1430:
31:
1374:, itself a constant of nature, approx. 1.44 solar masses) and an electron approximates to 10, an interesting variation on the 10 and 10 that are typically associated with Dirac and Eddington respectively. (The physics defining the Chandrasekhar mass produces a ratio that is the â3/2 power of the gravitational fine-structure constant, 10.)
1330:: In 1978, G. Blake argued that paleontological data is consistent with the "multiplicative" scenario but not the "additive" scenario. Arguments both for and against LNH are also made from astrophysical considerations. For example, D. Falik argued that LNH is inconsistent with experimental results for
274:
1369:
Various authors have introduced new sets of numbers into the original "coincidence" considered by Dirac and his contemporaries, thus broadening or even departing from Dirac's own conclusions. Jordan (1947) noted that the mass ratio for a typical star (specifically, a star of the
503:
392:
725:
1414:(for example Planck density). This ratio of densities, and other ratios (using four fundamental constants: speed of light in vacuum c, Newtonian constant of gravity G, reduced Planck constant â, and Hubble constant H) computes to an exact number,
1090:
1309:
Dirac's theory has inspired and continues to inspire a significant body of scientific literature in a variety of disciplines, with it sparking off many speculations, arguments and new ideas in terms of applications. In the context of
1292:
that describes the structure of spacetime in terms of a ratio of gravitational and electromagnetic units. He also provided alternative scenarios for the continuous creation of matter, one of the other significant issues in LNH:
921:
173:
577:
817:
1326:
demonstrated in 1962 how a simple revision of the parameters (in this case, the age of the Solar System) can invalidate Teller's conclusions. The debate is further complicated by the choice of LNH
398:
285:
631:
1210:
142:
107:
1559:
1268:
1177:
1150:
1886:
58:
in the present cosmological epoch. According to Dirac's hypothesis, the apparent similarity of these ratios might not be a mere coincidence but instead could imply a
1007:
1234:
1116:
948:
2224:
2154:
851:
751:. For Milne, space was not a structured object but simply a system of reference in which relations such as this could accommodate Einstein's conclusions:
269:{\displaystyle {\frac {R_{\text{U}}}{r_{\text{e}}}}\approx {\frac {r_{\text{H}}}{r_{\text{e}}}}\approx 4.1666763\cdot 10^{42}\approx 10^{42.62\ldots },}
156:
LNH was Dirac's personal response to a set of large number "coincidences" that had intrigued other theorists of his time. The "coincidences" began with
1455:
508:
1429:
2464:
1706:
1669:
757:
2439:
1318:
seemed to raise a serious objection to LNH in 1948 when he argued that variations in the strength of gravity are not consistent with
2429:
167:, might also be the hypothetical radius of a particle whose rest energy is equal to the gravitational self-energy of the electron:
2474:
1395:
1443:
498:{\displaystyle r_{\text{H}}={\frac {e^{2}}{4\pi \epsilon _{0}\ m_{\text{H}}c^{2}}}\approx 1.5671987\cdot 10^{27}\,\mathrm {m} }
387:{\displaystyle r_{\text{e}}={\frac {e^{2}}{4\pi \epsilon _{0}\ m_{\text{e}}c^{2}}}\approx 3.7612682\cdot 10^{-16}\mathrm {m} }
1410:
in the universe. Valev (2019) found an equation connecting cosmological parameters (for example density of the universe) and
1331:
2434:
1960:
V. Canuto, S. Hsieh (1978). "The 3 K blackbody radiation, Dirac's Large
Numbers Hypothesis, and scale-covariant cosmology".
747:
a few years before Dirac formulated LNH. Milne was inspired not by large number coincidences but by a dislike of
Einstein's
1350:, it simply states that the large numbers in LNH are a necessary coincidence for intelligent beings since they parametrize
2312:
1383:
55:
748:
720:{\displaystyle {\frac {e^{2}}{4\pi \epsilon _{0}\ Gm_{\text{e}}^{2}}}\approx 4.1666763\cdot 10^{42}\approx {\sqrt {N}}}
2479:
2459:
1722:
J. P.Uzan (2003). "The fundamental constants and their variation, Observational status and theoretical motivations".
1274:
noted that such a temporal variation does not necessarily follow from Dirac's assumptions, a corresponding change of
2310:
C.-G. Shao; J. Shen; B. Wang; R.-K. Su (2006). "Dirac
Cosmology and the Acceleration of the Contemporary Universe".
