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In [[physics]], the '''proton-to-electron mass ratio''', '''&mu;''' or '''&beta;''', is simply the [[rest mass]] of the [[proton mass|proton]] divided by that of the [[electron mass|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:
:&mu; = {{physconst|mpome|symbol=yes|after=.}}
The number enclosed in parentheses is the [[measurement uncertainty]] on the last two digits. The value of &mu; is known to about 0.4 parts per billion.


==Discussion==
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&mu; is a [[fundamental physical constant]] because:
*Nearly all of science deals with [[baryonic matter]] and how the [[fundamental interaction]]s affect such matter. Baryonic matter consists of [[quarks]] and particles made from quarks, like [[proton]]s and [[Neutron#Stability_and_beta_decay|neutron]]s. 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 decay]] predict that the proton has a [[half life]] on the order of at least [[1_E19_s_and_more|10<sup>32</sup> years]]. To date, there is no experimental evidence of proton decay.);
* The [[proton]] is the most important [[baryon]], while the [[electron]] is the most important [[lepton]];
*&mu; and the [[fine structure constant]] &alpha; are the two [[dimensionless quantities]] emerging in elementary physics, and two of the three dimensionless quantities discussed in Barrow (2002);
* The [[proton mass]] ''m''<sub>p</sub> is composed primarily of [[gluon]]s, and not of the [[quark]]s (the [[up quark]] and [[down quark]]) making up the proton. Hence ''m''<sub>p</sub>, and therefore the ratio ''&mu;'', are easily measurable consequences of the [[strong force]]. In fact, in the [[chiral]] limit, ''m''<sub>p</sub> is proportional to the [[Quantum_chromodynamics|QCD]] energy scale, &Lambda;<sub>QCD</sub>. At a given energy scale, the [[strong force|strong]] [[coupling constant]] ''&alpha;''<sub>s</sub> is related to the QCD scale (and thus ''&mu;'') as
:<math>\alpha_s=-\frac{2\pi}{\beta_0 \ln(E/\Lambda_{QCD})}</math>
:where ''&beta;''<sub>0</sub> = −11 + 2''n''/3, with ''n'' being the number of [[flavor (particle physics)|flavor]] of [[quark]]s.
 
==Does ''&mu;'' vary over time?==
Astrophysicists have tried to find evidence that ''&mu;'' 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 ''&mu;'' have typically examined the [[Lyman series]] and [[Werner transition]]s 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 ''&mu;'' were to change, then the change in the wavelength ''&lambda;<sub>i</sub>'' of each [[rest frame]] [[wavelength]] can be parameterised as:
:<math>\ \lambda_i=\lambda_0[1+K_i(\Delta\mu/\mu)],</math>
where &Delta;''&mu;''/''&mu;'' is the proportional change in ''&mu;'' and ''K<sub>i</sub>'' 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 ''&mu;'' by analysing the molecular hydrogen [[absorption spectra]] of [[quasar]]s Q0405-443 and Q0347-373. They found that &Delta;''&mu;''/''&mu;'' = (2.4 ± 0.6){{e|-5}}. King et al. (2008) reanalysed the spectral data of Reinhold et al. and collected new data on another quasar, Q0528-250. They estimated that &Delta;''&mu;''/''&mu;'' = (2.6 ± 3.0){{e|-6}}, different from the estimates of Reinhold et al. (2006).
 
Murphy et al. (2008) used the inversion transition of ammonia to conclude that |&Delta;''&mu;''/''&mu;''| < 1.8{{e|-6}} at redshift ''z'' = 0.68.
 
Bagdonaite et al. (2013) used [[methanol]] transitions in the spiral lens [[galaxy]] PKS 1830-211 to find (∆μ/μ) = (0.0 ± 1.0) × 10<sup>-7</sup> at z = 0.89, a stringent limit at this [[redshift]].<ref name="Science-20121213">{{cite journal |last1=Bagdonaitel |first1=Julija |last2=Jensen |first2=Paul |last3=Henkel |first3=Christian |last4=Bethlem |first4=Hendrick L. |last5=Menten |first5=Karl M. |last6=Ubachs |first6=Wim |title=A Stringent Limit on a Drifting Proton-to-Electron Mass Ratio from Alcohol in the Early Universe |url=http://www.sciencemag.org/content/early/2012/12/12/science.1224898.abstract |date=December 13, 2012 |journal=[[Science (journal)]] |doi=10.1126/science.1224898 |accessdate=December 14, 2012 |bibcode = 2013Sci...339...46B }}</ref><ref name="Space-20121213">{{cite web |last=Moskowitz |first=Clara |title=Phew! Universe's Constant Has Stayed Constant |url=http://www.space.com/18894-galaxy-alcohol-fundamental-constant.html |date=December 13, 2012 |publisher=[[Space.com]] |accessdate=December 14, 2012 }}</ref>
 
Note that any comparison between values of &Delta;''&mu;''/''&mu;'' at substantially different redshifts will need a particular model to govern the evolution of &Delta;''&mu;''/''&mu;''. That is, results consistent with zero change at lower redshifts do not rule out significant change at higher redshifts.
 
==See also==
* [[Dimensionless physical constant]]
* [[Electron]]
* [[Fine structure constant]]
* [[Proton]]
* [[Quark]]
* [[Quantum_chromodynamics|QCD]]
 
==Footnotes==
{{reflist}}
 
==References==
*[[John D. Barrow|Barrow, John D.]], 2002. ''The Constants of Nature: From Alpha to Omega--the Numbers That Encode the Deepest Secrets of the Universe''. London: Vintage. ISBN 0-09-928647-5.
*——— and [[Frank J. Tipler]], 1986. ''[[The Cosmological Anthropic Principle]]''. Oxford Univ. Press.
* Reinhold. E., Buning, R., Hollenstein, U., Ivanchik, A., Petitjean, P., Ubachs, W., 2006, "Indication of a Cosmological Variation of the Proton-Electron Mass Ratio based on Laboratory Measurement and Reanalysis of H2 spectra," ''Physical Review Letters'' '''96'''(15): 151101.
* King, J., Webb, J., Murphy, M., Carswell, R., 2008, "[http://arxiv.org/abs/0807.4366 arXiv:0807.4366 Stringent Null Constraint on Cosmological Evolution of the Proton-to-Electron Mass Ratio,]" ''Physical Review Letters'' '''101''': 251304.
* Murphy, M., Flambaum, V., Muller, S., Henkel, C., 2008, "[http://arxiv.org/abs/0806.3081 Strong Limit on a Variable Proton-to-Electron Mass Ratio from Molecules in the Distant Universe]", ''Science'' '''320''' 1611-
 
[[Category:Fundamental constants]]

Latest revision as of 11:07, 14 May 2014

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