1235:
Despite its common description, it has been noted that the conjecture is not entirely defined within the realms of Nelson's stochastic mechanics, but can also be thought of as a means of inquiring into the statistical effects of interaction with distant masses in the universe and was expected by
929:
then the order of magnitude of the associated angular momentum has the same value. Calogero himself suggests that these findings, originally based on the simplified model of the universe "are affected (and essentially, unaffected) by the possible presence in the mass of the
Universe of a large
106:
1124:
1032:
1253:
in which he discussed the compatibility of the conjecture with present bounds on variation of fundamental constants, but also outlined his focus on the modification of the relation between
1257:
and distance, and of the estimations attained from observations of elapsed time from the production of cosmic radiation and implications—both being related also, to the observed
1207:
1229:
1176:
1151:
891:
372:
873:
580:
124:
36:
353:
536:
459:
1249:
After the publication of
Calogero's original paper, " osmic origin of quantization" a response was published by Giuseppe Gaeta of the
1043:
119:
208:
315:
295:
866:
163:
285:
1250:
555:
939:
595:
333:
233:
348:
531:
526:
497:
129:
310:
300:
565:
482:
1452:
859:
511:
430:
516:
477:
405:
328:
188:
914:
is a fluctuating space-time, and that there are further mathematical relations between the involved quantities.
600:
911:
769:
487:
445:
395:
343:
109:
1154:
895:
774:
492:
400:
320:
290:
253:
243:
228:
155:
1457:
804:
560:
472:
198:
922:
659:
467:
385:
213:
193:
145:
1431:
903:
380:
305:
238:
150:
1423:
1390:
1342:
1307:
899:
814:
789:
729:
724:
624:
590:
570:
168:
27:
1290:
Gaeta, Giuseppe (2000-06-28). "On the cosmological implications of the
Calogero conjecture".
1415:
1382:
1334:
1299:
918:
819:
809:
799:
699:
679:
664:
634:
502:
390:
1209:
represents the radius of the universe accessible by gravitational interactions in time, t.
1183:
926:
844:
714:
694:
440:
280:
1236:
Calogero himself to be within the same order of magnitude as quantum mechanical effects.
1214:
1161:
1136:
779:
739:
719:
689:
669:
619:
585:
435:
425:
218:
1338:
1446:
1435:
907:
839:
834:
764:
734:
704:
575:
521:
248:
223:
933:
Essentially, the relation explained by
Calogero can be expressed with the formulas:
829:
824:
759:
744:
709:
203:
925:
provides an action purported by that motion within the order of magnitude of the
794:
749:
684:
639:
1419:
1386:
1303:
1258:
784:
754:
674:
649:
644:
629:
1427:
1394:
1346:
1311:
101:{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }
275:
1254:
654:
1373:
Calogero, Francesco (2004-02-20). "Cosmic origin of quantization".
902:, originally stipulated in 1997 and further republished in 2004 by
906:
that suggests the classical stochastic background field to which
1119:{\displaystyle h\equiv h(t)=A{\sqrt {R(t)}}=h_{0}{\sqrt {a(t)}}}
1406:
Gaeta, Giuseppe (2000). "Calogero
Conjecture and Hubble Law".
930:
component made up of particles much lighter than nucleons".
1414:(5). Springer Science and Business Media LLC: 1339–1350.
910:
attributes quantum mechanical behavior in his theory of
1325:
Calogero, F (1997). "Cosmic origin of quantization".
1217:
1186:
1164:
1139:
1046:
1027:{\displaystyle h\approx \alpha G^{1/2}m^{3/2}^{1/2}.}
942:
39:
1223:
1201:
1170:
1145:
1118:
1026:
100:
1381:(4–05). World Scientific Pub Co Pte Lt: 519–525.
1298:(20). World Scientific Pub Co Pte Lt: 1329–1339.
867:
8:
1408:International Journal of Theoretical Physics
892:minority interpretation of quantum mechanics
95:
69:
16:Minority interpretation of quantum mechanics
1368:
1366:
1364:
1362:
1360:
1358:
1356:
917:The hypothesis itself suggests that if the
874:
860:
18:
1375:International Journal of Modern Physics B
1285:
1283:
1281:
1279:
1277:
1275:
1273:
1216:
1185:
1163:
1138:
1100:
1094:
1071:
1045:
1011:
1007:
978:
974:
960:
956:
941:
921:associated with a stochastic tremor with
87:
76:
75:
61:
46:
38:
1245:Compatibility with fundamental constants
1269:
1178:represents the mass of a hydrogen atom.
