Fine-structure constant: Difference between revisions

Revision as of 15:37, 19 January 2025

Latest revision as of 18:42, 27 August 2025

(31 intermediate revisions by 14 users not shown)

Line 44:

{{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.

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>

Line 52:

{{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}}.}}

Line 354:

| 2022 Dec

| 0.0072973525643(11)

| 137.035999177035999206(21)

| CODATA 2022

|-

Line 404:

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 ===

Line 738:

|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

Line 745:

|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>

Line 780:

== 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.

Line 825:

}}</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