2965:
1216:
interference pattern is actually very low: "Because this signal (disruption) from the second, middle picture is small (equivalently, it only affects a very small portion of the photons), the contrast V is also very small, and goes to zero for infinitely thin wires." He also argues that the experiment can be understood with classical electrodynamics and has "nothing to do with quantum mechanics".
1004:
1012:
996:
1255:
which-path information when both pinholes are open. But this experiment is still subject to Motl's objection that the 2 beams have a sub-microscopic diffraction pattern created by the convergence of the beams before the slits; the result would have been the measuring of which slit was open before the wires were ever reached.
1047:. A grid of thin wires is placed just before the lens (Fig. 2) so that the wires lie in the dark fringes of an interference pattern which is produced by the dual pinhole setup. If one of the pinholes is blocked, the interference pattern will no longer be formed, and the grid of wires causes appreciable
1184:
Reitzner performed numerical simulations, published in a preprint, of Afshar's arrangement and obtained the same results that Afshar obtained experimentally. From this he argues that the photons exhibit wave behavior, including high fringe visibility but no which-way information, up to the point they
1051:
in the light and blocks some of it from detection by the corresponding photon detector. However, when both pinholes are open, the effect of the wires is negligible, comparable to the case in which there are no wires placed in front of the lens (Fig. 3), because the wires lie in the dark fringes of an
1241:
Argues that Afshar's claim to violate complementarity is a simple logical inconsistency: by setting up the experiment so that photons are spatially coherent over the two pinholes, the pinholes are necessarily indistinguishable by those photons. “In other words, Afshar et al. claim in one breath to
1199:
Unruh, like
Kastner, proceeds by setting up an arrangement that he feels is equivalent but simpler. The size of the effect is larger so that it is easier to see the flaw in the logic. In Unruh's view that flaw is, in the case that an obstacle exists at the position of the dark fringes, "drawing the
1035:
refocuses the light so that the image of each pinhole falls on separate photon-detectors (Fig. 1). With pinhole 2 closed, a photon that goes through pinhole 1 impinges only on photon detector 1. Similarly, with pinhole 1 closed, a photon that goes through pinhole 2 impinges only on photon detector
1228:
Steuernagel makes a quantitative analysis of the various transmitted, refracted, and reflected modes in a setup that differs only slightly from Afshar's. He concludes that the
Englert-Greenberger duality relation is strictly satisfied, and in particular that the fringe visibility for thin wires is
1101:
A number of scientists have published criticisms of Afshar's interpretation of his results, some of which reject the claims of a violation of complementarity, while differing in the way they explain how complementarity copes with the experiment. For example, one paper contests Afshar's core claim,
1125:
and applying Afshar's logic to it to expose its flaw. She proposes that Afshar's experiment is equivalent to preparing an electron in a spin-up state and then measuring its sideways spin. This does not imply that one has found out the up-down spin state and the sideways spin state of any electron
1060:
Afshar's conclusion is that, when both pinholes are open, the light exhibits wave-like behavior when going past the wires, since the light goes through the spaces between the wires but avoids the wires themselves, but also exhibits particle-like behavior after going through the lens, with photons
1254:
Afshar's coauthors
Eduardo Flores and Ernst Knoesel criticize Kastner's setup and propose an alternative experimental setup. By removing the lens of Afshar and causing two beams to overlap at a small angle, Flores et al. aimed to show that conservation of momentum guarantee the preservation of
1106:
is violated. The researchers re-ran the experiment, using a different method for measuring the visibility of the interference pattern than that used by Afshar, and found no violation of complementarity, concluding "This result demonstrates that the experiment can be perfectly explained by the
1215:
Motl's criticism, published in his blog, is based on an analysis of Afshar's actual setup, instead of proposing a different experiment like Unruh and
Kastner. In contrast to Unruh and Kastner, he believes that which-way information always exists, but argues that the measured contrast of the
1200:
inference that IF the particle was detected in detector 1, THEN it must have come from path 1. Similarly, IF it were detected in detector 2, then it came from path 2." In other words, he accepts the existence of an interference pattern but rejects the existence of which-way information.
