Talk:Fine-structure constant/Archive 2

Definition

Where is the reference for: alpaha is: "the ratio between the electron velocity in Bohr's model of the atom and the speed of light;" should this fact have a reference on the wiki page?

Definition on constant

Okey, I'm not a phycisist. But the def. of the constant seems a little odd.

"It can be defined as

$\alpha ={\frac {e^{2}}{\hbar c4\pi \epsilon _{0}}}\$

where $e\$ is the elementary charge, $\hbar =h/(2\pi )\$ is the

reduced Planck's constant, $c\$ is the speed of light in a vacuum, and

$\epsilon _{0}\$ is the permittivity of free space."

Why don't define it like this:

$\alpha ={\frac {e^{2}}{hc2\epsilon _{0}}}\$

Does anyone know why "they" define it this way? Thechamelon 16:41, 26 Apr 2005 (UTC)

Why define $\alpha$ in terms of $\hbar$ instead of h... well there are a number of reasons.

The $\alpha$ factor comes from a combination of the equation of electrostatic potential, the Schrödinger equation and something I can't remeber right now. As the Schrödinger equation is defined in terms of $\hbar$ then we tend to define $\alpha$ using these terms.

However that just shifts the problem into why the Schrödinger equation is defined in terms of $\hbar$... well this is a little bit of waffle, but as we define wavefunctions as linear sums of eigenfunctions which are normally expressed in exponential functions. These are periodic with a period of 2 $\pi$, and I suspect it has something to do with that... But I can't manage to make the conceptual leap to give a coherant explanation why... sorry.

As one reaches deeper levels of physics, ones tends to use $\hbar$ a lot more as this simplifies a lot of equations, but it is an arbitary choice in certain situations. Neo (ages ago...)

Okey then. I don't actually now anything about any of these levels of physics you are reffering to, but I understand now. Thanks! Thechamelon 19:21, 26 Apr 2005 (UTC)

Actually that is a rough rationalization for the existence of the reduced planck constant, not for its use in this context. As both the h and $\hbar$ are commonly used, and h is used in another "standard definition", it seems that the formula using h is simpler and therefore a better definition. I do not see any references supporting that the 3 given formulas are "standard definitions". Lacking other justification, i think that the formula $\alpha ={\frac {e^{2}}{\hbar c4\pi \epsilon _{0}}}\$ should be replaced by its simpler form ${\begin{aligned}\alpha ={\frac {e^{2}}{2hc\epsilon _{0}}}\end{aligned}}$ Bcharles (talk) 00:00, 15 February 2010 (UTC)

B, I have to disagree. We should use the expression that NIST uses which is

$\alpha ={\frac {e^{2}}{(4\pi \epsilon _{0})\hbar c}}$ .

I think that it is a good idea to contain the (4πε₀) factor in parenths because it is common for physicists to express α in cgs electrostatic units which are defined so that 4πε₀ = 1. They like to say that

$\alpha ={\frac {e^{2}}{\hbar c}}$ .

One of those two expressions for α is what is used nearly 100% of the time in the lit. 64.223.106.116 (talk) 20:14, 16 February 2010 (UTC)

Numerical value

Measurement accuracy

It's stated in this article that the fine structure constant is measured to 0.7 pbb and that this is 10 times more accurate than it's rivals.

However in the Rydberg constant article: http://en.wikipedia.org/wiki/Rydberg_constant

It says the Rydberg constant is measured to 7 ppt, or 0.007 ppb. Am I missing something?

The point is that the method described in th article for measuring then fine structure constant is claimed to be 10 times more accurate then the second best. But that does not mean that other physical constants cannot be known with greater accuracies. Dauto 02:36, 4 April 2007 (UTC)

Perhaps this isn't the best place for this comment, but the article describes measurement in a lab setting. The discovery of the constant varying over a dipole of the universe as seen from our location suggests there is a remote measuring technique also. Can someone who knows about this add that to the article? Victor Engel (talk) 16:39, 13 September 2010 (UTC)

New measurement

G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, and B. Odom, New Determination of the Fine Structure Constant from the Electron g Value and QED, Phys. Rev. Lett. 97, 030802 (2006), doi:10.1103/PhysRevLett.97.030802 describes a new measurement. Here is the abstract:

Quantum electrodynamics (QED) predicts a relationship between the dimensionless magnetic moment of the electron (g) and the fine structure constant $(\alpha )$. A new measurement of g using a one-electron quantum cyclotron, together with a QED calculation involving 891 eighth-order Feynman diagrams, determine $\alpha ^{-1}$=137.035 999 710 (96) [0.70 ppb]. The uncertainties are 10 times smaller than those of nearest rival methods that include atom-recoil measurements. Comparisons of measured and calculated g test QED most stringently, and set a limit on internal electron structure.

Someone who understands this better than me (I'm a mere mathematician) please edit the article. By the way, is there a Wikipedia article that explains how to read notations like "137.035 999 710 (96) [0.70 ppb]"? McKay 15:13, 4 August 2006 (UTC)

I added it to the "measurements" section of the article, along with a note on how to read the notation. I haven't learned how to format references properly yet; could someone more wiki-savvy than me please fix it up? Thanks! 72.57.79.40 15:23, 8 October 2006 (UTC) (Sorry, forgot to log in. HEL 15:24, 8 October 2006 (UTC))

Will someone now update the 2002 value of alpha quoted in the introduction to the new experimental result? I am not bold enough. :P HEL 15:30, 8 October 2006 (UTC)

The reference you added is more than acceptable for now (although I'll than likely update the formatting some time soon). Thanks for your contribution! Chovain 15:34, 8 October 2006 (UTC)

Correction to CODATA 2006 recommended value

Very unfortunately, within months of publication of the CODATA 2006 recommended values, an error was discovered in the calculation leading to the Gabrielse fine-structure constant value, which was by far the most influential input datum for the CODATA value of α: G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, and B. Odom, 'Erratum: New Determination of the Fine Structure Constant from the Electron g Value and QED', Phys. Rev. Lett. 97, 030802 (2006), (Dated: Submitted: 24 June 2007) (the erratum is appended at the end of that text).

The consequences of this correction are as follows. - Though a full discussion of the 2006 CODATA least squares adjustment of the physical constants has not yet been published, the CODATA recommended value for the fine-structure constant was apparently derived from the following experimental data for 1/α:

1. 137.035 999 710 (96) - from electron g value and QED, Gabrielse et al. 2006;
2. 137.035 998 80 (52) - from electron g value and QED, Van Dyck et al., 1987;
3. 137.035 998 78 (91) - from rubidium measurement (atom recoil of a rubidium atom in an optical lattice), Cladé et al., 2006;
4. 137.036 000 00 (110) - from cesium measurement (atomic recoil frequency shift of photons absorbed and emitted by cesium atoms), Wicht et al., 2002. A preliminary value 137.036 0001 (11) was already used in the CODATA 2002 adjustment, pp. 53-54;
5. Several other lower precision pre-2002 measurements that are specified in the discussion of the 2002 CODATA least squares adjustment, pp. 19-39.

The weighted average of all values is 137.035 999 674 (93), which is virtually the same as the 2006 CODATA recommendation, 137.035 999 679 (94).

Using the corrected Gabrielse value that is given in their erratum, 137.035 999 068 (96), and also correcting the Van Dyck datum to which exactly the same correction applies, one finds the following corrected value for the weighted means:

1 / α = 137.035 999 044 (93), or α = 0.007 297 352 5714 (50)

One may note that the Gabrielse datum, because of its small error compared with the other input data, contributes nearly 95% of the weight in the weighted average. Therefore, any change in its value heavily influences the weighted average. In fact, the Erratum correction amounts to a six standard deviations shift in the value of α, which is huge.

The correction has a series of consequences, some of which are quite serious:

1. Apparently the CODATA 2006 recommended value is (more than) six standard deviations off the value that currently may be considered the "best" value.
2. About a dozen physical quantities are closely related to α. Among these are e²/h (= 2α/μ_oc), h/m_e (= α²c/2R_∞), the Von Klitzing constant R_K, the conductance quantum G₀, and the Bohr radius a₀. It follows that all these quantities are off by six standard deviations too.
3. In recent years CODATA recommendations have been issued every four years (1998, 2002, 2006). Unless a new adjustment is done earlier, wrong values will remain in use until 2010.
4. The new value for alpha is very near the 2002 CODATA recommended value; however, its error is five times smaller.
5. The corrected α value is not consistent with the set of values for h, e, m_e, etcetera, that were adopted in the 2006 CODATA adjustment. (For example, because α is equivalent to e²/h, a change in the value of α implies also changes in either e, or h, or both.) However, the inconsistencies are minor: typically a one-tenth standard deviation shift in the values of h, e, etc., would suffice to restore consistency.
6. The new α value virtually rules out several numerological theories.

