Как пишется константа в физике

Физическая константа

Полезное

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 contrasted with 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 a 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 signifies a maximum speed for any object and its dimension is length divided by time; while the fine-structure constant α, which characterizes the strength of the electromagnetic interaction, is dimensionless.

The term fundamental physical constant is sometimes used to refer to universal-but-dimensioned physical constants such as those mentioned above.^[1] Increasingly, however, physicists only use fundamental physical constant for dimensionless physical constants, such as the fine-structure constant α.

Physical constant, as discussed here, should not be confused with other quantities called «constants», which are assumed to be constant in a given context without being fundamental, such as the «time constant» characteristic of a given system, or material constants (e.g., Madelung constant, electrical resistivity, and heat capacity).

Since May 2019, all of the SI base units have been defined in terms of physical constants. As a result, five constants: the speed of light in vacuum, c; the Planck constant, h; the elementary charge, e; the Avogadro constant, N_A; and the Boltzmann constant, k_B, have known exact numerical values when expressed in SI units. The first three of these constants are fundamental constants, whereas N_A and k_B are of a technical nature only: they do not describe any property of the universe, but instead only give a proportionality factor for defining the units used with large numbers of atomic-scale entities.

Choice of units[edit]

Whereas the physical quantity indicated by a physical constant does not depend on the unit system used to express the quantity, the numerical values of dimensional physical constants do depend on choice of unit system.
The term «physical constant» refers to the physical quantity, and not to the numerical value within any given system of units. For example, the speed of light is defined as having the numerical value of 299792458 when expressed in the SI unit metres per second, and as having the numerical value of 1 when expressed in the natural units Planck length per Planck time. While its numerical value can be defined at will by the choice of units, the speed of light itself is a single physical constant.

Any ratio between physical constants of the same dimensions results in a dimensionless physical constant, for example, the proton-to-electron mass ratio. Any relation between physical quantities can be expressed as a relation between dimensionless ratios via a process known as nondimensionalisation.

The term of «fundamental physical constant» is reserved for physical quantities which, according to the current state of knowledge, are regarded as immutable and as non-derivable from more fundamental principles. Notable examples are the speed of light c, and the gravitational constant G.

The fine-structure constant α 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. Introduced by Arnold Sommerfeld, its value as determined at the time was consistent with 1/137. This motivated Arthur Eddington (1929) to construct an argument why its value might be 1/137 precisely, which related to the Eddington number, his estimate of the number of protons in the Universe.^[2] By the 1940s, it became clear that the value of the fine-structure constant deviates significantly from the precise value of 1/137, refuting Eddington’s argument.^[3]

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.^{[citation needed]} In light of that, some theoretical physicists still hope for continued progress in explaining the values of other dimensionless physical constants.

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 values of some of the dimensionless fundamental physical constants.

Natural units[edit]

It is possible to combine dimensional universal physical constants to define fixed quantities of any desired dimension, and this property has been used to construct various systems of natural units of measurement. Depending on the choice and arrangement of constants used, the resulting natural units may be convenient to an area of study. For example, Planck units, constructed from c, G, ħ, and k_B give conveniently sized measurement units for use in studies of quantum gravity, and Hartree atomic units, constructed from ħ, m_e, e and 4πε₀ give convenient units in atomic physics. The choice of constants used leads to widely varying quantities.

Number of fundamental constants[edit]

The number of fundamental physical constants depends on the physical theory accepted as «fundamental».
Currently, this is the theory of general relativity for gravitation and the Standard Model for electromagnetic, weak and strong nuclear interactions and the matter fields.
Between them, these theories account for a total of 19 independent fundamental constants.
There is, however, no single «correct» way of enumerating them, as it is a matter of arbitrary choice which quantities are considered «fundamental» and which as «derived». Uzan (2011) lists 22 «unknown constants» in the fundamental theories, which give rise to 19 «unknown dimensionless parameters», as follows:

• the gravitational constant G,
• the speed of light c,
• the Planck constant h,
• the 9 Yukawa couplings for the quarks and leptons (equivalent to specifying the rest mass of these elementary particles),
• 2 parameters of the Higgs field potential,
• 4 parameters for the quark mixing matrix,
• 3 coupling constants for the gauge groups SU(3) × SU(2) × U(1) (or equivalently, two coupling constants and the Weinberg angle),
• a phase for the QCD vacuum.

The number of 19 independent fundamental physical constants is subject to change under possible extensions of the Standard Model, notably by the introduction of neutrino mass (equivalent to seven additional constants, i.e. 3 Yukawa couplings and 4 lepton mixing parameters).^[4]

The discovery of variability in any of these constants would be equivalent to the discovery of «new physics».^[5]

The question as to which constants are «fundamental» is neither straightforward nor meaningless, but a question of interpretation of the physical theory regarded as fundamental; as pointed out by Lévy-Leblond 1977, not all physical constants are of the same importance, with some having a deeper role than others.
Lévy-Leblond 1977 proposed a classification schemes of three types of constants:

• A: physical properties of particular objects
• B: characteristic of a class of physical phenomena
• C: universal constants

The same physical constant may move from one category to another as the understanding of its role deepens; this has notably happened to the speed of light, which was a class A constant (characteristic of light) when it was first measured, but became a class B constant (characteristic of electromagnetic phenomena) with the development of classical electromagnetism, and finally a class C constant with the discovery of special relativity.^[6]

Tests on time-independence[edit]

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).^[7]

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.^[8] 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.^[9]

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.^[10][11]

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.^[12][13][14]

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 ratio e²/(4πε₀ħc) (the fine-structure constant) remained unchanged.^[15]

Fine-tuned universe[edit]

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. However, the phase space of the possible constants and their values is unknowable, so any conclusions drawn from such arguments are unsupported. 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 ours 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.

