5455:. It would be fair enough to say that numerology was the origin of the theories of electromagnetism, quantum mechanics, gravitation. ... So I intend no disparagement when I describe a formula as numerological. When a numerological formula is proposed, then we may ask whether it is correct. ... I think an appropriate definition of correctness is that the formula has a good explanation, in a Platonic sense, that is, the explanation could be based on a good theory that is not yet known but 'exists' in the universe of possible reasonable ideas." â
5120:â the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.)
99:
2603:
1920:
3638:
5291:"Among other substances tried in the preliminary experiments, were thallium, lithium, and hydrogen. ... It may be noted, that in case of the red hydrogen line, the interference phenomena disappeared at about 15,000 wave-lengths, and again at about 45,000 wave-lengths: So that the red hydrogen line must be a double line with the components about one-sixtieth as distant as the sodium lines."
2344:
4562:
4982:
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,
4281:
4359:
2598:{\displaystyle \alpha =\left.{\left({\frac {e^{2}}{4\pi \varepsilon _{0}d}}\right)}\right/{\left({\frac {hc}{\lambda }}\right)}={\frac {e^{2}}{4\pi \varepsilon _{0}d}}\times {\frac {2\pi d}{hc}}={\frac {e^{2}}{4\pi \varepsilon _{0}d}}\times {\frac {d}{\hbar c}}={\frac {e^{2}}{4\pi \varepsilon _{0}\hbar c}}.}
4981:
separately suggested various approaches of how Webb's observations may be wrong. Orzel argues that the study may contain wrong data due to subtle differences in the two telescopes a totally different approach; he looks at the fine-structure constant as a scalar field and claims that if the telescopes
5123:
Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by humans. You might say the "hand
4953:
per year. A present day null constraint on the time variation of alpha does not necessarily rule out time variation in the past. Indeed, some theories that predict a variable fine-structure constant also predict that the value of the fine-structure constant should become practically fixed in its
4113:
5124:
of God" wrote that number, and "we don't know how He pushed His pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out â without putting it in secretly!
4800:
has changed in the past 2 billion years by 45 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 to be verified.
5001:
is an argument about 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 is that, if modern grand unified theories are correct, then
2916:
4690:
1505:
8946:
December 2, 2020). The value of this constant is given here as 1/137.035999206 (note the difference in the last three digits). It was determined by a team of four physicists led by SaĂŻda
Guellati-Khélifa at the Kastler Brossel Laboratory in
4557:{\displaystyle {\frac {\ \Delta \alpha \ }{\alpha }}~~{\overset {\underset {\mathsf {~def~}}{}}{=}}~~{\frac {\ \alpha _{\mathrm {prev} }-\alpha _{\mathrm {now} }\ }{\alpha _{\mathrm {now} }}}~~=~~\left(-5.7\pm 1.0\right)\times 10^{-6}~.}
7567:
Murphy, M.T.; Webb, J.K.; Flambaum, V.V. (6 December 2007). "Comment on 'Limits on the time
Variation of the electromagnetic fine-structure constant in the low energy limit from absorption lines in the spectra of distant quasars'".
8746:, 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).
7503:
Srianand, R.; Chand, H.; Petitjean, P.; Aracil, B. (26 March 2004). "Limits on the time variation of the electromagnetic fine-structure constant in the low energy limit from absorption lines in the spectra of distant quasars".
2131:, as measured by these different methods. The preferred methods in 2019 are measurements of electron anomalous magnetic moments and of photon recoil in atom interferometry. The theory of QED predicts a relationship between the
8414:
da Fonseca, Vitor; Barreiro, Tiago; Nunes, Nelson J.; Cristiani, Stefano; Cupani, Guido; D'Odorico, Valentina; et al. (2022). "Fundamental physics with ESPRESSO: Constraining a simple parametrisation for varying α".
3306:, and as a result its light absorption and transmission properties can be expressed in terms of the fine-structure constant alone. The absorption value for normal-incident light on graphene in vacuum would then be given by
5181:
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
5407:"If alpha were bigger than it really is, we should not be able to distinguish matter from ether , and our task to disentangle the natural laws would be hopelessly difficult. The fact however that alpha has just its value
3664:
to include elliptical orbits and relativistic dependence of mass on velocity. He introduced a term for the fine-structure constant in 1916. The first physical interpretation of the fine-structure constant
3681:
allowed by relativity for a closed orbit, and the minimum angular momentum allowed for it by quantum mechanics. It appears naturally in
Sommerfeld's analysis, and determines the size of the splitting or
4276:{\displaystyle {\frac {\ \Delta \alpha \ }{\alpha }}~~{\overset {\underset {\mathsf {~def~}}{}}{=}}~~{\frac {\ \alpha _{\mathrm {prev} }-\alpha _{\mathrm {now} }\ }{\alpha _{\mathrm {now} }}}~~=~~0~,}
5147:
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.
4598:
7324:
Webb, J.K.; Murphy, M.T.; Flambaum, V.V.; Dzuba, V.A.; Barrow, J.D.; Churchill, C.W.; et al. (9 August 2001). "Further evidence for cosmological evolution of the fine structure constant".
3270:
1408:
6293:
Nair, R. R.; Blake, P.; Grigorenko, A. N.; Novoselov, K. S.; Booth, T. J.; Stauber, T.; Peres, N. M. R.; Geim, A. K. (2008). "Fine
Structure Constant Defines Visual Transparency of Graphene".
3703:
has broadened from a spectroscopic phenomenon to a general coupling constant for the electromagnetic field, determining the strength of the interaction between electrons and photons. The term
1740:
1812:
2787:
2792:
5028:, his estimate of the number of protons in the universe. This led him in 1929 to conjecture that the reciprocal of the fine-structure constant was not approximately but precisely the
1910:
8081:
Webb, J. K.; King, J. A.; Murphy, M. T.; Flambaum, V. V.; Carswell, R. F.; Bainbridge, M. B. (31 October 2011). "Indications of a spatial variation of the fine structure constant".
7208:
Webb, John K.; Flambaum, Victor V.; Churchill, Christopher W.; Drinkwater, Michael J.; Barrow, John D. (February 1999). "Search for time variation of the fine structure constant".
2952:
7692:
King, J. A.; Mortlock, D. J.; Webb, J. K.; Murphy, M. T. (2009). "Markov chain Monte Carlo methods applied to measuring the fine structure constant from quasar spectroscopy".
3157:
3212:
2718:
8375:
7637:
7393:
7269:
7448:
Chand, H.; Srianand, R.; Petitjean, P.; Aracil, B. (April 2004). "Probing the cosmological variation of the fine-structure constant: Results based on VLT-UVES sample".
6753:
Parker, Richard H.; Yu, Chenghui; Zhong, Weicheng; Estey, Brian; MĂŒller, Holger (2018). "Measurement of the fine-structure constant as a test of the
Standard Model".
6234:
6193:
6614:
3381:
The fine-structure constant gives the maximum positive charge of an atomic nucleus that will allow a stable electron-orbit around it within the Bohr model (element
5811:
5746:
5716:
5686:
5656:
5626:
5604:
5492:
1215:
6698:
Aoyama, Tatsumi; Kinoshita, Toichiro; Nio, Makiko (8 February 2018). "Revised and improved value of the QED tenth-order electron anomalous magnetic moment".
5140:
argued that a numerological explanation would only be acceptable if it could be based on a good theory that is not yet known but "exists" in the sense of a
4816:
during the epoch before the formation of the first stars. In principle, this technique provides enough information to measure a variation of 1 part in
5561:
268:
8470:
5423:
is certainly no chance but itself a law of nature. It is clear that the explanation of this number must be the central problem of natural philosophy." â
3690:. This constant was not seen as significant until Paul Dirac's linear relativistic wave equation in 1928, which gave the exact fine structure formula.
308:
6069:
4054:
Physicists have pondered whether the fine-structure constant is in fact constant, or whether its value differs by location and over time. A varying
8260:
Wilczynska, Michael R.; Webb, John K.; Bainbridge, Matthew; Barrow, John D.; Bosman, Sarah E. I.; Carswell, Robert F.; et al. (1 April 2020).
1930:
on electron self-interaction. The arrowed horizontal line represents the electron, the wavy lines are virtual photons, and the circles are virtual
4049:
3496:
3523:
are soon unimportant, making the perturbation theory practical in this case. On the other hand, the large value of the corresponding factors in
3642:
5331:
hinzu, die zugleich mit der
Kenntnis des Wasserstoffdubletts oder des Heliumtripletts in §10 oder irgend einer analogen Struktur bekannt ist."
8889:
8813:
8780:
8724:
8688:
8652:
8589:
7748:
7192:
7159:
7122:
5787:
5579:
4894:
to the current level of quasar constraints is on the order of 100 square kilometers, which is economically impracticable at present.
4314:. Their findings were consistent with no variation in the fine-structure constant between these two vastly separated locations and times.
1073:
4732:
from the quasar spectra, and have found that the algorithm appears to produce correct uncertainties and maximum likelihood estimates for
8355:
3621:
theories. If quantum electrodynamics were an exact theory, the fine-structure constant would actually diverge at an energy known as the
2127:. Other methods include the A.C. Josephson effect and photon recoil in atom interferometry. There is general agreement for the value of
8234:
1697:
7878:
Khatri, Rishi; Wandelt, Benjamin D. (14 March 2007). "21 cm radiation: A new probe of variation in the fine-structure constant".
5274:
for a charged particle to the electromagnetic field. There are analogous coupling constants that give the interaction strength of the
1208:
1769:
6270:
4966:
Researchers from
Australia have said they had identified a variation of the fine-structure constant across the observable universe.
5209:â 1/137 â has been recognized and discussed for decades. The second mystery â the range of its domain â is generally unrecognized.
2052:, 0.8 times the standard uncertainty away from its old defined value, with the mean differing from the old value by only 0.13
838:
7143:
6467:
4969:
These results have not been replicated by other researchers. In
September and October 2010, after released research by Webb
9026:
3731:
8939:
8979:
6534:
5236:
4793:
4311:
1252:
111:
8929:
2172:
using a one-electron so-called "quantum cyclotron" apparatus, together with a calculation via the theory of QED that involved
9036:
7764:
Lamoreaux, S. K.; Torgerson, J. R. (2004). "Neutron moderation in the Oklo natural reactor and the time variation of alpha".
1879:
7820:
386:
8156:
Searching for variations in the fine-structure constant and the proton-to-electron mass ratio using quasar absorption lines
4322:
1668:
1201:
225:
185:
7263:
Murphy, M.T.; Webb, J.K.; Flambaum, V.V.; Dzuba, V.A.; Churchill, C.W.; Prochaska, J.X.; et al. (11 November 2001).
4040:
The CODATA values in the above table are computed by averaging other measurements; they are not independent experiments.
4820:(4 orders of magnitude better than the current quasar constraints). However, the constraint which can be placed on
3217:
943:
868:
215:
7265:"Possible evidence for a variable fine-structure constant from QSO absorption lines: motivations, analysis and results"
6966:
Uzan, J.-P. (2003). "The fundamental constants and their variation: Observational status and theoretical motivations".
5368:
which is known at once from knowledge of the hydrogen doublet or the helium triplet in §10 or any analogous structure.)
381:
6401:
4842:
4809:
3091:
3087:
1256:
318:
7450:
6529:
6497:
6243:
5435:"There have been a few examples of numerology that have led to theories that transformed society: See the mention of
3587:
is the asymptotic value of the fine-structure constant at zero energy. At higher energies, such as the scale of the
2911:{\displaystyle U_{\text{el}}=m_{\text{e}}v_{\text{e}}^{2}=m_{\text{e}}(\alpha c)^{2}=\alpha ^{2}(m_{\text{e}}c^{2}).}
8369:
MilakoviÄ, Dinko; Lee, Chung-Chi; Carswell, Robert F.; Webb, John K.; Molaro, Paolo; Pasquini, Luca (5 March 2021).
7998:
Barrow, John D.; Sandvik, HĂ„vard Bunes; Magueijo, JoĂŁo (21 February 2002). "Behavior of varying-alpha cosmologies".
5518:
2746:
9041:
8906:
7023:
6546:
6502:
5567:
4914:
in single-ion optical atomic clocks to place a very stringent constraint on the present-time temporal variation of
2970:
1053:
220:
371:
9031:
6968:
6153:
4580:. This is a very small value, but the error bars do not actually include zero. This result either indicates that
2958:
2120:
313:
9009:
8545:
8333:
5395:
4706:
873:
498:
391:
328:
288:
8209:
7941:
Rosenband, T.; Hume, D. B.; Schmidt, P. O.; Chou, C. W.; Brusch, A.; Lorini, L.; et al. (28 March 2008).
4685:{\displaystyle {\frac {\Delta \alpha }{\alpha _{\mathrm {em} }}}\ =\ \left(-0.6\pm 0.6\right)\times 10^{-6}~.}
863:
1694:, as commonly found in older physics literature, where the expression of the fine-structure constant becomes
8764:
8680:
8083:
7880:
7730:
7570:
7506:
7326:
7210:
6931:
6891:
6018:
5948:
5261:
5156:
5107:
3694:
3614:
3568:
3540:
3500:
3110:
3024:
2304:
2108:
1664:
1569:
1153:
613:
421:
416:
258:
2921:
1500:{\displaystyle \alpha ={\frac {e^{2}}{2\varepsilon _{0}hc}}={\frac {e^{2}}{4\pi \varepsilon _{0}\hbar c}},}
8177:
7111:
The
Constants of Nature: From Alpha to Omega â the Numbers That Encode the Deepest Secrets of the Universe
5006:
needs to be between around 1/180 and 1/85 to have proton decay to be slow enough for life to be possible.
