View source for Physics:Time-variation of fundamental constants

The term [[Physics:Physical constant|physical constant]] expresses the notion of a [[Physics:Physical quantity|physical quantity]] subject to experimental measurement which is independent of the time or location of the experiment. The constancy (immutability) of any "physical constant" is thus subject to experimental verification.
[[Biography:Paul Dirac|Paul Dirac]] in 1937 [[Astronomy:Dirac large numbers hypothesis|speculated]] that physical constants such as the [[Physics:Gravitational constant|gravitational constant]] or the [[Physics:Fine-structure constant|fine-structure constant]] might be subject to change over time in proportion of the [[Astronomy:Age of the universe|age of the universe]].<ref>{{cite journal|author=P.A.M. Dirac|year=1938 |title=A New Basis for Cosmology |journal=Proceedings of the Royal Society A |volume=165 |issue=921 |pages=199–208 |doi=10.1098/rspa.1938.0053 |bibcode = 1938RSPSA.165..199D |doi-access= }}</ref>
Experiments conducted since then have put upper bounds on their time-dependence. This concerns the fine-structure constant, the gravitational constant and the [[Proton-to-electron mass ratio|proton-to-electron mass ratio]] specifically, for all of which there are ongoing efforts to improve tests on their time-dependence.<ref>[http://physics.nist.gov/cuu/Constants/Preprints/lsa2010.pdf CODATA Recommended Values of the Fundamental Physical Constants: 2010]" (March 15, 2012):
"Although the possible time variation of the constants continues to be an active field of both experimental and theoretical research, there is no observed variation relevant to the data on which the 2010 recommended values are based; see, for example, the recent reviews by Uzan (2011) and Chiba (2011). Other references may be found in the FCDC bibliographic database at [http://physics.nist.gov/ physics.nist.gov/constantsbib] using, for example, the keywords 'time variation' or 'constants.'".</ref>

The immutability of these fundamental constants is an important cornerstone of the laws of physics as currently known; the postulate of the time-independence of physical laws is tied to that of the [[Physics:Conservation of energy|conservation of energy]] ([[Physics:Noether's theorem|Noether's theorem]]), so that the discovery of any variation would imply the discovery of a previously unknown law of force.<ref>"Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free fall. Thus, it is of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy." Uzan (2011)</ref>

In a more [[Philosophy:Philosophy of science|philosophical]] context, the conclusion that these quantities are constant raises the question of why they have the specific value they do in what appears to be a "[[Astronomy:Fine-tuned universe|fine-tuned universe]]", while their being variable would mean that their known values are merely an accident of the [[Astronomy:Cosmic time|current time]] at which we happen to measure them.<ref>Uzan (2011), chapter 7: "Why Are The Constants Just So?": "The numerical values of the fundamental constants are not determined by the laws of nature in which they appear. One can wonder why they have the values we observe. In particular, as pointed out by many authors (see below), the constants of nature seem to be fine-tuned [Leslie (1989)]. Many physicists take this fine-tuning to be an explanandum that cries for an explanans, hence following Hoyle [(1965)] who wrote that 'one must at least have a modicum of curiosity about the strange dimensionless numbers that appear in physics.'"
</ref>

==Dimensionality==
{{Further|System of measurement|Natural units}}
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 a system of units may arbitrarily select any physical constant as its basis, making the question of which constant is undergoing change an artefact of the choice of units.<ref name="hep-th1412.2040">{{cite journal |title=How fundamental are fundamental constants?|arxiv=1412.2040|year=2014|last1=Duff |first1=M. J.|doi=10.1080/00107514.2014.980093|journal=Contemporary Physics|volume=56|issue=1|pages=35–47|bibcode=2015ConPh..56...35D |hdl=10044/1/68485 |s2cid=118347723 |url=https://www.tandfonline.com/doi/abs/10.1080/00107514.2014.980093}}</ref><ref>{{cite arXiv |last1=Duff |first1=M. J. |date=13 August 2002 |title=Comment on time-variation of fundamental constants |eprint=hep-th/0208093}}</ref><ref>{{cite journal |last1=Duff |first1=M. J. |last2=Okun |first2=L. B. |last3=Veneziano |first3=G. |title=Trialogue on the number of fundamental constants |journal=Journal of High Energy Physics |date=2002 |volume=2002 |issue= 3|pages=023 |arxiv=physics/0110060 |bibcode=2002JHEP...03..023D |doi=10.1088/1126-6708/2002/03/023|s2cid=15806354 }}</ref>