The fundamental constants and quantities of nature have been discovered to be fine-tuned to such an extraordinarily narrow range that if it were not, the origin and evolution of conscious life in the universe would not be permitted.^[16]

Table of physical constants[edit]

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

Quantity	Symbol	Value[17]	Relative standard uncertainty
elementary charge		1.602176634×10−19 C[18]	0
Newtonian constant of gravitation		6.67430(15)×10−11 m3⋅kg−1⋅s−2[19]	2.2×10−5
Planck constant		6.62607015×10−34 J⋅Hz−1[20]	0
speed of light in vacuum		299792458 m⋅s−1[21]	0
vacuum electric permittivity		8.8541878128(13)×10−12 F⋅m−1[22]	1.5×10−10
vacuum magnetic permeability		1.25663706212(19)×10−6 N⋅A−2[23]	1.5×10−10
electron mass		9.1093837015(28)×10−31 kg[24]	3.0×10−10
fine-structure constant		7.2973525693(11)×10−3[25]	1.5×10−10
Josephson constant		483597.8484…×109 Hz⋅V−1[26]	0
Rydberg constant		10973731.568160(21) m−1[27]	1.9×10−12
von Klitzing constant		25812.80745… Ω[28]	0

See also[edit]

• List of common physics notations

References[edit]

• Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). «CODATA Recommended Values of the Fundamental Physical Constants: 2006» (PDF). Reviews of Modern Physics. 80 (2): 633–730. arXiv:0801.0028. Bibcode:2008RvMP…80..633M. doi:10.1103/RevModPhys.80.633. Archived from the original (PDF) on 2017-10-01.

• Barrow, John D. (2002), The Constants of Nature; From Alpha to Omega — The Numbers that Encode the Deepest Secrets of the Universe, Pantheon Books, ISBN 978-0-375-42221-8.

External links[edit]

• Sixty Symbols, University of Nottingham
• IUPAC — Gold Book

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 contrasted with 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 a 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 signifies a maximum speed for any object and its dimension is length divided by time; while the fine-structure constant α, which characterizes the strength of the electromagnetic interaction, is dimensionless.

The term fundamental physical constant is sometimes used to refer to universal-but-dimensioned physical constants such as those mentioned above.^[1] Increasingly, however, physicists only use fundamental physical constant for dimensionless physical constants, such as the fine-structure constant α.

Physical constant, as discussed here, should not be confused with other quantities called «constants», which are assumed to be constant in a given context without being fundamental, such as the «time constant» characteristic of a given system, or material constants (e.g., Madelung constant, electrical resistivity, and heat capacity).

Since May 2019, all of the SI base units have been defined in terms of physical constants. As a result, five constants: the speed of light in vacuum, c; the Planck constant, h; the elementary charge, e; the Avogadro constant, N_A; and the Boltzmann constant, k_B, have known exact numerical values when expressed in SI units. The first three of these constants are fundamental constants, whereas N_A and k_B are of a technical nature only: they do not describe any property of the universe, but instead only give a proportionality factor for defining the units used with large numbers of atomic-scale entities.

Choice of units[edit]

Whereas the physical quantity indicated by a physical constant does not depend on the unit system used to express the quantity, the numerical values of dimensional physical constants do depend on choice of unit system.
The term «physical constant» refers to the physical quantity, and not to the numerical value within any given system of units. For example, the speed of light is defined as having the numerical value of 299792458 when expressed in the SI unit metres per second, and as having the numerical value of 1 when expressed in the natural units Planck length per Planck time. While its numerical value can be defined at will by the choice of units, the speed of light itself is a single physical constant.

Any ratio between physical constants of the same dimensions results in a dimensionless physical constant, for example, the proton-to-electron mass ratio. Any relation between physical quantities can be expressed as a relation between dimensionless ratios via a process known as nondimensionalisation.

The term of «fundamental physical constant» is reserved for physical quantities which, according to the current state of knowledge, are regarded as immutable and as non-derivable from more fundamental principles. Notable examples are the speed of light c, and the gravitational constant G.

The fine-structure constant α 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. Introduced by Arnold Sommerfeld, its value as determined at the time was consistent with 1/137. This motivated Arthur Eddington (1929) to construct an argument why its value might be 1/137 precisely, which related to the Eddington number, his estimate of the number of protons in the Universe.^[2] By the 1940s, it became clear that the value of the fine-structure constant deviates significantly from the precise value of 1/137, refuting Eddington’s argument.^[3]

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.^{[citation needed]} In light of that, some theoretical physicists still hope for continued progress in explaining the values of other dimensionless physical constants.

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 values of some of the dimensionless fundamental physical constants.