3524:
3102:
2741:
2721:
2611:
2060:
1386:
1263:
1023:
1003:
493:
426:
323:
283:
8805:
6010:
5301:"Wir fĂŒgen den Bohrschen Gleichungen (46) und (47) die charakteristische Konstante unserer Feinstrukturen
3353:
or 97.75% (experimentally observed to be between 97.6% and 97.8%). The reflection would then be given by
165:
5377:
Numbers in parentheses (e.g. the "(11)" appearing at the end of the value "137.035999206(11)") give its
5015:
3544:
3459:
1278:
908:
763:
459:
396:
303:
8640:
5939:
Aoyama, T.; Hayakawa, M.; Kinoshita, T.; Nio, M. (2012). "Tenth-order QED contribution to the electron
5452:
2107:
can be determined from estimates of the constants that appear in any of its definitions, the theory of
8054:
5220:
When I die my first question to the Devil will be: What is the meaning of the fine structure constant?
5164:, and the fine-structure constant was one of several universal constants that suggested the idea of a
3116:
8963:
8479:
8434:
8285:
8169:
8102:
8019:
7954:
7899:
7785:
7711:
7656:
7589:
7525:
7469:
7412:
7345:
7288:
7229:
7147:
7083:
7042:
6987:
6940:
6900:
6852:
6774:
6719:
6580:
6455:
6410:
6365:
6314:
6158:(in German) (2 ed.). Braunschweig, DE: Friedr. Vieweg & Sohn. pp. 241â242, Equation 8.
6107:
6037:
5967:
5911:
5861:
5378:
5275:
4592:
4299:
The first experimenters to test whether the fine-structure constant might actually vary examined the
3528:
3273:
1158:
933:
464:
348:
298:
210:
90:
8182:
4321:
at much larger distances and to a much greater accuracy. In 1999, a team led by John K. Webb of the
3166:
3090:
is treated as a mixture of interactions associated with the electroweak fields. The strength of the
8984:
8529:
6521:
6489:
6009:
Bouchendira, Rym; Cladé, Pierre; Guellati-Khélifa, Saïda; Nez, François; Biraben, François (2011).
5571:
5241:
5165:
4998:
3649:
3160:
3106:
2116:
1924:
1638:
1375:
1168:
878:
603:
488:
7943:"Frequency ratio of Al and Hg single-ion optical clocks; metrology at the 17th decimal place"
7175:
Fujii, Yasunori (2004). "Oklo constraint on the time-variability of the fine-structure constant".
4110: . If the fine-structure constant really is a constant, then any experiment should show that
778:
653:
8570:
8562:
8503:
8450:
8424:
8384:
8275:
8159:
8136:
8092:
8035:
8009:
7980:
7923:
7889:
7847:
7801:
7775:
7701:
7674:
7646:
7613:
7579:
7549:
7515:
7485:
7459:
7430:
7402:
7369:
7335:
7306:
7278:
7245:
7219:
7058:
7032:
7003:
6977:
6868:
6798:
6764:
6735:
6709:
6663:
6655:
6471:
6445:
6381:
6338:
6304:
6131:
6061:
6027:
5991:
5957:
5851:
5523:
5279:
4059:
3669:
was as the ratio of the velocity of the electron in the first circular orbit of the relativistic
3063:
2696:
2144:
2132:
1178:
1103:
1033:
913:
898:
828:
788:
543:
503:
273:
235:
190:
178:
155:
150:
7389:"Further evidence for a variable fine-structure constant from Keck/HIRES QSO absorption spectra"
5779:
5769:
5114:
There is a most profound and beautiful question associated with the observed coupling constant,
4804:
In 2007, Khatri and
Wandelt of the University of Illinois at Urbana-Champaign realized that the
4283:
or as close to zero as experiment can measure. Any value far away from zero would indicate that
2234:
Further refinement of the experimental value was published by the end of 2020, giving the value
738:
8951:
8902:. Introduction to the constants for nonexperts. National Institute of Standards and Technology.
5340:(We add, to Bohr's equations (46) and (47), the characteristic constant of our fine structures
8885:
8809:
8776:
8720:
8716:
8684:
8648:
8495:
8311:
8128:
8000:
7972:
7915:
7766:
7744:
7740:
7605:
7541:
7361:
7188:
7155:
7118:
6790:
6755:
6700:
6560:
6530:"Method of making the wave-length of sodium light the actual and practical standard of length"
6498:"Method of making the wave-length of sodium light the actual and practical standard of length"
6330:
6295:
6266:
6149:
6123:
6090:
6053:
5983:
5877:
5783:
5575:
5514:
5271:
4755:
for particular models. This suggests that the statistical uncertainties and best estimate for
4304:
4075:
3657:
3618:
3596:
3079:
3032:
2666:
2053:
1815:
1515:
1398:
1353:
1271:
1133:
1063:
948:
938:
848:
783:
718:
688:
658:
518:
513:
343:
263:
253:
145:
8672:
6204:
6163:
6091:"Determination of the fine-structure constant with an accuracy of 81 parts per trillion"
1385:
Why the constant should have this value is not understood, but there are a number of ways to
8877:
8858:
8801:
8554:
8521:
8487:
8442:
8438:
8394:
8301:
8293:
8266:
8187:
8118:
8110:
8027:
7962:
7907:
7793:
7664:
7597:
7533:
7477:
7473:
7420:
7353:
7296:
7237:
7180:
7091:
7050:
6995:
6948:
6908:
6860:
6843:
6782:
6727:
6647:
6638:
Kragh, Helge (July 2003). "Magic number: A partial history of the fine-structure constant".
6588:
6525:
6493:
6463:
6418:
6373:
6322:
6115:
6098:
6045:
5975:
5919:
5869:
5436:
5025:
5021:
3727:
3678:
3653:
3071:
3067:
3056:
2680:
2180:
1927:
1379:
1173:
1088:
1068:
1038:
988:
808:
798:
793:
678:
663:
593:
278:
205:
195:
130:
6399:
Bedford, D.; Krumm, P. (2004). "Heisenberg indeterminacy and the fine structure constant".
5064:, including the fine-structure constant, which he also noted approximates the prime number
4317:
Improved technology at the dawn of the 21st century made it possible to probe the value of
1814:
As such, the fine-structure constant is just a quantity determining (or determined by) the
8704:
8644:
8634:
8609:"Number archetypes and 'background' control theory concerning the fine structure constant"
8351:
6824:
6011:"New determination of the fine-structure constant and test of the quantum electrodynamics"
5839:
5557:
5448:
5151:
5129:
5103:
4978:
4845:
4330:
2337:
1542:
1299:
1267:
1118:
1113:
1083:
1078:
1048:
1008:
978:
958:
858:
748:
743:
708:
693:
668:
648:
628:
558:
548:
469:
431:
333:
293:
125:
103:
98:
3559:
is linked to the observed value of this coupling associated with the energy scale of the
8862:
8829:
8483:
8289:
8173:
8106:
8023:
7958:
7903:
7789:
7715:
7660:
7593:
7529:
7416:
7349:
7292:
7233:
7151:
7087:
7046:
6991:
6944:
6904:
6856:
6778:
6723:
6584:
6459:
6414:
6369:
6318:
6111:
6041:
5971:
5915:
5865:
2720:
is the ratio of the potential energy of the electron in the first circular orbit of the
8997:
8993:
8975:
8769:
8760:
8709:
8491:
8306:
8261:
6564:
5775:
5141:
5057:
4071:
3683:
3674:
3610:
3052:
2737:
2674:
2658:
1611:
1371:
1367:
1143:
1093:
1013:
998:
983:
963:
928:
923:
918:
903:
893:
888:
853:
843:
768:
703:
673:
608:
573:
563:
538:
409:
366:
230:
17:
3609:
As the energy scale increases, the strength of the electromagnetic interaction in the
3543:, the more thorough quantum field theory underlying the electromagnetic coupling, the
9020:
8636:
Deciphering the Cosmic Number: The Strange Friendship of Wolfgang Pauli and Carl Jung
8574:
8454:
8059:
8039:
7984:
7825:
7805:
7736:
7669:
7632:
7425:
7388:
7301:
7264:
7078:
7007:
6739:
6667:
6135:
5803:
5440:
5024:
argued that the value could be "obtained by pure deduction" and he related it to the
4805:
4300:
4067:
3563:: the electron's mass gives a lower bound for this energy scale, because it (and the
3560:
1745:
1148:
1138:
1128:
1123:
1043:
1028:
823:
818:
643:
638:
598:
568:
533:
523:
454:
449:
8507:
8140:
7927:
7678:
7617:
7553:
7489:
7434:
7373:
7310:
7249:
7076:
Olive, K.; Qian, Y.-Z. (2003). "Were fundamental constants different in the past?".
7062:
6475:
6065:
5995:
5601:
CODATA Internationally recommended 2018 values of the fundamental physical constants
5205:
is actually a double mystery: The first mystery â the origin of its numerical value
2231:. This value and uncertainty are about the same as the latest experimental results.
1919:
27:
Dimensionless number that quantifies the strength of the electromagnetic interaction
8918:
8899:
8114:
7852:
7114:
6926:
6886:
6872:
6802:
6606:
6385:
6356:
Chandrasekhar, S. (1 April 1984). "On stars, their evolution and their stability".
6342:
6049:
5979:
5873:
5065:
5032:
4063:
3687:
3637:
3626:
3552:
3508:
3504:
3083:
1848:
1183:
1108:
993:
968:
953:
883:
803:
758:
753:
633:
623:
618:
583:
578:
553:
508:
376:
338:
160:
140:
8446:
7911:
7601:
7537:
7357:
5678:
5596:
5484:
7481:
7184:
7021:
Uzan, J.-P. (2004). "Variation of the constants in the late and early universe".
6260:
5738:
9005:
8881:
7848:"Scientists discover one of the constants of the universe might not be constant"
6816:
5186:
must be regarded as a variable, too. The value 1/137 is the asymptotic value of
4955:
3622:
2983:
2688:
1163:
1098:
1058:
1018:
973:
833:
733:
728:
713:
698:
683:
8031:
7797:
7241:
6952:
6912:
6731:
5708:
5648:
5618:
5390:
This is not an experimentally measured value; instead it is a value determined
8668:
8329:
8262:"Four direct measurements of the fine-structure constant 13 billion years ago"
6999:
6838:
6651:
6377:
6119:
5456:
5444:
5161:
5137:
5061:
5014:
As a dimensionless constant which does not seem to be directly related to any
4974:
4694:
However, in 2007 simple flaws were identified in the analysis method of Chand
3661:
3382:
3109:, the fine-structure constant is one fourth the product of the characteristic
2329:
1357:
813:
723:
588:
528:
200:
135:
8399:
8370:
6592:
4989:
Other research finds no meaningful variation in the fine structure constant.
4074:
of particle physics have led to theoretical interest in whether the accepted
2610:
The ratio of the velocity of the electron in the first circular orbit of the
8210:"Taking a second look at evidence for the 'varying' fine-structure constant"
7967:
6786:
6326:
5069:
3670:
3548:
2278:, which has a significant discrepancy from the previous experimental value.
8543:
Whittaker, Edmund (1945). "Eddington's theory of the constants of nature".
8499:
8315:
8297:
8132:
7976:
7919:
7609:
7545:
7365:
6794:
6681:
6334:
6127:
6057:
5987:
5924:
5899:
5881:
8608:
5838:
Fan, X.; Myers, T. G.; Sukra, B. A. D.; Gabrielse, G. (13 February 2023).
8673:"A quantal hypothesis for hadrons and the judging of physical numerology"
8123:
8014:
7894:
7651:
7520:
7464:
7407:
7340:
7283:
7224:
7037:
5898:
Yu, C.; Zhong, W.; Estey, B.; Kwan, J.; Parker, R.H.; MĂŒller, H. (2019).
5424:
5073:
5068:. This constant so intrigued him that he collaborated with psychoanalyst
4709:
methods to investigate the algorithm used by the UNSW group to determine
4338:
4287:
does change over time. So far, most experimental data is consistent with
3625:â this fact undermines the consistency of quantum electrodynamics beyond
3564:
3277:
3036:
2685:
2136:
2124:
1935:
1931:
773:
8468:
Barrow, John D. (2001). "Cosmology, life, and the anthropic principle".
8191:
7780:
6659:
6089:
Morel, Léo; Yao, Zhibin; Cladé, Pierre; Guellati-Khélifa, Saïda (2020).
8566:
7633:"Revision of VLT/UVES constraints on a varying fine-structure constant"
6982:
6607:"Current advances: The fine-structure constant and quantum Hall effect"
6468:
10.1002/1521-3978(200205)50:5/7<518::AID-PROP518>3.0.CO;2-F
6450:
5029:
3588:
3462:
momentum/position uncertainty relationship of such an electron is just
1229:
7095:
7054:
6422:
4356:
over the last 10â12 billion years. Specifically, they found that
1667:, the only quantity in this list that does not have an exact value in
8771:
Quarks and Leptons: An Introductory Course in Modern Particle Physics
8748:
Quarks and Leptons: An Introductory Course in Modern Particle Physics
7140:
The Natural Laws of the Universe: Understanding fundamental constants
6929:(1967). "Variability of elementary charge and quasistellar objects".
6864:
4808:
of the early universe leaves a unique absorption line imprint in the
4584:
is not constant or that there is experimental error unaccounted for.
4334:
3677:
in the vacuum. Equivalently, it was the quotient between the minimum
3095:
3040:
2315:
2064:
1943:
8558:
8371:"A new era of fine structure constant measurements at high redshift"
7942:
8429:
8389:
8280:
6769:
6714:
5856:
4812:
radiation. They proposed using this effect to measure the value of
4352:
found that their spectra were consistent with a slight increase in
3547:
dictates how the strength of the electromagnetic interaction grows
8164:
8097:
7706:
7584:
6309:
6032:
5962:
3648:
Based on the precise measurement of the hydrogen atom spectrum by
3636:
2918:
Essentially this ratio follows from the electron's velocity being
2163:
obtained experimentally (as of 2023) is based on a measurement of
1918:
1245:
6436:
Fritzsch, Harald (2002). "Fundamental constants at high energy".