Question now is: how to integrate this information into the article. I think it would still be good to give the CODATA 2006 recommendation, but somehow a warning should be added that a better, and quite different value is now available. Hans van Deukeren 16:37, 23 August 2007 (UTC)

I have corrected the preceding calculation of the weighted means: my original calculation included the Wicht result twice, because I overlooked that it had already been used in the CODATA 2002 adjustment. Hans van Deukeren 13:50, 26 August 2007 (UTC)

I also had overlooked that the University of Washington value (Van Dyck 1987) that was the single most important input datum for the CODATA 2002 adjustment, should be updated: this alpha value was calculated from an electron magnetic moment measurement (g_e = 1.001 159 652 1883 (42)), and the correction communicated in the Gabrielse Erratum therefore also applies to this datum. Hans van Deukeren 20:28, 2 September 2007 (UTC)

Fine structure constant formula by Mikhail Vlasov

Fine structure constant α is linked with constant π, natural logarithm base e and natural number 138 by next equation :

                   α = sinc(1-(1/π)×tanh(π/138)),

where

    sinc(x) = (sin(πx))/πx,             normalized sinc function
    tanh(x)=(e^x-e^(-x))/(e^x+e^(-x)),  hyperbolic tangent function
    138 = 2*3*23,                       represents electric field quanta -
                                        number of electric field states

where

    multiplicand 2   represents positive and negative electric charge,
    multiplicand 3   represents number of electric charge values 1/3, 2/3, 1,
    multiplicand 23  is hypothetically (Mikhail Vlasov) related to the strings
                     of the M-theory (Duff,Michael J. )
                     which are 1-dimensional slices of a 2-dimensional membrane
                     vibrating in 11-dimensional space.
                     As illustration, product (1+x)^11×(1+x)^11 contains 23 additives.

Following formula (modified) has greater accuracy 1.5x10-13

  α = sinc( 1 - (1/π) × (tanh(π/138)) × (1-(π/138)^3)^(1/5) × (1-(π/138)^4)^(1/12) )

Please, see my article http://www.vmig-ip.com/FineStructureConstant.html

Mikhail Vlasov Korablino (talk) 20:31, 3 October 2010 (UTC)

Calculated value of alpha

The Feynman quote was good, but it sure didn't look like the rest of the section was physics. If we're going to have a section on a calculated value of $\alpha \$, i think i've seen closer guesses than that (some English math prof named "Gilson" had a good one), but i think they're all numerology. What should a good section on this topic be? I am not sure, but i didn't think this last one was particularly good. any other ideas? r b-j 01:37, 9 Apr 2005 (UTC)

Why was the "α in the International System of Units" section removed? See this old version The apparent inconsistency in the current set of SI recommended values and the CODATA one is certainly worth mentioning. I'll put it back in if I don't see a good argument materialise here. Urhixidur 13:19, 2005 Apr 9 (UTC)

there is no inconsistency in the most current value of $\alpha \$ outside of the normal experimental variance. it's just a number that we determine experimentally that presently is 1/137.03599911 . they used to think it was 1/137.03599976 . not much different. in that version, showing $\alpha \$ to 30+ digits is just very stupid. also, the expression of $\alpha \$ in terms of other fundamental constants was done both ways, using SI and cgs. it's the same number, but in cgs, they don't have an $\epsilon _{0}\$ (they set $4\pi \epsilon _{0}\$ to the dimensionless 1 by their choice of the unit charge statcoulomb ). r b-j 15:03, 9 Apr 2005 (UTC)

Calculations by W. Smilga and F. D. Smith

In 2004, W. Smilga [1] published a result based on quantum and group theory, supporting a formula previously found by F. D. Smith in 1985. Their theoretical value is:

${\frac {9}{(2\pi )^{4}}}{\sqrt[{4}]{\frac {\pi ^{5}}{5!}}}\approx {\frac {1}{137.03608245}}$

This looks very sensible, and I would like to add it to the Physical approaches section. Comments?

--Vernanimalcula 19:01, 4 August 2006 (UTC)

Actually, they uploaded a paper to arXiv, but it hasn't been published. I wouldn't even call it a reliable source, let alone notable enough to describe here. Melchoir 19:15, 4 August 2006 (UTC)

Another way to calculate the fine structure constant

$\alpha ={\sqrt {\frac {-2n^{2}E_{n}}{E_{r}}}}$

where,

$n\$ is the principal quantum number

$E_{n}\$ is the $n^{th}$ energy level

$E_{r}\$ is the rest energy of an electron? ($E_{r}=m_{e}c^{2}$)

By the way, $2n^{2}\$ is the total number of electrons that the electron shell can hold.

The energy level of an electron in the $n^{th}\$ shell is given by the following equation:

$E_{n}={\frac {E_{r}\alpha ^{2}}{-2n^{2}}}$

where,

$E_{n}$ is the energy level

$E_{r}$ is the rest energy of the electron

$\alpha$ is the fine structure constant

$n$ is the principal quantum number.

GoldenBoar 03:12, 18 December 2005 (UTC)

okay, Golden, i'm doing a little work that i was hoping you would do:

$E_{n}=-c2\pi \hbar R_{\infty }{\frac {(Q/e)^{2}}{n^{2}}}\$

$R_{\infty }={\frac {m_{e}e^{4}}{(4\pi \epsilon _{0})^{2}\hbar ^{3}4\pi c}}$

$E_{n}=-c2\pi \hbar {\frac {m_{e}e^{4}}{(4\pi \epsilon _{0})^{2}\hbar ^{3}4\pi c}}{\frac {(Q/e)^{2}}{n^{2}}}\$

$=-{\frac {m_{e}c^{2}e^{4}}{(4\pi \epsilon _{0})^{2}\hbar ^{2}c^{2}}}{\frac {(Q/e)^{2}}{2n^{2}}}\$

$=-m_{e}c^{2}\alpha ^{2}{\frac {(Q/e)^{2}}{2n^{2}}}\$

for the Hydrogen atom (i presume that is what you're doing), Q = e:

$E_{n}=-m_{e}c^{2}\alpha ^{2}{\frac {1}{2n^{2}}}\$

$=-E_{r}\alpha ^{2}{\frac {1}{2n^{2}}}\$

if you want, Golden, go ahead and put this factoid into the Physical interpretation section. r b-j 05:18, 18 December 2005 (UTC)

i reverted this in the article for the reasons stated in the edit summary. if this checks out, perhaps including a note that the energy level of a (what? an electron in the n^th shell?) is

$E_{n}=-\left({\frac {\alpha }{n}}\right)^{2}{\frac {E_{r}}{2}}\$

as a sorta useful factoid that uses the Fine-structure constant, fine. but it doesn't seem to me to rise to the level of definition. it's more of a result. if thid is the case, might E_r be replaced by m_e c² ? r b-j 17:41, 17 December 2005 (UTC)

Positronium

What's this Positronium stuff? Am I clueless or is this just nonsense, or one authors opinion? I've moved from the article here:

Physical approaches

Some attempts have also been made to understand the fine-structure constant in a physical way, for instance from thermodynamic considerations. Calculating the annihilation temperature and the decay ratio of 2-gamma and 3-gamma events at the positronium decay by thermodynamics (Thermodynamic consideration of the positronium decay Nuovo Cimento B, Vol 121 Issue 02 Month February pp. 175-191, ISSN 1826-9877 [2]), a result of $\alpha \approx$ 1/128 was obtained.

Another approach was the calculation of interaction entropy of electrons and photons, with a result of $\alpha \approx$ 1/137.135... (Statistical approach to Sommerfelds fine-structure constant Nuovo Cimento B, Vol. 121, issue no. 3 (2006) pp235-240 [3]).

Following these thermo-statistical approaches, charge could be seen in some kind of conflict: On one hand, it would like to emit a photon, because thus entropy could be generated - but on the other hand, the emission of a photon is "construction expensive" and could tell an observer where the charge is located. Putting this antagonism into physical formulas, the value of the fine-structure constant could be obtained.

Can some subscriber check the alleged Nuovo Cimento references? --Pjacobi 12:07, 29 September 2006 (UTC)

removed 2008 value from lead paragraph

The first paragraph gives values for $\alpha$ and ${\begin{aligned}{\frac {1}{\alpha }}\end{aligned}}$ that differ from the CODATA 2006 values given in the following section. As these values are not referenced, as they lead to confusion with the "standard" values given, and as the CODATA 2006 values were republished in 2008, i will remove the sentence with these alternate values. Various other values are discussed in the section on measurements. Bcharles (talk) 00:44, 15 February 2010 (UTC)

Variation of value with energy

Running value

I hope I'm not being dense, but the phrase "....contribute to the running." doesn't make any sense to me. What's really meant?

