Fine-structure constant: Difference between revisions

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{{Quantum field theory}}

In [[physics]], the '''fine-structure constant''', also known as the '''Sommerfeld constant''', commonly denoted by {{mvar|α}} (the [[Alpha|Greek letter ''alpha'']]), is a [[Dimensionless physical constant|fundamental physical constant]] whichthat quantifies the strength of the [[electromagnetic interaction]] between elementary charged particles.

It is a [[dimensionless quantity]] ([[dimensionless physical constant]]), independent of the [[system of units]] used, which is related to the strength of the coupling of an [[elementary charge]] ''e'' with the [[electromagnetic field]], by the formula {{math|1=4''πε''{{sub|0}}''ħcα'' = ''e''{{sup|2}}}}. Its [[numerical value]] is approximately {{nowrap|{{physconst|alpha|round=13|ref=no}} ≈ {{sfrac|{{physconst|alphainv|round=9|ref=no}}}}}}, with a relative uncertainty of {{physconst|alpha|after=.|runc=yes}}

The constant was named by [[Arnold Sommerfeld]], who introduced it in 1916<ref name=Sommerfeld-1916>{{cite journal |author=Sommerfeld, Arnold |author-link=Arnold Sommerfeld |year=1916 |title=Zur Quantentheorie der Spektrallinien |journal=[[Annalen der Physik]] |volume=4 |issue=51 |pages=51–52 |url=https://babel.hathitrust.org/cgi/pt?id=nyp.33433090771183&view=1up&seq=65 |access-date=2020-12-06 }}

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<math display="block"> \alpha = \frac{e^2}{\hbar c} .</math>

A nondimensionalised system [[natural units|commonly used in high energy physics]] sets {{math|1=''ε''{{sub|0}} = ''c'' = ''ħ'' = 1}}, where the expressionsexpression for the fine-structure constant becomes<ref>

{{cite book |last1=Peskin |first1=M. |last2=Schroeder |first2=D. |year=1995 |title=An Introduction to Quantum Field Theory |publisher=[[Westview Press]] |isbn=978-0-201-50397-5 |page=[https://archive.org/details/introductiontoqu0000pesk/page/125 125] |url=https://archive.org/details/introductiontoqu0000pesk/page/125}}</ref><math display="block"> \alpha = \frac{e^2}{4 \pi} .</math>As such, the fine-structure constant is chiefly a quantity determining (or determined by) the [[elementary charge]]: {{math|1=''e'' = {{sqrt|4''πα''}} ≈ {{val|0.30282212}}}} in terms of such a natural unit of charge.

<math display="block"> \alpha = \frac{e^2}{4 \pi} .</math>

As such, the fine-structure constant is just a quantity determining (or determined by) the [[elementary charge]]: {{math|1=''e'' = {{sqrt|4''πα''}} ≈ {{val|0.30282212}}}} in terms of such a natural unit of charge.

In the system of [[atomic units]], which sets {{math|1=''e'' = ''m''{{sub|e}} = ''ħ'' = 4''πε''{{sub|0}} = 1}}, the expression for the fine-structure constant becomes

<math display="block">\alpha = \frac{1}{c} .</math>

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{{block indent|{{math|1=''α'' = {{sfrac|''e''{{sup|2}}| 4''πε''{{sub|0}}''ħc''}}}} {{=}} {{physconst|alpha|ref=no}}.}} This has a relative standard uncertainty of {{physconst|alpha|runc=yes|after=.}}

This value for {{math|''α''}} gives the following value for the [[Vacuum permeability|vacuum magnetic permeability]] (magnetic constant): {{nowrap|1={{mvar|µ}}{{sub|0}} = 4''π'' × {{val|0.99999999987|(16)|e=-7|u=H.m-1}}}}, 0.8 times the standard uncertainty away from its old defined value, with the mean differing from the old defined value by only 0.13&nbsp;[[parts per billion]], 0.8 times the standard uncertainty (0.16 parts per billion) of its recommended measured value.

Historically, the value of the [[multiplicative inverse|reciprocal]] of the fine-structure constant is often given. The [[CODATA]] recommended value is {{physconst|alphainv|ref=only}}

{{block indent|{{math|{{sfrac|1|''α''}}}} {{=}} {{physconst|alphainv|ref=no}}.}}

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| 2022 Dec

| 0.0072973525643(11)

| 137.035999177035999206(21)

| CODATA 2022

|-

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In the experiments below, {{math|Δ''α''}} represents the change in {{mvar|α}} over time, which can be computed by {{mvar|α}}_prev − {{mvar|α}}_now&nbsp;. If the fine-structure constant really is a constant, then any experiment should show that

<math display="block">\frac{\ \Delta \alpha\ }{\alpha} ~~ \overset{\underset{\mathsf{~def~}}{}}{=} ~~ \frac{\ \alpha _\mathrm{prev}-\alpha _\mathrm{now}\ }{\alpha_\mathrm{now}} ~~=~~ 0 ~,</math>

or as close to zero as experiment can measure. Any value far away from zero would indicate that {{mvar|α}} does change over time. So far, most experimental data is consistent with {{mvar|α}} being constant, up to 10 digits of accuracy.