3385:). For an electron orbiting an atomic nucleus with atomic number
8940:
Physicists Nail Down the âMagic Numberâ That Shapes the Universe
8911:
5900:"Atom-interferometry measurement of the fine structure constant"
5053:
deviated sufficiently from 137 to refute Eddington's arguments.
4824:
is strongly dependent upon effective integration time, going as
4790:
4587:
In 2004, a smaller study of 23 absorption systems by Chand
4566:
In other words, they measured the value to be somewhere between
4308:
2143:(the magnetic moment of the electron is also referred to as the
1766:, where the expressions for the fine-structure constant becomes
5150:
In the early 21st century, multiple physicists, including
5110:(QED), referred to the fine-structure constant in these terms:
5106:, one of the originators and early developers of the theory of
8334:"Why I'm Skeptical about the changing fine-structure constant"
5018:, the fine-structure constant has long fascinated physicists.
3592:
1680:
7179:. Lecture Notes in Physics. Vol. 648. pp. 167â185.
3743:
Successive values determined for the fine-structure constant
1270:
used, which is related to the strength of the coupling of an
8830:"137 | The Fine Structure Constant, Physics - ArsMagine.com"
3726:
is engraved on the tombstone of one of the pioneers of QED,
8524:(1956). "The constants of nature". In Newman, J. R. (ed.).
2402:
2355:
1374:
of the hydrogen atom, which had been measured precisely by
3059:, whose value is not determined within the Standard Model.
7387:
Murphy, M.T.; Webb, J.K.; Flambaum, V.V. (October 2003).
4871:
to about 0.3%. The collecting area required to constrain
3507:
expansions for physical results are expressed as sets of
1876:, the expression for the fine-structure constant becomes
2669:'s original physical interpretation. Then the square of
8750:. John Wiley & Sons. ISBN 978-0-471-88741-6, p. 13.
7631:
Murphy, M.T.; Webb, J.K.; Flambaum, V.V. (March 2008).
6611:
The NIST Reference on Constants, Units, and Uncertainty
5946:
and an improved value of the fine structure constant".
5808:
The NIST Reference on Constants, Units, and Uncertainty
5743:
The NIST Reference on Constants, Units, and Uncertainty
5713:
The NIST Reference on Constants, Units, and Uncertainty
5683:
The NIST Reference on Constants, Units, and Uncertainty
5653:
The NIST Reference on Constants, Units, and Uncertainty
5623:
The NIST Reference on Constants, Units, and Uncertainty
5489:
The NIST Reference on Constants, Units, and Uncertainty
5080:
differed, the universe would degenerate, and thus that
8834:
Ars Magine - Umetnost promiĆĄljanja i uobrazilje | ŚŚŚŚ
5072:
in a quest to understand its significance. Similarly,
3490:
is the reciprocal of the fine-structure constant, 137.
3228:
1671:
units is the electric constant (vacuum permittivity).
8607:
VĂĄrlaki, PĂ©ter; NĂĄdai, LĂĄszlĂł; Bokor, JĂłzsef (2008).
8590:"Cosmic numbers: Pauli and Jung's love of numerology"
6207:
6166:
4601:
4362:
4116:
3220:
3169:
3119:
2924:
2795:
2749:
2699:
2684:= approximately twice its ionization energy) and the
2347:
1882:
1772:
1700:
1411:
5804:"2022 CODATA Value: inverse fine-structure constant"
4303:
of distant astronomical objects and the products of
3555:
increases. The value of the fine-structure constant
3043:. The theory does not predict its value. Therefore,
3035:
determining the strength of the interaction between
2957:
The two ratios of three characteristic lengths: the
4806:
21 cm hyperfine transition in neutral hydrogen
2063:of the fine-structure constant is often given. The
8768:
8708:
8356:"The fine structure constant is probably constant"
8203:
8201:
6567:[On the quantum theory of spectral lines]
6228:
6187:
5595:Mohr, P. J.; Taylor, B. N.; Newell, D. B. (2019).
5381:referred to the least significant preceding digit.
4684:
4556:
4275:
4058:has been proposed as a way of solving problems in
3280:for visible frequencies is theoretically given by
3265:{\displaystyle \alpha ={\tfrac {1}{4}}Z_{0}G_{0}.}
3264:
3206:
3151:
2946:
2910:
2781:
2712:
2597:
1904:
1806:
1734:
1499:
8376:Monthly Notices of the Royal Astronomical Society
7638:Monthly Notices of the Royal Astronomical Society
7394:Monthly Notices of the Royal Astronomical Society
7270:Monthly Notices of the Royal Astronomical Society
5739:"2022 CODATA Value: vacuum electric permittivity"
5479:
5477:
5475:
2736:equivalent to the mass of an electron. Using the
1735:{\displaystyle \alpha ={\frac {e^{2}}{\hbar c}}.}
6613:. Introduction to the Constants for Nonexperts.
5447:(1962) p. 316 ... and one can well include
7177:Astrophysics, Clocks, and Fundamental Constants
6889:(1967). "Electricity, gravity, and cosmology".
6615:National Institute for Standards and Technology
6265:(third ed.). World Scientific. p. 4.
5394:from an experimentally determined value of the
5218:
5199:
5175:
5112:
4789:Lamoreaux and Torgerson analyzed data from the
1807:{\displaystyle \alpha ={\frac {e^{2}}{4\pi }}.}
1356:, who introduced it in 1916 when extending the
8628:
8626:
7142:. Springer-Praxis Books in Popular Astronomy.
5605:National Institute of Standards and Technology
4325:claimed the first detection of a variation in
2782:{\displaystyle U_{\text{el}}=2U_{\text{kin}},}
7082:. Vol. 57, no. 10. pp. 40â45.
6633:
6631:
5840:"Measurement of the Electron Magnetic Moment"
5709:"2022 CODATA Value: speed of light in vacuum"
5552:
5550:
1209:
8:
6821:Relativity, Gravitation, and World Structure
6084:
6082:
5679:"2022 CODATA Value: reduced Planck constant"
5485:"2022 CODATA Value: fine-structure constant"
3047:must be determined experimentally. In fact,
2004:This has a relative standard uncertainty of
5563:QED: The Strange Theory of Light and Matter
4954:value once the universe enters its current
1844:in terms of such a natural unit of charge.
8952:"Quotes about the fine structure constant"
8471:Annals of the New York Academy of Sciences
7821:"Speed of light may have changed recently"
7694:Memorie della Societa Astronomica Italiana
3571:can contribute to the running. Therefore,
1216:
1202:
97:
86:
31:
8863:"Theories of the fine structure constant
8428:
8398:
8388:
8305:
8279:
8181:
8163:
8122:
8096:
8055:"Changes spotted in fundamental constant"
8013:
7966:
7893:
7873:
7871:
7779:
7705:
7668:
7650:
7583:
7519:
7463:
7424:
7406:
7339:
7300:
7282:
7223:
7036:
6981:
6768:
6713:
6449:
6308:
6262:A Modern Introduction to Particle Physics
6218:
6212:
6206:
6177:
6171:
6165:
6031:
5961:
5923:
5893:
5891:
5855:
4667:
4617:
4616:
4602:
4600:
4539:
4480:
4479:
4458:
4457:
4434:
4433:
4423:
4397:
4390:
4363:
4361:
4234:
4233:
4212:
4211:
4188:
4187:
4177:
4151:
4144:
4117:
4115:
4070:and other proposals for going beyond the
3253:
3243:
3227:
3219:
3196:
3190:
3174:
3168:
3137:
3124:
3118:
2929:
2923:
2896:
2886:
2873:
2860:
2841:
2828:
2823:
2813:
2800:
2794:
2770:
2754:
2748:
2704:
2698:
2577:
2560:
2554:
2536:
2521:
2504:
2498:
2472:
2457:
2440:
2434:
2411:
2406:
2385:
2368:
2362:
2357:
2346:
1889:
1881:
1785:
1779:
1771:
1713:
1707:
1699:
1479:
1462:
1456:
1438:
1424:
1418:
1410:
8241:. Australian Government. 27 October 2020
3741:
3519:is much less than one, higher powers of
2290:, has several physical interpretations.
6565:"Zur Quantentheorie der Spektrallinien"
5771:An Introduction to Quantum Field Theory
5519:"Zur Quantentheorie der Spektrallinien"
5471:
5253:
5035:. By the 1940s experimental values for
4050:Time-variation of fundamental constants
3567:) is the lightest charged object whose
2583:
2542:
2223:has a relative standard uncertainty of
1905:{\displaystyle \alpha ={\frac {1}{c}}.}
1720:
1485:
89:
8935:from the original on 16 February 2008.
8679:. By Grimmett, G. R.; Welsh, D. J. A.
6841:(1937). "The cosmological constants".
5619:"2022 CODATA Value: elementary charge"
4407:
4404:
4401:
4161:
4158:
4155:
3730:, referring to his calculation of the
3478:. The relativistic limiting value for
1259:between elementary charged particles.
8970:– via scienceworld.wolfram.com.
8775:. John Wiley & Sons. p. 13.
6640:Archive for History of Exact Sciences
6075:from the original on 4 November 2018.
5833:
5831:
5829:
5270:is proportional to the square of the
5195:Francis Halzen and Alan Martin (1984)
4986:., previously stated in their study.
4962:Spatial variation â Australian dipole
4096:over time, which can be computed by
2947:{\displaystyle v_{\text{e}}=\alpha c}
2159:). One of the most precise values of
1255:which quantifies the strength of the
7:
5649:"2022 CODATA Value: Planck constant"
2307:between two electrons a distance of
1746:commonly used in high energy physics
8154:King, Julian A. (1 February 2012).
8492:10.1111/j.1749-6632.2001.tb02133.x
7138:Uzan, J.-P.; Leclercq, B. (2008).
5768:Peskin, M.; Schroeder, D. (1995).
4621:
4618:
4605:
4487:
4484:
4481:
4465:
4462:
4459:
4444:
4441:
4438:
4435:
4369:
4241:
4238:
4235:
4219:
4216:
4213:
4198:
4195:
4192:
4189:
4123:
3331:or 2.24%, and the transmission by
2303:the energy needed to overcome the
25:
8968:Eric Weisstein's World of Physics
8053:Johnston, H. (2 September 2010).
6544:â Article reprinted same year in
4595:, found no measurable variation:
3892:Gabrielse (2008), Hanneke (2008)
3613:approaches that of the other two
3527:makes calculations involving the
1341:, with a relative uncertainty of
8744:for larger observation distances
7670:10.1111/j.1365-2966.2007.12695.x
7426:10.1046/j.1365-8711.2003.06970.x
7302:10.1046/j.1365-8711.2001.04840.x
5160:, began exploring the idea of a
4848:would only be able to constrain
3732:anomalous magnetic dipole moment
3486:, and so the limiting value for
3152:{\displaystyle Z_{0}=\mu _{0}c,}
3094:varies with the strength of the
3082:associated with the electroweak
3053:parameters in the Standard Model
2139:and the fine-structure constant
2111:(QED) provides a way to measure
8876:. Vol. 3. pp. 73â84.
6535:The American Journal of Science
6259:Riazuddin, Fayyazuddin (2012).
5237:Dimensionless physical constant
5060:commented on the appearance of
4794:natural nuclear fission reactor
4312:natural nuclear fission reactor
8208:Zyga, Lisa (21 October 2010).
8115:10.1103/PhysRevLett.107.191101
6050:10.1103/PhysRevLett.106.080801
5980:10.1103/PhysRevLett.109.111807
5874:10.1103/PhysRevLett.130.071801
5076:believed that if the value of
4698:, discrediting those results.
3207:{\displaystyle G_{0}=2e^{2}/h}
2902:
2879:
2857:
2847:
2059:Historically the value of the
397:Renormalization group equation
1:
8998:"The fine structure constant"
8978:; Webb, John K. (June 2005).
8919:"CODATA recommended value of
8900:"The fine structure constant"
7912:10.1103/PhysRevLett.98.111301
7819:Reich, E. S. (30 June 2004).
7602:10.1103/PhysRevLett.99.239001
7538:10.1103/PhysRevLett.92.121302
7358:10.1103/PhysRevLett.87.091301
4323:University of New South Wales
4044:Potential variation over time
2286:The fine-structure constant,
2133:dimensionless magnetic moment
1253:fundamental physical constant
226:Spontaneous symmetry breaking
186:Symmetry in quantum mechanics
8677:Disorder in Physical Systems
8417:Astronomy & Astrophysics
7451:Astronomy & Astrophysics
7185:10.1007/978-3-540-40991-5_11
4906:used the frequency ratio of
4796:in 2004, and concluded that
2270:with a relative accuracy of
1744:A nondimensionalised system
1675:Alternative systems of units
8882:10.1007/978-1-4684-2961-9_4
8588:Falk, Dan (24 April 2009).
8447:10.1051/0004-6361/202243795
6402:American Journal of Physics
4810:cosmic microwave background
3535:Variation with energy scale
3092:electromagnetic interaction
3088:electromagnetic interaction
3078:is absorbed into two other
3031:is directly related to the
2713:{\displaystyle \alpha ^{2}}
1257:electromagnetic interaction
9058:
8613:Acta Polytechica Hungarica
8032:10.1103/PhysRevD.65.063504
7798:10.1103/PhysRevD.69.121701
7482:10.1051/0004-6361:20035701
7242:10.1103/PhysRevLett.82.884
7024:AIP Conference Proceedings
6953:10.1103/PhysRevLett.19.913
6913:10.1103/PhysRevLett.19.759
6732:10.1103/PhysRevD.97.036001
6575:. 4th series (in German).
6547:the Philosophical Magazine
6503:The Philosophical Magazine
6155:Atombau und Spektrallinien
5568:Princeton University Press
5062:certain numbers in physics
5010:Numerological explanations
4085:In the experiments below,
4047:
3697:(QED) the significance of
3617:, a feature important for
2971:reduced Compton wavelength
2299:The ratio of two energies:
1366:quantified the gap in the
1352:The constant was named by
221:Explicit symmetry breaking
8964:"Fine structure constant"
8715:. Bantam Books. pp.
