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Fundamental physical constants

Fundamental physical constants are constants included in equations describing the fundamental laws of nature and the properties of matter [1] . Fundamental physical constants arise in theoretical models of observed phenomena in the form of universal coefficients in the corresponding mathematical expressions.

Content

  • 1 Review
  • 2 Fundamental physical constants
  • 3 Planck quantities (dimensional combinations of the constants c, G, h, k )
  • 4 Constants linking different systems of units and conversion factors
  • 5 Electromagnetic constants
  • 6 Some other physical constants
  • 7 See also
  • 8 Notes
  • 9 References

Overview

The word "constant" in physics is used in a double sense:

  • the numerical value of a certain value does not depend on any external parameters at all and does not change with time,
  • a change in the numerical value of a certain quantity is not essential for the problem under consideration.

For example, the heliocentric constant, equal to the product of the gravitational constant by the mass of the Sun , decreases due to a decrease in the mass of the Sun, resulting from the radiation of energy from it and the emission of the solar wind . However, since the relative decrease in the mass of the Sun is of the order of 10 -14 , the heliocentric constant can be regarded as a constant with satisfactory accuracy for most tasks of celestial mechanics . Also in high-energy physics , the fine structure constant , which characterizes the intensity of the electromagnetic interaction , increases with the transfer of the momentum (at small distances), however, its change is not essential for a wide range of ordinary phenomena, for example, for spectroscopy.

Physical constants are divided into two main groups - dimensional and dimensionless constants. The numerical values ​​of dimensional constants depend on the choice of units. The numerical values ​​of dimensionless constants do not depend on systems of units and should be determined purely mathematically in the framework of a unified theory. Among dimensional physical constants, it is necessary to distinguish constants that do not form dimensionless combinations among themselves, their maximum number is equal to the number of basic units of measurement - these are actually the fundamental physical constants ( speed of light , Planck's constant , etc.). All other dimensional physical constants are reduced to combinations of dimensionless constants and fundamental dimensional constants. From the point of view of fundamental constants, the evolution of the physical picture of the world is a transition from physics without fundamental constants (classical physics) to physics with fundamental constants (modern physics). At the same time, classical physics retains its significance as the limiting case of modern physics, when the characteristic parameters of the phenomena under study are far from fundamental constants.

The speed of light appeared back in classical physics in the 17th century, but then it did not play a fundamental role. The speed of light acquired fundamental status after the creation of electrodynamics by J. K. Maxwell and the special theory of relativity by A. Einstein (1905). After the creation of quantum mechanics (1926), Planck's constant h acquired fundamental status, introduced by M. Planck in 1901 as a dimensional coefficient in the law of thermal radiation. The fundamental constants also include a number of scientists the gravitational constant G , the Boltzmann constant k , the elementary charge e (or the fine structure constant α ) and the cosmological constant Λ . Fundamental physical constants are the natural scales of physical quantities, the transition to them as units of measurement underlies the construction of a natural (Planck) system of units . By virtue of historical tradition, some other physical constants associated with specific bodies (for example, masses of elementary particles ) also belong to fundamental constants, however, these constants should, according to modern concepts, be derived in some unknown way from a more fundamental scale of mass (energy ), the so-called Higgs vacuum mean field .

An internationally accepted set of values ​​of fundamental physical constants and coefficients for their translation is regularly published [2] by the CODATA Working Group on Fundamental Constants.

Fundamental Physical Constants

Here and below are the values ​​recommended by CODATA in 2018.