Natural units[edit]

It is possible to combine dimensional universal physical constants to define fixed quantities of any desired dimension, and this property has been used to construct various systems of natural units of measurement. Depending on the choice and arrangement of constants used, the resulting natural units may be convenient to an area of study. For example, Planck units, constructed from c, G, ħ, and k_B give conveniently sized measurement units for use in studies of quantum gravity, and Hartree atomic units, constructed from ħ, m_e, e and 4πε₀ give convenient units in atomic physics. The choice of constants used leads to widely varying quantities.

Number of fundamental constants[edit]

The number of fundamental physical constants depends on the physical theory accepted as «fundamental».
Currently, this is the theory of general relativity for gravitation and the Standard Model for electromagnetic, weak and strong nuclear interactions and the matter fields.
Between them, these theories account for a total of 19 independent fundamental constants.
There is, however, no single «correct» way of enumerating them, as it is a matter of arbitrary choice which quantities are considered «fundamental» and which as «derived». Uzan (2011) lists 22 «unknown constants» in the fundamental theories, which give rise to 19 «unknown dimensionless parameters», as follows:

• the gravitational constant G,
• the speed of light c,
• the Planck constant h,
• the 9 Yukawa couplings for the quarks and leptons (equivalent to specifying the rest mass of these elementary particles),
• 2 parameters of the Higgs field potential,
• 4 parameters for the quark mixing matrix,
• 3 coupling constants for the gauge groups SU(3) × SU(2) × U(1) (or equivalently, two coupling constants and the Weinberg angle),
• a phase for the QCD vacuum.

The number of 19 independent fundamental physical constants is subject to change under possible extensions of the Standard Model, notably by the introduction of neutrino mass (equivalent to seven additional constants, i.e. 3 Yukawa couplings and 4 lepton mixing parameters).^[4]

The discovery of variability in any of these constants would be equivalent to the discovery of «new physics».^[5]

The question as to which constants are «fundamental» is neither straightforward nor meaningless, but a question of interpretation of the physical theory regarded as fundamental; as pointed out by Lévy-Leblond 1977, not all physical constants are of the same importance, with some having a deeper role than others.
Lévy-Leblond 1977 proposed a classification schemes of three types of constants:

• A: physical properties of particular objects
• B: characteristic of a class of physical phenomena
• C: universal constants

The same physical constant may move from one category to another as the understanding of its role deepens; this has notably happened to the speed of light, which was a class A constant (characteristic of light) when it was first measured, but became a class B constant (characteristic of electromagnetic phenomena) with the development of classical electromagnetism, and finally a class C constant with the discovery of special relativity.^[6]

Tests on time-independence[edit]

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).^[7]

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.^[8] 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.^[9]

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.^[10][11]

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.^[12][13][14]

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 ratio e²/(4πε₀ħc) (the fine-structure constant) remained unchanged.^[15]

Fine-tuned universe[edit]

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. However, the phase space of the possible constants and their values is unknowable, so any conclusions drawn from such arguments are unsupported. 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 ours 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.

The fundamental constants and quantities of nature have been discovered to be fine-tuned to such an extraordinarily narrow range that if it were not, the origin and evolution of conscious life in the universe would not be permitted.^[16]

Table of physical constants[edit]

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

Quantity	Symbol	Value[17]	Relative standard uncertainty
elementary charge		1.602176634×10−19 C[18]	0
Newtonian constant of gravitation		6.67430(15)×10−11 m3⋅kg−1⋅s−2[19]	2.2×10−5
Planck constant		6.62607015×10−34 J⋅Hz−1[20]	0
speed of light in vacuum		299792458 m⋅s−1[21]	0
vacuum electric permittivity		8.8541878128(13)×10−12 F⋅m−1[22]	1.5×10−10
vacuum magnetic permeability		1.25663706212(19)×10−6 N⋅A−2[23]	1.5×10−10
electron mass		9.1093837015(28)×10−31 kg[24]	3.0×10−10
fine-structure constant		7.2973525693(11)×10−3[25]	1.5×10−10
Josephson constant		483597.8484…×109 Hz⋅V−1[26]	0
Rydberg constant		10973731.568160(21) m−1[27]	1.9×10−12
von Klitzing constant		25812.80745… Ω[28]	0

See also[edit]

• List of common physics notations

References[edit]

• Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). «CODATA Recommended Values of the Fundamental Physical Constants: 2006» (PDF). Reviews of Modern Physics. 80 (2): 633–730. arXiv:0801.0028. Bibcode:2008RvMP…80..633M. doi:10.1103/RevModPhys.80.633. Archived from the original (PDF) on 2017-10-01.

• Barrow, John D. (2002), The Constants of Nature; From Alpha to Omega — The Numbers that Encode the Deepest Secrets of the Universe, Pantheon Books, ISBN 978-0-375-42221-8.

External links[edit]

• Sixty Symbols, University of Nottingham
• IUPAC — Gold Book

The constants listed here are known values of physical constants expressed in SI units; that is, physical quantities that are generally believed to be universal in nature and thus are independent of the unit system in which they are measured. Many of these are redundant, in the sense that they obey a known relationship with other physical constants and can be determined from them.