The observed value of \alpha \ is associated with the energy scale of the electron mass; the energy scale does not run below this because the electron (and the positron) is the lightest charged object whose quantum loops can contribute to the running. Sesquiannual

Variation of value with time

Variation with time

Which Theories suggested that the fine structure constant should change?

JeffBobFrank 04:27, 2 Mar 2004 (UTC)

I think certain cosmic inflation models but I'm not sure. Sanders muc 21:02, 16 Apr 2004 (UTC)

---

String Theory and other multi-dementional theories provide potential mechanisms for alpha to change. The basic idea is that there is an over all constant that is smeared over all the dimensions. If one of the dimensions changes size then the weighting that each dimension feels of the constant changes, even though if you added up the contributions from all the dimensions then you'd still get the same constant. ie if a fifth dimension expanded then the electromagnetic force would weaken in our 3+1 dimensions as it would be acting over a greater volume and so alpha would appear to decrease, even though over all when all dimensions are taken into account it stays constant. Complicated stuff!! K.D.B 1May 2006 (See book by J.D.Barrow The constants of nature, from alpha to omega)

Varying fine structure constant

Dear all,

I was just reading the bit about varying-alpha and it occured to me that as it stands it contains some erroneous information. Firstly it quotes the Tzanavaris et al. paper as being a stronger bound on the constancy of alpha than the earlier Webb et al. work, which is simply inaccurate. The Tzanavaris work is a very important study because they have looked at the variation of the quantity x = \alpha^2 g_p m_e / m_p, and so they can derive bounds on g_p, and mu = m_p / m_e as well as \alpha. They find a slight indication of a change in x (very very slight, just over 1 sigma), by comparison the Webb et. al. results were consistent with a change in alpha at the far more significant level of six sigma.

The quoted error bars on the Chand et. al. results found using the VLT/UVES are very small (unbelievably small), and the team lead by Webb and Murphy have a number of issues with the Chand et al. analysis. The concenus seems to be that reanalysis is needed (and currently proceeding) to understand the accuracy that Chand et al. claim.

Also John's paper on spatial variations doesn't place any limits on the time variation in alpha, it is just considering spatial variation, so it is inaccurate to cite it as a better bound than the Webb result (although it is an important work in its own right).

I think, if I were rewriting the section, I would say something like this: " Physicists have been wondering whether the fine structure constant is really a constant, i.e. whether it always had the same value over the history of the universe, as some theories had been suggested which implied this not to be the case. First experimental tests of this question, most notably examination of spectral lines of distant astronomical objects and of the Oklo natural nuclear fission reactor, found results consistent with no change.

More recently, technology improvements have made it possible to probe the value of $\alpha$ at much larger distances, and to much greater accuracy. In 1999, a team lead by John Webb of the UNSW announced results that may prove to be the first detection of a variation in $\alpha$. Using the Keck telescope and a data set of 128 quasars at redshifts 0.5<z<3, Webb et al. found their absorption spectra were consistent with a slight increase in $\alpha$ over the last 10-12 Gyrs. Precisely the found that $\Delta \alpha /\alpha \equiv \alpha _{then}-\alpha _{now}/\alpha _{now}=-0.57\pm 0.10\times 10^{-5}$. In the seven years since their results were first announced, extensive analysis has yet to identity any systematic effect that could explain either its magnitude or sign. This said, a smaller study of 23 absorption systems by Chand et al. found a result consistent with no variation: $\Delta \alpha /\alpha _{em}=-0.6\pm 0.6\times 10^{-6}$. This result was found using the VLT telescope. The Chand et al. result seems to be rule out variation at the level claimed by Webb et al., however, it was found using a simplified version of the method used by the UNSW team and concerns remain about calibrations and the noisiness of the data fits. Later in 2006, a major effort to produce a very large new data set should be reported and this will hopefully clarify the status of these earlier investigations.

All other results that have been found to date are consistent with no variation, however none could of these had the precision to see the level of variation reported by Webb et al.

If a variation in $\alpha$ can be detected then it will be the first clear sign for the existent of physics beyond the standard model of particle physics. "

What do you think? If people are happy with the change I will make it (and include the appropriate references).

I don't mean to step on anyone's toes with this proposed change, but I have had some experience in this field and so I would like to make this article as accurate as possible.

Doug

--Djshaw 13:17, 7 August 2006 (UTC)

New paper: Evidence for spatial variation of the fine structure constant J. K. Webb et.al http://arxiv.org/abs/1008.3907v1 —Preceding unsigned comment added by Thinkclearniac (talk • contribs) 17:40, 3 September 2010 (UTC)

It is less than helpful to read that a study has found something, but later dismissed as faulty (the bit about the alpha having not changed in a smaller study.) I don't dare touch these articles of physics, but is there any reason to keep that reference? Esben (talk) 07:51, 6 September 2010 (UTC)

Numerology

Numerology: Eddington

The section "Arthur Eddington and the fine structure constant" seems to contradict what it says at Eddington number. Here it states that he thought 137, then in 1938 changed to 136. There is says he started with 136 in 1938 and later changed it to 137. DÅ‚ugosz

I dont know too much about Eddington, but I would guess that when early measurements gave roughly 1/136 he said that was its exact value, and when the more accurate approximation 1/137 was known he changed it to that. It would seem a bit odd if he did it the other way around JeffBobFrank 16:04, 2 Apr 2004 (UTC)

Removing personal criticism

Hi everyone. I'm new to Wikipedia. I removed the reference to Eddington because it was accompanied with the word 'numerological'. A mathematical physicist should not be accused of numerology as it turns the encyclopaedia into a critical review (a review with spiteful tendencies). If criticism is to be made, it should be in the context of a larger appraisal of a person's work, so that the reader gets a balanced view of that person's achievements. This I believe is consistent with the 5 Pillars.Lucretius 13:33, 30 December 2005 (UTC)

i reverted this deletion and added links to where this info might have come from. i realize that this numerical navel gazing is probably not physics but it is an interesting aspect of the fine-structure constant. it should remain, but we should be clear it's numerology, not physics. r b-j 04:56, 31 December 2005 (UTC)

Lucretius - Thanks RBJ for your input. I concede that Eddington's suggestion is of interest in the FSC section but I still think the word 'numerology' packs a nasty punch and the reader here would think Eddington was a nincompoop, which he most certainly was not. I think we can reach an agreement here - we retain the reference to Eddington and Gielson but change the heading to 'Numerical Hypotheses' then leave the readers to make up their own minds whether it is in fact numerology. We have to be careful not to sit in judgement in an article page and therefore we should not 'be clear' that Eddington's work here is numerology. I've made the change accordingly. Thanks again Lucretius 06:08, 31 December 2005 (UTC)

Lucretius, you do not understand that there are a lot of super-duper physicists, some Nobel winners, that have also overreached and put forth crackpot ideas. William Shockley is one example. This 1931 contribution from Eddington is documented and it is speculated by many that he was publishing a spoof or hoax in the similar sense of the Sokal Affair. Perhaps he was serious as in the Bogdanov Affair, but whether or not it is a spoof, the content of that publication is at best numerology. i'll let this sit for a couple days to see what other input there is, but the fact that Eddington said this stuff is, in fact, numerology (whether he was serious or not) and the article needs to say it. r b-j 18:16, 31 December 2005 (UTC)

Again thanks RBJ for your measured response. I am aware of super-duper physicists who tested the boundaries between numerology and science, such as Dirac and his large number hypothesis, which is based simply on numerical co-incidence. You might dispute whether or not Dirac's hypothesis is numerology but that would also prove my point - what you call a 'spade' others will call a 'blunt-nosed shovel' and you can't, as a contributor to an encyclopaedia, make qualitative judgements. Make no mistake about this - referring to a physicist in terms of numerology is a qualitative judgement about their competence. Yes, even super-duper physicists get it wrong sometimes, but you can't ridicule them in an encyclopaedia. The reference to numerology is simply unnecessary and I think the argument, after the changes you have made, is now much more informative and balanced. Thanks again.Lucretius 01:33, 1 January 2006 (UTC)

i am not "referring to a physicist in terms of numerology". not directly. i am referring to a publication (by a particularly physicist) in terms of numerology. there is no controversy in the physics community, that i know of, that any argument that 1/α is precisely an integer is made from a numerological basis. Eddington was a great physicist, but whether that 1931 publication was meant as tongue-in-cheek or not, the content of that publication is widely considered to be a numerological argument. whether the physicist who wrote it is considered to be a numerologist or not or a great physicist or not, is another matter. r b-j 02:15, 5 January 2006 (UTC)

Sorry Rbj but I hope you'll give ground on this just as I gave ground on the Planck page. The word 'numerological' is simply unnecessary and readers can make up their own minds without prompting from us. Cheers Lucretius 09:47, 7 January 2006 (UTC)

Arthur_Eddington#Fundamental_theory: During 1920s until his death, he increasingly concentrated on what he called "fundamental theory" which was intended to be a unification of quantum theory, relativity and gravitation. At first he progressed along "traditional" lines, but turned increasingly to an almost numerological analysis of the dimensionless ratios of fundamental constants. His work was increasingly seen as "crankish", and he became something of a science pariah in his later years.