1694:
1657:
845:
The Weyl and
Eddington ratios above can be rephrased in a variety of ways, as for instance in the context of time:
1418:. This provides evidence of the Dirac large numbers hypothesis by connecting the macro-world and the micro-world.
1382:
Several authors have recently identified and pondered the significance of yet another large number, approximately
1282:
is constant, otherwise the law of conserved energy is violated. Dirac met this difficulty by introducing into the
2099:
2003:
1962:
1925:
1724:
590:
1283:
732:
1636:
1213:
67:
1858:
1398:
identified 10 with the ratio of the universe's volume to the volume of a typical nucleon bounded by its
1391:
1343:
1182:
983:
2484:
2395:
2374:
A. Unzicker (2009). "A Look at the
Abandoned Contributions to Cosmology of Dirac, Sciama and Dicke".
2331:
2282:
2233:
2194:
2163:
2049:
2012:
1971:
1934:
1895:
1827:
1790:
1743:
1568:
1557:
A. Eddington (1931). "Preliminary Note on the Masses of the
Electron, the Proton, and the Universe".
1531:
1490:
114:
77:
2469:
1390:, which Nottale (1993) and Matthews (1997) associated in an LNH context with a scaling law for the
1371:
1347:
744:
736:
71:
1239:
1155:
1128:
2411:
2385:
2376:
2360:
2347:
2321:
2298:
2272:
2249:
2210:
2129:
1759:
1733:
1584:
1522:
1481:
1399:
1300:'multiplicative' creation (new matter is created where there are already concentrations of mass).
979:
59:
1778:
1698:
1606:
2128:
H. Lyre (2003). "C. F. Weizsäcker's
Reconstruction of Physics: Yesterday, Today and Tomorrow".
2263:
1862:
1702:
1665:
1449:
1661:
1651:
147:
Physical constants are actually not constant. Their values depend on the age of the
Universe.
2403:
2339:
2290:
2241:
2202:
2185:
2171:
2108:
2057:
2020:
1979:
1942:
1903:
1835:
1798:
1751:
1576:
1539:
1498:
1085:{\displaystyle {\frac {e^{2}}{4\pi \epsilon _{0}Gm_{\text{p}}m_{\text{e}}}}\approx 10^{40}.}
618:
1818:
1096:
2399:
2335:
2286:
2237:
2198:
2167:
2053:
2016:
1975:
1938:
1899:
1831:
1794:
1747:
1572:
1535:
1494:
1687:
1435:
1351:
1219:
1101:
951:
933:
625:, the estimated number of charged particles in the universe, with the following ratio:
54:
to that of force scales. The ratios constitute very large, dimensionless numbers: some
2343:
2261:
G. A. Mena
Marugan; S. Carneiro (2002). "Holography and the large number hypothesis".
2076:
1386:. This is for example the ratio of the theoretical and observational estimates of the
17:
2453:
2351:
2302:
2253:
1763:
1653:
Cosmology and
Controversy: The historical development of two theories of the universe
1588:
1387:
1338:
consistent. One argument that has created significant controversy was put forward by
1315:
987:
916:{\displaystyle {\frac {c\,t}{r_{\text{e}}}}\approx 3.47\cdot 10^{41}\approx 10^{42},}
2444:
2415:
1923:
D. Falik (1979). "Primordial Nucleosynthesis and Dirac's Large Numbers Hypothesis".
731:
In addition to the examples of Weyl and Eddington, Dirac was also influenced by the
2214:
1411:
1339:
1323:
1319:
1271:
157:
2359:
S. Ray; U. Mukhopadhyay; P. P. Ghosh (2007). "Large Number Hypothesis: A Review".
1407:
2294:
2222:
P. A. M. Dirac (1974). "Cosmological Models and the Large Numbers Hypothesis".
2113:
2094:
2077:"Mach's Principle, Dirac's Large Numbers and the Cosmological Constant Problem"
30:
1908:
1881:
1802:
1755:
1580:
1425:
1311:
111:
The mass of the universe is proportional to the square of the universe's age:
47:
2407:
2061:
1543:
1502:
1327:
2245:
2175:
1839:
1777:
Saibal, Ray; Mukhopadhyay, Utpal; Ray, Soham; Bhattacharjee, Arjak (2019).