Table of physical constants[edit]

Symbol	Quantity	Value[a][b]	Relative standard uncertainty	Ref
	Newtonian constant of gravitation	6.67430(15)×10−11 m3⋅kg−1⋅s−2	2.2×10−5	[1]
	speed of light in vacuum	299792458 m⋅s−1	0	[2]
	Planck constant	6.62607015×10−34 J⋅Hz−1	0	[3]
	reduced Planck constant	1.054571817…×10−34 J⋅s	0	[4]
	vacuum magnetic permeability	1.25663706212(19)×10−6 N⋅A−2	1.5×10−10	[5]
	characteristic impedance of vacuum	376.730313668(57) Ω	1.5×10−10	[6]
	vacuum electric permittivity	8.8541878128(13)×10−12 F⋅m−1	1.5×10−10	[7]
	Coulomb constant	8.9875517923(14)×109 N⋅m2⋅C−2	1.5×10−10	[8]
	Boltzmann constant	1.380649×10−23 J⋅K−1	0	[9]
	Stefan–Boltzmann constant	5.670374419…×10−8 W⋅m−2⋅K−4	0	[10]
	first radiation constant	3.741771852…×10−16 W⋅m2	0	[11]
	first radiation constant for spectral radiance	1.1910429723971884140794892×10−16 W⋅m2⋅sr−1	0	[12]
	second radiation constant	1.438776877…×10−2 m⋅K	0	[13]
[c]	Wien wavelength displacement law constant	2.897771955…×10−3 m⋅K	0	[14]
[d]	Wien frequency displacement law constant	5.878925757…×1010 Hz⋅K−1	0	[15]
	Wien entropy displacement law constant	3.002916077…×10−3 m⋅K	0	[16]
	elementary charge	1.602176634×10−19 C	0	[17]
	conductance quantum	7.748091729…×10−5 S	0	[18]
	inverse conductance quantum	12906.40372… Ω	0	[19]
	von Klitzing constant	25812.80745… Ω	0	[20]
	Josephson constant	483597.8484…×109 Hz⋅V−1	0	[21]
	magnetic flux quantum	2.067833848…×10−15 Wb	0	[22]
	fine-structure constant	7.2973525693(11)×10−3	1.5×10−10	[23]
	inverse fine-structure constant	137.035999084(21)	1.5×10−10	[24]
	electron mass	9.1093837015(28)×10−31 kg	3.0×10−10	[25]
	proton mass	1.67262192369(51)×10−27 kg	3.1×10−10	[26]
	neutron mass	1.67492749804(95)×10−27 kg	5.7×10−10	[27]
	muon mass	1.883531627(42)×10−28 kg	2.2×10−8	[28]
	tau mass	3.16754(21)×10−27 kg	6.8×10−5	[29]
	top quark mass	3.0784(53)×10−25 kg	1.7×10−3	[30]
	proton-to-electron mass ratio	1836.15267343(11)	6.0×10−11	[31]
	W-to-Z mass ratio	0.88153(17)	1.9×10−4	[32]
	weak mixing angle	0.22290(30)	1.3×10−3	[33]
	electron g-factor	−2.00231930436256(35)	1.7×10−13	[34]
	muon g-factor	−2.0023318418(13)	6.3×10−10	[35]
	proton g-factor	5.5856946893(16)	2.9×10−10	[36]
	quantum of circulation	3.6369475516(11)×10−4 m2⋅s−1	3.0×10−10	[37]
	Bohr magneton	9.2740100783(28)×10−24 J⋅T−1	3.0×10−10	[38]
	nuclear magneton	5.0507837461(15)×10−27 J⋅T−1	3.1×10−10	[39]
	classical electron radius	2.8179403262(13)×10−15 m	4.5×10−10	[40]
	Thomson cross section	6.6524587321(60)×10−29 m2	9.1×10−10	[41]
	Bohr radius	5.29177210903(80)×10−11 m	1.5×10−10	[42]
	Hartree energy	4.3597447222071(85)×10−18 J	1.9×10−12	[43]
	Rydberg unit of energy	2.1798723611035(42)×10−18 J	1.9×10−12	[44]
	Rydberg constant	10973731.568160(21) m−1	1.9×10−12	[45]
	Fermi coupling constant	1.1663787(6)×10−5 GeV−2	5.1×10−7	[46]
	Avogadro constant	6.02214076×1023 mol−1	0	[47]
	molar gas constant	8.31446261815324 J⋅mol−1⋅K−1	0	[48]
	Faraday constant	96485.3321233100184 C⋅mol−1	0	[49]
	molar Planck constant	3.9903127128934314×10−10 J⋅s⋅mol−1	0	[50]
	atomic mass of carbon-12	1.99264687992(60)×10−26 kg	3.0×10−10	[51]
	molar mass of carbon-12	11.9999999958(36)×10−3 kg⋅mol−1	3.0×10−10	[52]
	atomic mass constant	1.66053906660(50)×10−27 kg	3.0×10−10	[53]
	molar mass constant	0.99999999965(30)×10−3 kg⋅mol−1	3.0×10−10	[54]
	molar volume of silicon	1.205883199(60)×10−5 m3⋅mol−1	4.9×10−8	[55]
	hyperfine transition frequency of 133Cs	9192631770 Hz	0	[56]

Uncertainties[edit]

While the values of the physical constants are independent of the system of units in use, each uncertainty as stated reflects our lack of knowledge of the corresponding value as expressed in SI units, and is strongly dependent on how those units are defined. For example, the atomic mass constant is exactly known when expressed using the dalton (its value is exactly 1 Da), but the kilogram is not exactly known when using these units, the opposite of when expressing the same quantities using the kilogram.