Anthropic Reasoning and the Contemporary Design Argument in Astrophysics: A Reply to Robert Klee ...Eddington's numerology takes historical precedence. The appeal to numerology turns on the idea that the fundamental constants of our universe are in some sort of "mysterious" or "occult" numerological relationships. ... Surely we can imagine a universe that exhibits all sorts of Eddington numerology, but is inhospitable to life (imagine radiation levels too high to allow life to develop). Conversely, we can imagine a universe where the physical parameters are finely tuned for life, but the parameters themselves do not exhibit any Eddington numerology. Thus, any critique of Eddingtonian numerology leaves the anthropic principle unscathed; to claim otherwise is a non sequitur.

Cosmic Numerology: Active in physics, astronomy, and mathematics, Arthur S. Eddington (1882–1944) made important contributions to the general theory of relativity, providing the first experimental confirmation that gravity can bend light. At the same time, he was fascinated by the fundamental constants of nature, particularly what he termed surprising numerical coincidences among these constants. Eddington insisted, for example, that the fine structure constant, now known to be 1/137.036, had to be precisely 1/137, and the number 137 was itself significant.

Numerology: The great scientist Sir Arthur Eddington "derived" the fine structure constant from an equation based on simple ideas. At the time the measured value was about 1/136. Eddington assumed that the denominator was a whole number. When the value was measured more accurately and found to be close to 1/137, Eddington had to change his theory. In fact the actual number is 1/137.03604. Nobody to this day knows the origin of this number, nor even whether it has meaning. Arthur Eddington probably did not know the following fact. If you write Arthur Stanley Eddington, and if you set 1 for A, 2 for B, etc, the total of all the numbers from the letters is 274, which is 2 X 137. The 2 can be identified with the electron gyromagnetic ratio: 137 we have met already. Had Eddington been aware of this, he might have reflected on the wisdom of believing something just because the numbers agree with something else. That his idea did not lead to anything does not detract from Eddington's great work in physics and astronomy: quite a few scientists have had sidelines which were not rated highly by other scientists.

A parody paper in solid state physics, published in 1931: The paper parodies certain types of "numerology", notably that of Sir Arthur Eddington. Eddington was a famous and highly accomplished physicist, who toward the end of his career began to delve into poorly-founded speculations. One of these involved the fine-structure constant alpha, a number which arises in quantum physics. It is a pure number, without dimensions or units, and is equal to about 1/137.04. At Eddington's time, alpha was known less accurately and the experimental value was consistent with 1/137 exactly. Eddington and others, attempting to figure out why alpha should be the value that it is, engaged in various hand-waving efforts to justify the number 137 as derivable from some kind of fundamental principle.

The fine-structure constant before quantum mechanics: The physicist Arthur Eddington ... fine-structure constant α, which had been measured at approximately 1/137, should be exactly 1/137... (not a free paper, but this is what Google extracted from it.)

Numerology in science]: Number-coincidence arguments are still used in science, although there is great controversy about their validity. The physicist Arthur Eddington at one time thought the fine-structure constant α, which had been measured at approximately 1/137, should be exactly 1/137, based on aesthetic and numerological arguments. Careful measurements have shown this not to be the case: the value of α is currently estimated at 1/137.03599976(50). When another (erroneous) measurement showed α to have a value nearer 1/136, Eddington constructed an argument relating the number 136 to the Eddington number, his best estimate of the number of electrons in the Universe. (of course Eddington didn't estimate the number of electrons in the Universe to be 136, but i think it was e¹³⁶ or 2¹³⁶.)

okay Lucretius, you have to produce citable evidence to support your position that either Eddington didn't say this or that it is not considered to be numerology. This is what we call a "slam-dunk" on this side of the pond. r b-j 18:12, 7 January 2006 (UTC)

Not to insult Lucretius, but I'll just pop in here to say I support r b-j, and anyone interested in the removal and restoration of the content in question might want to check out Talk:Numerology#Personal_criticism as well. Melchoir 19:21, 7 January 2006 (UTC)

My problem with a 'numerology' reference to Eddington here is this - the only 2 things most amateurs and students know about Eddington is that he made 2 egregious mistakes. First there is his fine structure hypothesis, after which the satirical magazine Punch immortalized him as "Sir Arthur Adding-one", and secondly, he designed a flawed experiment to 'prove' Einstein's theory that the sun bends light - he simply got the test result he wanted. It's not right that a brilliant physicist should be remembered as a dolt on the basis of 2 bad mistakes and I don't think Wikipedia is setting the record straight with references like this. By all means let's expand the section on 'Numerology', with Eddington in it among other brilliant physicists, but please let's leave the 'numerology' reference out of the FSC article, where it really is unnecessary. I can add Dirac and his large number hypothesis and maybe Rbj and Melchoir can add some others. Does this sound like a fair comrpomise? Lucretius 03:17, 8 January 2006 (UTC)

Not to me. I know nothing about the Dirac large numbers hypothesis, but if the Wikipedia article is to be believed, it is motivated more by cosmology than by alpha. There's an e^2 in there, but it's hardly the central idea. On the other hand, Eddington's ideas about the value of alpha were motivated by alpha itself and directed towards alpha itself. You say it's unnecessary to an article on alpha; I respectfully find that absurd. Melchoir 04:17, 8 January 2006 (UTC)

I meant Dirac should be included in the Numerology article(my phrasing above was however sloppy and I blame myself for the misunderstanding). I also offered this compromise on the basis of what you wrote me, Melchoir, that the Numerology article could be expanded and that there might then be no need for two 'numerology' references to Eddington. I thought your suggestion was a good one and I'm now puzzled as to why you find it absurd.Lucretius 04:44, 8 January 2006 (UTC)

first of all, i never heard that Eddington's trip down to the Amazon (or wherever it was) to check out Einstein's GR hypothesis on bending of light was flawed. everything i've ever seen on it was that Eddington came back with the evidence that was consistent with Einstein's prediction. second of all, i do not think about Eddington entirely in terms of this alpha thing, but it is there. and not only has Eddington tried to come up with a mathematical explanation for α, many others have. now you are suggesting that we have an article about α and not mention that many people have proposed mathematical definitions of it? or that we include the other numerolgical theories but leave out any mention of Eddington's efforts? that makes no sense.

this numerology does not define Eddington nor is his principle history just as racism and eugenics do not define William Shockley. i think of Shockley as a Nobel winning physicist who, along with two other physicist, invented the transistor and that's a big deal. but any biography of Shockley cannot responsibly leave off the eugenics.

lastly, someday they might come up with a pure mathematical expression for α, but they need to do that on a physical basis and not a coincidence of number to avoid the "numerology" label. it's sorta like first measuring the exponent in the denominator of Coulomb's law to be some number very close to 2. so they first measure the electrostatic force to be an inverse-square law within some tolerance of error. but just because it comes out to be soooo close to 2 in experiment is not sufficient to demand that that exponent must be exactly 2 because it looks elegant mathematically (because maybe it's really 2.00000001 or 1.99999999). you need a physical reason or a physical theory to say it's exactly 2. and they came up with one: it's called flux and is the basis of Gauss's law (and the divergence operator in Maxwell's equations).

so far no one has come up with real physics to create a pure mathematical expression for α. but maybe someday, perhaps using the weak anthropic principle, they'll come up with independent expressions that will limit the range of α so that the universe doesn't turn into a tomato or something. and maybe that independently derived "range of possible α for a universe to be like the one we see" will get narrowed down so much that it is simply equal to what we've been measuring (within the tolerance of error). r b-j 05:28, 8 January 2006 (UTC)

Lucretius, I apologize if I misled you on your talk page; I certainly didn't mean to misrepresent my own intentions for this article. I think my mind at the time was more on the Numerology article. Since numerology is so broad a topic and the fine-structure constant is relatively narrow, it makes more sense to me to split that article into multiple pieces, and alpha would go into the Science piece. This article, on the other hand, ought to fully describe the history of thought of the fine-structure constant, which would be incomplete without a section on numerology... and that section would be incomplete without Eddington. In Numerology the reference is unfairly selective, in that other areas of science, and other scientists, need to be mentioned; but here it is completely fair and appropriate. See what I mean? Melchoir 06:24, 8 January 2006 (UTC)

Ok so now we have two references to Eddington in terms of 'numerology'. I think this is disproportionate. The FSC article mentioned that his theory is considered a 'spoof' or a 'hoax'. Surely that was enough.