For example, in SI units, the speed of light has been given a ''defined'' value in 1983. Thus, it was meaningful to experimentally measure the speed of light in SI units prior to 1983, but it is not so now.
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 ratio ''e''<sup>2</sup>:''c'' (the fine-structure constant) remained unchanged.<ref>{{citation|  last=Barrow| first=John D.| title=The Constants of Nature; From Alpha to Omega - The Numbers that Encode the Deepest Secrets of the Universe| publisher=Pantheon Books| year=2002| isbn=0-375-42221-8| url-access=registration| url=https://archive.org/details/constantsofnatur0000barr}}
"[An] important lesson we learn from the way that pure numbers like α define the World is what it really means for worlds to be different. The pure number we call the fine-structure constant and denote by α is a combination of the electron charge, ''e'', the speed of light, ''c'', and Planck's constant, ''h''. At first, we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If ''c'', ''h'', and ''e'' were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be ''observationally indistinguishable'' from our World. The only thing that counts in the definition of worlds are the values of the dimensionless constants of Nature. If all masses were doubled in value you cannot tell, because all the pure numbers defined by the ratios of any pair of masses are unchanged."</ref>

[[Natural units]] are systems of units entirely based in fundamental constants. In such systems, it is meaningful to measure any specific quantity which is ''not'' used in the definition of units. For example, in [[Stoney units]], the elementary charge is set to {{nowrap|1=''e'' = 1}} while the [[Physics:Reduced Planck constant|reduced Planck constant]] is subject to measurement, {{nowrap|''ħ'' ≈ 137.03}}, and in [[Planck units]], the [[Physics:Reduced Planck constant|reduced Planck constant]] is set to {{nowrap|1=''ħ'' = 1}}, while the elementary charge is subject to measurement, {{nowrap|''e'' ≈ (137.03)<sup>1/2</sup>}}. The 2019 redefinition of SI base units expresses all SI base units in terms of fundamental physical constants, effectively transforming the SI system into a system of natural units.

==Fine-structure constant==
In 1999, evidence for time variability of the [[Physics:Fine-structure constant|fine-structure constant]] based on observation of [[Astronomy:Quasar|quasar]]s was announced<ref>{{cite journal | last1 = Webb | first1 = J. K. | display-authors = etal | year = 2001 | title = Further evidence for cosmological evolution of the fine structure constant | arxiv=astro-ph/0012539v3 | journal = [[Physics:Physical Review Letters|Physical Review Letters]] | volume = 87 | issue = 9| page = 091301 |bibcode = 2001PhRvL..87i1301W |doi = 10.1103/PhysRevLett.87.091301 | pmid=11531558| s2cid = 40461557 }}</ref> but a much more precise study based on CH molecules did not find any variation.<ref>{{cite journal|title=A search for varying fundamental constants using hertz-level frequency measurements of cold CH molecules|date=15 October 2013|doi=10.1038/ncomms3600|last1=Truppe|first1=S.|last2=Hendricks|first2=R.J.|last3=Tokunaga|first3=S.K.|last4=Lewandowski|first4=H.J.|last5=Kozlov|first5=M.G.|last6=Henkel|first6=Christian|last7=Hinds|first7=E.A.|last8=Tarbutt|first8=M.R.|journal=Nature Communications|volume=4|page=2600|pmid=24129439|pmc=3826645|arxiv=1308.1496|bibcode=2013NatCo...4.2600T}}</ref><ref>{{cite web|url=https://www.forbes.com/sites/startswithabang/2017/01/05/distant-quasars-show-that-fundamental-constants-never-change/#7a3054a847ee|title=Distant Quasars Show That Fundamental Constants Never Change|website={{wipe|Forbes}}|date=5 January 2017}}</ref> An upper bound of 10<sup>−17</sup> per year for the time variation, based on laboratory measurements, was published in 2008.<ref>
{{Cite journal
 | first = T.
 | last = Rosenband
 | display-authors = etal
 | year = 2008
 | title = Frequency Ratio of Al<sup>+</sup> and Hg<sup>+</sup> Single-Ion Optical Clocks; Metrology at the 17th Decimal Place
 | journal = Science
 | volume = 319 | issue = 5871 | pages = 1808–12
 | bibcode = 2008Sci...319.1808R
 | doi = 10.1126/science.1154622
 | pmid = 18323415
| s2cid = 206511320
 | url = https://zenodo.org/record/1230892
 | doi-access = free
 }}</ref> Observations of a quasar of the universe at only 0.8 billion years old with [[Artificial intelligence|AI]] analysis method employed on the [[Astronomy:Very Large Telescope|Very Large Telescope]] (VLT) found a spatial variation preferred over a no-variation model at the <math>3.9\sigma</math> level.<ref>
{{Cite journal
 | first1 = Michael R.
 | last1 = Wilczynska
 | first2 = John K.
 | last2 = Webb
 | display-authors = etal
 | year = 2020
 | title =Four direct measurements of the fine-structure constant 13 billion years ago
 | journal = Science Advances
 | volume = 6 | issue = 17 | pages = 9672
 | bibcode = 2020SciA....6.9672W
 | doi = 10.1126/sciadv.aay9672
 | pmid = 32426462
| pmc = 7182409
 | arxiv = 2003.07627
 | doi-access = free
 }}</ref>