7000:10.1103/RevModPhys.75.403
6969:Reviews of Modern Physics
6652:10.1007/s00407-002-0065-7
6378:10.1103/RevModPhys.56.137
6358:Reviews of Modern Physics
6248:. Methuen & co. 1923.
6120:10.1038/s41586-020-2964-7
5597:"Fine-structure constant"
5136:Conversely, statistician
4092:represents the change in
2959:classical electron radius
2673:is the ratio between the
2121:anomalous magnetic moment
387:BargmannâWigner equations
314:Path Integral Formulation
9010:University of Nottingham
8796:MacGregor, M.H. (2007).
8739:The asymptotic value of
8546:The Mathematical Gazette
8526:The World of Mathematics
6593:10.1002/andp.19163561702
6022:(Submitted manuscript).
5396:electron magnetic moment
5177:For historical reasons,
4707:Markov chain Monte Carlo
3693:With the development of
3615:fundamental interactions
3051:is one of the empirical
2282:Physical interpretations
392:Schwinger-Dyson equation
9027:Dimensionless constants
8907:EncyclopĂŠdia Britannica
8711:A Brief History of Time
8681:Oxford University Press
8439:2022A&A...666A..57D
8084:Physical Review Letters
7968:10.1126/science.1154622
7881:Physical Review Letters
7732:The Singularity is Near
7571:Physical Review Letters
7507:Physical Review Letters
7474:2004A&A...417..853C
7327:Physical Review Letters
7211:Physical Review Letters
6932:Physical Review Letters
6892:Physical Review Letters
6787:10.1126/science.aap7706
6682:"The number 137.035..."
6506:(reprint). 5th series.
6438:Fortschritte der Physik
6327:10.1126/science.1156965
6229:{\displaystyle v_{1}/c}
6188:{\displaystyle v_{1}/c}
6019:Physical Review Letters
5949:Physical Review Letters
5844:Physical Review Letters
5543:"rund 7·10" (about ...)
5262:quantum electrodynamics
5157:A Brief History of Time
5108:quantum electrodynamics
3738:History of measurements
3695:quantum electrodynamics
3641:Sommerfeld memorial at
3541:quantum electrodynamics
3501:quantum electrodynamics
3111:impedance of free space
3025:quantum electrodynamics
2314:the energy of a single
2305:electrostatic repulsion
2109:quantum electrodynamics
1683:system implicitly sets
1665:2019 revision of the SI
1570:reduced Planck constant
1234:fine-structure constant
422:Electroweak interaction
417:Quantum electrodynamics
382:WheelerâDeWitt equation
259:Background field method
18:Fine Structure Constant
8980:"Inconstant constants"
8641:W. W. Norton & Co.
8633:Miller, A. I. (2009).
8400:10.1093/mnras/staa3217
8298:10.1126/sciadv.aay9672
8235:"Poles and directions"
6230:
6189:
5925:10.1002/andp.201800346
5228:
5217:
5198:
5134:
4898:Present rate of change
4686:
4558:
4333:and a data set of 128
4277:
3645:
3525:quantum chromodynamics
3266:
3208:
3153:
3103:electrical engineering
3086:. In this theory, the
2948:
2912:
2783:
2742:Bohr model of the atom
2722:Bohr model of the atom
2714:
2612:Bohr model of the atom
2599:
2067:recommended value is
1939:
1906:
1808:
1736:
1501:
1264:dimensionless quantity
1240:, commonly denoted by
427:Quantum chromodynamics
284:Effective field theory
9037:Fundamental constants
8532:. pp. 1074â1093.
7729:Kurzweil, R. (2005).
7109:Barrow, J.D. (2002).
6231:
6190:
5392:by the current theory
5214:M.H. MacGregor (2007)
5190:shown in Fig. 1.5a.
5016:mathematical constant
4993:Anthropic explanation
4687:
4559:
4278:
4048:Further information:
3640:
3545:renormalization group
3531:extremely difficult.
3460:uncertainty principle
3267:
3209:
3154:
2949:
2913:
2784:
2715:
2600:
1946:recommended value of
1922:
1907:
1809:
1737:
1502:
1279:electromagnetic field
1266:, independent of the
372:KleinâGordon equation
304:LSZ reduction formula
8942:(Natalie Wolchover,
8530:Simon & Schuster
6522:Michelson, Albert A.
6490:Michelson, Albert A.
6205:
6164:
5379:standard uncertainty
5276:nuclear strong force
5100:is a law of nature.
4599:
4593:Very Large Telescope
4360:
4114:
4010:0.0072973525643(11)
3978:0.0072973525693(11)
3960:0.0072973525713(14)
3942:0.0072973525657(18)
3928:0.0072973525664(17)
3914:0.0072973525698(24)
3900:0.0072973525717(48)
3886:0.0072973525692(27)
3872:0.0072973525376(50)
3858:0.0072973525700(52)
3643:University of Munich
3529:strong nuclear force
3274:optical conductivity
3218:
3167:
3117:
2922:
2793:
2747:
2697:
2679:27.2 eV = twice the
2345:
2219:This measurement of
1880:
1770:
1698:
1409:
1236:, also known as the
465:Theory of everything
299:Lattice field theory
269:Correlation function
91:Quantum field theory
8985:Scientific American
8910:, 15th ed. by
8484:2001NYASA.950..139B
8354:(18 October 2010).
8332:(14 October 2010).
8290:2020SciA....6.9672W
8174:2012PhDT........14K
8107:2011PhRvL.107s1101W
8024:2002PhRvD..65f3504B
7959:2008Sci...319.1808R
7953:(5871): 1808â1812.
7904:2007PhRvL..98k1301K
7790:2004PhRvD..69l1701L
7716:2009MmSAI..80..864K
7661:2008MNRAS.384.1053M
7594:2007PhRvL..99w9001M
7530:2004PhRvL..92l1302S
7417:2003MNRAS.345..609M
7350:2001PhRvL..87i1301W
7293:2001MNRAS.327.1208M
7234:1999PhRvL..82..884W
7152:2008nlu..book.....U
7088:2004PhT....57j..40O
7047:2004AIPC..736....3U
6992:2003RvMP...75..403U
6945:1967PhRvL..19..913G
6905:1967PhRvL..19..759G
6857:1937Natur.139..323D
6779:2018Sci...360..191P
6724:2018PhRvD..97c6001A
6585:1916AnP...356....1S
6460:2002ForPh..50..518F
6415:2004AmJPh..72..969B
6370:1984RvMP...56..137C
6319:2008Sci...320.1308N
6245:English translation
6112:2020Natur.588...61M
6042:2011PhRvL.106h0801B
5972:2012PhRvL.109k1807A
5916:2019AnP...53100346Y
5866:2023PhRvL.130g1801F
5242:Hyperfine structure
5166:fine-tuned universe
4999:anthropic principle
4902:In 2008, Rosenband
4295:Past rate of change
4024:0.0072973525649(8)
3992:0.0072973525628(6)
3906:Bouchendira (2010)
3844:0.007297352568(24)
3830:0.007297352533(27)
3816:0.007297352582(27)
3744:
3497:perturbation theory
3161:conductance quantum
3107:solid-state physics
2833:
2117:quantum Hall effect
2115:directly using the
2103:While the value of
1405:may be defined as:
1238:Sommerfeld constant
444:Incomplete theories
8904:(adapted from the
8798:The Power of Alpha
6573:Annalen der Physik
6226:
6185:
5904:Annalen der Physik
5524:Annalen der Physik
5515:Sommerfeld, Arnold
5280:nuclear weak force
5201:The mystery about
4958:-dominated epoch.
4682:
4554:
4414:
4273:
4168:
4076:physical constants
4027:137.035999166(15)
4013:137.035999177(21)
3995:137.035999206(11)
3981:137.035999084(21)
3963:137.035999046(27)
3945:137.035999150(33)
3931:137.035999139(31)
3917:137.035999074(44)
3903:137.035999037(91)
3889:137.035999084(51)
3875:137.035999679(94)
3861:137.035999070(98)
3802:0.00729735308(33)
3742:
3686:of the hydrogenic
3646:
3262:
3237:
3204:
3149:
3080:coupling constants
3064:electroweak theory
2944:
2908:
2819:
2779:
2710:
2595:
2330:angular wavelength
1940:
1902:
1804:
1732:
1679:The electrostatic
1497:
1399:physical constants
1397:In terms of other
309:Partition function
236:Topological charge
156:General relativity
151:Special relativity
9042:Arnold Sommerfeld
8891:978-1-4684-2963-3
8859:Adler, Stephen L.
8815:978-981-256-961-5
8782:978-0-471-88741-6
8726:978-0-553-05340-1
8690:978-0-19-853215-6
8654:978-0-393-06532-9
8001:Physical Review D
7767:Physical Review D
7750:978-0-670-03384-3
7194:978-3-540-21967-5
7161:978-0-387-73454-5
7124:978-0-09-928647-9
7096:10.1063/1.1825267
7055:10.1063/1.1835171
6763:(6385): 191â195.
6701:Physical Review D
6526:Morley, Edward W.
6494:Morley, Edward W.
6423:10.1119/1.1646135
5789:978-0-201-50397-5
5581:978-0-691-08388-9
5272:coupling constant
4678:
4637:
4631:
4627:
4550:
4509:
4506:
4500:
4497:
4493:
4473:
4428:
4422:
4419:
4415:
4412:
4400:
4396:
4395:
4389:
4386:
4382:
4377:
4368:
4305:radioactive decay
4269:
4263:
4260:
4254:
4251:
4247:
4227:
4182:
4176:
4173:
4169:
4166:
4154:
4150:
4149:
4143:
4140:
4136:
4131:
4122:
4082:) actually vary.
4038:
4037:
3864:Gabrielse (2007)
3847:137.03599911(46)
3833:137.03599976(50)
3819:137.03599883(51)
3788:0.0072973461(81)
3658:Arnold Sommerfeld
3619:grand unification
3458:. The Heisenberg
3236:
3101:In the fields of
3033:coupling constant
2932:
2889:
2844:
2826:
2816:
2803:
2789:which means that
2773:
2757:
2590:
2549:
2531:
2493:
2467:
2424:
2395:
2054:parts per billion
2049:10 H⋅m
1897:
1847:In the system of
1816:elementary charge
1799:
1727:
1639:electric constant
1516:elementary charge
1492:
1451:
1387:measure its value
1354:Arnold Sommerfeld
1302:is approximately
1281:, by the formula
1272:elementary charge
1226:
1225:
289:Expectation value
264:BRST quantization
211:Poincaré symmetry
166:YangâMills theory
146:Quantum mechanics
85:
84:
16:(Redirected from
9049:
9032:Electromagnetism
9013:
8989:
8971:
8959:
8944:Quanta magazine,
8936:
8934:
8927:
8922:
8903:
8895:
8871:
8866:
8846:
8845:
8843:
8841:
8826:
8820:
8819:
8802:World Scientific
8793:
8787:
8786:
8774:
8757:
8751:
8742:
8737:
8731:
8730:
8714:
8701:
8695:
8694:
8665:
8659:
8658:
8630:
8621:
8620:
8604:
8598:
8597:
8585:
8579:
8578:
8553:(286): 137â144.
8540:
8534:
8533:
8522:Eddington, A. S.
8518:
8512:
8511:
8465:
8459:
8458:
8432:
8411:
8405:
8404:
8402:
8392:
8366:
8360:
8359:
8348:
8342:
8341:
8338:ScienceBlogs.com
8326:
8320:
8319:
8309:
8283:
8274:(17): eaay9672.
8267:Science Advances
8257:
8251:
8250:
8248:
8246:
8231:
8225:
8224:
8222:
8220:
8205:
8196:
8195:
8185:
8167:
8151:
8145:
8144:
8126:
8100:
8078:
8072:
8071:
8069:
8067:
8050:
8044:
8043:
8017:
8015:astro-ph/0109414
7995:
7989:
7988:
7970:
7938:
7932:
7931:
7897:
7895:astro-ph/0701752
7875:
7866:
7865:
7863:
7861:
7844:
7838:
7837:
7835:
7833:
7816:
7810:
7809:
7783:
7761:
7755:
7754:
7726:
7720:
7719:
7709:
7689:
7683:
7682:
7672:
7654:
7652:astro-ph/0612407
7645:(3): 1053â1062.
7628:
7622:
7621:
7587:
7564:
7558:
7557:
7523:
7521:astro-ph/0402177
7500:
7494:
7493:
7467:
7465:astro-ph/0401094
7445:
7439:
7438:
7428:
7410:
7408:astro-ph/0306483
7384:
7378:
7377:
7343:
7341:astro-ph/0012539
7321:
7315:
7314:
7304:
7286:
7284:astro-ph/0012419
7277:(4): 1208â1222.
7260:
7254:
7253:
7227:
7225:astro-ph/9803165
7205:
7199:
7198:
7172:
7166:
7165:
7135:
7129:
7128:
7106:
7100:
7099:
7073:
7067:
7066:
7040:
7038:astro-ph/0409424
7018:
7012:
7011:
6985:
6963:
6957:
6956:
6923:
6917:
6916:
6883:
6877:
6876:
6865:10.1038/139323a0
6839:Dirac, Paul A.M.
6835:
6829:
6828:
6813:
6807:
6806:
6772:
6750:
6744:
6743:
6717:
6695:
6689:
6688:
6678:
6672:
6671:
6635:
6626:
6625:
6623:
6621:
6603:
6597:
6596:
6570:
6557:
6551:
6543:
6518:
6512:
6511:
6486:
6480:
6479:
6453:
6444:(5â7): 518â524.