Technical constants[edit]

Some of these constants are of a technical nature and do not give any true physical property, but they are included for convenience. Such a constant gives the correspondence ratio of a technical dimension with its corresponding underlying physical dimension. These include the Boltzmann constant , which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant , which gives the correspondence of the dimension of amount of substance with the dimension of count of entities (the latter formally regarded in the SI as being dimensionless). By implication, any product of powers of such constants is also such a constant, such as the molar gas constant .

See also[edit]

• List of mathematical constants
• Physical constant
• List of particles

Notes[edit]

References[edit]

The constants listed here are known values of physical constants expressed in SI units; that is, physical quantities that are generally believed to be universal in nature and thus are independent of the unit system in which they are measured. Many of these are redundant, in the sense that they obey a known relationship with other physical constants and can be determined from them.

Table of physical constants[edit]

Symbol	Quantity	Value[a][b]	Relative standard uncertainty	Ref
	Newtonian constant of gravitation	6.67430(15)×10−11 m3⋅kg−1⋅s−2	2.2×10−5	[1]
	speed of light in vacuum	299792458 m⋅s−1	0	[2]
	Planck constant	6.62607015×10−34 J⋅Hz−1	0	[3]
	reduced Planck constant	1.054571817…×10−34 J⋅s	0	[4]
	vacuum magnetic permeability	1.25663706212(19)×10−6 N⋅A−2	1.5×10−10	[5]
	characteristic impedance of vacuum	376.730313668(57) Ω	1.5×10−10	[6]
	vacuum electric permittivity	8.8541878128(13)×10−12 F⋅m−1	1.5×10−10	[7]
	Coulomb constant	8.9875517923(14)×109 N⋅m2⋅C−2	1.5×10−10	[8]
	Boltzmann constant	1.380649×10−23 J⋅K−1	0	[9]
	Stefan–Boltzmann constant	5.670374419…×10−8 W⋅m−2⋅K−4	0	[10]
	first radiation constant	3.741771852…×10−16 W⋅m2	0	[11]
	first radiation constant for spectral radiance	1.1910429723971884140794892×10−16 W⋅m2⋅sr−1	0	[12]
	second radiation constant	1.438776877…×10−2 m⋅K	0	[13]
[c]	Wien wavelength displacement law constant	2.897771955…×10−3 m⋅K	0	[14]
[d]	Wien frequency displacement law constant	5.878925757…×1010 Hz⋅K−1	0	[15]
	Wien entropy displacement law constant	3.002916077…×10−3 m⋅K	0	[16]
	elementary charge	1.602176634×10−19 C	0	[17]
	conductance quantum	7.748091729…×10−5 S	0	[18]
	inverse conductance quantum	12906.40372… Ω	0	[19]
	von Klitzing constant	25812.80745… Ω	0	[20]
	Josephson constant	483597.8484…×109 Hz⋅V−1	0	[21]
	magnetic flux quantum	2.067833848…×10−15 Wb	0	[22]
	fine-structure constant	7.2973525693(11)×10−3	1.5×10−10	[23]
	inverse fine-structure constant	137.035999084(21)	1.5×10−10	[24]
	electron mass	9.1093837015(28)×10−31 kg	3.0×10−10	[25]
	proton mass	1.67262192369(51)×10−27 kg	3.1×10−10	[26]
	neutron mass	1.67492749804(95)×10−27 kg	5.7×10−10	[27]
	muon mass	1.883531627(42)×10−28 kg	2.2×10−8	[28]
	tau mass	3.16754(21)×10−27 kg	6.8×10−5	[29]
	top quark mass	3.0784(53)×10−25 kg	1.7×10−3	[30]
	proton-to-electron mass ratio	1836.15267343(11)	6.0×10−11	[31]
	W-to-Z mass ratio	0.88153(17)	1.9×10−4	[32]
	weak mixing angle	0.22290(30)	1.3×10−3	[33]
	electron g-factor	−2.00231930436256(35)	1.7×10−13	[34]
	muon g-factor	−2.0023318418(13)	6.3×10−10	[35]
	proton g-factor	5.5856946893(16)	2.9×10−10	[36]
	quantum of circulation	3.6369475516(11)×10−4 m2⋅s−1	3.0×10−10	[37]
	Bohr magneton	9.2740100783(28)×10−24 J⋅T−1	3.0×10−10	[38]
	nuclear magneton	5.0507837461(15)×10−27 J⋅T−1	3.1×10−10	[39]
	classical electron radius	2.8179403262(13)×10−15 m	4.5×10−10	[40]
	Thomson cross section	6.6524587321(60)×10−29 m2	9.1×10−10	[41]
	Bohr radius	5.29177210903(80)×10−11 m	1.5×10−10	[42]
	Hartree energy	4.3597447222071(85)×10−18 J	1.9×10−12	[43]
	Rydberg unit of energy	2.1798723611035(42)×10−18 J	1.9×10−12	[44]
	Rydberg constant	10973731.568160(21) m−1	1.9×10−12	[45]
	Fermi coupling constant	1.1663787(6)×10−5 GeV−2	5.1×10−7	[46]
	Avogadro constant	6.02214076×1023 mol−1	0	[47]
	molar gas constant	8.31446261815324 J⋅mol−1⋅K−1	0	[48]
	Faraday constant	96485.3321233100184 C⋅mol−1	0	[49]
	molar Planck constant	3.9903127128934314×10−10 J⋅s⋅mol−1	0	[50]
	atomic mass of carbon-12	1.99264687992(60)×10−26 kg	3.0×10−10	[51]
	molar mass of carbon-12	11.9999999958(36)×10−3 kg⋅mol−1	3.0×10−10	[52]
	atomic mass constant	1.66053906660(50)×10−27 kg	3.0×10−10	[53]
	molar mass constant	0.99999999965(30)×10−3 kg⋅mol−1	3.0×10−10	[54]
	molar volume of silicon	1.205883199(60)×10−5 m3⋅mol−1	4.9×10−8	[55]
	hyperfine transition frequency of 133Cs	9192631770 Hz	0	[56]