The time-variation of fine-structure constant is equivalent to the time-variation of one or more of: [[Physics:Speed of light|speed of light]], [[Physics:Planck constant|Planck constant]], [[Physics:Vacuum permittivity|vacuum permittivity]], and [[Physics:Elementary charge|elementary charge]], since <math>\alpha=\frac{e^2}{2\epsilon_0ch}</math>.

==Speed of light==
{{excerpt|Variable speed of light}}

==Gravitational constant==
The [[Physics:Gravitational constant|gravitational constant]] {{math|''G''}} is 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.<ref name=anderson2015>{{Citation |first1=J. D. |last1=Anderson |first2=G. |last2=Schubert|first3=V. |last3=Trimble|first4=M. R. |last4=Feldman |title=Measurements of Newton's gravitational constant and the length of day |journal=EPL |date=April 2015 |volume=110 |issue=1|doi=10.1209/0295-5075/110/10002|arxiv = 1504.06604 |bibcode = 2015EL....11010002A |pages=10002|s2cid=119293843}}</ref>  However, while its value is not known to great precision, the possibility of observing type Ia supernovae which happened in the universe's remote past, paired with the assumption that the physics involved in these events is universal, allows for an upper bound of less than 10<sup>−10</sup> per year for <math>|\dot G/G|</math> over the last nine billion years.<ref>{{Citation |first1=J. |last1=Mould |first2=S. A. |last2=Uddin |title=Constraining a Possible Variation of G with Type Ia Supernovae |date=10 April 2014 |volume=31 |pages=e015 |doi=10.1017/pasa.2014.9 |journal=Publications of the Astronomical Society of Australia|arxiv = 1402.1534 |bibcode = 2014PASA...31...15M |s2cid=119292899 }}</ref> The quantity <math>|\dot G/G|</math> is simply the change in time of the gravitational constant, denoted by <math>\dot G</math>, divided by {{math|''G''}}.

As a dimensional quantity, the value of the gravitational constant and its possible variation will depend on the choice of units; in [[Planck units]], for example, its value is fixed at {{nowrap|1=''G'' = 1}} by definition. A meaningful test on the time-variation of ''G'' would require comparison with a non-gravitational force to obtain a dimensionless quantity, e.g. through the ratio of the gravitational force to the electrostatic force between two electrons, which in turn is related to the dimensionless [[Physics:Fine-structure constant|fine-structure constant]].

==Proton-to-electron mass ratio==
An upper bound of the change in the [[Proton-to-electron mass ratio|proton-to-electron mass ratio]]
has been placed at 10<sup>−7</sup> over a period of 7 billion years (or 10<sup>−16</sup> per year) in a 2012 study based on the observation of [[Chemistry:Methanol|methanol]] in a distant galaxy.<ref name="Science-20121213">{{cite journal |last1=Bagdonaite |first1=Julija |last2=Jansen |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=https://www.science.org/doi/abs/10.1126/science.1224898 |date=December 13, 2012 |journal=Science |doi=10.1126/science.1224898 |access-date=December 14, 2012 |bibcode = 2013Sci...339...46B |volume=339 |issue=6115 |pages=46–48 |pmid=23239626|s2cid=716087 |doi-access=free }}</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 |access-date=December 14, 2012 }}</ref>

==Cosmological constant==
{{Further|Astronomy:Cosmological constant|Physics:Vacuum energy|Astronomy:Dark energy}}