1036:
2. With both pinholes open, Afshar claims, citing
Wheeler in support, that pinhole 1 remains correlated to photon Detector 1 (and vice versa for pinhole 2 to photon Detector 2), and therefore that which-way information is preserved when both pinholes are open.
1185:
hit the detector: "In other words the two-peaked distribution is an interference pattern and the photon behaves as a wave and exhibits no particle properties until it hits the plate. As a result a which-way information can never be obtained in this way."
974:
feature article generated many responses, including various letters to the editor that appeared in the August 7 and August 14, 2004 issues, arguing against the conclusions being drawn by Afshar. The results were published in a
114:
1229:
small. Like some of the other critics, he emphasizes that inferring an interference pattern is not the same as measuring one: "Finally, the greatest weakness in the analysis given by Afshar is the
1242:
have set up the experiment so that pinholes A and B are inherently indistinguishable by certain photons , and in another breath to have distinguished pinholes A and B with those same photons.”
960:. The results were first presented at a seminar at Harvard in March 2004. The experiment was featured as the cover story in the July 24, 2004 edition of the popular science magazine
2092:
E. Flores and E. Knoesel (2007). "Why
Kastner analysis does not apply to a modified Afshar experiment". In Roychoudhuri, Chandrasekhar; Kracklauer, Al F; Creath, Katherine (eds.).
1653:
1356:
1162:
2209:
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936:
The experiment has been analyzed and repeated by a number of investigators. There are several theories that explain the effect without violating complementarity.
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380:
881:
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1103:
952:
Shahriar Afshar's experimental work was done initially at the
Institute for Radiation-Induced Mass Studies (IRIMS) in Boston and later reproduced at
2945:
2259:
588:
132:
1452:
S. S. Afshar (2005). Roychoudhuri, Chandrasekhar; Creath, Katherine (eds.). "Violation of the principle of complementarity, and its implications".
44:
925:
takes through the apparatus, while simultaneously allowing interference between the paths to be observed. According to Afshar, this violates the
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1285:
361:
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544:
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simultaneously. Applied to Afshar's experiment: "Nevertheless, even with the grid removed, since the photon is prepared in a superposition
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467:
1300:
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Below is a synopsis of papers by several critics highlighting their main arguments and the disagreements they have amongst themselves:
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Fig.3 Experiment with wire grid and both pinholes open. The wires lie in the dark fringes and thus block very little light
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603:
341:
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V. Jacques; et al. (2008). "Illustration of quantum complementarity using single photons interfering on a grating".
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in quantum mechanics, devised and carried out by
Shahriar Afshar in 2004. In the experiment, light generated by a
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to the extent that it shows both wave and particle characteristics in the same experiment for the same photons.
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1968:
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667:
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S. S. Afshar; E. Flores; K. F. McDonald; E. Knoesel (2007). "Paradox in wave-particle duality".
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35:
914:. In addition, a grid of thin wires is placed just before the lens on the dark fringes of an
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510:
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O. Steuernagel (2007). "Afshar's experiment does not show a violation of complementarity".
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722:
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1972:
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1419:
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a 'which-way' measurement (the term traditionally attached to the slit-basis observable
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interference pattern. The effect is not dependent on the light intensity (photon flux).
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conference proceedings in 2005. A follow-up paper was published in a scientific journal
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going to a correlated photo-detector. Afshar argues that this behavior contradicts the
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772:
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529:
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231:
1960:
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J. Zheng; C. Zheng (2011). "Variant simulation system using quaternion structures".