According to my pocket Oxford dictionary, numerology is 'divination by numbers; study of occult meaning of numbers'. Yes, some aspects of Eddington's work are more mathematical than scientific but that doesn't mean he should be accused of numerology. Dirac was sometimes more mathematical than scientific. So was Herman Weyl. So were many others. Accusing any of them of numerology would be an abuse of the English language. But it is always Eddington who gets tagged a numerologist and this is personal abuse as well as an abuse of language. I think Wikipedia should try to avoid using this handle on Eddington as it is already used too often. Give the man a fair go. Possibly there is an issue here about the standard of scientific debate and maybe there is a tendency for people to stretch the meaning of numerology simply to denigrate physicists they don't agree with. That should be mentioned in the Numerology article if we are to include physicists in it.

I'd like to add that I've also re-stated my argument on my user page in reply to Melchoir's letter. I thank Rbj and Melchoir for their conscientious efforts to argue their own case here on the discussion page. But I continue to hope they will change their minds. Lucretius 21:01, 8 January 2006 (UTC)

listen, Lucreius, i like Eddington. i'm not trying to do Eddington bashing. it's just that there are two important points that Melchoir made succintly that still stand: since α is dimensionless and either it is or some function of solely α is possibly the most fundamental physical number we know of. i like ${\sqrt {4\pi \alpha }}=0.30282212$ because in "rationalized Planck units", the set of units i personally think are the most natural, this number is the elemetary charge. α is said to define, relative to the other forces, the strength of the electromagnetic force, and one could argue that this relative strength is just a consequence of the product of each pair of charges relative to the natural unit of charge. but this is my personal mathematical pet. i'm not a famous physicist and i haven't published this anywhere.

but it's natural for all of us to wonder about the nature of α. how did it get to be what it is? it's similar for us to wonder about the nature of the inverse-square law. why not inverse-proportional or inverse-cubed or 1/r^5/2 or some other power? now, experiments have shown that for electrostatic forces the exponent in the denominator is virtually 2, but there is always a margin of error. for us to say it must be exactly 2 because 2 is a nice integer and it makes the equation look pretty, that would be numerology. on the other hand, for us to come up with a physical theory of flux to justify the exponent of 2 is physics. (but just a theory, maybe isotropic E&M fields are not conserved and distributed evenly over a spherical surface as the flux concept would dictate. but the experiments say it's super close to exactly an inverse square relationship, so the flux theory of the electrostatic field as well as Gauss's law survive.)

Eddington's theory that α = 1/136 and later α = 1/137 were based on aesthetics and had, as best as i can read, no physical foundation. and the only physical foundation i have ever come across that says anything about how α comes to be the number it is, is the weak anthropic principle (along with a shitload of nuclear physics). they have come up with ranges that α must be in order for atoms and matter to exist as it does. and maybe someday, from an independent physical argument, they'll narrow it down and we'll have an independently derived mathematical expression for α, but that day hasn't arrived yet. r b-j 03:37, 9 January 2006 (UTC)

Thanks again Rbj for your willingness to debate the issue. I am convinced that you respect Eddington as a physicist. Quite frankly I agree with you that his work on the FSC however was fanciful. But his theory was able to be disproved experimentally and it's only for that reason that it is no longer to be considered a scientific theory. Einstein's special theory of relativity looks fanciful too except it has been proved experimentally. The fact that a scientific theory appears to be more mathematical than scientific does not mean we are justified in calling it numerology. Eddington's theory was bad science(we can say this with hindsight) but that does not make it numerology. Astrology is numerology. Pythagorean mysticism is numerology. A failed scientific theory with a strong mathematical emphasis is not numerology. It doesn't come within the true definition of numerology. The words 'numerology' and 'numerological' are used in a scientific context simply to show how strongly we disapprove of a conclusion that appears to us to make little physical sense. But we are not supposed to record our feelings (at least not on the article page). This is supposed to be an encyclopaedia.

My opinion is that we should have an article about mathematics in physics, and there we can present the fact that physicists are sometimes accused of numerology. But we should point out that this is a pejorative word that lumps physicists with astrologers. We should not make any judgement about whose work is numerology or which physicist resembles an astrologer. We should merely present the case that this or that physicist has been accused of numerology. The references you supplied above would be good as these are written by people who are trying to show their personal disapproval of Eddington's work, for which they have their own reasons.

Again, please give careful thought to what we are actually doing when we label Eddington's work as 'numerology'. Lucretius 05:04, 9 January 2006 (UTC)

i am not the only one labeling Eddington's particular attempt to set α to 1/136 or 1/137 "numerology". i cited several other sources that say the same thing. i believe that this is the widely held belief of physicists today because Eddington's justification was that he thought that the integers 136 and 137 were special somehow.

in some sense every one of these lower integers is special, but it doesn't make physics. It was said of Srinivasa Ramanujan that every number was his friend and he had plainly thought about and stored away many interesting facts about most of the lower integers. ... one visitor told of a visit he made to Ramanujan "when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to me rather a dull one, and that I hoped it was not a bad omen." "No," he replied, "it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways." if 1729 is special, then 136 and 137 are at least as special. but to say that 1/α is precisely 136 or 137 because they are special integers is numerology. not occult or really mysticism, but it's not physics either. r b-j 05:44, 9 January 2006 (UTC)

Thanks again Rbj. You certainly are a fountain of interesting information. I think we agree about everything here except the use of the term 'numerology'. Yes, I've already conceded that Eddington's theory was bad science - I think even Einstein's theories would today be considered bad science if experimental results hadn't backed him up, and many people in his time thought he too was just being fanciful. My point is simply that numerolgy might be a term scientists sometimes use when they want to disparage someone's work but just because scientists or serious students of science sometimes use that word does not mean we can use it in an encyclopaedia, because then we also would appear to be trying to disparage someone's work. It's an emotive term when used in a scientific context and it communicates contempt. Yes I know you respect Eddington for his other work but maybe you haven't quite grasped the full significance of the language you are employing in this article, because it does express contempt for Eddington's theory. You might or you might not think contempt is a justifiable response in this particular FSC case, but that is a personal response and it doesn't belong on the article page. I am not disputing your grasp of scientific concepts. I am disputing your choice of words in an encyclopaedia. Maybe you give so much time to the science that you don't give enough time to the language issue. Forgive me if that sounds like personal criticism. It is not meant to be. There are other ways to phrase this article without the words 'numerology' or 'numerological'. I removed only those words from your version because it was in every other respect a good article. I'm hoping you'll return it to that previous condition. I won't do it unilaterally as I know you'll probably retaliate, which would get us nowhere. Lucretius 06:55, 9 January 2006 (UTC)

I've added a caveat in italics at the start of the article to let readers know that 'numerology' here does not imply that Eddington is some kind of astrologer or Pythagorean mystic. This is an important distinction and I hope it is an acceptable compromise to others who are interested in this article.—The preceding unsigned comment was added by Lucretius (talk • contribs) 03:38, 10 January 2006.

i can most certainly live with your latest edit, Lucretius. r b-j 03:53, 10 January 2006 (UTC)