The [[Astronomy:Cosmological constant|cosmological constant]] is a measure of the [[Physics:Energy density|energy density]] of the [[Physics:Vacuum|vacuum]]. It was first measured, and found to have a positive value, in the 1990s. It is currently (as of 2015) estimated at 10<sup>−122</sup> in [[Planck units]].<ref>{{cite journal |last1=Ade |first1=P. A. R. |last2=Aghanim |first2=N.|last3=Arnaud |first3=M. |last4=Ashdown |first4=M. |last5=Aumont |first5=J. |last6=Baccigalupi |first6=C. |collaboration=Planck Collaboration |title=Planck 2015 results: XIII. Cosmological parameters |journal=Astronomy & Astrophysics |date=October 2016 |volume=594 |pages=A13 |doi=10.1051/0004-6361/201525830 |arxiv=1502.01589 |bibcode=2016A&A...594A..13P |url=https://www.aanda.org/articles/aa/full_html/2016/10/aa25830-15/aa25830-15.html|doi-access=free }}</ref> Possible variations of the cosmological constant over time or space are not amenable to observation, but it has been noted that, in Planck units, its measured value is suggestively close to the reciprocal of the [[Astronomy:Age of the universe|age of the universe]] squared, Λ ≈ ''T''<sup>−2</sup>. Barrow and Shaw proposed a modified theory in which Λ is a field evolving in such a way that its value remains Λ ~ ''T''<sup>−2</sup> throughout the history of the universe.<ref>{{Citation |first1=John D. |last1=Barrow |first2=Douglas J.| last2=Shaw |title=The Value of the Cosmological Constant |journal=General Relativity and Gravitation |volume=43|issue=10 | pages=2555–2560 |year=2011 | doi=10.1007/s10714-011-1199-1 |arxiv=1105.3105 | bibcode=2011GReGr..43.2555B|s2cid=55125081 }}</ref>

==See also==
* [[Astronomy:Dirac large numbers hypothesis|Dirac large numbers hypothesis]]

==References==
{{reflist}}
*{{cite journal | last1 = Marciano | first1 = William J. | year = 1984 | title = Time Variation of the Fundamental "Constants" and Kaluza-Klein Theories | journal = Phys. Rev. Lett. | volume = 52 | issue = 7| pages = 489–491 | doi=10.1103/physrevlett.52.489| bibcode = 1984PhRvL..52..489M}}
*{{cite journal | last1 = Varshalovich | first1 = D. A. | last2 = Levshakov | first2 = S. A. | year = 1993 | title = On a time dependence of physical constants | journal = Pis'ma Zh. Eksp. Teor. Fiz. | volume = 58 | issue = 4| pages = 231–235 | bibcode=1993JETPL..58..237V}}
*{{cite journal | last1 = Dzuba | first1 = V. A. | last2 = Flambaum | first2 = V. V. | last3 = Webb | first3 = J. K. | year = 1999 | title = Space-Time Variation of Physical Constants and Relativistic Corrections in Atoms | journal = Phys. Rev. Lett. | volume = 82 | issue = 5| page = 888 | doi=10.1103/physrevlett.82.888| arxiv = physics/9802029 | bibcode = 1999PhRvL..82..888D | s2cid = 18462448 }}
*{{cite journal | last1 = Dzuba | first1 = V. A. | last2 = Flambaum | first2 = V. V. | last3 = Webb | first3 = J. K. | year = 1999 | title = Calculations of the relativistic effects in many-electron atoms and space-time variation of fundamental constants | journal = Phys. Rev. A | volume = 59 | issue = 1| pages = 230–237 | doi=10.1103/physreva.59.230| arxiv = physics/9808021 | bibcode = 1999PhRvA..59..230D | s2cid = 1427732 }}
*{{cite journal | last1 = Davies | first1 = Paul C. |  last2 = Davis | first2 = T. M. | last3 = Lineweaver | first3 = C. H. | year = 2002 | title = Cosmology: Black Holes Constrain Varying Constants | journal = Nature | volume = 418 | issue = 6898| pages = 602–3 | doi=10.1038/418602a | pmid=12167848|bibcode = 2002Natur.418..602D | s2cid = 1400235 }}
* Dara Faroughy, "Slowly evolving early universe and a phenomenological model for time-dependent fundamental constants and the leptonic masses" (2008), [https://arxiv.org/abs/0801.1935 arXiv:0801.1935].
* Jean-Philippe Uzan, [https://web.archive.org/web/20160401212131/http://relativity.livingreviews.org/Articles/lrr-2011-2/download/lrr-2011-2Color.pdf "Varying Constants, Gravitation and Cosmology"], Living Rev. Relativ., 14.2 (2011).
*{{cite journal | last1 = Chiba | first1 = Takeshi | year = 2011 | title = The Constancy of the Constants of Nature: Updates | journal = Progress of Theoretical Physics | volume = 126 | issue = 6| pages = 993–1019 | doi=10.1143/ptp.126.993| arxiv = 1111.0092| bibcode = 2011PThPh.126..993C| s2cid = 59381699 }}


[[Category:Physical constants]]
[[Category:Fundamental constants]]
[[Category:Time in physics]]

{{Sourceattribution|Time-variation of fundamental constants}}