572:{\displaystyle m_{\text{H}}c^{2}={\frac {Gm_{\text{e}}^{2}}{r_{\text{e}}}}}
1297:'additive' creation (new matter is created uniformly throughout space) and
739:, who lectured on the topic in Cambridge in 1933. The notion of a varying-
2134:
1458: â Hypothetical conflict with the laws of physics as currently known
1355:
1119:
998:
51:
1779:"Dirac's large number hypothesis: A journey from concept to implication"
1738:
2326:
2277:
978:, the age of the universe is about 10 units of time. This is the same
2206:
994:
1517:
1476:
1402:, and he identified this ratio with the sum of elementary events or
2025:
1998:
1983:
1946:
2390:
2365:
990:
812:{\displaystyle G=\left(\!{\frac {c^{3}}{M_{\text{U}}}}\!\right)t,}
29:
1999:"Primordial nucleosynthesis and Dirac's large numbers hypothesis"
160:(1919), who speculated that the observed radius of the universe,
1866:
1363:
1359:
1123:
840:
1403:
1278:
has not been found. According to general relativity, however,
1287:
27:
Hypothesis relating age of the universe to physical constants
1882:"The Large Numbers Hypothesis and the rotation of the Earth"
2430:
Audio of Dirac talking about the large numbers hypothesis
1816:
E. Teller (1948). "On the change of physical constants".
1216:
is approximately 10. Dirac interpreted this to mean that
1179:
of the proton and electron, and the permittivity factor
961:
is the classical electron radius. Hence, in units where
833:
is the age of the universe. According to this relation,
841:
Dirac's interpretation of the large number coincidences
2183:
P. A. M. Dirac (1937). "The Cosmological Constants".
1242:
1222:
1185:
1158:
1131:
1104:
1010:
936:
854:
760:
634:
511:
401:
288:
176:
117:
80:
2440:
Robert Matthews: Dirac's coincidences sixty years on
2152:
P. A. M. Dirac (1938). "A New Basis for Cosmology".
607:denotes the mass of the hypothetical particle, and
1686:
1560:Proceedings of the Cambridge Philosophical Society
1262:
1228:
1204:
1171:
1144:
1110:
1084:
942:
915:
811:
719:
571:
497:
386:
268:
136:
101:
1887:Monthly Notices of the Royal Astronomical Society
797:
772:
1518:"Eine neue Erweiterung der Relativitätstheorie"
1212:in atomic units (equal to 1), the value of the
66:The strength of gravity, as represented by the
50:in 1937 relating ratios of size scales in the
2040:P. Jordan (1947). "Die Herkunft der Sterne".
8:
2225:Proceedings of the Royal Society of London A
2155:Proceedings of the Royal Society of London A
1607:"Evidence of Dirac large numbers hypothesis"
2389:
2364:
2325:
2276:
2133:
2112:
2024:
1907:
1783:International Journal of Modern Physics D
1737:
1252:
1241:
1221:
1196:
1184:
1163:
1157:
1136:
1130:
1103:
1073:
1057:
1047:
1034:
1017:
1011:
1009:
935:
904:
891:
870:
861:
855:
853:
789:
779:
773:
759:
710:
701:
679:
674:
658:
641:
635:
633:
617:The coincidence was further developed by
561:
550:
545:
535:
526:
516:
510:
490:
489:
483:
461:
451:
438:
421:
415:
406:
400:
379:
370:
348:
338:
325:
308:
302:
293:
287:
254:
241:
220:
210:
204:
193:
183:
177:
175:
128:
116:
98:
90:
79:
1334:whereas Canuto and Hsieh argued that it
1633:Relativity, Gravity and World Structure
1467:
1456:Time-variation of fundamental constants
1446: â Physical constant with no units
743:cosmology first appears in the work of
621:(1931) who related the above ratios to
1305:Later developments and interpretations
2445:The Mysterious EddingtonâDirac Number
2095:"Dirac's coincidences sixty years on"
7:
1600:
1598:
1614:Proceedings of the Romanian Academy
1452: â Unsolved problem in physics
70:, is inversely proportional to the
2435:Full transcript of Dirac's speech.
1205:{\displaystyle 4\pi \epsilon _{0}}
491:
380:
25:
1428:
829:is the mass of the universe and
1444:Dimensionless physical constant
1332:microwave background radiation
137:{\displaystyle M\propto t^{2}}
102:{\displaystyle G\propto 1/t\,}
40:Dirac large numbers hypothesis
1:
2313:Classical and Quantum Gravity
1805:– via World Scientific.