=== Past rate of change ===

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}}</ref> This suggests that the statistical uncertainties and best estimate for {{sfrac|{{math|Δ''α''}} | {{mvar|α}} }} stated by Webb ''et al.'' and Murphy ''et al.'' are robust.

Lamoreaux and Torgerson analyzed data from the [[Oklo]] [[natural nuclear fission reactor]] in 2004, and concluded that {{mvar|α}} has changed in the past 2&nbsp;billion years by 45&nbsp;parts per billion. They claimed that this finding was "probably accurate to within 20%". Accuracy is dependent on estimates of impurities and temperature in the natural reactor. These conclusions have yet to be verified.<ref>

{{cite book

|last=Kurzweil |first=R.

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|website=ScienceBlogs.com

}}</ref>

that the study may contain wrong data due to subtle differences in the two telescopes.<ref>

{{cite web

|first=S. M. |last=Carroll |author-link=Sean M. Carroll

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|url=http://www.preposterousuniverse.com/blog/2010/10/18/the-fine-structure-constant-is-probably-constant/

}}</ref>

aCarroll totallytakes an altogether different approach;: he looks at the fine-structure constant as a scalar field and claims that if the telescopes are correct and the fine-structure constant varies smoothly over the universe, then the scalar field must have a very small mass. However, previous research has shown that the mass is not likely to be extremely small. Both of these scientists' early criticisms point to the fact that different techniques are needed to confirm or contradict the results, a conclusion Webb, ''et al''., previously stated in their study.<ref name=Zyga-2010-10-21/>

Other research finds no meaningful variation in the fine structure constant.<ref>

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== Anthropic explanation ==

The [[anthropic principle]] isprovides an argument aboutas to the reason the fine-structure constant has the value it does: stable matter, and therefore life and intelligent beings, could not exist if its value were very different. One example isFor thatinstance, if modern grand unified theories are correct, then {{mvar|α}} needs to be between around 1/180 and 1/85 to have proton decay to be slow enough for life to be possible.<ref>

{{cite journal

|last=Barrow |first=John D.

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}}</ref>

Physicist [[Wolfgang Pauli]] commented on the appearance of [[Numerology#Related uses|certain numbers in physics]], including the fine-structure constant, which he also noted approximates reciprocal of the prime number [[137 (number)#Physics|137]].<ref>{{cite journal |url=https://www.newscientist.com/article/mg20227051.800-cosmic-numbers-pauli-and-jungs-love-of-numerology.html |title=Cosmic numbers: Pauli and Jung's love of numerology |first=Dan |last=Falk |issue=2705 |date=24 April 2009 |journal=New Scientist}}</ref> This constant so intrigued him that he collaborated with psychoanalyst [[Carl Jung]] in a quest to understand its significance.<ref>

{{cite journal

|last1=Várlaki |first1=Péter

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Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time. However, no numerological explanation has ever been accepted by the physics community.

In the earlylate 20th 21st&nbsp;century, multiple physicists, including [[Stephen Hawking]] in his 1988 book ''[[A Brief History of Time]]'', began exploring the idea of a [[multiverse]], and the fine-structure constant was one of several universal constants that suggested the idea of a [[fine-tuned universe]].<ref name=Hawking-1988>

{{cite book

|last=Hawking |first=S. |author-link=Stephen Hawking

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== Quotes ==

{{blockquote|

For historical reasons, {{mvar|α}} is known as the fine structure constant. Unfortunately, this name conveys a false impression. We have seen that the charge of an electron is not strictly constant but varies with distance because of quantum effects; hence {{mvar|α}} must be regarded as a variable, too. The value 1/137 is the asymptotic value of {{mvar|α}} shown in Fig. 1.5a.<ref>The asymptotic value of {{mvar|α}} ''for larger observation distances'', is intended here. Caption: Fig 1.5. Screening of the (a) electric charge and (b) the color charge in quantum field theory. Graph of Electron charge versus Distance from the bare e^-− charge. From: Halzen, F.; Martin, A.D. (1984). ''Quarks and Leptons: An Introductory Course in Modern Particle Physics''. John Wiley & Sons. ISBN 978-0-471-88741-6, p. 13.</ref> | Francis Halzen and Alan Martin (1984)<ref>

{{cite book

|last1=Halzen

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{{blockquote|

When I die my first question to the Devil will be: What is the meaning of the fine structure constant?|Wolfgang Pauli <ref> {{Cite web |title=137 {{!}} The Fine Structure Constant, Physics - ArsMagine.com |url=https://arsmagine.com/others/fine-structure-constant/ |access-date=2024-06-28 |website=Ars Magine - Umetnost promišljanja i uobrazilje {{!}} אהיה |language=sr-rs}} </ref>|source=}}

== See also ==