6433:
6427:
6426:
6396:
6390:
6389:
6353:
6347:
6346:
6312:
6290:
6284:
6283:
6281:
6279:
6256:
6250:
6249:
6241:
6239:
6235:
6233:
6232:
6227:
6222:
6217:
6216:
6198:
6194:
6192:
6191:
6186:
6181:
6176:
6175:
6146:
6140:
6139:
6095:
6086:
6077:
6076:
6074:
6035:
6015:
6006:
6000:
5999:
5965:
5945:
5936:
5930:
5929:
5927:
5895:
5886:
5885:
5859:
5835:
5824:
5823:
5821:
5819:
5800:
5794:
5793:
5765:
5759:
5758:
5756:
5754:
5735:
5729:
5728:
5726:
5724:
5705:
5699:
5698:
5696:
5694:
5675:
5669:
5668:
5666:
5664:
5645:
5639:
5638:
5636:
5634:
5615:
5609:
5608:
5592:
5586:
5585:
5554:
5545:
5540:
5538:
5536:
5511:
5505:
5504:
5502:
5500:
5481:
5460:
5433:
5427:
5422:
5420:
5419:
5416:
5413:
5405:
5399:
5388:
5382:
5375:
5369:
5367:
5366:
5364:
5363:
5358:
5355:
5337:
5329:
5328:
5326:
5325:
5320:
5317:
5298:
5292:
5289:
5283:
5269:
5258:
5226:
5215:
5208:
5204:
5196:
5189:
5185:
5180:
5132:
5119:
5099:
5097:
5096:
5093:
5090:
5083:
5079:
5052:
5050:
5049:
5048:
5044:
5041:
5026:Eddington number
5022:Arthur Eddington
5005:
4952:
4950:
4946:
4940:
4938:
4937:
4936:
4932:
4929:
4928:
4925:
4917:
4913:
4909:
4893:
4891:
4890:
4889:
4885:
4882:
4881:
4878:
4870:
4868:
4867:
4866:
4862:
4859:
4858:
4855:
4840:
4839:
4838:
4837:
4836:
4828:
4823:
4819:
4815:
4799:
4777:
4775:
4774:
4773:
4769:
4766:
4765:
4754:
4752:
4751:
4750:
4746:
4743:
4742:
4731:
4729:
4728:
4727:
4723:
4720:
4719:
4691:
4689:
4688:
4683:
4676:
4675:
4674:
4659:
4655:
4635:
4629:
4628:
4626:
4625:
4624:
4611:
4603:
4583:
4579:
4578:
4572:
4571:
4563:
4561:
4560:
4555:
4548:
4547:
4546:
4531:
4527:
4507:
4504:
4498:
4495:
4494:
4492:
4491:
4490:
4474:
4471:
4470:
4469:
4468:
4449:
4448:
4447:
4426:
4424:
4420:
4417:
4416:
4413:
4410:
4398:
4391:
4387:
4384:
4383:
4378:
4375:
4366:
4364:
4355:
4347:
4328:
4320:
4291:being constant.
4290:
4286:
4282:
4280:
4279:
4274:
4267:
4261:
4258:
4252:
4249:
4248:
4246:
4245:
4244:
4228:
4225:
4224:
4223:
4222:
4203:
4202:
4201:
4180:
4178:
4174:
4171:
4170:
4167:
4164:
4152:
4145:
4141:
4138:
4137:
4132:
4129:
4120:
4118:
4106:
4099:
4095:
4091:
4081:
4057:
3805:137.0359895(61)
3774:0.007297351(11)
3763:
3755:
3745:
3728:Julian Schwinger
3725:
3724:
3722:
3721:
3715:
3712:
3702:
3679:angular momentum
3668:
3605:
3591:, about 90
3586:
3584:
3583:
3580:
3577:
3558:
3551:as the relevant
3522:
3518:
3514:
3503:, the resulting
3489:
3485:
3481:
3477:
3457:
3456:
3454:
3453:
3448:
3445:
3434:
3432:
3431:
3422:
3419:
3412:
3410:
3409:
3404:
3401:
3389:the relation is
3388:
3377:
3376:
3374:
3373:
3366:
3363:
3352:
3351:
3349:
3348:
3341:
3338:
3330:
3329:
3327:
3326:
3319:
3316:
3305:
3298:
3296:
3295:
3292:
3289:
3271:
3269:
3268:
3263:
3258:
3257:
3248:
3247:
3238:
3229:
3213:
3211:
3210:
3205:
3200:
3195:
3194:
3179:
3178:
3158:
3156:
3155:
3150:
3142:
3141:
3129:
3128:
3077:
3072:electromagnetism
3068:weak interaction
3057:particle physics
3050:
3046:
3030:
3019:
2993:
2981:
2973:of the electron
2968:
2953:
2951:
2950:
2945:
2934:
2933:
2930:
2917:
2915:
2914:
2909:
2901:
2900:
2891:
2890:
2887:
2878:
2877:
2865:
2864:
2846:
2845:
2842:
2832:
2827:
2824:
2818:
2817:
2814:
2805:
2804:
2801:
2788:
2786:
2785:
2780:
2775:
2774:
2771:
2759:
2758:
2755:
2735:
2719:
2717:
2716:
2711:
2709:
2708:
2683:
2672:
2664:
2656:
2655:
2653:
2652:
2647:
2644:
2636:
2634:
2633:
2624:
2621:
2604:
2602:
2601:
2596:
2591:
2589:
2582:
2581:
2565:
2564:
2555:
2550:
2548:
2537:
2532:
2530:
2526:
2525:
2509:
2508:
2499:
2494:
2492:
2484:
2473:
2468:
2466:
2462:
2461:
2445:
2444:
2435:
2430:
2429:
2425:
2420:
2412:
2405:
2401:
2400:
2396:
2394:
2390:
2389:
2373:
2372:
2363:
2334:
2327:
2310:
2293:
2289:
2277:
2275:
2266:
2264:
2261:
2255:
2254:
2252:
2251:
2246:
2243:
2230:
2228:
2222:
2215:
2213:
2210:
2204:
2203:
2201:
2200:
2195:
2192:
2181:Feynman diagrams
2178:
2177:
2171:
2162:
2158:
2148:
2142:
2130:
2114:
2106:
2099:
2097:
2094:
2088:
2087:
2085:
2084:
2079:
2076:
2051:
2050:
2048:
2044:
2041:
2038:
2025:
2020:
2011:
2009:
2000:
1998:
1995:
1992:
1986:
1985:
1983:
1982:
1970:
1967:
1951:
1928:Feynman diagrams
1911:
1909:
1908:
1903:
1898:
1890:
1875:
1843:
1842:
1841:
1838:
1832:
1831:
1813:
1811:
1810:
1805:
1800:
1798:
1790:
1789:
1780:
1765:
1741:
1739:
1738:
1733:
1728:
1726:
1718:
1717:
1708:
1693:
1658:
1655:
1653:
1649:
1646:
1633:
1627:
1624:
1622:
1619:
1609:
1603:
1600:
1598:
1594:
1591:
1585:
1567:
1561:
1558:
1556:
1553:
1550:
1540:
1534:
1531:
1529:
1526:
1523:
1513:
1506:
1504:
1503:
1498:
1493:
1491:
1484:
1483:
1467:
1466:
1457:
1452:
1450:
1443:
1442:
1429:
1428:
1419:
1404:
1365:
1348:
1346:
1340:
1339:
1337:
1336:
1335:
1334:
1331:
1325:
1322:
1315:
1314:
1311:
1308:
1297:
1243:
1218:
1211:
1204:
279:Effective action
206:Lorentz symmetry
131:Electromagnetism
101:
87:
81:
79:
76:
67:
57:
55:
52:
49:
40:
32:
21:
9057:
9056:
9052:
9051:
9050:
9048:
9047:
9046:
9017:
9016:
8994:Eaves, Laurence
8992:
8974:
8962:
8950:
8932:
8925:
8920:
8917:
8898:
8892:
8869:
8864:
8857:
8854:
8849:
8839:
8837:
8828:
8827:
8823:
8816:
8795:
8794:
8790:
8783:
8759:
8758:
8754:
8740:
8738:
8734:
8727:
8703:
8702:
8698:
8691:
8683:. p. 141.
8667:
8666:
8662:
8655:
8632:
8631:
8624:
8606:
8605:
8601:
8587:
8586:
8582:
8559:10.2307/3609461
8542:
8541:
8537:
8528:. Vol. 2.
8520:
8519:
8515:
8467:
8466:
8462:
8413:
8412:
8408:
8368:
8367:
8363:
8350:
8349:
8345:
8328:
8327:
8323:
8259:
8258:
8254:
8244:
8242:
8233:
8232:
8228:
8218:
8216:
8207:
8206:
8199:
8183:10.1.1.750.8595
8153:
8152:
8148:
8080:
8079:
8075:
8065:
8063:
8052:
8051:
8047:
7997:
7996:
7992:
7940:
7939:
7935:
7877:
7876:
7869:
7859:
7857:
7846:
7845:
7841:
7831:
7829:
7818:
7817:
7813:
7781:nucl-th/0309048
7763:
7762:
7758:
7751:
7728:
7727:
7723:
7691:
7690:
7686:
7630:
7629:
7625:
7566:
7565:
7561:
7502:
7501:
7497:
7447:
7446:
7442:
7386:
7385:
7381:
7323:
7322:
7318:
7262:
7261:
7257:
7207:
7206:
7202:
7195:
7174:
7173:
7169:
7162:
7144:Springer Praxis
7137:
7136:
7132:
7125:
7108:
7107:
7103:
7075:
7074:
7070:
7020:
7019:
7015:
6965:
6964:
6960:
6939:(16): 913â914.
6925:
6924:
6920:
6899:(13): 759â761.
6885:
6884:
6880:
6837:
6836:
6832:
6825:Clarendon Press
6815:
6814:
6810:
6752:
6751:
6747:
6697:
6696:
6692:
6680:
6679:
6675:
6637:
6636:
6629:
6619:
6617:
6605:
6604:
6600:
6568:
6559:
6558:
6554:
6542:(204): 427â430.
6520:
6519:
6515:
6510:(151): 463â466.
6488:
6487:
6483:
6435:
6434:
6430:
6398:
6397:
6393:
6355:
6354:
6350:
6292:
6291:
6287:
6277:
6275:
6273:
6258:
6257:
6253:
6242:
6237:
6208:
6203:
6202:
6201:[The ratio
6196:
6167:
6162:
6161:
6160:Das VerhÀltnis
6148:
6147:
6143:
6106:(7836): 61â65.
6093:
6088:
6087:
6080:
6072:
6013:
6008:
6007:
6003:
5940:
5938:
5937:
5933:
5897:
5896:
5889:
5837:
5836:
5827:
5817:
5815:
5802:
5801:
5797:
5790:
5767:
5766:
5762:
5752:
5750:
5737:
5736:
5732:
5722:
5720:
5707:
5706:
5702:
5692:
5690:
5677:
5676:
5672:
5662:
5660:
5647:
5646:
5642:
5632:
5630:
5617:
5616:
5612:
5594:
5593:
5589:
5582:
5556:
5555:
5548:
5534:
5532:
5513:
5512:
5508:
5498:
5496:
5483:
5482:
5473:
5469:
5464:
5463:
5434:
5430:
5417:
5414:
5411:
5410:
5408:
5406:
5402:
5389:
5385:
5376:
5372:
5359:
5356:
5350:
5349:
5347:
5341:
5339:
5335:
5333:
5321:
5318:
5312:
5311:
5309:
5303:
5299:
5295:
5290:
5286:
5265:
5259:
5255:
5250:
5233:
5227:
5225:Wolfgang Pauli
5224:
5216:
5213:
5206:
5202:
5197:
5194:
5187:
5183:
5178:
5174:
5152:Stephen Hawking
5133:
5128:
5115:
5104:Richard Feynman
5094:
5091:
5088:
5087:
5085:
5081:
5077:
5046:
5045:
5042:
5039:
5038:
5036:
5012:
5003:
4995:
4964:
4948:
4944:
4942:
4934:
4933:
4930:
4926:
4923:
4922:
4921:
4919:
4915:
4911:
4907:
4900:
4887:
4886:
4883:
4879:
4876:
4875:
4874:
4872:
4864:
4863:
4860:
4856:
4853:
4852:
4851:
4849:
4846:radio telescope
4841:. The European
4834:
4833:
4831:
4830:
4826:
4825:
4821:
4817:
4813:
4797:
4778:stated by Webb
4771:
4770:
4767:
4760:
4759:
4758:
4756:
4748:
4747:
4744:
4737:
4736:
4735:
4733:
4725:
4724:
4721:
4714:
4713:
4712:
4710:
4663:
4642:
4638:
4612:
4604:
4597:
4596:
4581:
4576:
4574:
4569:
4567:
4535:
4514:
4510:
4475:
4453:
4429:
4425:
4365:
4358:
4357:
4353:
4341:
4331:Keck telescopes
4326:
4318:
4297:
4288:
4284:
4229:
4207:
4183:
4179:
4119:
4112:
4111:
4109:
4104:
4102:
4097:
4093:
4086:
4079:
4055:
4052:
4046:
3758:
3751:
3740:
3716:
3713:
3708:
3707:
3705:
3704:
3698:
3666:
3635:
3603:
3581:
3578:
3575:
3574:
3572:
3556:
3549:logarithmically
3537:
3520:
3516:
3512:
3493:
3487:
3483:
3479:
3476:
3472:
3469:
3466:
3463:
3452:
3449:
3446:
3444:
3441:
3438:
3437:
3435:
3430:
3427:
3423:
3420:
3417:
3416:
3414:
3408:
3405:
3402:
3400:
3397:
3394:
3393:
3391:
3390:
3386:
3371:
3367:
3364:
3362:
3358:
3357:
3355:
3354:
3346:
3342:
3339:
3336:
3335:
3333:
3332:
3324:
3320:
3317:
3315:
3311:
3310:
3308:
3307:
3304:
3301:
3293:
3290:
3288:
3285:
3284:
3282:
3281:
3249:
3239:
3216:
3215:
3186:
3170:
3165:
3164:
3133:
3120:
3115:
3114:
3075:
3048:
3044:
3028:
3018:
3008:
3001:
2995:
2992:
2986:
2980:
2974:
2967:
2961:
2925:
2920:
2919:
2892:
2882:
2869:
2856:
2837:
2809:
2796:
2791:
2790:
2766:
2750:
2745:
2744:
2731:
2725:
2724:and the energy
2700:
2695:
2694:
2691:(511 keV).