ValueSymbolValueNote
speed of light in vacuumc{\ displaystyle \ c}  299 792 458 m s −1
= 2.99792458⋅10 8 m s −1		for sure
gravitational constantG{\ displaystyle \ G}  6.674 30 (15) ⋅ 10 −11 m 3 kg −1 s −2
Planck's constant (elementary quantum of action)h{\ displaystyle \ h}  6.626 070 15⋅10 −34 J · sfor sure
Dirac constant (reduced Planck constant )ℏ=h/2π{\ displaystyle \ hbar = h / 2 \ pi}  1,054 571 817 ... ⋅10 −34 J s
elemental chargee{\ displaystyle \ e}  1,602 176 634⋅10 −19 Clfor sure
Boltzmann constantk{\ displaystyle \ k}  1,380 649⋅10 −23 J · K −1for sure

Planck quantities (dimensional combinations of the constants c, G, h, k )

TitleSymbolValue
Planck massmp=(ℏc/G)one/2{\ displaystyle m_ {p} = (\ hbar c / G) ^ {1/2}}  2.176 434 (24) ⋅10 −8 kg [3]
Planck lengthlp=(ℏG/c3)one/2{\ displaystyle l_ {p} = (\ hbar G / c ^ {3}) ^ {1/2}}  1,616 255 (18) ⋅10 −35 m [4] [5]
Planck timetp=(ℏG/c5)one/2{\ displaystyle t_ {p} = (\ hbar G / c ^ {5}) ^ {1/2}}  5.391 247 (60) ⋅10 −44 s [6]
Planck temperatureTp=onek(ℏc5/G)one/2{\ displaystyle T_ {p} = {\ frac {1} {k}} (\ hbar c ^ {5} / G) ^ {1/2}}  1.416 784 (16) ⋅10 32 K [7]

Constant, connecting different systems of units, and translation factors

TitleSymbolValueNote
fine structure constantα=e2/fourπε0ℏc{\ displaystyle \ alpha = e ^ {2} / 4 \ pi \ varepsilon _ {0} \ hbar c}   ( SI system )7.297 352 5693 (11) ⋅10 −3
α-one{\ displaystyle \ alpha ^ {- 1}}  137,035 999 084 (21)
electric constantε0=one/(μ0c2){\ displaystyle \ varepsilon _ {0} = 1 / (\ mu _ {0} c ^ {2})}  8.854 187 8128 (13) ⋅ 10 −12 F · m −1
atomic mass unitmu{\ displaystyle \ m_ {u}}   = 1 a. eat.1,660 539 066 60 (50) ⋅ 10 −27 kg
1 amu1.492 418 085 60 (45) ⋅ 10 −10 J
= 931.494 102 42 (28) ⋅10 6 Ev
= 931.494 102 42 (28) MeV [8]
Avogadro constantNA{\ displaystyle \ N_ {A}}  6.022 140 76⋅10 23 mol −1 [9]for sure
1 electronvolteV1,602 176 634⋅10 −19 J
= 1.602 176 634⋅10 −12 erg		for sure
1 calorie (international)1 cal4.1868 Jfor sure
liter atmosphere1 L atm101.325 J
2.30259 RT [10]5.706 kJ mol −1 (at 298 K)
1 kJ mol −183.593 cm −1 [11]

Electromagnetic Constants

The following constants were accurate prior to changes in the definitions of the basic SI units of 2018-2019 , but became experimentally determined values ​​as a result of these changes.

TitleSymbolValueNote
magnetic constant [12]μ0=one/(ε0c2){\ displaystyle \ mu _ {0} = 1 / (\ varepsilon _ {0} c ^ {2})}  1.256 637 062 12 (19) ⋅10 -6 GN · m −1 = 1.256 637 062 12 (19) ⋅10 -6 N · A −2 (through the basic SI units: kg · m · s -2 · A -2 )earlier exactlyfourπ×10-7 {\ displaystyle 4 \ pi \ times 10 ^ {- 7}}   GN / m
vacuum impedance [13]Z0=μ0c=oneε0c{\ displaystyle Z_ {0} = \ mu _ {0} c = {\ frac {1} {\ varepsilon _ {0} c}}}  ≈376.73{\ displaystyle \ approx 376.73}   Ohm.
electric constantε0=one/(μ0c2){\ displaystyle \ varepsilon _ {0} = 1 / (\ mu _ {0} c ^ {2})}  8.854 187 8128 (13) ⋅10 −12 F · m −1 (through the basic SI units: kg −1 · m −3 · s 4 · А 2 )
pendant constantk=onefourπε0{\ displaystyle k = {\ frac {1} {4 \ pi \ varepsilon _ {0}}}}  ≈ 8.987 55 ⋅10 9 F −1 · m (through the basic units: kg · m 3 · s −4 · A −2 )

