Proton-to-electron mass ratio
Encyclopedia
In physics
, the proton-to-electron mass ratio, μ or β, is simply the rest mass of the proton divided by that of the electron. Because this is a ratio of like-dimensioned physical quantity
, it is a dimensionless quantity
, a function of the dimensionless physical constant
s, and has numerical value independent of the system of units, namely:
The number enclosed in parentheses is the measurement uncertainty
on the last two digits. The value of μ is known to about 0.4 parts per billion.
Astronomical searches for time-varying μ have typically examined the Lyman series
and Werner transitions of molecular hydrogen which, given a sufficiently large redshift
, occur in the optical region and so can be observed with ground-based spectrograph
s.
If μ were to change, then the change in the wavelength λi of each rest frame
wavelength
can be parameterised as:
where Δμ/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
variation in μ by analysing the molecular hydrogen absorption spectra of quasar
s Q0405-443 and Q0347-373. They found that Δμ/μ = (2.4 ± 0.6). King et al. (2008) reanalysed the spectral data of Reinhold et al. and collected new data on another quasar, Q0528-250. They estimated that Δμ/μ = (2.6 ± 3.0), which is inconsistent with the estimates of Reinhold et al. (2006) and implies that μ does not change over time.
Murphy et al. (2008) used the inversion transition of ammonia to conclude that |Δμ/μ| < 1.8 at redshift z = 0.68.
Note that any comparison between values of Δμ/μ at substantially different redshifts will need a particular model to govern the evolution of Δμ/μ. That is, results consistent with zero change at low redshifts do not rule out significant change at high redshifts.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, the proton-to-electron mass ratio, μ or β, is simply the rest mass of the proton divided by that of the electron. Because this is a ratio of like-dimensioned physical quantity
Physical quantity
A physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.-Definition of a physical quantity:Formally, the International Vocabulary of Metrology, 3rd edition defines quantity as:...
, it is a dimensionless quantity
Dimensionless quantity
In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a "pure" number, and as such always has a dimension of 1. Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and...
, a function of the dimensionless physical constant
Dimensionless physical constant
In physics, a dimensionless physical constant is a universal physical constant that is dimensionless - having no unit attached, so its numerical value is the same under all possible systems of units...
s, and has numerical value independent of the system of units, namely:
- μ =
The number enclosed in parentheses is the measurement uncertainty
Measurement uncertainty
In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity. The uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity. All measurements are subject to uncertainty and a measured...
on the last two digits. The value of μ is known to about 0.4 parts per billion.
Discussion
μ is a fundamental physical constant because:- Nearly all of science deals with baryonic matter and how the fundamental interactionFundamental interactionIn particle physics, fundamental interactions are the ways that elementary particles interact with one another...
s affect such matter. Baryonic matter consists of protonProtonThe proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
s, electronElectronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s, and neutrons. Free neutrons have a half life of 613.9 seconds. Electrons and protons appear to be stable, to the best of current knowledge. (Theories of proton decayProton decayIn particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron...
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.); - The protonProtonThe proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
is the most important baryonBaryonA baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...
, while the electronElectronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
is the most important leptonLeptonA lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
; - μ and the fine structure constant α are the two dimensionless quantities emerging in elementary physics, and two of the three dimensionless quantities discussed in Barrow (2002);
- The proton mass mp is composed primarily of gluonGluonGluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....
s, and not of the quarkQuarkA quark is an 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 nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s (the up quarkUp quarkThe up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...
and down quarkDown quarkThe down quark or d quark is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...
) making up the proton. Hence mp, and therefore the ratio μ, are easily measurable consequences of the strong force. In fact, in the chiral limit, mp is proportional to the QCDQuantum chromodynamicsIn theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
energy scale, ΛQCD. At a given energy scale, the strong coupling constantCoupling constantIn physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. Usually the Lagrangian or the Hamiltonian of a system can be separated into a kinetic part and an interaction part...
αs is related to the QCD scale (and thus μ) as
- where β0 = −11 + 2n/3, with n being the number of flavor of quarkQuarkA quark is an 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 nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s.
Does μ vary 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.) 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
Lyman series
In physics and chemistry, the Lyman series is the series of transitions and resulting ultraviolet emission lines of the hydrogen atom as an electron goes from n ≥ 2 to n = 1...
and Werner transitions of molecular hydrogen which, given a sufficiently large redshift
Redshift
In physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...
, occur in the optical region and so can be observed with ground-based spectrograph
Spectrograph
A spectrograph is an instrument that separates an incoming wave into a frequency spectrum. There are several kinds of machines referred to as spectrographs, depending on the precise nature of the waves...
s.
If μ were to change, then the change in the wavelength λi of each rest frame
Rest frame
In special relativity the rest frame of a particle is the coordinate system in which the particle is at rest.The rest frame of compound objects is taken to be the frame of reference in which the average momentum of the particles which make up the substance is zero In special relativity the rest...
wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
can be parameterised as:
where Δμ/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
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
variation in μ by analysing the molecular hydrogen absorption spectra of quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...
s Q0405-443 and Q0347-373. They found that Δμ/μ = (2.4 ± 0.6). King et al. (2008) reanalysed the spectral data of Reinhold et al. and collected new data on another quasar, Q0528-250. They estimated that Δμ/μ = (2.6 ± 3.0), which is inconsistent with the estimates of Reinhold et al. (2006) and implies that μ does not change over time.
Murphy et al. (2008) used the inversion transition of ammonia to conclude that |Δμ/μ| < 1.8 at redshift z = 0.68.
Note that any comparison between values of Δμ/μ at substantially different redshifts will need a particular model to govern the evolution of Δμ/μ. That is, results consistent with zero change at low redshifts do not rule out significant change at high redshifts.
See also
- Dimensionless physical constantDimensionless physical constantIn physics, a dimensionless physical constant is a universal physical constant that is dimensionless - having no unit attached, so its numerical value is the same under all possible systems of units...
- ElectronElectronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
- Fine structure constant
- ProtonProtonThe proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
- QuarkQuarkA quark is an 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 nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
- QCDQuantum chromodynamicsIn theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...