2678:
2670:
2662:
2648:
2645:
2640:
2639:
2637:
2632:
2629:
2625:
2622:
2619:
2618:
2616:
2615:
2607:
2573:
2566:
2556:
2541:
2517:
2510:
2500:
2485:
2474:
2453:
2446:
2436:
2413:
2407:
2381:
2374:
2364:
2358:
2354:
2343:
2342:
2338:Planck relation
2332:
2319:
2308:
2291:
2287:
2284:
2273:
2271:
2268:
2262:
2259:
2257:
2247:
2244:
2241:
2240:
2238:
2237:
2226:
2224:
2220:
2217:
2211:
2208:
2206:
2196:
2193:
2190:
2189:
2187:
2186:
2175:
2173:
2170:
2164:
2160:
2157:
2151:
2146:
2140:
2128:
2112:
2104:
2101:
2095:
2092:
2090:
2080:
2077:
2074:
2073:
2071:
2070:
2046:
2042:
2039:
2036:
2034:
2028:
2023:
2022:
2016:
2015:This value for
2007:
2005:
2002:
1996:
1993:
1990:
1988:
1978:
1971:
1968:
1963:
1962:
1960:
1955:
1947:
1917:
1878:
1877:
1873:
1862:
1852:
1839:
1836:
1834:
1826:
1824:
1819:
1791:
1781:
1768:
1767:
1755:
1749:
1719:
1709:
1696:
1695:
1691:
1684:
1677:
1656:
1651:
1647:
1644:
1642:
1636:
1631:
1625:
1620:
1617:
1615:
1607:
1601:
1596:
1592:
1589:
1587:
1573:
1565:
1559:
1554:
1551:
1548:
1546:
1543:Planck constant
1538:
1532:
1527:
1524:
1521:
1519:
1511:
1475:
1468:
1458:
1434:
1430:
1420:
1407:
1406:
1402:
1395:
1361:
1344:
1342:
1332:
1329:
1327:
1326:
1323:
1320:
1319:
1317:
1312:
1309:
1306:
1304:
1303:
1300:numerical value
1289:
1282:
1268:system of units
1241:
1222:
1193:
1192:
1191:
1189:
483:
475:
474:
470:Quantum gravity
445:
437:
436:
432:Higgs mechanism
412:
402:
401:
377:Proca equations
362:
354:
353:
349:Wightman Axioms
334:Renormalization
294:Feynman diagram
249:
241:
240:
181:
171:
170:
121:
106:
104:Feynman diagram
77:
74:
72:
63:
53:
50:
47:
45:
36:
28:
23:
22:
15:
12:
11:
5:
9055:
9053:
9045:
9044:
9039:
9034:
9029:
9019:
9018:
9015:
9014:
8990:
8972:
8960:
8948:
8937:
8915:
8896:
8890:
8874:Atomic Physics
8853:
8852:External links
8850:
8848:
8847:
8821:
8814:
8788:
8781:
8752:
8732:
8725:
8696:
8689:
8660:
8653:
8622:
8599:
8580:
8535:
8513:
8478:(1): 139â153.
8460:
8406:
8361:
8352:Carroll, S. M.
8343:
8321:
8252:
8226:
8197:
8146:
8091:(19): 191101.
8073:
8045:
7990:
7933:
7888:(11): 111301.
7867:
7839:
7811:
7774:(12): 121701.
7756:
7749:
7737:Viking Penguin
7721:
7684:
7623:
7578:(23): 239001.
7559:
7514:(12): 121302.
7495:
7458:(3): 853â871.
7440:
7401:(2): 609â638.
7379:
7316:
7255:
7218:(5): 884â887.
7200:
7193:
7167:
7160:
7130:
7123:
7101:
7068:
7013:
6983:hep-ph/0205340
6976:(2): 403â455.
6958:
6918:
6878:
6830:
6808:
6745:
6690:
6673:
6646:(5): 395â431.
6627:
6598:
6561:Sommerfeld, A.
6552:
6538:. 3rd series.
6513:
6481:
6451:hep-ph/0201198
6428:
6391:
6364:(2): 137â147.
6348:
6303:(5881): 1308.
6285:
6271:
6251:
6225:
6221:
6215:
6211:
6184:
6180:
6174:
6170:
6150:Sommerfeld, A.
6141:
6078:
6001:
5956:(11): 111807.
5931:
5910:(5): 1800346.
5887:
5825:
5795:
5788:
5776:Westview Press
5760:
5730:
5700:
5670:
5640:
5610:
5587:
5580:
5558:Feynman, R. P.
5546:
5541:Equation 12a,
5506:
5470:
5468:
5465:
5462:
5461:
5451:on account of
5428:
5400:
5383:
5370:
5293:
5284:
5252:
5251:
5249:
5246:
5245:
5244:
5239:
5232:
5229:
5222:
5211:
5192:
5173:
5170:
5142:Platonic Ideal
5126:
5058:Wolfgang Pauli
5011:
5008:
4994:
4991:
4963:
4960:
4899:
4896:
4681:
4673:
4670:
4666:
4662:
4658:
4654:
4651:
4648:
4645:
4641:
4634:
4623:
4620:
4615:
4610:
4607:
4553:
4545:
4542:
4538:
4534:
4530:
4526:
4523:
4520:
4517:
4513:
4503:
4489:
4486:
4483:
4478:
4467:
4464:
4461:
4456:
4452:
4446:
4443:
4440:
4437:
4432:
4409:
4406:
4403:
4394:
4381:
4374:
4371:
4301:spectral lines
4296:
4293:
4272:
4266:
4257:
4243:
4240:
4237:
4232:
4221:
4218:
4215:
4210:
4206:
4200:
4197:
4194:
4191:
4186:
4163:
4160:
4157:
4148:
4135:
4128:
4125:
4107:
4100:
4072:Standard Model
4045:
4042:
4036:
4035:
4028:
4025:
4022:
4018:
4017:
4014:
4011:
4008:
4004:
4003:
3996:
3993:
3990:
3986:
3985:
3982:
3979:
3976:
3972:
3971:
3964:
3961:
3958:
3954:
3953:
3946:
3943:
3940:
3936:
3935:
3932:
3929:
3926:
3922:
3921:
3918:
3915:
3912:
3908:
3907:
3904:
3901:
3898:
3894:
3893:
3890:
3887:
3884:
3880:
3879:
3876:
3873:
3870:
3866:
3865:
3862:
3859:
3856:
3852:
3851:
3848:
3845:
3842:
3838:
3837:
3834:
3831:
3828:
3824:
3823:
3820:
3817:
3814:
3810:
3809:
3806:
3803:
3800:
3796:
3795:
3792:
3791:137.03612(15)
3789:
3786:
3782:
3781:
3778:
3777:137.03602(21)
3775:
3772:
3768:
3767:
3764:
3756:
3749:
3739:
3736:
3688:spectral lines
3684:fine-structure
3675:speed of light
3634:
3631:
3611:Standard Model
3536:
3533:
3499:is applied to
3492:
3491:
3474:
3470:
3467:
3464:
3450:
3442:
3439:
3428:
3425:
3406:
3398:
3395:
3379:
3369:
3360:
3344:
3322:
3313:
3302:
3299:
3286:
3261:
3256:
3252:
3246:
3242:
3235:
3232:
3226:
3223:
3203:
3199:
3193:
3189:
3185:
3182:
3177:
3173:
3148:
3145:
3140:
3136:
3132:
3127:
3123:
3099:
3060:
3021:
3016:
3006:
2999:
2990:
2978:
2965:
2955:
2943:
2940:
2937:
2928:
2907:
2904:
2899:
2895:
2885:
2881:
2876:
2872:
2868:
2863:
2859:
2855:
2852:
2849:
2840:
2836:
2831:
2822:
2812:
2808:
2799:
2778:
2769:
2765:
2762:
2753:
2738:virial theorem
2729:
2707:
2703:
2692:
2681:Rydberg energy
2675:Hartree energy
2659:speed of light
2630:
2627:
2608:
2606:
2605:
2594:
2588:
2585:
2580:
2576:
2572:
2569:
2563:
2559:
2553:
2547:
2544:
2540:
2535:
2529:
2524:
2520:
2516:
2513:
2507:
2503:
2497:
2491:
2488:
2483:
2480:
2477:
2471:
2465:
2460:
2456:
2452:
2449:
2443:
2439:
2433:
2428:
2423:
2419:
2416:
2410:
2404:
2399:
2393:
2388:
2384:
2380:
2377:
2371:
2367:
2361:
2356:
2353:
2350:
2318:of wavelength
2312:
2300:
2296:
2283:
2280:
2236:
2185:
2168:
2155:
2069:
2026:
1976:
1954:
1916:
1913:
1901:
1896:
1893:
1888:
1885:
1871:
1860:
1803:
1797:
1794:
1788:
1784:
1778:
1775:
1753:
1731:
1725:
1722:
1716:
1712:
1706:
1703:
1689:
1676:
1673:
1661:
1660:
1634:
1629:
1612:speed of light
1605:
1563:
1536:
1496:
1490:
1487:
1482:
1478:
1474:
1471:
1465:
1461:
1455:
1449:
1446:
1441:
1437:
1433:
1427:
1423:
1417:
1414:
1394:
1391:
1372:spectral lines
1368:fine structure
1287:
1224:
1223:
1221:
1220:
1213:
1206:
1198:
1195:
1194:
1187:
1186:
1181:
1176:
1171:
1166:
1161:
1156:
1151:
1146:
1141:
1136:
1131:
1126:
1121:
1116:
1111:
1106:
1101:
1096:
1091:
1086:
1081:
1076:
1071:
1066:
1061:
1056:
1051:
1046:
1041:
1036:
1031:
1026:
1021:
1016:
1011:
1006:
1001:
996:
991:
986:
981:
976:
971:
966:
961:
956:
951:
946:
941:
936:
931:
926:
921:
916:
911:
906:
901:
896:
891:
886:
881:
876:
871:
866:
861:
856:
851:
846:
841:
836:
831:
826:
821:
816:
811:
806:
801:
796:
791:
786:
781:
776:
771:
766:
761:
756:
751:
746:
741:
736:
731:
726:
721:
716:
711:
706:
701:
696:
691:
686:
681:
676:
671:
666:
661:
656:
651:
646:
641:
636:
631:
626:
621:
616:
611:
606:
601:
596:
591:
586:
581:
576:
571:
566:
561:
556:
551:
546:
541:
536:
531:
526:
521:
516:
511:
506:
501:
496:
491:
485:
484:
481:
480:
477:
476:
473:
472:
467:
462:
457:
452:
446:
443:
442:
439:
438:
435:
434:
429:
424:
419:
413:
410:Standard Model
408:
407:
404:
403:
400:
399:
394:
389:
384:
379:
374:
369:
367:Dirac equation
363:
360:
359:
356:
355:
352:
351:
346:
344:Wick's theorem
341:
336:
331:
329:Regularization
326:
321:
316:
311:
306:
301:
296:
291:
286:
281:
276:
271:
266:
261:
256:
250:
247:
246:
243:
242:
239:
238:
233:
231:Noether charge
228:
223:
218:
216:Gauge symmetry
213:
208:
203:
198:
193:
188:
182:
177:
176:
173:
172:
169:
168:
163:
158:
153:
148:
143:
138:
133:
128:
122:
119:
118:
115:
114:
108:
107:
102:
94:
93:
83:
82:
69:
68:
59:
58:
42:
41:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
9054:
9043:
9040:
9038:
9035:
9033:
9030:
9028:
9025:
9024:
9022:
9011:
9007:
9003:
9002:Sixty Symbols
8999:
8995:
8991:
8987:
8986:
8981:
8977:
8973:
8969:
8965:
8961:
8957:
8953:
8949:
8945:
8941:
8938:
8931:
8924:
8916:
8913:
8909:
8908:
8901:
8897:
8893:
8887:
8883:
8879:
8875:
8868:
8860:
8856:
8855:
8851:
8835:
8831:
8825:
8822:
8817:
8811:
8807:
8803:
8799:
8792:
8789:
8784:
8778:
8773:
8772:
8766:
8762:
8756:
8753:
8749:
8745:
8736:
8733:
8728:
8722:
8718:
8713:
8712:
8706:
8700:
8697:
8692:
8686:
8682:
8678:
8674:
8670:
8664:
8661:
8656:
8650:
8646:
8642:
8638:
8637:
8629:
8627:
8623:
8618:
8614:
8610:
8603:
8600:
8595:
8594:New Scientist
8591:
8584:
8581:
8576:
8572:
8568:
8564:
8560:
8556:
8552:
8548:
8547:
8539:
8536:
8531:
8527:
8523:
8517:
8514:
8509:
8505:
8501:
8497:
8493:
8489:
8485:
8481:
8477:
8473:
8472:
8464:
8461:
8456:
8452:
8448:
8444:
8440:
8436:
8431:
8426:
8422:
8418:
8410:
8407:
8401:
8396:
8391:
8386:
8382:
8378:
8377:
8372:
8365:
8362:
8357:
8353:
8347:
8344:
8339:
8335:
8331:
8325:
8322:
8317:
8313:
8308:
8303:
8299:
8295:
8291:
8287:
8282:
8277:
8273:
8269:
8268:
8263:
8256:
8253:
8240:
8236:
8230:
8227:
8215:
8211:
8204:
8202:
8198:
8193:
8189:
8184:
8179:
8175:
8171:
8166:
8161:
8157:
8150:
8147:
8142:
8138:
8134:
8130:
8125:
8124:1959.3/207294
8120:
8116:
8112:
8108:
8104:
8099:
8094:
8090:
8086:
8085:
8077:
8074:
8062:
8061:
8060:Physics World
8056:
8049:
8046:
8041:
8037:
8033:
8029:
8025:
8021:
8016:
8011:
8008:(6): 063504.