I would hope that the difference between numerology and theoretical physics could be more clearly defined. I would propose that theoretical physics, while it can include a lot of mathematics, should also have a coherent physical model of some part of the Universe, which should be self-consistent, and should take account of all relevant experimental data. Now if one obtains a value of "alpha" simply by playing around with numbers, without providing a coherent physical picture of how these numbers get there, it is simply numerology. In my field (theoretical particle physics) there is a general consensus that Eddington did not have a coherent physical model. (For comparison, Dirac's 'large numbers' work gave a clear picture of the evolution of fundamental parameters over time and made testable predictions - which have now been falsified). To be blunt, everyone I have discussed it with sees Eddington's work on 'alpha' as both worthless and extremely misguided. As to other mathematical expressions for alpha, their status strongly depends on whether they come out of a coherent/self-consistent physical model. --Tdent 23:25, 1 December 2006 (UTC)

last two equations - numerological explanations

Lucretius wrote this: can someone supply a reference or link for the last 2 equations in 'Numerological explanations'? Or are they part of Gilson's theory? It needs to be explained because they are presented here as if they came from nowhere. Also can 1.000042 really be described as 'high precision'? I think even G has more precision that that and G is usually said to be imprecise. I'm not much good as a mathematician so I need someone else's input here.Lucretius 00:25, 11 January 2006 (UTC)

hi, L. i didn't put those last two in (with the log(cos) stuff). it didn't come from Gilson AFAIK. you'll have to check the article history (the "diffs") to figure out who put it in. you can yank it out AFAIC and see if someone squawks or not (i won't), or you can track down the editor who stuck it in and ask them about it or you can yank it out and tell that editor or any other combination. BTW, G is accurate to 150 ppm where that number above is 42 ppm (better than G but not much better). nonetheless, we know α to about 3 ppb and Gilson's numerology is accurate to about twice that error. r b-j 02:52, 11 January 2006 (UTC)

Thanks again Rbj. I'll take the lazy option, remove it and see what happens. Lucretius 03:06, 11 January 2006 (UTC)

removal of "non-notable" Gilson numerology

Pjacobi, are you sure that the Gilson equation is so non-notable to be removed from the numerology section? excluding mirrors of WP and Gilson's own site i find some references that seem to indicate some notability: [4], [5],[6], [7], [8], [9] including hits in Google Scholar. i think that the physics community still regards Gilsons discovery to be numerology and little more, but it is of enough note that it belongs in the numerology section of the article. no? r b-j 16:39, 16 October 2006 (UTC)

Hmm. Very mixed bag of references. I typically don't include contributorts to Galilean Electrodynamics ino the scientific community. --Pjacobi 17:30, 16 October 2006 (UTC)

it is a mixed bag. i didn't look at them all closely, enough to see it wasn't a WP reflection. i am not saying that Gilson is "right" or his conclusion is, but neither was Eddington's numerology regarding the FSC. there is an infinite bag of numerology that can hit the FSC to whatever degree of accuracy you spec, but a reasonably accurate hit with an expression that is compact is notable to within the scope of just this section, no? maybe the section itself shouldn't be there at all. r b-j 18:17, 16 October 2006 (UTC)

From 137 (number)

I removed the following paragraph from 137 (number) as unnecessarily detailed for that page:

The importance of the constant is that it measures the strength of the electromagnetic interaction. It is precisely because the constant is so small (i.e. 1/137 as opposed to 1/3 or 5 or 100...) that quantum electrodynamics (QED) works so amazingly well as a quantum theory of electromagnetism. It means that when we go to calculate simple processes, such as two electrons scattering off one another through the exchange of photons, we only need to consider the simple case of one photon exchange -- every additional photon you consider is less important by a factor of 1/137. This is why theorists have been so successful at making incredibly accurate predictions using QED. By contrast, the equivalent 'fine-structure' constant for the theory of strong interactions (quantum chromodynamics or QCD) is just about 1 at laboratory energy scales. This makes calculating things in QCD much, much more involved.

According to my rough and hazy understanding of how QED works, the point this paragraph makes appears to be valid, but should rather be made in this article. It's not here already, but I don't feel fully competent to insert it; it needs at least some copyediting to trim away the superlatives. Any comments before I just brutally insert it here at a place where it seems to fit? –Henning Makholm 16:02, 13 May 2007 (UTC)

Culetto and Culetto original research

The section in Numerology on the "Culetto and Culetto" theory seems like obvious original research. I'll tag it and if no reputable sources are given I'll delete it. Dark Formal (talk) 18:06, 22 November 2009 (UTC)

Deletion accomplished. Dark Formal (talk) 02:42, 15 December 2009 (UTC)

Miscellaneous

Nonsense?

The stuff at http://www.fine-structure-constant.org looks like nonsense to me. If someone can convince me that it really belongs here, I'll put it back. --Lee Daniel Crocker

Yup, you're right, it's bogus. AxelBoldt

References

Does anyone object to me changing the reference style? They are currently inconsistent with WP:CITET. If anyone knows of a good reason to leave them as they are, then please speak up, otherwise I'll convert them over in the next day or so. Chovain 13:44, 10 August 2006 (UTC)

Please do change them. I didn't know how to do them properly when I did them, I was hoping someone with the know how would come along and make them right. Thanks. Doug

Ok - I've started on this, but am going to need to do it iteratively (It's a lot more work than I realised :)). It'd be great if you could review my changes. I'm fistly going to break the current references up into separate refs (rather than the multiple refs per footnote that are there at the moment, then go through and update a few refs at a time.

I should warn you that I know virtually nothing about physics beyond my high school physics classes, so have not even been able to sanity-check my changes. Chovain 03:51, 12 August 2006 (UTC)

Picture Caption

The article has a picture with some Feynman graphs that are claimed to be contibutions to th electron`s magnetic moment. To me they look like self-energy graphs that contribute to the electrons mass renormalization. Dauto 03:33, 4 April 2007 (UTC)

Using <math> for α in paragraphs

I don't think it is necessary to use $\alpha \,$ in paragraphs where the single greek character α could be used. Is there any advantage to using <math> for a single greek letter? — PhilHibbs | talk 12:25, 26 November 2007 (UTC)

consistency of style Dauto (talk) 23:26, 19 July 2008 (UTC)

Constant?

Lee Smolin, in What's Wrong with Physics?, notes studies that criticizes the Australians' claim that alpha is not constant. I'll seek and add in such cites. Bearian (talk) 19:39, 20 February 2008 (UTC)

Ampere definition?

I can't get over the feeling that I'm being tricked somehow by this "dimensionless" unit. What comes to mind is that the definition of the ampere arbitrarily chooses to measure the force generated by two wires one meter apart. If it measured the force between two wires one kilometer apart, even if it measured it over a full kilometer, the force would be 1000 less per a given current, so the ampere would be defined as a 1000 times greater amount of current. So in the formula, the charge on the electron would be 1000 times lower, and the mu-zero conversion factor (newtons per amperes squared) would be the same... I think. (Using a different unit of length would throw the newton-to-joule ratio off by 1000, but c would also be lower; these length units cancel out in the math without resorting to the definition of the ampere). Now admittedly, when I start wondering if all physicists are wrong it usually means I have a deficit in my understanding ;), but this one has me stumped. Wnt (talk) 19:00, 10 July 2008 (UTC)

There were a series of "Practical Systems" for which one might couple units like volt-ohm-ampere etc, with a given national system, eg foot, inch, or centimetre. The "Practical system" itself has the volt-ohm-second as the derived EMU, that is, has a unit of length = 10,000 km, and a mass of 10 picograms. Generally, the practical systems set the length as x metres, and the mass as 1/x² kilograms. Gustave Mie used x=0.01 (ie cm), while Giorgi uses x=1. You could easily use x=0,3048 (ie foot). The decision to use a four-dimensional system, with a fourth, electrical unit, comes because the EMU system requires that x=10^7, and any other value supposes that a fourth dimension is needed to eliminate 10^7/x.

Since this supposes a definition that involves both electrical and magnetic properties, we see then that a value of 1E7 appears somewhere in the definition for the mksA system. The 2 is an integration (specifically, surface of sphere/ perimeter of circle = 4pi/2pi = 2). We then have by using 2, that A² = 1E-7 N is an equity when the size of the square (length of wire + separation) is any unit, eg foot, metre, cm, km. They cancell out. However, the newton involves a length, (kg,m/s²), but as long as one gets "newton" as the force, one could have, eg Newton = gram.millimetre/millisecond² without general loss.

The fine structure constant (1/137), is indeed dimensionless. We see it as a ratio of lengths (the radius of a electron, calculated that mc² = e²/r (ESU), is (1/137)² of the classical bohr radius, calculated as momentum = e²/r² = ma²/t², is quantised (ie h-bar). It is dimensionless in the six-dimensional scale of Leo Young (1962 "Systems of Units in Electromagnetics"),

--Wendy.krieger (talk) 09:50, 28 May 2010 (UTC)

Possible Variation due to Distance from the Sun

It has been suggested by some physicists at Brookhaven that the fine structure constant might be modulated by the distance of the Earth from the sun. Here's an interesting paper that posits this as a possible explanation of some observed variable decay rates:

http://arxiv.org/abs/0808.3283v1 —Preceding unsigned comment added by Gmcastil (talk • contribs) 17:36, 29 August 2008 (UTC)

Another Numerical Approximation

$\alpha \quad \approx \quad {\frac {19^{17}}{17^{19}}}\ {\frac {1}{\pi }}\qquad ={\frac {1}{137.047}}$

Not that close, but pretty.