Some other physical constants

TitleSymbolValueNote
Masses of elementary particles:
electron mass		me{\ displaystyle \ m_ {e}}  9.109 383 7015 (28) ⋅ 10 −31 kg (absolute)
= 0,000548579909065 (16) a.u. (rel.)
proton massmp{\ displaystyle \ m_ {p}}  1,672 621 923 69 (51) ⋅ 10 −27 kg
= 1.007276466621 (53)
neutron massmn{\ displaystyle \ m_ {n}}  1.674 927 498 04 (95) ⋅ 10 −27 kg
= 1.008 664 915 60 (57)
M proton plus electron (absolute mass of a hydrogen atom is 1 H )mp+e{\ displaystyle \ m_ {p + e}}  ≈ 1,673 5328⋅10 −27 kg
= 1.007825 amu ( rel. )
electron magnetic momentμe{\ displaystyle \ mu _ {e}}  −928,476 470 43 (28) ⋅10 −26 J · T −1
proton magnetic momentμp{\ displaystyle \ mu _ {p}}  1.410 606 797 36 (60) ⋅ 10 −26 J · T −1
magneton boraμB=eℏ/2me{\ displaystyle \ mu _ {B} = e \ hbar / 2m_ {e}}  927.401 007 83 (28) ⋅10 −26 J · T −1 [14]
nuclear magnetonμN{\ displaystyle \ mu _ {N}}  5.050 783 7461 (15) ⋅ 10 −27 J
g is the free electron factorge=2μe/μB{\ displaystyle g_ {e} = 2 \ mu _ {e} / \ mu _ {B}}  2.002 319 304 362 56 (35)
gyromagnetic ratio of protonγp=2μp/ℏ{\ displaystyle \ gamma _ {p} = 2 \ mu _ {p} / \ hbar}  2.675 221 8744 (11) ⋅10 8 s −1
Faraday constantF=NAe{\ displaystyle \ F = N_ {A} e}  96 485.332 12 ... Cl mol −1
universal gas constantR=kNA{\ displaystyle \ R = kN_ {A}}  8.314 462 618 ... J · K −1 · mol −1
≈ 0.082057 l · atm · K −1 · mol −1
molar volume of an ideal gas (at 273.15 K, 101.325 kPa)Vm{\ displaystyle \ V_ {m}}  22,413 969 54 ... ⋅10 −3 m³ mol −1
standard atmospheric pressure ( n.o. )atm101 325 Pafor sure
Borovsky radiusa0=α/(fourπR∞){\ displaystyle a_ {0} = \ alpha / (4 \ pi R _ {\ infty})}  0.529 177 210 903 (80) ⋅ 10 −10 m
hartree energyEh=2R∞hc{\ displaystyle E_ {h} = 2R _ {\ infty} hc}  4.359 744 722 2071 (85) ⋅ 10 −18 J
Rydberg constantR∞=α2mec/2h{\ displaystyle R _ {\ infty} = \ alpha ^ {2} m_ {e} c / 2h}  10 973 731.568 160 (21) m −1
first radiation constantcone=2πhc2{\ displaystyle c_ {1} = 2 \ pi hc ^ {2}}  3.741 771 852 ... ⋅10 −16 W m²
second radiation constantc2=hc/k{\ displaystyle c_ {2} = hc / k}  1.438 776 877 ... ⋅10 −2 mK
Stefan-Boltzmann constantσ=(π2/60)kfour/ℏ3c2{\ displaystyle \ sigma = (\ pi ^ {2} / 60) k ^ {4} / \ hbar ^ {3} c ^ {2}}  5,670 374 419 ... ⋅10 −8 W m −2 K −4
guilt constantb=c2/four,965114231 ...{\ displaystyle b = c_ {2} / 4,965114231 ...}  2,897 771 955 ... ⋅10 −3 m
standard acceleration of gravity on the Earth's surface (averaged)gn{\ displaystyle g_ {n}}  9.806 65 m s −2for sure
Triple point temperature of waterT0{\ displaystyle T_ {0}}  273.16 K