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1808:
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1011:
837:
832:
767:
752:
717:
211:
1121:
Kastner's criticism, published in a peer-reviewed paper, proceeds by setting up a
1651:
R. Kastner (2005). "Why the Afshar experiment does not refute complementarity?".
1585:
2725:
1684:
1190:
1169:
Daniel
Reitzner, Research Center for Quantum Information, Institute of Physics,
1048:
995:
802:
757:
692:
647:
2070:
1507:
S. S. Afshar (2006). "Violation of Bohr's complementarity: One slit or both?".
17:
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2008:
1742:
1427:
1174:
792:
762:
682:
657:
652:
637:
1634:
109:{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }
2579:
2275:
283:
1357:"Waving Copenhagen Good-bye: Were the founders of Quantum Mechanics wrong?"
1164:), because it cannot tell us 'which slit the photon actually went through.'
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1823:
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1608:
2102:
1992:
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662:
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Afshar claimed that the experiment gives information about which path a
2111:
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one can observe that there are regions that the photons avoid, called
922:
2187:
1263:
adopts Afshar's interpretation of the experiment to support his own
2053:
1007:
Fig.2 Experiment with obstructing wire grid and one pinhole covered
1783:
1114:
Ruth
Kastner, Committee on the History and Philosophy of Science,
1024:
994:
906:
passes through two closely spaced pinholes, and is refocused by a
903:
2168:
The Quantum Handshake: Entanglement, Nonlocality and Transactions
2191:
1855:
1221:
Ole Steuernagel, School of Physics, Astronomy and Mathematics,
2037:
Andrew Knight (2020). "No Paradox in Wave-Particle Duality".
1149:
1068:
Afshar asserts that there is simultaneously high visibility
1238:
Andrew Knight, Department of Physics, New York University
1986:
D. Reitzner (2007). "Comment on Afshar's experiments".
1856:"Institute for Radiation-Induced Mass Studies (IRIMS)"
910:
so that the image of each pinhole falls on a separate
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47:
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The experiment uses a setup similar to that for the
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2706:
2638:
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2485:
2449:
2403:
2268:
2225:
1654:
Studies in History and Philosophy of Modern Physics
1076:(corresponding to which-path information), so that
1072:of interference as well as high distinguishability
1156:
108:
1704:
1702:
1107:Copenhagen interpretation of quantum mechanics."
1031:pinholes (not slits). After the dual pinholes, a
944:of quantum mechanics over other interpretations.
940:claims the experiment provides evidence for the
1824:"Quantum histories and quantum complementarity"
1609:"Quantum Histories and Quantum Complementarity"
1762:
1760:
1233:that an interference pattern must be present."
999:Fig.1 Experiment without obstructing wire grid
2203:
1965:APS Meeting, March 13–17, Baltimore, Maryland
1646:
1644:
875:
8:
1447:
1445:
1389:
1387:
1385:
1383:
1381:
1350:
1348:
1023:. In Afshar's variant, light generated by a
966:endorsed by professor John G. Cramer of the
103:
77:
1961:"The Afshar Experiment and Complementarity"
1319:
1317:
1315:
2210:
2196:
2188:
1946:Mathematical foundations of quantum theory
1458:. The Nature of Light: What Is a Photon?.
1039:When the light acts as a wave, because of
882:
868:
26:
2101:
2052:
1991:
1839:
1782:
1724:
1666:
1624:
1522:
1467:
1409:
1208:, Former Assistant Professor of Physics,
1148:
1147:
1145:
1130:, the measurement at the final screen at
95:
84:
83:
69:
54:
46:
1010:
1002:
1311:
51:
34:
2094:The Nature of Light: What Are Photons?
2171:. Springer Verlag. pp. 111–112.
7:
1116:University of Maryland, College Park
1104:Englert–Greenberger duality relation
2096:. Vol. 6664. pp. 66640O.
1286:Wheeler's delayed choice experiment
2009:"Shahriar Afshar – Quantum Rebel?"
1918:"Quantum rebel wins over doubters"
1027:passes through two closely spaced
414:Sum-over-histories (path integral)
100:
74:
30:Part of a series of articles about
25:
2964:
2963:
983:in January 2007 and featured in
2140:Analog Science Fiction and Fact
2024:"Violation of complementarity?"