--Vibritannia (talk) 16:53, 4 September 2008 (UTC)

A Similar but Closer Numerical Approximation

$\alpha \quad \approx \quad {\frac {\pi ^{e}}{e^{\pi }}}\ {\frac {1}{7}}\ {\frac {1}{19}}\qquad ={\frac {1}{137.03595}}$

Spooky!

--Vibritannia (talk) 07:07, 5 September 2008 (UTC)

Simple Rational Approximation

$\alpha \quad \approx {\frac {3\times 7\times 11\times 19}{601451}}={\frac {1}{137.0359990886}}$

Rumpuscat (talk) 21:14, 25 September 2008 (UTC)

2 × 53 × 16699/12917 is much closer, 137.03599907099. (How did I find it? See continued fraction.) -- A r m y 1 9 8 7 ! ! !  22:13, 25 September 2008 (UTC)

deleted personal research

I deleted this since it's unreferenced and looks certainly like personal research:

An example of one of many approximations found since is

${\frac {1}{\alpha }}\quad \approx \quad 7\cdot 19\cdot {\frac {e^{\pi }}{\pi ^{e}}}\qquad =137.03595$

This observation was inserted by Vibritannia - please don't use public space for private theorizing. Lucretius (talk) 21:44, 25 September 2008 (UTC)

Revised value

Kleppner, Daniel (2006-07-28). "A More Precise Fine Structure Constant". Science. 313 (5786): 448–449. doi:10.1126/science.1131834.

—RJH (talk) 20:03, 14 November 2008 (UTC)

I believe that this is the same value discussed above. Bcharles (talk) 00:20, 15 February 2010 (UTC)

'Numerological' caveat

I restored this caveat to the section 'Numerological explanations': Note: within the scientific community, 'numerology' has a colloquial significance and it is mostly used to refer to any scientific theory that appears to be more mathematical than scientific in its approach. The caveat is necessary because Eddington and others were not engaged in the occult study of numbers (OED definition of 'numerology'). The caveat helps to distance the article from a POV common among many physicists that Eddington and others are guilty of crappy science on a par with astrology and palm reading. Lucretius (talk) 04:41, 21 November 2008 (UTC)

The caveat was removed again and I have now reinstated it once again. Mathematical physics is not numerology (the occult study of numbers). Some physicists seem to get too mathematical according to the POV of other physicists but the only real test of a scientific theory is experimental proof for or against. Eddington made exact predictions that have been disproved experimentally. It's a failed theory by an eminent scientist. It's overly mathematical in the opinion of most physicists but that still doesn't make it numerology. The caveat is necessary. Lucretius (talk) 23:23, 29 November 2008 (UTC)

About alpha, Eddington, and numerology

Eddington was seriously proposing that the reciprocal of α must be an integer, originally 136 and later changed to 137.

This Gilson mathematician seems to think that it is

$\alpha ={\frac {\cos \left(\pi /137\right)}{137}}\ {\frac {\tan \left(\pi /(137\cdot 29)\right)}{\pi /(137\cdot 29)}}$.

User:Lucretius evidently doesn't think that it's

$\alpha ^{-1}=\quad 7\cdot 19\cdot {\frac {e^{\pi }}{\pi ^{e}}}$

User:Alphatronic seems to think that α is

$\alpha ^{-1}=4\pi ^{3}+(1-180^{-2})\pi ^{2}+\pi \$.

Without a physical theory to support why α would be forced to take on any of these values, the fact that one can come up a mathematical expression of some simplicity that gets close enough to the measured α to be plausible, that is what mathematicians and scientists call "numerology". It has nothing to do with the occult but it has everything to do with valuing certain numbers essentially for aesthetic reasons. It's numerology because there is no currently known reason for either e or π or 29 or 180 or even 137 to have any association with the physics that makes the fine-structure constant.

Even the Wikipedia defining statement is congruent with the above being numerology, given our present understanding of the relevant physics: Numerology is any of many systems, traditions or beliefs in a mystical or esoteric relationship between numbers and physical objects or living things. Until there is a working physical theory that makes the connection, it is numerology to esoterically relate these simple numbers to physical objects such as the velocities of light and the Bohr model electron. These velocities are related to each other by the ratio of 137.035999... and no physical reason to associate that to the numbers above has been put forth.

To "soften" the meaning of this speculation regarding applying what the discipline of physics labels as "numerology", what fits the definition of numerology, to soften that and call it "mathematics", is to insert a non-neutral point-of-view and is contrary to the guidelines of the Wikipedia project. 96.237.148.44 (talk) 20:43, 27 June 2009 (UTC)

User 96.237.148.44

You are right about the need for a physical theory to avoid the pejorative term "numerology" though evidently you did not read the paper about

$\alpha ^{-1}=4\pi ^{3}+(1-180^{-2})\pi ^{2}+\pi \ =137.035\,999\,16$

as this came from the interpretation of Wolfgang Pauli's World Clock, something he spent years of research on its physical basis, his key to finding the fourth quantum number too. Pauli also felt Eddington's work was "nonsense." I would suggest "mathematical" is the neutral point of view whereas "numerology" is the colloquial expression unsuitable for an encyclopedia. Lucretius has been through this several times and makes several excellent points.

Quotes above from Lucretius:

"A mathematical physicist should not be accused of numerology as it turns the encyclopaedia into a critical review (a review with spiteful tendencies). If criticism is to be made, it should be in the context of a larger appraisal of a person's work, so that the reader gets a balanced view of that person's achievements."

" ... you can't, as a contributor to an encyclopaedia, make qualitative judgements. Make no mistake about this - referring to a physicist in terms of numerology is a qualitative judgement about their competence. Yes, even super-duper physicists get it wrong sometimes, but you can't ridicule them in an encyclopaedia. The reference to numerology is simply unnecessary...."

"I think Wikipedia should try to avoid using this handle on Eddington as it is already used too often. Give the man a fair go. Possibly there is an issue here about the standard of scientific debate and maybe there is a tendency for people to stretch the meaning of numerology simply to denigrate physicists they don't agree with."

"A failed scientific theory with a strong mathematical emphasis is not numerology. It doesn't come within the true definition of numerology. The words 'numerology' and 'numerological' are used in a scientific context simply to show how strongly we disapprove of a conclusion that appears to us to make little physical sense. But we are not supposed to record our feelings (at least not on the article page). This is supposed to be an encyclopaedia."

"... maybe you haven't quite grasped the full significance of the language you are employing in this article, because it does express contempt for Eddington's theory. You might or you might not think contempt is a justifiable response in this particular FSC case, but that is a personal response and it doesn't belong on the article page. I am not disputing your grasp of scientific concepts. I am disputing your choice of words in an encyclopaedia. Maybe you give so much time to the science that you don't give enough time to the language issue."

Then we have QED itself that has parts of which could be considered "numerology" too ... As Feynman himself says:

"The shell game that we play ... is technically called 'renormalization'. But no matter how clever the word, it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It's surprising that the theory still hasn't been proved self-consistent one way or the other by now; I suspect that renormalization is not mathematically legitimate."

Feynman, Richard P., QED, The Strange Theory of Light and Matter, p. 128, Penguin (1990).

Should we make note of this in the article? Maybe someone with more editing experience can help us? Alphatronic (talk) 22:14, 27 June 2009 (UTC)

You quote Lucretius as if he or she is some authority of the subject. What are his/her qualifications or credentials to declare Eddington's or Gilson's or yours as "non-numerology" when above there are several cited references that are verifiable where physicists in the literature and online have called it "numerology"?

Perhaps renormalization is a false theory. It seems to be embraced or, at least referenced, by physicists in a variety of forums. There are plenty of literature references about it and it's taught in textbooks regarding quantum field theory. But even if it may someday be shown to be false, it is not numerology so your example has no traction. It isn't an expression that, as far as the accepted physics is concerned, was merely happened upon (no derivation from existing physical relationships) mathematically. Not all rejected or not-yet-to-be-accepted scientific theories are rejected or not-yet-accepted because they are numerology. They might just be a poor theory. But renormalization is not even that. It appears to be widely accepted among physicists. String theory may become a rejected theory and it is presently not accepted by everyone, but it is not numerology. The reason that α is not 1/137 is that there is no physical basis for saying so. To say that it is, because 1 and 137 are esoterically and aesthetically simple and pleasing numbers, is, by definition, numerology. To call it "mathematical" instead of "numerological" because there is mathematics expressed in it, does not make it non-numerological. What does make it non-numerological is a theory regarding principles of physics, not principles of nice simple numbers.

