Physical constant
A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement.
There are many physical constants in science, some of the most widely recognized being the
The term "fundamental physical constant" is sometimes used to refer to universal-but-dimensioned physical constants such as those mentioned above.
Physical constant, as discussed here, should not be confused with
) of a particular material or substance.Characteristics
Physical constants are parameters in a physical theory that cannot be explained by that theory. This may be due to the apparent fundamental nature of the constant or due to limitations in the theory. Consequently, physical constants must be measured experimentally.[3]: 9
The set of parameters considered physical constants change as physical models change and how fundamental they appear can change. For example, the speed of light was originally considered a property of light, a specific system. The discovery and verification of Maxwell's equations connect the same quantity an entire system, electromagnetism. When the theory of special relativity emerged, the quantity came to be understood as the basis of causality.[3] The speed of light is so fundamental it now defines the international unit of length.
Relationship to units
Numerical values
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
International System of Units
Since May 2019, all of the units in the
: 128As a result of the new definitions, an SI unit like the kilogram can be written in terms of fundamental constants and one experimentally measured constant, ΔνCs:[4]: 131
- 1 kg = (299792458)2/(6.62607015×10−34)(9192631770)hΔνCs/c2.
Natural units
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,
. The choice of constants used leads to widely varying quantities.Number of fundamental constants
The number of fundamental physical constants depends on the
- the gravitational constant G,
- the speed of light c,
- the Planck constant h,
- the 9 elementary particles),
- 2 parameters of the Higgs fieldpotential,
- 4 parameters for the quark mixing matrix,
- 3 coupling constants for the 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
The discovery of variability in any of these constants would be equivalent to the discovery of "
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.[5]
Tests on time-independence
By definition, fundamental physical constants are subject to measurement, so that their being constant (independent on both the time and position of the performance of the measurement) is necessarily an experimental result and subject to verification.
Paul Dirac in 1937 speculated that physical constants such as the gravitational constant or the fine-structure constant might be subject to change over time in proportion of the age of the universe. Experiments can in principle only put an upper bound on the relative change per year. For the fine-structure constant, this upper bound is comparatively low, at roughly 10−17 per year (as of 2008).[6]
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.
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.[9][10]
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.[11][12][13]
For example, in
Tests on the immutability of physical constants look at dimensionless quantities, i.e. ratios between quantities of like dimensions, in order to escape this problem. Changes in physical constants are not meaningful if they result in an observationally indistinguishable universe. For example, a "change" in the speed of light c would be meaningless if accompanied by a corresponding change in the elementary charge e so that the expression e2/(4πε0ħc) (the fine-structure constant) remained unchanged.[14]
Dimensionless physical constants
Any ratio between physical constants of the same dimensions results in a dimensionless physical constant, for example, the proton-to-electron mass ratio. The fine-structure constant α 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 and uncertainty 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.[15] 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.[16]
Fine-tuned universe
Some physicists have explored the notion that if the
Table of physical constants
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[18] | Relative standard uncertainty |
---|---|---|---|
elementary charge | 1.602176634×10−19 C[19] | 0 | |
Newtonian constant of gravitation | 6.67430(15)×10−11 m3⋅kg−1⋅s−2[20] | 2.2×10−5 | |
Planck constant | 6.62607015×10−34 J⋅Hz−1[21] | 0 | |
speed of light in vacuum | 299792458 m⋅s−1[22] | 0 | |
vacuum electric permittivity | 8.8541878128(13)×10−12 F⋅m−1[23] | 1.5×10−10 | |
vacuum magnetic permeability | 1.25663706212(19)×10−6 N⋅A−2[24] | 1.5×10−10 | |
electron mass | 9.1093837015(28)×10−31 kg[25] | 3.0×10−10 | |
fine-structure constant | 7.2973525693(11)×10−3[26] | 1.5×10−10 | |
Josephson constant
|
483597.8484...×109 Hz⋅V−1[27] | 0 | |
Rydberg constant | 10973731.568160(21) m−1[28] | 1.9×10−12 | |
von Klitzing constant
|
25812.80745... Ω[29] | 0 |
See also
References
- ^ "Fundamental Physical Constants from NIST". Archived from the original on 2016-01-13. Retrieved 2016-01-14. NIST
- ^ "ISO 80000-1:2022 Quantities and units — Part 1: General". iso.org. Retrieved 2023-08-31.
- ^ PMID 28179829.
- ^ ISBN 978-92-822-2272-0
- S2CID 121022139.Lévy-Leblond, J.-M. (1979). "The importance of being (a) Constant". In Toraldo di Francia, G. (ed.). Problems in the Foundations of Physics, Proceedings of the International School of Physics 'Enrico Fermi' Course LXXII, Varenna, Italy, July 25 – August 6, 1977. New York: NorthHolland. pp. 237–263.
- ^
T. Rosenband; et al. (2008). "Frequency Ratio of Al+ and Hg+ Single-Ion Optical Clocks; Metrology at the 17th Decimal Place". S2CID 206511320.
- S2CID 119293843
- S2CID 119292899
- S2CID 716087.
- ^ Moskowitz, Clara (December 13, 2012). "Phew! Universe's Constant Has Stayed Constant". Space.com. Archived from the original on December 14, 2012. Retrieved December 14, 2012.
- S2CID 118347723.
- arXiv:hep-th/0208093.
- S2CID 15806354.
- ISBN 978-0-375-42221-8
- ^ A.S Eddington (1956). "The Constants of Nature". In J.R. Newman (ed.). The World of Mathematics. Vol. 2. Simon & Schuster. pp. 1074–1093.
- ^
H. Kragh (2003). "Magic Number: A Partial History of the Fine-Structure Constant". S2CID 118031104.
- ISBN 1573922501.
- least significant digitsof the value.
- ^ "2018 CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
- ^ "2018 CODATA Value: Newtonian constant of gravitation". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
- ^ "2018 CODATA Value: Planck constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2021-04-28.
- ^ "2018 CODATA Value: speed of light in vacuum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
- ^ "2018 CODATA Value: vacuum electric permittivity". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
- ^ "2018 CODATA Value: vacuum magnetic permeability". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
- ^ "2018 CODATA Value: electron mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
- ^ "2018 CODATA Value: fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
- ^ "2018 CODATA Value: Josephson constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
- ^ "2018 CODATA Value: Rydberg constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
- ^ "2018 CODATA Value: von Klitzing constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
- Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006" (PDF). doi:10.1103/RevModPhys.80.633. Archived from the original(PDF) on 2017-10-01.
External links
- Sixty Symbols, University of Nottingham
- IUPAC – Gold Book