1301:Wheeler–Feynman absorber theory
2913:Relativistic quantum mechanics
1801:10.1088/1367-2630/10/12/123009
1607:Georgiev, Danko (2012-01-26).
1267:of quantum mechanics over the
1195:University of British Columbia
1157:{\displaystyle {\mathcal {O}}}
1086:wave-particle duality relation
1055:
564:Relativistic quantum mechanics
96:
89:
70:
1:
2891:Quantum statistical mechanics
2668:Quantum differential calculus
2590:Delayed-choice quantum eraser
2373:Symmetry in quantum mechanics
1291:Delayed choice quantum eraser
604:Quantum statistical mechanics
1586:10.1080/09500340.2011.636152
1361:Harvard Seminar Announcement
1265:transactional interpretation
1063:principle of complementarity
942:transactional interpretation
2693:Quantum stochastic calculus
2683:Quantum measurement problem
2605:Mach–Zehnder interferometer
2135:"A farewell to Copenhagen?"
1685:10.1016/j.shpsb.2005.04.006
1223:University of Hertfordshire
574:Quantum information science
3016:
2071:10.1007/s10701-020-00379-9
1948:. Elsevier. pp. 9–48.
1510:AIP Conference Proceedings
1273:many-worlds interpretation
1193:, Professor of Physics at
1171:Slovak Academy of Sciences
956:, while he was there as a
2959:
2753:Quantum complexity theory
2731:Quantum cellular automata
2436:Path integral formulation
1879:Afshar's Quantum Bomshell
1828:ISRN Mathematical Physics
1743:10.1007/s10701-007-9153-5
1613:ISRN Mathematical Physics
1428:10.1007/s10701-006-9102-8
1269:Copenhagen interpretation
927:complementarity principle
2820:Quantum machine learning
2800:Quantum key distribution
2790:Quantum image processing
2780:Quantum error correction
2630:Wheeler's delayed choice
1565:Journal of Modern Optics
968:University of Washington
609:Quantum machine learning
362:Wheeler's delayed-choice
2736:Quantum finite automata
1933:(subscription required)
1822:D. D. Georgiev (2012).
1341:(subscription required)
1056:Afshar's interpretation
319:Leggett–Garg inequality
2840:Quantum neural network
2040:Foundations of Physics
1959:R. E. Kastner (2006).
1944:Wheeler, John (1978).
1916:Chown, Marcus (2007).
1770:New Journal of Physics
1712:Foundations of Physics
1397:Foundations of Physics
1324:Chown, Marcus (2004).
1158:
1021:double-slit experiment
1016:
1008:
1000:
981:Foundations of Physics
912:single-photon detector
900:double-slit experiment
898:is a variation of the
110:
3000:Philosophy of physics
2865:Quantum teleportation
2393:Wave–particle duality
2133:J. G. Cramer (2005).
1893:"Bohr is still wrong"
1891:J. G. Cramer (2004).
1355:S. S. Afshar (2004).
1159:
1014:
1006:
998:
304:Elitzur–Vaidman
294:Davisson–Germer
111:
2896:Quantum field theory
2825:Quantum metamaterial
2770:Quantum cryptography
2500:Consistent histories
1144:
1041:quantum interference
916:interference pattern
569:Quantum field theory
481:Consistent histories
118:Schrödinger equation
45:
2995:Physics experiments
2990:Quantum measurement
2881:Quantum fluctuation
2850:Quantum programming
2810:Quantum logic gates
2795:Quantum information
2775:Quantum electronics
2250:Classical mechanics
2165:Cramer, JG (2015).