From your user page, it appears obvious that you have a non-neutral POV in favor of numerological expressions of α. That should disqualify you right away regarding this content issue. Perhaps someday, some physicist will discover and publish in journals that are widely accepted in the physics community as reputable, a physical justification for why α must take on the value:

$\alpha ^{-1}=4\pi ^{3}+(1-180^{-2})\pi ^{2}+\pi \$

But we're not there yet.

Now, it is perfectly appropriate that a scientific and neutral discussion of α include a reference to the numerological interest in its value. Perhaps someday one of those numerical conjectures will be shown to have physical justification. (But we're not there yet.) This is especially appropriate regarding Eddington, since he is an important and legitimate figure in historical physics. Whether Gilson's conjecture is included or not is not so important, but some current numerological hypothesis by identifiable persons who have some credentials is appropriate. Otherwise it will appear that perhaps this numerological hypothesizing ended with Eddington and it hasn't, of course.

Gilson and his credentials are more clearly identified than that of anonymous Wikipedia editors Alphatronic or Lucretius, whom I suspect are neither physicists. If anyone comes up with a paper by some identified physicist other than and more current than Eddington) that proposes a purely mathematical evaluation of α we should include it. If it has a real physical theory that has gained some acceptance of plausibility (with the reviewers and editors of these reputable journals of physics), then this should be included and not be under a heading of "numerological explanations". If it is published by a reputable journal but, in the academic/scholarly discourse remains largely rejected as having insufficient physical basis, then it should be included in the Numerological explanations section, and possibly replace the entry regarding Gilson (but not replacing the entry regarding Eddington, he is too important). But, as you can see in the discussion above, everyone and their dog seem to have their favorite mathematical expression, so notability considerations must be made. That is why Gilson is favored over either of two or three anonymous Wikipedia editors (to avoid OR). 96.237.148.44 (talk) 23:20, 27 June 2009 (UTC)

According to an Arcturan prospector visiting our asteroid belt whom I ran across in the late nineties when he responded to my CQ DX while working skip on 40 meters after a long night (I have never heard English spoken with an accent like his), 1/α is well known where he comes from to be

$-\alpha /4!+4\pi ^{3}+\pi ^{2}+\pi$,

a value he observed changes when α does. I tried pointing out to him that when you solve the quadratic you get 137.035999719522... but he seemed not to know about solving quadratics and kept insisting the formula varied with α ("transparent it is, schmuck, that α govern value−how else feedback gonna work, huh?"). Evidently he was a product of No Arcturan Left Behind and could only work to the test. I offered to buy him a beer if he would drop by California but he said the pickings were slim in our solar system and his boss had told him to move on to Alpha Centauri toot sweet (his French was less execrable than his English).

To this day I don't know if he was pulling my leg, but when those Harvard physicists announced their estimate in 2006 of a value in the range 137.0359996 to 137.0359998 I nearly dropped my Jarvis Lake William---their number lent a certain corroborative detail to that innumerate prospector dude's story, especially when they pegged the middle of their range at 137.035999710. How often do you get 11 decimal digits of agreement from a sum of four simple terms containing only the integers 2, 3, and 4 and the constant pi? --Vaughan Pratt (talk) 22:32, 30 October 2009 (UTC)

Unfortunately the 11 digits of agreement is with the erroneously calculated 2006 CODATA value of 137.035 999 679 (94). When the corrected number of 137.035 999 044 (93) is used as per the relevant section above, agreement is only with the first nine decimal digits. Not quite as impressive, though α/4! still seems less of a kludge than 1 - 1/180². There are too many such kludges, for example $(4-319^{-2})\pi ^{3}+\pi ^{2}+\pi$ = 137.035 999 078…. Why is 180 better than 319 if it only gets you down to 137.035 999 158…? --Vaughan Pratt (talk) 02:17, 2 November 2009 (UTC)

Woof woof woof series:

$137+{\frac {ln137}{137}}+{\frac {ln\,ln137}{137^{2}}}+{\frac {ln137}{137^{3}}}+{\frac {ln\,ln137}{137^{4}}}+{\frac {ln137}{137^{5}}}+\ \cdots \ \ =137.0359990777649$

Woof average woof woof two woof woof experimental woof, 137.035999070 woof 137.035999084, woof woof 137.035999077 woof. -- Professor Dog Biscuit (talk), 11:34, 10 November 2009 (UTC)

Get down, SineBot, you bad dog. --Vibritannia (talk) 11:49, 10 November 2009 (UTC)

History of FSC, Sommerfeld, relation to splitting of lines in H atom.

This is for consideration for inclusion to the Physical interpretations or to the History section. In the latter section it says The FSC "appears naturally in Sommerfeld's analysis, and determines the size of the splitting or fine-structure of the hydrogenic spectral lines." Can we show more clearly, quantitatively, how this number is related to this splitting?

Is not the relation thus:

${\frac {1.41\mathrm {A} }{1215.67\mathrm {A} }}={\frac {\alpha }{2\pi }}={\frac {e^{2}}{(4\pi \epsilon _{0})hc}}$

the 1.41 A being the fine-structure splitting of the 1215.67 Angstrom bottom line of the Lyman series?

Can someone confirm/deny/elucidate this? I have some memory of this from my college days, but I cannot seem to confirm or refute this. 64.223.106.116 (talk) 19:34, 16 February 2010 (UTC)

Mathematical derivation

Now that I have removed the Extended Heim Theory-related content (the main article is up for deletion, too), is it necessary to include the other mathematical derivation? Has it been cited in any peer-reviewed source, or is it otherwise in any way notable? - Mike Rosoft (talk) 08:38, 4 August 2010 (UTC)

From Google search I find 16 citations for Gilson's paper:

Calculating the Fine‐Structure Constant

JG Gilson - Physics Essays, 1996 - link.aip.org

This paper presents an introductory review of the origins of the fine‐structure constant problem and some of its historical connections to angular momenta in Maxwell's electromagnetic theory and to Planck's frequency‐to‐energy conversion factor h. ... Cited by 16 - Alphatronic (talk) 12:27, 4 August 2010 (UTC)

I don't consider Gilson's thing to be particularly "good science" (it's not), but serves as a modern example of numerology in that it makes a pretty good estimate of the measured FSC from a few different simple constants (pi, 29, 137). I think that it should be included with Eddington's history of numerology regarding the FSC. 71.169.182.131 (talk) 15:12, 4 August 2010 (UTC)

reciprocal of the square

Repeatedly in the article alpha is mentioned as 1/137. Surely it should be α² = 1/137 ? Wizzy…☎ 10:12, 11 September 2010 (UTC)

Check out this. 70.109.189.83 (talk) 01:39, 12 September 2010 (UTC)

variation with direction: Yahoo Science News story

"New Physics? Fundamental Cosmic Constant Now Seems Shifty - Yahoo! News". Retrieved 2010-09-15. Yahoo News features a Nes story that cites a new Phys. Rev. Letters paper with "evidence" of variabilty of electromagnetic force (hence alpha coupling) with cosmic direction. 164.55.254.106 (talk) 22:22, 15 September 2010 (UTC)

Proposal for section titled "Derivation"

I am new to Wikipedia so am not fully aware of the proper way to do things here. I think that there should be a new heading entitled: "Derivation". I have derived the fine structure constant by deduction using a dimensional method. You can review it at www.vixra.org/abs/1008.0007. It is only about 3 pages and is well worth the time to read. I would appreciate any comments or advice on how to proceed. Thanks! RBDowd (talk) 19:02, 12 November 2010 (UTC)

So you're new here. Welcome. My first suggestion is not to start a new topic inside an old topic, but to start a new section at the bottom (there's a convenient tab for that) and write it there. I have done that for you. If you don't like the title of the section I gave it, please change it to your liking (between the == delimiters).

That said, I haven't yet looked at your derivation, but I'll bet money that, cite unseen, it's numerology, not physics. I'll take a look. 71.169.188.72 (talk) 05:27, 13 November 2010 (UTC)

So now I just took a look at your paper, Richard, and I would not attach any practical nor scholarly value to it. I wouldn't necessarily call it numerology (since you do not derive the FSC from fundamental mathematical constants nor do you derive it from any other dimensionless physical constants, but it certainly looks like crackpottery. The gravitational constant has nothing whatsoever to do with the FSC. Whatever it is, the derivation literally offers nothing to the body of knowledge. The only advice I would offer is to withdraw it before you get embarrassed. 71.169.188.72 (talk) 05:39, 13 November 2010 (UTC)