Uncertainties[edit]

While the values of the physical constants are independent of the system of units in use, each uncertainty as stated reflects our lack of knowledge of the corresponding value as expressed in SI units, and is strongly dependent on how those units are defined. For example, the atomic mass constant is exactly known when expressed using the dalton (its value is exactly 1 Da), but the kilogram is not exactly known when using these units, the opposite of when expressing the same quantities using the kilogram.

Technical constants[edit]

Some of these constants are of a technical nature and do not give any true physical property, but they are included for convenience. Such a constant gives the correspondence ratio of a technical dimension with its corresponding underlying physical dimension. These include the Boltzmann constant , which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant , which gives the correspondence of the dimension of amount of substance with the dimension of count of entities (the latter formally regarded in the SI as being dimensionless). By implication, any product of powers of such constants is also such a constant, such as the molar gas constant .

See also[edit]

• List of mathematical constants
• Physical constant
• List of particles

Notes[edit]

References[edit]

Универсальная и неизменная физическая величина

A физическая константа, иногда фундаментальная физическая постоянная или универсальная константа — это физическая величина, которая обычно считается универсальной по природе и имеет постоянную значение во времени. Это контрастирует с математической константой , которая имеет фиксированное числовое значение, но не включает напрямую никаких физических измерений.

В науке существует множество физических констант, некоторые из наиболее широко признанных — это скорость света в вакууме c, гравитационная постоянная G, Постоянная Планка h, электрическая постоянная ε0и элементарный заряд e. Физические константы могут принимать многие размерные формы: скорость света означает максимальную скорость для любого объекта, а его размер равен длине, деленной на время ; в то время как постоянная тонкой структуры α, которая характеризует силу электромагнитного взаимодействия, безразмерна.

Термин фундаментальная физическая постоянная иногда используется для обозначения универсального но размерные физические константы, такие как упомянутые выше. Однако все чаще физики используют фундаментальную физическую постоянную только для безразмерных физических констант, таких как постоянная тонкой структуры α.

Физическую константу, как обсуждается здесь, не следует путать с другими величинами, называемыми «константами», которые считаются постоянными в данном контексте, но не являются фундаментальными, такими как «постоянная времени «характеристика данной системы или константы материала (например, постоянная Маделунга, удельное электрическое сопротивление и теплоемкость ).

С мая 2019 года все базовые единицы СИ были определены в терминах физических констант. В результате пять констант: скорость света в вакууме, c; постоянная Планка, ч; элементарный заряд, э; константа Авогадро, N A ; и постоянная Больцмана, k B, имеют точные числовые значения, когда они выражены в единицах СИ. Первые три из этих констант являются фундаментальными константами, тогда как N A и k B имеют только технический характер: они не описывают никаких свойств вселенной, а вместо этого только дают коэффициент пропорциональности для определения единиц, используемых с большим количеством объектов атомарного масштаба.

Содержание

• 1 Выбор единиц
  • 1.1 Натуральные единицы
• 2 Количество фундаментальных констант
• 3 Тесты на независимость от времени
• 4 Точно настроенная вселенная
• 5 Таблица физических констант
• 6 См. Также
• 7 Ссылки
• 8 Внешние ссылки

Выбор единиц

В то время как физическая величина, обозначенная физической константой, не зависит от единицы системы, используемой для выражения количества, числовые значения размерных физических констант действительно зависят от выбора системы единиц. Термин «физическая постоянная» относится к физической величине, а не к числовому значению в любой данной системе единиц. Например, скорость света определяется как имеющая числовое значение 299792458 при выражении в единицах СИ метров в секунду и как имеющее числовое значение 1 при выражении в натуральные единицы Планковская длина за планковское время. Хотя ее числовое значение может быть определено по желанию путем выбора единиц, скорость света сама по себе является единственной физической константой.

Любое соотношение между физическими константами одинаковых размеров приводит к безразмерной физической постоянной, например, отношение масс протона к электрону. Любая связь между физическими величинами может быть выражена как связь между безразмерными отношениями с помощью процесса, известного как обезразмеривание.

Термин «фундаментальная физическая константа» зарезервирован для физических величин, которые, согласно текущему уровню знаний, являются рассматривается как неизменный и не вытекающий из более фундаментальных принципов. Яркими примерами являются скорость света c и гравитационная постоянная G.