See also

  • Astronomical constants

Notes

  1. ↑ Fundamental physical constants // Physical Encyclopedia, vol. 5. M .: Big Russian Encyclopedia, 1998, p. 381-383.
  2. ↑ 1 2 CODATA Internationally recommended values ​​of the Fundamental Physical Constants
  3. ↑ Planck mass (unopened) (inaccessible link) . physics.nist.gov. Date of treatment June 28, 2015. Archived June 14, 2015.
  4. ↑ NIST 's “ Planck length ”, NIST's published CODATA constants
  5. ↑ Fundamental Physical Constants - Complete Listing
  6. ↑ Planck time (unopened) (inaccessible link) . physics.nist.gov. Date of treatment June 28, 2015. Archived June 14, 2015.
  7. ↑ Planck temperature (unopened) (inaccessible link) . physics.nist.gov. Date of treatment June 28, 2015. Archived June 14, 2015.
  8. ↑ from the relation E = mc 2
  9. ↑ Avogadro constant - CODATA Internationally recommended values ​​of the Fundamental Physical Constants
  10. ↑ from the relation determining the dependence of free energy on concentration (partial pressure):G=G∘+RTln(pp∘) {\ displaystyle G = G ^ {\ circ} + RT ~ \ mathrm {ln} \ left ({\ frac {p} {\ displaystyle {p ^ {\ circ}}} \ right)}  
    2,30259 - transition module (logarithms)
  11. ↑ from the relationE=hv=hcv¯ {\ displaystyle E = hv = hc {\ bar {v}}}   wherev¯ {\ displaystyle {\ bar {v}}}   expressed in inverse centimeters cm −1
  12. ↑ CODATA Value: Vacuum permeability
  13. ↑ CODATA Value: Characteristic impedance of vacuum (link not available)
  14. ↑ Bohr magneton (neopr.) . physics.nist.gov.

Links

  • Fundamental Physical Constants - Complete Listing .
  • Cohen ER, Crowe CM, Dumond JWM Fundamental constants of physics. NY, L., 1957, 287 p.
  • Barrow JD The Constants of Nature: From Alpha to Omega. London: Jonathan Cape, 2002. NY: Pantheon, 2003, 353 p.
  • Wilczek F. Fundamental Constants // arXiv: 0708.4361v1 (pdf), same: Frank Wilczek website .
  • Perch L. B. Fundamental constants of physics // UFN, 161 (9) p. 177-194 (1991) (pdf).
  • Karshenboim S.G. Fundamental physical constants: role in physics and metrology and recommended values // UFN, 175, No. 3, p.271-298 (2005) (pdf).
  • Rubakov V.A. Hierarchies of fundamental constants (to points 16, 17 and 27 from the list of V. L. Ginzburg) // UFN, 177, No. 4, p.407-414 (2007) (pdf).
  • Fritzs X. Fundamental physical constants // UFN, 179, No. 4, p. 383-392 (2009) (pdf).
  • Tomilin K. A. Fundamental physical constants in historical and methodological aspects. M .: Fizmatlit, 2006, 368 p. (djvu)
  • Spiridonov O.P. Fundamental physical constants. M .: Higher school, 1991, 238 p.
  • Sagitov M. U. The constant of gravity and the mass of the Earth. M .: Nauka, 1969, 188 p.
  • Quantum metrology and fundamental constants. M .: Mir, 1981, 368 p.
Source - https://ru.wikipedia.org/w/index.php?title=Fundamental_physical_constants&oldid=100654091


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