8007:
8003:
8002:
7994:
7991:
7986:
7982:
7978:
7974:
7969:
7964:
7960:
7956:
7952:
7948:
7944:
7937:
7934:
7929:
7925:
7921:
7917:
7913:
7909:
7905:
7901:
7896:
7891:
7887:
7883:
7882:
7874:
7872:
7868:
7856:. 12 May 2005
7855:
7854:
7849:
7843:
7840:
7828:
7827:
7826:New Scientist
7822:
7815:
7812:
7807:
7803:
7799:
7795:
7791:
7787:
7782:
7777:
7773:
7769:
7768:
7760:
7757:
7752:
7746:
7742:
7738:
7734:
7733:
7725:
7722:
7717:
7713:
7708:
7703:
7699:
7695:
7688:
7685:
7680:
7676:
7671:
7666:
7662:
7658:
7653:
7648:
7644:
7640:
7639:
7634:
7627:
7624:
7619:
7615:
7611:
7607:
7603:
7599:
7595:
7591:
7586:
7581:
7577:
7573:
7572:
7563:
7560:
7555:
7551:
7547:
7543:
7539:
7535:
7531:
7527:
7522:
7517:
7513:
7509:
7508:
7499:
7496:
7491:
7487:
7483:
7479:
7475:
7471:
7466:
7461:
7457:
7453:
7452:
7444:
7441:
7436:
7432:
7427:
7422:
7418:
7414:
7409:
7404:
7400:
7396:
7395:
7390:
7383:
7380:
7375:
7371:
7367:
7363:
7359:
7355:
7351:
7347:
7342:
7337:
7334:(9): 091301.
7333:
7329:
7328:
7320:
7317:
7312:
7308:
7303:
7298:
7294:
7290:
7285:
7280:
7276:
7272:
7271:
7266:
7259:
7256:
7251:
7247:
7243:
7239:
7235:
7231:
7226:
7221:
7217:
7213:
7212:
7204:
7201:
7196:
7190:
7186:
7182:
7178:
7171:
7168:
7163:
7157:
7153:
7149:
7145:
7141:
7134:
7131:
7126:
7120:
7116:
7112:
7105:
7102:
7097:
7093:
7089:
7085:
7081:
7080:
7079:Physics Today
7072:
7069:
7064:
7060:
7056:
7052:
7048:
7044:
7039:
7034:
7030:
7026:
7025:
7017:
7014:
7009:
7005:
7001:
6997:
6993:
6989:
6984:
6979:
6975:
6971:
6970:
6962:
6959:
6954:
6950:
6946:
6942:
6938:
6934:
6933:
6928:
6922:
6919:
6914:
6910:
6906:
6902:
6898:
6894:
6893:
6888:
6882:
6879:
6874:
6870:
6866:
6862:
6858:
6854:
6851:(3512): 323.
6850:
6846:
6845:
6840:
6834:
6831:
6826:
6822:
6818:
6812:
6809:
6804:
6800:
6796:
6792:
6788:
6784:
6780:
6776:
6771:
6766:
6762:
6758:
6757:
6749:
6746:
6741:
6737:
6733:
6729:
6725:
6721:
6716:
6711:
6708:(3): 036001.
6707:
6703:
6702:
6694:
6691:
6686:
6683:
6677:
6674:
6669:
6665:
6661:
6657:
6653:
6649:
6645:
6641:
6634:
6632:
6628:
6616:
6612:
6608:
6602:
6599:
6594:
6590:
6586:
6582:
6578:
6574:
6566:
6562:
6556:
6553:
6549:
6548:
6541:
6537:
6536:
6531:
6527:
6523:
6517:
6514:
6509:
6505:
6504:
6499:
6495:
6491:
6485:
6482:
6477:
6473:
6469:
6465:
6461:
6457:
6452:
6447:
6443:
6439:
6432:
6429:
6424:
6420:
6416:
6412:
6408:
6404:
6403:
6395:
6392:
6387:
6383:
6379:
6375:
6371:
6367:
6363:
6359:
6352:
6349:
6344:
6340:
6336:
6332:
6328:
6324:
6320:
6316:
6311:
6306:
6302:
6298:
6297:
6289:
6286:
6274:
6272:9789814338837
6268:
6264:
6263:
6255:
6252:
6247:
6246:
6223:
6219:
6213:
6209:
6200:
6182:
6178:
6172:
6168:
6157:
6156:
6151:
6145:
6142:
6137:
6133:
6129:
6125:
6121:
6117:
6113:
6109:
6105:
6101:
6100:
6092:
6085:
6083:
6079:
6071:
6067:
6063:
6059:
6055:
6051:
6047:
6043:
6039:
6034:
6029:
6026:(8): 080801.
6025:
6021:
6020:
6012:
6005:
6002:
5997:
5993:
5989:
5985:
5981:
5977:
5973:
5969:
5964:
5959:
5955:
5951:
5950:
5943:
5935:
5932:
5926:
5921:
5917:
5913:
5909:
5905:
5901:
5894:
5892:
5888:
5883:
5879:
5875:
5871:
5867:
5863:
5858:
5853:
5850:(7): 071801.
5849:
5845:
5841:
5834:
5832:
5830:
5826:
5813:
5809:
5805:
5799:
5796:
5791:
5785:
5781:
5777:
5773:
5772:
5764:
5761:
5748:
5744:
5740:
5734:
5731:
5718:
5714:
5710:
5704:
5701:
5688:
5684:
5680:
5674:
5671:
5658:
5654:
5650:
5644:
5641:
5628:
5624:
5620:
5614:
5611:
5606:
5602:
5598:
5591:
5588:
5583:
5577:
5573:
5569:
5565:
5564:
5559:
5553:
5551:
5547:
5544:
5530:
5526:
5525:
5520:
5516:
5510:
5507:
5494:
5490:
5486:
5480:
5478:
5476:
5472:
5466:
5458:
5454:
5453:his third law
5450:
5446:
5442:
5438:
5432:
5429:
5426:
5404:
5401:
5397:
5393:
5387:
5384:
5380:
5374:
5371:
5362:
5354:
5345:
5332:
5324:
5316:
5307:
5302:
5297:
5294:
5288:
5285:
5281:
5277:
5273:
5268:
5263:
5257:
5254:
5247:
5243:
5240:
5238:
5235:
5234:
5230:
5221:
5210:
5191:
5171:
5169:
5167:
5163:
5159:
5158:
5153:
5148:
5145:
5143:
5139:
5131:
5130:R. P. Feynman
5125:
5121:
5118:
5111:
5109:
5105:
5101:
5075:
5071:
5067:
5063:
5059:
5054:
5034:
5031:
5027:
5023:
5019:
5017:
5009:
5007:
5000:
4992:
4990:
4987:
4985:
4980:
4976:
4973:, physicists
4972:
4967:
4961:
4959:
4957:
4905:
4897:
4895:
4847:
4844:
4811:
4807:
4802:
4795:
4792:
4787:
4785:
4781:
4764:
4741:
4718:
4708:
4704:
4699:
4697:
4692:
4679:
4671:
4668:
4664:
4660:
4656:
4652:
4649:
4646:
4643:
4639:
4632:
4613:
4608:
4594:
4590:
4585:
4564:
4551:
4543:
4540:
4536:
4532:
4528:
4524:
4521:
4518:
4515:
4511:
4501:
4476:
4454:
4450:
4430:
4392:
4379:
4372:
4351:
4345:
4340:
4336:
4332:
4324:
4315:
4313:
4310:
4306:
4302:
4294:
4292:
4270:
4264:
4255:
4230:
4208:
4204:
4184:
4146:
4133:
4126:
4090:
4083:
4077:
4073:
4069:
4068:String theory
4065:
4061:
4051:
4043:
4041:
4033:
4029:
4026:
4023:
4020:
4019:
4015:
4012:
4009:
4006:
4005:
4001:
3997:
3994:
3991:
3988:
3987:
3983:
3980:
3977:
3974:
3973:
3969:
3965:
3962:
3959:
3956:
3955:
3951:
3947:
3944:
3941:
3938:
3937:
3933:
3930:
3927:
3924:
3923:
3919:
3916:
3913:
3910:
3909:
3905:
3902:
3899:
3896:
3895:
3891:
3888:
3885:
3882:
3881:
3877:
3874:
3871:
3868:
3867:
3863:
3860:
3857:
3854:
3853:
3849:
3846:
3843:
3840:
3839:
3835:
3832:
3829:
3826:
3825:
3821:
3818:
3815:
3812:
3811:
3807:
3804:
3801:
3798:
3797:
3793:
3790:
3787:
3784:
3783:
3779:
3776:
3773:
3770:
3769:
3765:
3762:
3757:
3754:
3750:
3747:
3746:
3737:
3735:
3733:
3729:
3720:
3711:
3701:
3696:
3691:
3689:
3685:
3680:
3676:
3672:
3663:
3660:extended the
3659:
3655:
3651:
3644:
3639:
3632:
3630:
3628:
3624:
3620:
3616:
3612:
3607:
3602:
3598:
3594:
3590:
3570:
3569:quantum loops
3566:
3562:
3561:electron mass
3554:
3550:
3546:
3542:
3534:
3532:
3530:
3526:
3510:
3506:
3502:
3498:
3461:
3384:
3380:
3279:
3275:
3259:
3254:
3250:
3244:
3240:
3233:
3230:
3224:
3221:
3201:
3197:
3191:
3187:
3183:
3180:
3175:
3171:
3162:
3146:
3143:
3138:
3134:
3130:
3125:
3121:
3112:
3108:
3104:
3100:
3097:
3093:
3089:
3085:
3081:
3073:
3069:
3066:unifying the
3065:
3061:
3058:
3054:
3042:
3038:
3034:
3026:
3022:
3015:
3012:
3005:
2998:
2989:
2985:
2977:
2972:
2964:
2960:
2956:
2941:
2938:
2935:
2926:
2905:
2897:
2893:
2883:
2874:
2870:
2866:
2861:
2853:
2850:
2838:
2834:
2829:
2820:
2810:
2806:
2797:
2776:
2767:
2763:
2760:
2751:
2743:
2739:
2734:
2728:
2723:
2705:
2701:
2693:
2690:
2687:
2682:
2676:
2668:
2660:
2651:
2643:
2613:
2609:
2592:
2586:
2578:
2574:
2570:
2567:
2561:
2557:
2551:
2545:
2538:
2533:
2527:
2522:
2518:
2514:
2511:
2505:
2501:
2495:
2489:
2486:
2481:
2478:
2475:
2469:
2463:
2458:
2454:
2450:
2447:
2441:
2437:
2431:
2426:
2421:
2417:
2414:
2408:
2397:
2391:
2386:
2382:
2378:
2375:
2369:
2365:
2359:
2351:
2348:
2340:
2339:
2331:
2326:
2322:
2317:
2313:
2306:
2302:
2301:
2298:
2297:
2295:
2281:
2279:
2250:
2235:
2232:
2199:
2184:
2182:
2167:
2154:
2150:
2138:
2134:
2126:
2122:
2118:
2110:
2083:
2068:
2066:
2062:
2057:
2055:
2032:
2019:
2013:
1981:
1975:
1966:
1958:
1953:
1950:
1945:
1937:
1933:
1929:
1926:
1921:
1914:
1912:
1899:
1894:
1891:
1886:
1883:
1870:
1866:
1859:
1855:
1851:, which sets
1850:
1845:
1830:
1822:
1817:
1801:
1795:
1792:
1786:
1782:
1776:
1773:
1763:
1759:
1752:
1747:
1742:
1729:
1723:
1714:
1710:
1704:
1701:
1688:
1682:
1674:
1672:
1670:
1666:
1640:
1630:
1613:
1606:
1584:
1580:
1576:
1571:
1564:
1544:
1537:
1517:
1510:
1509:
1508:
1494:
1488:
1480:
1476:
1472:
1469:
1463:
1459:
1453:
1447:
1444:
1439:
1435:
1431:
1425:
1421:
1415:
1412:
1400:
1392:
1390:
1388:
1383:
1381:
1377:
1373:
1369:
1364:
1360:of the atom.
1359:
1355:
1350:
1301:
1296:
1292:
1286:
1280:
1276:
1273:
1269:
1265:
1260:
1258:
1254:
1250:
1249:
1246:Greek letter
1239:
1235:
1231:
1219:
1214:
1212:
1207:
1205:
1200:
1199:
1197:
1196:
1190:
1185:
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1177:
1175:
1172:
1170:
1167:
1165:
1162:
1160:
1159:Zamolodchikov
1157:
1155:
1154:Zamolodchikov
1152:
1150:
1147:
1145:
1142:
1140:
1137:
1135:
1132:
1130:
1127:
1125:
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1120:
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987:
985:
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965:
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950:
947:
945:
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935:
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927:
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917:
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907:
905:
902:
900:
897:
895:
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890:
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885:
882:
880:
877:
875:
872:
870:
867:
865:
862:
860:
857:
855:
852:
850:
847:
845:
842:
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837:
835:
832:
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827:
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822:
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815:
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807:
805:
802:
800:
797:
795:
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787:
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747:
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742:
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712:
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495:
492:
490:
487:
486:
479:
478:
471:
468:
466:
463:
461:
458:
456:
455:Supersymmetry
453:
451:
450:String theory
448:
447:
441:
440:
433:
430:
428:
425:
423:
420:
418:
415:
414:
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137:
134:
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123:
117:
116:
113:
110:
109:
105:
100:
96:
95:
92:
88:
71:
70:
66:
61:
60:
44:
43:
39:
34:
33:
30:
19:
9001:
8983:
8976:Barrow, J.D.
8967:
8955:
8943:
8905:
8873:
8838:. Retrieved
8836:(in Serbian)
8833:
8824:
8797:
8791:
8770:
8765:Martin, A.D.
8755:
8747:
8743:
8735:
8710:
8699:
8676:
8663:
8635:
8619:(2): 71â104.