постоянная тонкой структуры α является наиболее известной безразмерной фундаментальной физической постоянной. Это значение элементарного заряда в квадрате, выраженное в единицах Планка. Это значение стало стандартным примером при обсуждении выводимости или невозможности вывода физических констант. Введенный Арнольдом Зоммерфельдом, его значение, определенное в то время, соответствовало 1/137. Это побудило Артура Эддингтона (1929) создать аргумент, почему его значение может быть точно 1/137, что связано с числом Эддингтона, его оценкой количества протонов во Вселенной.. К 1940-м годам стало ясно, что значение постоянной тонкой структуры значительно отклоняется от точного значения 1/137, опровергая аргумент Эддингтона.

С развитием квантовой химии в Однако в 20 веке огромное количество необъяснимых ранее безразмерных физических констант было успешно вычислено на основе теории. В свете этого некоторые физики-теоретики все еще надеются на дальнейший прогресс в объяснении значений других безразмерных физических констант.

Известно, что Вселенная была бы совсем другой, если бы эти константы принимали значения, значительно отличающиеся от тех, которые мы наблюдаем. Например, изменения значения постоянной тонкой структуры на несколько процентов будет достаточно, чтобы исключить такие звезды, как наше Солнце. Это вызвало попытки антропных объяснений значений некоторых безразмерных фундаментальных физических констант.

Натуральные единицы

Можно комбинировать размерные универсальные физические константы для определения фиксированных величин любого желаемого измерения, и это свойство использовалось для построения различных систем естественных единиц измерения. В зависимости от выбора и расположения используемых констант полученные натуральные единицы могут быть удобны для области исследования. Например, единицы Планка, построенные из c, G, ħ, и kB дают единицы измерения удобного размера для использования в исследованиях квантовой гравитации и атомных единиц Хартри, построенные из ħ, me, e и 4πε0, дают удобные единицы в атомной физике. Выбор используемых констант приводит к широкому изменению величин.

Количество фундаментальных констант

Количество фундаментальных физических констант зависит от физической теории, принятой в качестве «фундаментальной». В настоящее время это теория общей теории относительности для гравитации и Стандартная модель для электромагнитных, слабых и сильных ядерных взаимодействий и полей материи. Вместе эти теории составляют 19 независимых фундаментальных констант. Однако не существует единого «правильного» способа их перечисления, поскольку это вопрос произвольного выбора, какие величины считать «основными», а какие — «производными». Узан (2011) перечисляет 22 «неизвестных константы» в фундаментальных теориях, которые приводят к 19 «неизвестным безразмерным параметрам», а именно:

• гравитационная постоянная G,
• скорость света c,
• постоянная Планка h,
• 9 связи Юкавы для кварков и лептонов (что эквивалентно заданию массы покоя этих элементарных частиц ),
• 2 параметров потенциала поля Хиггса,
• 4 параметра для матрицы смешения кварков,
• 3 константы связи для калибровочных групп SU (3) × SU (2) × U (1) (или, что эквивалентно, две константы связи и угол Вайнберга ),
• фаза для вакуума КХД.

Число 19 независимых фундаментальных физических константы могут быть изменены в рамках возможных расширений Стандартной модели, в частности, путем введения массы нейтрино (что эквивалентно семи дополнительным константам, т. е. 3 связи Юкавы и 4 лептонного смешения параметры).

Открытие y изменения любой из этих констант было бы эквивалентно открытию «новой физики «.

. Вопрос о том, какие константы являются« фундаментальными », не является ни прямым, ни бессмысленным, это вопрос интерпретации рассматриваемой физической теории как фундаментальный; как указано Леви-Леблон 1977 г., не все физические константы имеют одинаковое значение, причем некоторые имеют более глубокую роль, чем другие. Леви-Леблон 1977 предложил схемы классификации трех типов констант:

• A: физические свойства отдельных объектов
• B: характеристика класса физических явлений
• C: универсальные константы

Одна и та же физическая константа может переходить из одной категории в другую по мере углубления понимания ее роли; в частности, это произошло с скоростью света, которая была константой класса A (характеристика света ), когда она была впервые измерена, но стала константой класса B (характеристика электромагнитные явления ) с развитием классического электромагнетизма и, наконец, константа класса C с открытием специальной теории относительности.

Тесты на независимость от времени

Автор По определению, фундаментальные физические константы подлежат измерению, так что их постоянство (независимо от времени и положения выполнения измерения) обязательно является экспериментальным результатом и подлежит проверке.

Поль Дирак в 1937 году предположил, что физические константы, такие как гравитационная постоянная или постоянная тонкой структуры, могут изменяться со временем пропорционально возраст вселенной. Эксперименты, в принципе, могут установить только верхнюю границу относительного изменения за год. Для постоянной тонкой структуры эта верхняя граница сравнительно низкая, примерно 10 в год (по состоянию на 2008 г.).

Гравитационную постоянную гораздо труднее измерить с точностью, и противоречивые измерения в 2000-х гг. вдохновил спорные предположения о периодическом изменении его стоимости в статье 2015 года. Однако, хотя его значение неизвестно с большой точностью, возможность наблюдения сверхновых типа Ia, которые произошли в далеком прошлом Вселенной, в сочетании с предположением, что физика, вовлеченная в эти события, является универсальной, позволяет верхняя граница менее 10 в год для гравитационной постоянной за последние девять миллиардов лет.

Аналогично, верхняя граница изменения отношения масс протона к электрону была помещен в 10 в течение 7 миллиардов лет (или 10 в год) в исследовании 2012 года, основанном на наблюдении метанола в далекой галактике.