1689:Dirac: A Scientific Biography
1396:Carl Friedrich von Weizsäcker
614:is its electrostatic radius.
600:is the mass of the electron,
62:with these unusual features:
2465:Obsolete scientific theories
1997:V. Canuto, S. Hsieh (1980).
1388:energy density of the vacuum
1263:{\displaystyle G\approx 1/t}
1172:{\displaystyle m_{\text{e}}}
1145:{\displaystyle m_{\text{p}}}
930:is the age of the universe,
749:general theory of relativity
46:) is an observation made by
2344:10.1088/0264-9381/23/11/003
1366:would not arise otherwise.
2501:
2295:10.1103/PhysRevD.65.087303
2100:Astronomy & Geophysics
1695:Cambridge University Press
1658:Princeton University Press
1288:
2042:Astronomische Nachrichten
2004:The Astrophysical Journal
1963:The Astrophysical Journal
1926:The Astrophysical Journal
1803:10.1142/S0218271819300143
1756:10.1103/RevModPhys.75.403
1725:Reviews of Modern Physics
1581:10.1017/S0305004100009269
1477:"Zur Gravitationstheorie"
591:classical electron radius
2408:10.1002/andp.20095210108
2114:10.1093/astrog/39.6.6.19
2062:10.1002/asna.19472751012
1544:10.1002/andp.19193641002
1503:10.1002/andp.19173591804
1284:Einstein field equations
1095:Hence, interpreting the
733:primeval-atom hypothesis
2475:Astronomical hypotheses
1909:10.1093/mnras/185.2.399
1637:Oxford University Press
1384:120 orders of magnitude
1362:and hence carbon-based
2246:10.1098/rspa.1974.0095
2176:10.1098/rspa.1938.0053
1840:10.1103/PhysRev.73.801
1789:(8): 1930014â1930096.
1342:in 1961. Known as the
1264:
1230:
1214:gravitational constant
1206:
1173:
1146:
1112:
1086:
944:
917:
813:
721:
573:
499:
388:
270:
138:
103:
68:gravitational constant
56:40 orders of magnitude
35:
18:EddingtonâDirac number
1392:cosmological constant
1344:anthropic coincidence
1265:
1231:
1207:
1174:
1147:
1113:
1087:
945:
918:
837:increases over time.
814:
722:
574:
500:
389:
271:
139:
104:
33:
2093:R. Matthews (1998).
1861:. pp. 138â141.
1631:E. A. Milne (1935).
1240:
1236:varies with time as
1220:
1183:
1156:
1129:
1102:
1008:
982:as the ratio of the
934:
852:
758:
632:
509:
399:
286:
174:
115:
78:
2400:2009AnP...521...57U
2336:2006CQGra..23.3707S
2287:2002PhRvD..65h7303M
2238:1974RSPSA.338..439D
2199:1937Natur.139..323D
2168:1938RSPSA.165..199D
2054:1947dhds.book.....J
2017:1980ApJ...239L..91C
1976:1978ApJ...224..302C
1939:1979ApJ...231L...1F
1900:1978MNRAS.185..399B
1832:1948PhRv...73..801T
1795:2019IJMPD..2830014R
1748:2003RvMP...75..403U
1573:1931PCPS...27...15E
1536:1919AnP...364..101W
1495:1917AnP...359..117W
1348:fine-tuned universe
745:Edward Arthur Milne
684:
555:
72:age of the universe
2480:1937 introductions
2460:Physical cosmology
2377:Annalen der Physik
1523:Annalen der Physik
1482:Annalen der Physik
1400:Compton wavelength
1372:Chandrasekhar mass
1260:
1226:
1202:
1169:
1142:
1108:
1082:
980:order of magnitude
940:
913:
809:
717:
670:
569:
541:
495:
384:
266:
134:
99:
36:
2320:(11): 3707â3720.
2264:Physical Review D
2232:(1615): 439â446.
1880:G. Blake (1978).
1853:G. Gamow (1962).
1708:978-0-521-38089-8
1685:H. Kragh (1990).
1671:978-0-691-02623-7
1650:H. Kragh (1996).
1605:D. Valev (2019).
1450:Hierarchy problem
1286:a gauge function
1229:{\displaystyle G}
1166:
1139:
1111:{\displaystyle e}
1064:
1060:
1050:
943:{\displaystyle c}
876:
873:
795:
792:
715:
686:
677:
666:
567:
564:
548:
519:
468:
454:
446:
409:
355:
341:
333:
296:
226:
223:
213:
199:
196:
186:
16:(Redirected from
2492:
2419:
2393:
2370:
2368:
2355:
2329:
2306:
2280:
2257:
2218:
2207:10.1038/139323a0
2179:
2162:(921): 199â208.