43:
26:
7:
406:Sum-over-histories (path integral)
92:
66:
22:Part of a series of articles about
14:
1261:of background cosmic radiation.
1196:
1190:
1111:
1105:
1082:
1076:
1062:
1056:
1004:
1000:
994:
988:
556:Relativistic quantum mechanics
88:
81:
62:
1:
1339:10.1016/s0375-9601(97)00107-2
596:Quantum statistical mechanics
1333:(6). Elsevier BV: 335–346.
566:Quantum information science
1474:
1231:is a dimensional constant.
1387:10.1142/s0217979204024136
1304:10.1142/s0217732300001614
1292:Modern Physics Letters A
601:Quantum machine learning
354:Wheeler's delayed-choice
1420:10.1023/a:1003647122051
912:stochastic quantization
311:Leggett–Garg inequality
1259:blackbody distribution
1225:
1203:
1172:
1155:gravitational constant
1147:
1120:
1028:
898:explanation involving
102:
1226:
1204:
1173:
1148:
1121:
1029:
296:Elitzur–Vaidman
286:Davisson–Germer
103:
1215:
1202:{\displaystyle R(t)}
1184:
1162:
1137:
1044:
940:
561:Quantum field theory
473:Consistent histories
110:Schrödinger equation
37:
888:Calogero conjecture
349:Stern–Gerlach
146:Classical mechanics
1251:University of Rome
1221:
1199:
1168:
1143:
1116:
1024:
904:Francesco Calogero
537:Von Neumann–Wigner
517:Objective-collapse
316:Mach–Zehnder
306:Leggett inequality
301:Franck–Hertz
151:Old quantum theory
98:
1453:Quantum mechanics
1327:Physics Letters A
1224:{\displaystyle A}
1171:{\displaystyle m}
1146:{\displaystyle G}
1114:
1085:
923:spatial coherence
900:quantum mechanics
884:
883:
591:Scattering theory
571:Quantum computing
344:Schrödinger's cat
276:Bell's inequality
84:
59:
28:Quantum mechanics
1465:
1439:
1399:
1398:
1370:
1351:
1350:
1322:
1316:
1315:
1287:
1230:
1228:
1227:
1222:
1208:
1206:
1205:
1200:
1177:
1175:
1174:
1169:
1152:
1150:
1149:
1144:
1125:
1123:
1122:
1117:
1115:
1101:
1099:
1098:
1086:
1072:
1033:
1031:
1030:
1025:
1020:
1019:
1015:
987:
986:
982:
969:
968:
964:
919:angular momentum
876:
869:
862:
503:Superdeterminism
156:Bra–ket notation
107:
105:
104:
99:
91:
86:
85:
77:
65:
60:
58:
47:
19:
1473:
1472:
1468:
1467:
1466:
1464:
1463:
1462:
1443:
1442:
1405:
1402:
1372:
1371:
1354:
1324:
1323:
1319:
1289:
1288:
1271:
1267:
1247:
1242:
1213:
1212:
1182:
1181:
1160:
1159:
1153:represents the
1135:
1134:
1090:
1042:
1041:
1003:
970:
952:
938:
937:
927:Planck constant
880:
851:
850:
849:
614:
606:
605:
551:
550:Advanced topics
543:
542:
541:
493:Hidden-variable
483:de Broglie–Bohm
462:
460:Interpretations
452:
451:
450:
420:
412:
411:
410:
368:
360:
359:
358:
325:
281:CHSH inequality
270:
262:
261:
260:
189:Complementarity
183:
175:
174:
173:
141:
112:
51:
35:
34:
17:
12:
11:
5:
1471:
1469:
1461:
1460:
1455:
1445:
1444:
1441:
1440:
1401:
1400:
1352:
1317:
1268:
1266:
1263:
1246:
1243:
1241:
1238:
1233:
1232:
1220:
1210:
1198:
1195:
1192:
1189:
1179:
1167:
1157:
1142:
1128:
1127:
1113:
1110:
1107:
1104:
1097:
1093:
1089:
1084:
1081:
1078:
1075:
1070:
1067:
1064:
1061:
1058:
1055:
1052:
1049:
1035:
1034:
1023:
1018:
1014:
1010:
1006:
1002:
999:
996:
993:
990:
985:
981:
977:
973:
967:
963:
959:
955:
951:
948:
945:
882:
881:
879:
878:
871:
864:
856:
853:
852:
848:
847:
842:
837:
832:
827:
822:
817:
812:
807:
802:
797:
792:
787:
782:
777:
772:
767:
762:
757:
752:
747:
742:
737:
732:
727:
722:
717:
712:
707:
702:
697:
692:
687:
682:
677:
672:
667:
662:
657:
652:
647:
642:
637:
632:
627:
622:
616:
615:
612:
611:
608:
607:
604:
603:
598:
593:
588:
586:Density matrix
583:
578:
573:
568:
563:
558:
552:
549:
548:
545:
544:
540:
539:
534:
529:
524:
519:
514:
509:
508:
507:
506:
505:
490:
485:
480:
475:
470:
464:
463:
458:
457:
454:
453:
449:
448:
443:
438:
433:
428:
422:
421:
418:
417:
414:
413:
409:
408:
403:
398:
393:
388:
383:
377:
376:
375:
369:
366:
365:
362:
361:
357:
356:
351:
346:
340:
339:
338:
337:
336:
334:Delayed-choice
329:Quantum eraser
324:
323:
318:
313:
308:
303:
298:
293:
288:
283:
278:
272:
271:
268:
267:
264:
263:
259:
258:
257:
256:
246:
241:
236:
231:
226:
221:
219:Quantum number
216:
211:
206:
201:
196:
191:
185:
184:
181:
180:
177:
176:
172:
171:
166:
160:
159:
158:
153:
148:
142:
139:
138:
135:
134:
133:
132:
127:
122:
114:
113:
108:
97:
94:
90:
83:
80:
74:
71:
68:
64:
57:
54:
50:
45:
42:
31:
30:
24:
23:
15:
13:
10:
9:
6:
4:
3:
2:
1470:
1459:
1456:
1454:
1451:
1450:
1448:
1437:
1433:
1429:
1425:
1421:
1417:
1413:
1409:
1404:
1403:
1396:
1392:
1388:
1384:
1380:
1376:
1369:
1367:
1365:
1363:
1361:
1359:
1357:
1353:
1348:
1344:
1340:
1336:
1332:
1328:
1321:
1318:
1313:
1309:
1305:
1301:
1297:
1293:
1286:
1284:
1282:
1280:
1278:
1276:
1274:
1270:
1264:
1262:
1260:
1256:
1252:
1244:
1239:
1237:
1218:
1211:
1193:
1187:
1180:
1165:
1158:
1156:
1140:
1133:
1132:
1131:
1108:
1102:
1095:
1091:
1087:
1079:
1073:
1068:
1065:
1059:
1053:
1050:
1047:
1040:
1039:
1038:
1037:Furthermore:
1021:
1016:
1012:
1008:
997:
991:
983:
979:
975:
971:
965:
961:
957:
953:
949:
946:
943:
936:
935:
934:
931:
928:
924:
920:
915:
913:
909:
908:Edward Nelson
905:
901:
897:
893:
889:
877:
872:
870:
865:
863:
858:
857:
855:
854:
846:
843:
841:
838:
836:
833:
831:
828:
826:
823:
821:
818:
816:
813:
811:
808:
806:
803:
801:
798:
796:
793:
791:
788:
786:
783:
781:
778:
776:
773:
771:
768:
766:
763:
761:
758:
756:
753:
751:
748:
746:
743:
741:
738:
736:
733:
731:
728:
726:
723:
721:
718:
716:
713:
711:
708:
706:
703:
701:
698:
696:
693:
691:
688:
686:
683:
681:
678:
676:
673:
671:
668:
666:
663:
661:
658:
656:
653:
651:
648:
646:
643:
641:
638:
636:
633:
631:
628:
626:
623:
621:
618:
617:
610:
609:
602:
599:
597:
594:
592:
589:
587:
584:
582:
579:
577:
576:Quantum chaos
574:
572:
569:
567:
564:
562:
559:
557:
554:
553:
547:
546:
538:
535:
533:
532:Transactional
530:
528:
525:
523:
522:Quantum logic
520:
518:
515:
513:
510:
504:
501:
500:
499:
496:
495:
494:
491:
489:
486:
484:
481:
479:
476:
474:
471:
469:
466:
465:
461:
456:
455:
447:
444:
442:
439:
437:
434:
432:
429:
427:
424:
423:
416:
415:
407:
404:
402:
399:
397:
394:
392:
389:
387:
384:
382:
379:
378:
374:
371:
370:
364:
363:
355:
352:
350:
347:
345:
342:
341:
335:
332:
331:
330:
327:
326:
322:
319:
317:
314:
312:
309:
307:
304:
302:
299:
297:
294:
292:
289:
287:
284:
282:
279:
277:
274:
273:
266:
265:
255:
252:
251:
250:
249:Wave function
247:
245:
242:
240:
237:
235:
232:
230:
229:Superposition
227:
225:
222:
220:
217:
215:
212:
210:
207:
205:
202:
200:
197:
195:
192:
190:
187:
186:
179:
178:
170:
167:
165:
162:
161:
157:
154:
152:
149:
147:
144:
143:
137:
136:
131:
128:
126:
123:
121:
118:
117:
116:
115:
111:
78:
72:
55:
52:
48:
40:
33:
32:
29:
25:
21:
20:
1411:
1407:
1378:
1374:
1330:
1326:
1320:
1295:
1291:
1248:
1234:
1129:
1036:
932:
916:
896:quantization
887:
885:
431:Klein–Gordon
367:Formulations
204:Energy level
199:Entanglement
182:Fundamentals
169:Interference
120:Introduction
1458:Conjectures
820:von Neumann
805:Schrödinger
581:EPR paradox
512:Many-worlds
446:Schrödinger
401:Schrödinger
396:Phase-space
386:Interaction
291:Double-slit
269:Experiments
244:Uncertainty
214:Nonlocality
209:Measurement
194:Decoherence
164:Hamiltonian
1447:Categories
1265:References
894:. It is a
815:Sommerfeld
730:Heisenberg
725:Gutzwiller
665:de Broglie
613:Scientists
527:Relational
478:Copenhagen
381:Heisenberg
239:Tunnelling
140:Background
1436:118571985
1428:0020-7748
1395:0217-9792
1347:0375-9601
1312:0217-7323
1126:Const G,m
1051:≡
950:α
947:≈
845:Zeilinger
690:Ehrenfest
419:Equations
96:⟩
93:Ψ
82:^
70:⟩
67:Ψ
44:ℏ
1255:redshift
1240:Analysis
770:Millikan
695:Einstein
680:Davisson
635:Blackett
620:Aharonov
488:Ensemble
468:Bayesian
373:Overview
254:Collapse
234:Symmetry
125:Glossary
1130:Where:
810:Simmons
800:Rydberg
765:Moseley
745:Kramers
735:Hilbert
720:Glauber
715:Feynman
700:Everett
670:Compton
441:Rydberg
130:History
1434:
1426:
1393:
1345:
1310:
840:Zeeman
835:Wigner
785:Planck
755:Landau
740:Jordan
391:Matrix
321:Popper
1432:S2CID
890:is a
795:Raman
780:Pauli
775:Onnes
710:Fermi
685:Debye
675:Dirac
640:Bloch
630:Bethe
498:Local
436:Pauli
426:Dirac
224:State
1424:ISSN
1391:ISSN
1343:ISSN
1308:ISSN
886:The
830:Wien
825:Weyl
790:Rabi
760:Laue
750:Lamb
705:Fock
660:Bose
655:Born
650:Bohr
645:Bohm
625:Bell
1416:doi
1383:doi
1335:doi
1331:228
1300:doi
1449::
1430:.
1422:.
1412:39
1410:.
1389:.
1379:18
1377:.
1355:^
1341:.
1329:.
1306:.
1296:15
1294:.
1272:^
1438:.
1418::
1397:.
1385::
1349:.
1337::
1314:.
1302::
1219:A
1197:)
1194:t
1191:(
1188:R
1166:m
1141:G
1112:)
1109:t
1106:(
1103:a
1096:0
1092:h
1088:=
1083:)
1080:t
1077:(
1074:R
1069:A
1066:=
1063:)
1060:t
1057:(
1054:h
1048:h
1022:.
1017:2
1013:/
1009:1
1005:]
1001:)
998:t
995:(
992:R
989:[
984:2
980:/
976:3
972:m
966:2
962:/
958:1
954:G
944:h
875:e
868:t
861:v
89:|
79:H
73:=
63:|
56:t
53:d
49:d
41:i
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