Проблематично обсуждать предложенное скорость изменения (или ее отсутствия) отдельно взятой одномерной физической постоянной. Причина этого в том, что выбор единиц измерения произвольный, поэтому вопрос о том, претерпевает ли константа изменение, является артефактом выбора (и определения) единиц.

Например, в SI единиц, скорость света получила определенное значение в 1983 году. Таким образом, до 1983 года имело смысл экспериментально измерить скорость света в единицах СИ, но сейчас это не так. Аналогичным образом, начиная с мая 2019 года, постоянная Планка имеет определенное значение, так что все базовые единицы СИ теперь определены в терминах фундаментальных физических констант. С этим изменением, международный прототип килограмма удаляется как последний физический объект, используемый в определении любой единицы СИ.

В тестах на неизменность физических констант изучаются безразмерные величины, то есть отношения между величинами одинаковых размеров, чтобы избежать этой проблемы. Изменения физических констант не имеют смысла, если они приводят к неразличимой с точки зрения наблюдений Вселенной. Например, «изменение» скорости света c было бы бессмысленным, если бы сопровождалось соответствующим изменением элементарного заряда e, так что отношение e / (4πε 0 ħc) (постоянная тонкой структуры) осталась неизменной.

Тонко настроенная вселенная

Некоторые физики исследовали идею о том, что если безразмерные физические константы имеют достаточно разные значения, наши Вселенная будет настолько радикально отличаться от других, что разумная жизнь, вероятно, не возникнет, и поэтому наша Вселенная кажется тонко настроенной для разумной жизни. Однако фазовое пространство возможных констант и их значений неизвестно, поэтому любые выводы, сделанные на основе таких аргументов, не подтверждаются. Антропный принцип устанавливает логический трюизм : факт нашего существования в качестве разумных существ, которые могут измерять физические константы, требует, чтобы эти константы были такими, чтобы существа, подобные нам, могли существовать. Существует множество интерпретаций значений констант, включая интерпретацию божественного творца (кажущаяся точная настройка фактическая и преднамеренная), или то, что наша вселенная — одна из многих в мультивселенной (например, интерпретация многих миров из квантовой механики ) или даже так, если информация является врожденным свойством вселенной и логически неотделима от сознание, вселенная без способности к сознательным существам существовать не может.

Было обнаружено, что фундаментальные константы и количества природы точно настроены на такой чрезвычайно узкий диапазон, что, если бы это было не так, происхождение и эволюция сознательной жизни во Вселенной не допускается.

Таблица физических констант

В таблице ниже перечислены некоторые часто используемые константы и их рекомендуемые значения CODATA. Более подробный список см. В Список физических констант.

Количество	Символ	Значение	Относительная. стандартная. неопределенность
элементарный заряд	e { displaystyle e}	1,602176634 × 10 C	0
Ньютоновская постоянная гравитации	G { displaystyle G}	6,67430 (15) × 10 м⋅кг⋅с	2,2 × 10
постоянная Планка	h { displaystyle h}	6,62607015 × 10 Дж / с	0
скорость света в вакууме	c { displaystyle c}	299792458 м ⋅s	0
электрическая диэлектрическая проницаемость вакуума	ε 0 = 1 / μ 0 c 2 { displaystyle varepsilon _ {0} = 1 / mu _ {0} c ^ {2}}	8.8541878128 (13) × 10 Ф · м	1,5 · 10
магнитная проницаемость вакуума	μ 0 { displaystyle mu _ {0}}	1,25663706212 (19) × 10 N⋅A	1,5 × 10
масса электрона	me { displaystyle m _ { mathrm {e}}}	9,1093837015 (28) × 10 кг	3,0 × 10
постоянная тонкой структуры	α = e 2/2 ε 0 hc { displaystyle alpha = e ^ {2} / 2 varepsilon _ {0} hc}	7.2973525693 (11) × 10	1,5 × 10
постоянная Джозефсона	KJ = 2 e / h { displaystyle K _ { mathrm {J}} = 2e / h}	483597.8484… × 10 Гц⋅V	0
постоянная Ридберга	R ∞ = α 2 mec / 2 час { displaystyle R _ { infty} = alpha ^ {2} m _ { mathrm {e}} c / 2h}	10973731.568160 (21) m	1,9 × 10
фон Константа Клитцинга	RK = h / e 2 { displaystyle R _ { mathrm {K}} = h / e ^ {2}}	25812.80745… Ω	0

См. Также

• Список общих обозначения физики

Список литературы

• Мор, Питер Дж.; Тейлор, Барри Н.; Ньюэлл, Дэвид Б. (2008). «CODATA Рекомендуемые значения фундаментальных физических констант: 2006 г.» (PDF). Обзоры современной физики. 80(2): 633–730. arXiv : 0801.0028. Bibcode : 2008RvMP… 80..633M. doi : 10.1103 / RevModPhys.80.633. Архивировано из оригинального (PDF) 01.10.2017.

• Барроу, Джон Д. (2002), Константы природы; От альфы к омеге — числа, закодирующие самые глубокие тайны Вселенной, Pantheon Books, ISBN 978-0-375-42221-8.

Внешние ссылки

• Шестьдесят символов, Ноттингемский университет
• ИЮПАК — Золотая книга