2140:
2139:
2137:
2135:quant-ph/0309183
2125:
2119:
2118:
2116:
2090:
2084:
2083:
2081:
2072:
2066:
2065:
2037:
2031:
2030:
2028:
1994:
1988:
1987:
1957:
1951:
1950:
1920:
1914:
1913:
1911:
1877:
1871:
1870:
1850:
1844:
1843:
1813:
1807:
1806:
1774:
1768:
1767:
1741:
1719:
1713:
1712:
1692:
1682:
1676:
1675:
1647:
1641:
1640:
1628:
1622:
1621:
1611:
1602:
1593:
1592:
1554:
1548:
1547:
1516:H. Weyl (1919).
1513:
1507:
1506:
1475:H. Weyl (1917).
1472:
1438:
1433:
1432:
1417:
1314:, for instance,
1291:
1290:
1269:
1267:
1266:
1261:
1256:
1235:
1233:
1232:
1227:
1211:
1209:
1208:
1203:
1201:
1200:
1178:
1176:
1175:
1170:
1168:
1167:
1164:
1151:
1149:
1148:
1143:
1141:
1140:
1137:
1117:
1115:
1114:
1109:
1091:
1089:
1088:
1083:
1078:
1077:
1065:
1063:
1062:
1061:
1058:
1052:
1051:
1048:
1039:
1038:
1022:
1021:
1012:
977:
967:
949:
947:
946:
941:
922:
920:
919:
914:
909:
908:
896:
895:
877:
875:
874:
871:
865:
856:
818:
816:
815:
810:
802:
798:
796:
794:
793:
790:
784:
783:
774:
737:Georges LemaĂŽtre
726:
724:
723:
718:
716:
711:
706:
705:
687:
685:
683:
678:
675:
664:
663:
662:
646:
645:
636:
619:Arthur Eddington
578:
576:
575:
570:
568:
566:
565:
562:
556:
554:
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546:
536:
531:
530:
521:
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501:
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487:
469:
467:
466:
465:
456:
455:
452:
444:
443:
442:
426:
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416:
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410:
407:
393:
391:
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383:
378:
377:
356:
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353:
352:
343:
342:
339:
331:
330:
329:
313:
312:
303:
298:
297:
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275:
273:
272:
267:
262:
261:
246:
245:
227:
225:
224:
221:
215:
214:
211:
205:
200:
198:
197:
194:
188:
187:
184:
178:
143:
141:
140:
135:
133:
132:
108:
106:
105:
100:
94:
21:
2500:
2499:
2495:
2494:
2493:
2491:
2490:
2489:
2450:
2449:
2426:
2373:
2358:
2309:
2260:
2221:
2182:
2151:
2148:
2146:Further reading
2143:
2127:
2126:
2122:
2092:
2091:
2087:
2079:
2074:
2073:
2069:
2039:
2038:
2034:
1996:
1995:
1991:
1959:
1958:
1954:
1922:
1921:
1917:
1879:
1878:
1874:
1852:
1851:
1847:
1819:Physical Review
1815:
1814:
1810:
1776:
1775:
1771:
1721:
1720:
1716:
1709:
1684:
1683:
1679:
1672:
1649:
1648:
1644:
1630:
1629:
1625:
1609:
1604:
1603:
1596:
1556:
1555:
1551:
1530:(10): 101â133.
1515:
1514:
1510:
1489:(18): 117â145.
1474:
1473:
1469:
1465:
1434:
1427:
1424:
1415:
1380:
1322:data. However,
1320:paleontological
1307:
1238:
1237:
1218:
1217:
1192:
1181:
1180:
1159:
1154:
1153:
1132:
1127:
1126:
1100:
1099:
1069:
1053:
1043:
1030:
1023:
1013:
1006:
1005:
975:
969:
962:
960:
932:
931:
900:
887:
866:
857:
850:
849:
843:
828:
785:
775:
771:
767:
756:
755:
697:
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1324:George Gamow
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1408:information
1328:cosmologies
1270:. Although
2470:Paul Dirac
2454:Categories
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1463:References
1312:geophysics
993:between a
984:electrical
152:Background
48:Paul Dirac
34:Paul Dirac
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