10−10 J·s·mol−1 6.7 × 10−9
molar volume of an ideal gas at T=273.15 K and p=100 kPa $V_m = R T / p ,$ 22.710 981(40) × 10−3 m³·mol−1 1.7 × 10−6
at T=273.15 K and p=101.325 kPa 22.413 996(39) × 10−3 m³·mol−1 1.7 × 10−6
Sackur-Tetrode constant at T=1 K and p=100 kPa $S_0 / R = frac{5}{2}$
$+ lnleft[ (2pi m_u k T / h^2)^{3/2} k T / p right]$
−1.151 7047(44) 3.8 × 10−6
at T=1 K and p=101.325 kPa −1.164 8677(44) 3.8 × 10−6
second radiation constant $c_2 = h c / k ,$ 1.438 7752(25) × 10−2 m·K 1.7 × 10−6
Stefan-Boltzmann constant $sigma = (pi^2 / 60) k^4 / hbar^3 c^2$ 5.670 400(40) × 10−8 W·m−2·K−4 7.0 × 10−6
Wien displacement law constant $b = (h c / k) / ,$ 4.965 114 231... 2.897 7685(51) × 10−3 m·K 1.7 × 10−6

Look up si, Si, SI in Wiktionary, the free dictionary. ... The unified atomic mass unit (u), or dalton (Da), is a small unit of mass used to express atomic and molecular masses. ... Avogadros number, also called Avogadros constant (NA), named after Amedeo Avogadro, is formally defined to be the number of carbon-12 atoms in 12 grams (0. ... The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... I am the man. ... Avogadros number, also called Avogadros constant (NA), named after Amedeo Avogadro, is a constant used in chemistry and physics. ... The gas constant (also known as the molar, universal, or ideal gas constant, usually denoted by symbol R) is a physical constant which is featured in a large number of fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. ... In chemistry, the molar volume of a substance is the ratio of the volume of a sample of that substance to the amount of substance (usually in mole) in the sample. ... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ... In a simple derivation based on the ideal gas law, the entropy S is not an extensive variable as it must be, leading to an apparent paradox known as the Gibbs paradox. ... The Stefan-Boltzmann constant (also Stefans constant), denoted with a Greek letter σ, is a derivable physical constant, the constant of proportionality between the total energy radiated per unit surface area of a black body in unit time and the fourth power of the thermodynamic temperature, as per the... The wavelength corresponding to the peak emission in various black body spectra as a function of temperature Wiens displacement law is a law of physics that states that there is an inverse relationship between the wavelength of the peak of the emission of a black body and its temperature. ...

Quantity Symbol Value (SI units) Relative Standard Uncertainty
conventional value of Josephson constant[3] $K_{J-90} ,$ 483 597.9 × 109 Hz·V−1 defined
conventional value of von Klitzing constant[4] $R_{K-90} ,$ 25 812.807 Ω defined
molar mass constant $M_u = M(,^{12}mbox{C}) / 12$ 1 × 10−3 kg·mol−1 defined
of carbon-12 $M(,^{12}mbox{C}) = N_A m(,^{12}mbox{C})$ 12 × 10−3 kg·mol−1 defined
standard acceleration of gravity (gee, free fall on Earth) $g_n ,!$ 9.806 65 m·s−2 defined
standard atmosphere $mbox{atm} ,$ 101 325 Pa defined

Look up si, Si, SI in Wiktionary, the free dictionary. ... The magnetic flux quantum Φ0 is the quantum of magnetic flux passing through a superconductor. ... The quantum Hall effect is a quantum mechanical version of the Hall effect, observed in two-dimensional systems of electrons subjected to low temperatures and strong magnetic fields, in which the Hall conductance σ takes on the quantized values where e is the elementary charge and h is Plancks... Carbon 12 is a stable isotope of the element carbon. ... Gravity is a force of attraction that acts between bodies that have mass. ... g (also gee, g-force or g-load) is a non-SI unit of acceleration defined as exactly 9. ... For other uses, see Free-fall (disambiguation). ... Standard atmosphere (symbol: atm) is a unit of pressure. ...

An astronomical constant is a physical constant used in astronomy. ... Atomic units (au) form a system of units convenient for electromagnetism, atomic physics, and quantum electrodynamics, especially when the focus is on the properties of electrons. ... CODATA (Committee on Data for Science and Technology) was established in 1966 as an interdisciplinary committee of the International Council of Science (ICSU), formerly the International Council of Scientific Unions. ... In physics, fundamental physical constants are, in the strictest sense, physical constants that are independent of systems of units and hence are dimensionless numbers. ... In physics, natural units are physical units of measurement defined in terms of universal physical constants in such a manner that some chosen physical constants take on the numerical value of one when expressed in terms of a particular set of natural units. ... For a list of set rules, see Laws of science. ... In physics, Planck units are physical units of measurement defined exclusively in terms of the five universal physical constants shown in the table below in such a manner that all of these physical constants take on the numerical value of one when expressed in terms of these units. ... This is a list of physical and mathematical constants named after people. ... The International System of Units (symbol: SI) (for the French phrase Système International dUnités) is the most widely used system of units. ...

## Notes

1. ^ c, and ε0 now are defined numerical values, independent of experiment, so observations now are trained elsewhere, for example, upon a changing value of the meter.
2. ^ a b c The values are given in the so-called concise form; the number in brackets is the standard uncertainty, which is the value multiplied by the relative standard uncertainty.
3. ^ This is the value adopted internationally for realizing representations of the volt using the Josephson effect.
4. ^ This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect.

Josephson junction array chip developed by NIST as a standard volt. ... The Josephson effect is the phenomenon of current flow across two weakly coupled superconductors, separated by a very thin insulating barrier. ... The ohm (symbol: Î©) is the SI unit of electric resistance. ... The quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductance takes on the quantized values where is the elementary charge and is Plancks constant. ...

## References

• CODATA Recommendations - 2006 CODATA Internationally recommended values of the Fundamental Physical Constants
• Barrow, John D., The Constants of Nature; From Alpha to Omega - The Numbers that Encode the Deepest Secrets of the Universe. Pantheon Books, 2002. ISBN 0-375-42221-8.
• Mohr, Peter J., Taylor, Barry N., Newell, David B., CODATA Recommended Values of the Fundamental Physical Constants: 2006
John David Barrow FRS (born November 29, 1952, London) is an English cosmologist, theoretical physicist, and mathematician. ...

Results from FactBites:

 Physical constant - Wikipedia, the free encyclopedia (582 words) Constants can take many forms: the speed of light in a vacuum signifies a maximum speed limit of the universe; while the fine-structure constant α, which characterizes the interaction between electrons and photons, is dimensionless. Unless the system of natural units is used, the numerical values of dimensionful physical constants are artifacts of the unit system used, such as SI or cgs; that is, they are essentially conversion factors of human construct. Constants that are independent of systems of units are typically dimensionless numbers, known as fundamental physical constants, and are truly meaningful parameters of nature, not merely human constructs.
 Encyclopedia4U - Physical constant - Encyclopedia Article (260 words) In science, a physical constant is a physical quantity whose numerical value is fixed. There are many such constants used in science, some of the most famous of which being: Planck's constant, the gravitational constant and Avogadro's constant (better known as Avogadro's number). Constants can take many forms; some, such as the Planck length represents a fundamental physical distance, others such as the speed of light signifies the maximun speed limit of the universe, yet others are dimensionless quantities such as the fine-structure constant which embodies the interaction between electrons and photons.
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