8616:
8612:
8602:
8593:
8583:
8550:
8544:
8538:
8525:
8516:
8475:
8469:
8463:
8420:
8416:
8409:
8380:
8374:
8364:
8346:
8337:
8324:
8271:
8265:
8255:
8243:. Retrieved
8238:
8229:
8217:. Retrieved
8213:
8192:1959.4/50886
8155:
8149:
8088:
8082:
8076:
8066:11 September
8064:. Retrieved
8058:
8048:
8005:
7999:
7993:
7950:
7946:
7936:
7885:
7879:
7858:. Retrieved
7853:ScienceDaily
7851:
7842:
7830:. Retrieved
7824:
7814:
7771:
7765:
7759:
7731:
7724:
7697:
7693:
7687:
7642:
7636:
7626:
7575:
7569:
7562:
7511:
7505:
7498:
7455:
7449:
7443:
7398:
7392:
7382:
7331:
7325:
7319:
7274:
7268:
7258:
7215:
7209:
7203:
7176:
7170:
7139:
7133:
7110:
7104:
7077:
7071:
7028:
7022:
7016:
6973:
6967:
6961:
6936:
6930:
6921:
6896:
6890:
6881:
6848:
6842:
6833:
6820:
6817:Milne, E. A.
6811:
6760:
6754:
6748:
6705:
6699:
6693:
6684:
6676:
6643:
6639:
6618:. Retrieved
6610:
6601:
6579:(17): 1â94.
6576:
6572:
6555:
6545:
6539:
6533:
6516:
6507:
6501:
6484:
6441:
6437:
6431:
6406:
6400:
6394:
6361:
6357:
6351:
6300:
6294:
6288:
6276:. Retrieved
6261:
6254:
6244:
6159:
6154:
6144:
6103:
6097:
6023:
6017:
6004:
5953:
5947:
5941:
5934:
5907:
5903:
5847:
5843:
5816:. Retrieved
5807:
5798:
5770:
5763:
5751:. Retrieved
5742:
5733:
5721:. Retrieved
5712:
5703:
5691:. Retrieved
5682:
5673:
5661:. Retrieved
5652:
5643:
5631:. Retrieved
5622:
5613:
5600:
5590:
5562:
5542:
5533:. Retrieved
5528:
5522:
5509:
5497:. Retrieved
5488:
5431:
5403:
5391:
5386:
5373:
5360:
5352:
5343:
5330:
5322:
5314:
5305:
5300:
5296:
5287:
5266:
5256:
5219:
5200:
5176:
5155:
5154:in his book
5149:
5146:
5135:
5122:
5116:
5113:
5102:
5055:
5020:
5013:
4996:
4988:
4983:
4979:S.M. Carroll
4970:
4968:
4965:
4903:
4901:
4803:
4788:
4786:are robust.
4783:
4779:
4762:
4739:
4716:
4702:
4700:
4695:
4693:
4591:, using the
4588:
4586:
4565:
4349:
4343:
4329:. Using the
4316:
4298:
4088:
4084:
4064:astrophysics
4053:
4039:
4031:
4016:CODATA 2022
3999:
3984:CODATA 2018
3967:
3966:Parker, Yu,
3949:
3934:CODATA 2014
3920:CODATA 2010
3878:CODATA 2006
3850:CODATA 2002
3836:CODATA 1998
3808:CODATA 1986
3794:CODATA 1973
3780:CODATA 1969
3760:
3752:
3718:
3709:
3699:
3692:
3647:
3629:expansions.
3627:perturbative
3608:
3600:
3599:measures an
3553:energy scale
3538:
3509:power series
3505:perturbative
3494:
3084:gauge fields
3013:
3010:
3003:
2996:
2987:
2975:
2962:
2732:
2726:
2649:
2641:
2336:
2324:
2320:
2285:
2269:
2248:
2233:
2218:
2197:
2179:tenth-order
2165:
2152:
2102:
2081:
2058:
2030:
2017:
2014:
2003:
1979:
1973:
1964:
1956:
1948:
1941:
1868:
1864:
1857:
1853:
1849:atomic units
1846:
1828:
1820:
1761:
1757:
1750:
1743:
1686:
1678:
1662:
1582:
1578:
1574:
1557:10 Jâ
Hz
1396:
1384:
1362:
1351:
1294:
1290:
1284:
1274:
1261:
1247:
1237:
1233:
1227:
1188:
1034:Stueckelberg
764:Jona-Lasinio
339:Vacuum state
324:Quantization
161:Gauge theory
141:Strong force
126:Field theory
64:
37:
29:
9006:Brady Haran
8705:Hawking, S.
8669:Good, I. J.
8214:Physics.org
7739:. pp.
6195:nennen wir
5531:(51): 51â52
4956:dark energy
4782:and Murphy
3623:Landau pole
2984:Bohr radius
2689:rest energy
2661:in vacuum,
2614:, which is
1915:Measurement
1654:10 Fâ
m
1599:10 Jâ
s
1174:Zinn-Justin
1024:Sommerfield
949:Pomeranchuk
914:Osterwalder
909:Oppenheimer
839:ĆopuszaĆski
659:Fredenhagen
460:Technicolor
9021:Categories
8956:Good Reads
8804:. p.
8761:Halzen, F.
8430:2204.02930
8390:2008.10619
8281:2003.07627
8239:Antarctica
8158:(Thesis).
7860:30 January
7832:30 January
6770:1812.04130
6715:1712.06060
6409:(7): 969.
5857:2209.13084
5814:. May 2024
5778:. p.
5749:. May 2024
5719:. May 2024
5689:. May 2024
5659:. May 2024
5629:. May 2024
5570:. p.
5535:6 December
5495:. May 2024
5467:References
5457:I. J. Good
5162:multiverse
5138:I. J. Good
5056:Physicist
4705:have used
4078:(not just
3822:Kinoshita
3662:Bohr model
3656:in 1887,
3582:137.03600
3515:. Because
3383:feynmanium
2982:, and the
2667:Sommerfeld
2665:. This is
2311:apart, and
2061:reciprocal
1663:Since the
1393:Definition
1358:Bohr model
1169:Zimmermann
1064:Vainshtein
939:Polchinski
799:Kontsevich
744:Iliopoulos
719:Heisenberg
544:Bogoliubov
482:Scientists
319:Propagator
201:T-symmetry
196:P-symmetry
191:C-symmetry
179:Symmetries
136:Weak force
120:Background
8575:125122360
8455:247996839
8330:Orzel, C.
8178:CiteSeerX
8165:1202.6365
8098:1008.3907
8040:118077783
7985:206511320
7806:119337838
7707:0910.2699
7585:0708.3677
7008:118684485
6927:Gamow, G.
6887:Gamow, G.
6740:118922814
6668:118031104
6310:0803.3718
6136:227259475
6033:1012.3627
5963:1205.5368
5437:Kirchhoff
5248:Footnotes
5070:Carl Jung
4918:, namely
4669:−
4661:×
4650:±
4644:−
4614:α
4609:α
4606:Δ
4541:−
4533:×
4522:±
4516:−
4477:α
4455:α
4451:−
4431:α
4380:α
4373:α
4370:Δ
4342:0.5 <
4339:redshifts
4231:α
4209:α
4205:−
4185:α
4134:α
4127:α
4124:Δ
4060:cosmology
4034:. (2023)
4021:2023 Feb
4007:2022 Dec
4002:. (2020)
3989:2020 Dec
3975:2019 May
3970:. (2018)
3957:2018 Dec
3952:. (2017)
3939:2017 Jul
3925:2015 Jun
3911:2011 Jun
3897:2010 Dec
3883:2008 Jul
3869:2008 Jun
3855:2007 Jul
3827:2000 Apr
3799:1987 Jan
3771:1969 Jul
3671:Bohr atom
3650:Michelson
3606:â 1/127.
3601:effective
3222:α
3135:μ
3037:electrons
2939:α
2871:α
2851:α
2702:α
2657:, to the
2584:ℏ
2575:ε
2571:π
2543:ℏ
2534:×
2519:ε
2515:π
2479:π
2470:×
2455:ε
2451:π
2422:λ
2383:ε
2379:π
2349:α
2145:electron
1884:α
1796:π
1774:α
1721:ℏ
1702:α
1623: mâ
s
1530:10 C
1486:ℏ
1477:ε
1473:π
1436:ε
1413:α
1382:in 1887.
1376:Michelson
1277:with the
1104:Wetterich
1089:Weisskopf
1039:Sudarshan
989:Schwinger
899:Nishijima
864:Maldacena
829:Leutwyler
789:Kinoshita
689:Goldstone
679:Gell-Mann
594:Doplicher
361:Equations
62:Value of
35:Value of
9008:for the
8996:(2009).
8930:Archived
8928:. 2010.
8861:(1973).
8767:(1984).
8707:(1988).
8671:(1990).
8643:p.
8508:33396683
8500:11797744
8383:: 1â21.
8316:32917582
8141:23236775
8133:22181590
7977:18323415
7928:43502450
7920:17501040
7679:10476451
7618:29266168
7610:18233422
7554:29581666
7546:15089663
7490:17863903
7435:13182756
7374:40461557
7366:11531558
7311:14294586
7250:55638644
7063:15435796
7031:: 3â20.
6819:(1935).
6795:29650669
6660:41134170
6620:11 April
6563:(1916).
6528:(1887).
6496:(1887).
6476:18481179
6335:18388259
6278:20 April
6236:we call
6152:(1921).
6128:33268866
6070:Archived
6066:47470092
6058:21405559
5996:14712017
5988:23005618
5882:36867820
5560:(1985).
5517:(1916).
5425:Max Born
5278:and the
5231:See also
5223:â
5212:â
5193:â
5127:â
5074:Max Born
4975:C. Orzel
3766:Sources
3565:positron
3368:4 (1 + Ï
3278:graphene
3159:and the
2686:electron
2137:electron
2125:electron
1936:positron
1932:electron
1262:It is a
1251:), is a
1119:Wightman
1084:Weinberg
1074:Virasoro
1054:Tomonaga
1049:Thirring
1044:Symanzik
1004:Semenoff
979:Schrader
944:Polyakov
859:Majorana
794:Klebanov
749:Ivanenko
739:'t Hooft
709:Guralnik
654:Fröhlich
649:Fritzsch
644:Frampton
559:Buchholz
504:Bargmann
494:Anderson
274:Crossing
8840:28 June
8719:, 125.
8596:(2705).
8567:3609461
8480:Bibcode
8435:Bibcode
8423:: A57.
8307:7182409
8286:Bibcode
8245:26 July
8219:27 July
8170:Bibcode
8103:Bibcode
8020:Bibcode
7955:Bibcode
7947:Science
7900:Bibcode
7786:Bibcode
7741:139â140
7712:Bibcode
7700:: 864.
7657:Bibcode
7590:Bibcode
7526:Bibcode
7470:Bibcode
7413:Bibcode
7346:Bibcode
7289:Bibcode
7230:Bibcode
7148:Bibcode
7115:Vintage
7084:Bibcode
7043:Bibcode
6988:Bibcode
6941:Bibcode
6901:Bibcode
6873:4106534
6853:Bibcode
6803:4875011
6775:Bibcode
6756:Science
6720:Bibcode
6581:Bibcode
6456:Bibcode
6411:Bibcode
6386:2317589
6366:Bibcode
6343:3024573
6315:Bibcode
6296:Science
6108:Bibcode
6038:Bibcode
5968:Bibcode
5912:Bibcode
5862:Bibcode
5421:
5409:
5365:
5353:πe
5348:
5327:
5315:πe
5310:
5098:
5086:
5051:
5037:
5030:integer
4939:
4920:
4892:
4873:
4869:
4850:
4832:√
4829:⁄
4776:
4757:
4753:
4734:
4730:
4711:
4348:, Webb
4335:quasars
4307:in the
3948:Aoyama
3723:
3706:
3673:to the
3633:History
3597:instead
3589:Z boson
3585:
3573:
3455:
3436:
3433:
3415:
3411:
3392:
3375:
3356:
3350:
3334:
3328:
3309:
3297:
3283:
3062:In the
3041:photons
2740:in the
2654:
2638:
2635:
2617:
2328:(or of
2258:137.035
2253:
2239:
2207:137.035
2202:
2188:
2149:-factor
2135:of the
2123:of the
2119:or the
2091:137.035
2086:
2072:
1984:
1961:
1923:Eighth-
1825:√
1657:
1637:is the
1626:
1610:is the
1602:
1568:is the
1560:
1541:is the
1533:
1514:is the
1370:of the
1338:
1328:137.035
1318:
1230:physics
1129:Wilczek
1094:Wentzel
1069:Veltman
1014:Shirkov
1009:Shifman
999:Seiberg
984:Schwarz
964:Rubakov
884:Naimark
834:Lipatov
824:Lehmann
804:Kreimer
784:Kendall
674:Gelfand
669:Glashow
629:Feynman
609:Faddeev
604:Englert
574:Coleman
564:Cachazo
549:Brodsky
534:Bjorken
524:Berezin
514:Belavin
254:Anomaly
112:History
73:137.035
8947:Paris.
8888:
8812:
8779:
8723:
8687:
8651:
8573:
8565:
8506:
8498:
8453:
8314:
8304:
8180:
8139:
8131:
8038:
7983:
7975:
7926:
7918:
7804:
7747:
7677:
7616:
7608:
7552:
7544:
7488:
7433:
7372:
7364:
7309:
7248:
7191:
7158:
7121:
7061:
7006:
6871:
6844:Nature
6801:
6793:
6738:
6666:
6658:
6474:
6384:
6341:
6333:
6269:
6240:.]
6134:
6126:
6099:Nature
6064:
6056:
5994:
5986:
5880:
5818:18 May
5786:
5753:18 May
5723:18 May
5693:18 May
5663:18 May
5633:18 May
5578:
5499:18 May
5459:(1990)
5449:Kepler
5441:Balmer
5344:α
5338:
5334:
5306:α
5172:Quotes
4971:et al.
4904:et al.
4784:et al.
4780:et al.
4703:et al.
4696:et al.
4677:
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