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In
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
, the proton-to-electron mass ratio (symbol ''μ'' or ''β'') is the
rest mass The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, ...
of the
proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...
(a
baryon In particle physics, a baryon is a type of composite particle, composite subatomic particle that contains an odd number of valence quarks, conventionally three. proton, Protons and neutron, neutrons are examples of baryons; because baryons are ...
found in
atoms Atoms are the basic particles of the chemical elements. An atom consists of a nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other ...
) divided by that of the
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
(a
lepton In particle physics, a lepton is an elementary particle of half-integer spin (Spin (physics), spin ) that does not undergo strong interactions. Two main classes of leptons exist: electric charge, charged leptons (also known as the electron-li ...
found in atoms), a
dimensionless quantity Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...
, namely: :''μ'' = The number in parentheses is the measurement uncertainty on the last two digits, corresponding to a relative standard uncertainty of


Discussion

''μ'' is an important fundamental physical constant because: * Baryonic matter consists of quarks and particles made from quarks, like
proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...
s and
neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...
s. Free neutrons have a
half-life Half-life is a mathematical and scientific description of exponential or gradual decay. Half-life, half life or halflife may also refer to: Film * Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang * ''Half Life: ...
of 613.9 seconds. Electrons and protons appear to be stable, to the best of current knowledge. (Theories of proton decay predict that the proton has a half life on the order of at least 1032 years. To date, there is no experimental evidence of proton decay.); * Because they are stable, are components of all normal atoms, and determine their chemical properties, the
proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...
is the most prevalent
baryon In particle physics, a baryon is a type of composite particle, composite subatomic particle that contains an odd number of valence quarks, conventionally three. proton, Protons and neutron, neutrons are examples of baryons; because baryons are ...
, while the
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
is the most prevalent
lepton In particle physics, a lepton is an elementary particle of half-integer spin (Spin (physics), spin ) that does not undergo strong interactions. Two main classes of leptons exist: electric charge, charged leptons (also known as the electron-li ...
; * The proton mass ''m''p is composed primarily of
gluon A gluon ( ) is a type of Massless particle, massless elementary particle that mediates the strong interaction between quarks, acting as the exchange particle for the interaction. Gluons are massless vector bosons, thereby having a Spin (physi ...
s, and of the
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...
s (the
up quark The up quark or u quark (symbol: u) is the lightest of all quarks, a type of elementary particle, and a significant constituent of matter. It, along with the down quark, forms the neutrons (one up quark, two down quarks) and protons (two up quark ...
and
down quark The down quark (symbol: d) is a type of elementary particle, and a major constituent of matter. The down quark is the second-lightest of all quarks, and combines with other quarks to form composite particles called hadrons. Down quarks are most ...
) making up the proton. Hence ''m''p, and therefore the ratio ''μ'', are easily measurable consequences of the strong force. In fact, in the chiral limit, ''m''p is proportional to the
QCD In theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in ...
energy scale, ΛQCD. At a given energy scale, the strong coupling constant ''α''s is related to the QCD scale (and thus ''μ'') as ::\alpha_s=-\frac :where ''β''0 = −11 + 2''n''/3, with ''n'' being the number of
flavors Flavour or flavor is either the sensory perception of taste or smell, or a flavoring in food that produces such perception. Flavour or flavor may also refer to: Science * Flavors (programming language), an early object-oriented extension to L ...
of
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...
s.


Variation of ''μ'' over time

Astrophysicists have tried to find evidence that ''μ'' has changed over the history of the universe. (The same question has also been asked of the
fine-structure constant In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Alpha, Greek letter ''alpha''), is a Dimensionless physical constant, fundamental physical constant that quantifies the strength of the el ...
.) One interesting cause of such change would be change over time in the strength of the strong force. Astronomical searches for time-varying ''μ'' have typically examined the Lyman series and Werner transitions of
molecular hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
which, given a sufficiently large
redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and increase in frequency and e ...
, occur in the optical region and so can be observed with ground-based spectrographs. If ''μ'' were to change, then the change in the wavelength ''λ''''i'' of each rest frame
wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
can be parameterised as: :\ \lambda_i=\lambda_0 \left 1+K_i \frac\mu \right where Δ''μ''/''μ'' is the proportional change in ''μ'' and ''Ki'' is a constant which must be calculated within a theoretical (or semi-empirical) framework. Reinhold et al. (2006) reported a potential 4
standard deviation In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...
variation in ''μ'' by analysing the molecular hydrogen absorption spectra of
quasar A quasar ( ) is an extremely Luminosity, luminous active galactic nucleus (AGN). It is sometimes known as a quasi-stellar object, abbreviated QSO. The emission from an AGN is powered by accretion onto a supermassive black hole with a mass rangi ...
s Q0405-443 and Q0347-373. They found that . King et al. (2008) reanalysed the spectral data of Reinhold et al. and collected new data on another quasar, Q0528-250. They estimated that , different from the estimates of Reinhold et al. (2006). Murphy et al. (2008) used the inversion transition of ammonia to conclude that at redshift . Kanekar (2011) used deeper observations of the inversion transitions of ammonia in the same system at towards 0218+357 to obtain . Bagdonaite et al. (2013) used
methanol Methanol (also called methyl alcohol and wood spirit, amongst other names) is an organic chemical compound and the simplest aliphatic Alcohol (chemistry), alcohol, with the chemical formula (a methyl group linked to a hydroxyl group, often ab ...
transitions in the spiral lensing
galaxy A galaxy is a Physical system, system of stars, stellar remnants, interstellar medium, interstellar gas, cosmic dust, dust, and dark matter bound together by gravity. The word is derived from the Ancient Greek, Greek ' (), literally 'milky', ...
PKS 1830-211 to find at . Kanekar et al. (2015) used near-simultaneous observations of multiple methanol transitions in the same lens, to find at . Using three methanol lines with similar frequencies to reduce systematic effects, Kanekar et al. (2015) obtained . Note that any comparison between values of Δ''μ''/''μ'' at substantially different redshifts will need a particular model to govern the evolution of Δ''μ''/''μ''. That is, results consistent with zero change at lower redshifts do not rule out significant change at higher redshifts.


See also

*
Koide formula The Koide formula is an unexplained Empirical relationship, empirical equation discovered by Yoshio Koide in 1981. In its original form, it is not fully empirical but a set of guesses for a model for masses of quarks and leptons, as well as Cabibbo ...


Footnotes


References

* * * * * * {{cite journal , last1 = Kanekar , first1 = N. , last2 = Ubachs , first2 = W. , last3 = Menten , first3 = K. L. , last4 = Bagdonaite , first4 = J. , last5 = Brunthaler , first5 = A. , last6 = Henkel , first6 = C. , last7 = Muller , first7 = S. , last8 = Bethlem , first8 = H. L. , last9 = Dapra , first9 = M. , year = 2015 , title = Constraints on changes in the proton–electron mass ratio using methanol lines. , journal = Monthly Notices of the Royal Astronomical Society Letters , volume = 448 , issue = 1 , pages = L104 , doi=10.1093/mnrasl/slu206 , doi-access = free , arxiv = 1412.7757 , bibcode = 2015MNRAS.448L.104K Fundamental constants Proton Dimensionless constants Electron