2063:2020FoPh...50.1723K
1973:2006APS..MARD40011K
1841:10.5402/2012/327278
1793:2008NJPh...10l3009J
1735:2007FoPh...37.1370S
1677:2005SHPMP..36..649K
1626:10.5402/2012/327278
1578:2012JMOp...59..484Z
1533:2006AIPC..810..294A
1478:2005SPIE.5866..229A
1455:Proceedings of SPIE
1420:2007FoPh...37..295A
958:visiting researcher
357:Stern–Gerlach
154:Classical mechanics
2934:in popular culture
2716:Quantum algorithms
2564:Von Neumann–Wigner
2544:Objective collapse
2255:Old quantum theory
1210:Harvard University
1154:
1123:thought experiment
1097:Specific criticism
1017:
1009:
1001:
991:Experimental setup
987:in February 2007.
954:Harvard University
545:Von Neumann–Wigner
525:Objective-collapse
324:Mach–Zehnder
314:Leggett inequality
309:Franck–Hertz
159:Old quantum theory
106:
2977:
2976:
2951:Quantum mysticism
2929:Schrödinger's cat
2860:Quantum simulator
2830:Quantum metrology
2758:Quantum computing
2721:Quantum amplifier
2698:Quantum spacetime
2663:Quantum cosmology
2653:Quantum chemistry
2368:Scattering theory
2316:Zero-point energy
2311:Degenerate levels
2219:Quantum mechanics
2178:978-3-319-24642-0
2112:10.1117/12.730965
2047:(11): 1723–1727.
2007:W. Unruh (2004).
1541:10.1063/1.2158731
1486:10.1117/12.638774
931:quantum mechanics
896:Afshar experiment
892:
891:
599:Scattering theory
579:Quantum computing
352:Schrödinger's cat
284:Bell's inequality
92:
67:
36:Quantum mechanics
16:(Redirected from
3007:
2967:
2966:
2678:Quantum geometry
2673:Quantum dynamics
2530:Superdeterminism
2426:Matrix mechanics
2281:Bra–ket notation
2212:
2205:
2198:
2189:
2183:
2182:
2162:
2156:
2155:
2153:
2152:
2143:. Archived from
2130:
2124:
2123:
2105:
2103:quant-ph/0702210
2089:
2083:
2082:
2056:
2034:
2028:
2027:
2022:L. Motl (2004).
2019:
2013:
2012:
2004:
1998:
1997:
1995:
1993:quant-ph/0701152
1983:
1977:
1976:
1956:
1950:
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1907:
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1888:
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1728:
1726:quant-ph/0512123
1706:
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1668:quant-ph/0502021
1648:
1639:
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1604:
1598:
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1524:quant-ph/0701039
1504:
1498:
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1471:
1469:quant-ph/0701027
1449:
1440:
1439:
1413:
1411:quant-ph/0702188
1391:
1376:
1375:
1373:
1372:
1363:. Archived from
1352:
1343:
1342:
1339:
1321:
1296:Weak measurement
1249:Specific support
1163:
1161:
1160:
1155:
1153:
1152:
1084:> 1, and the
884:
877:
870:
511:Superdeterminism
164:Bra–ket notation
115:
113:
112:
107:
99:
94:
93:
85:
73:
68:
66:
55:
27:
21:
3015:
3014:
3010:
3009:
3008:
3006:
3005:
3004:
2980:
2979:
2978:
2973:
2955:
2941:Wigner's friend
2917:
2908:Quantum gravity
2869:
2855:Quantum sensing
2835:Quantum network
2815:Quantum machine
2785:Quantum imaging
2748:Quantum circuit
2743:Quantum channel
2702:
2648:Quantum biology
2634:
2610:Elitzur–Vaidman
2585:Davisson–Germer
2568:
2520:Hidden-variable
2510:de Broglie–Bohm
2487:Interpretations
2481:
2445:
2399:
2286:Complementarity
2264:
2221:
2216:
2186:
2179:
2164:
2163:
2159:
2150:
2148:
2132:
2131:
2127:
2091:
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2086:
2036:
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2020:
2016:
2006:
2005:
2001:
1985:
1984:
1980:
1958:
1957:
1953:
1943:
1942:
1938:
1932:
1915:
1914:
1910:
1890:
1889:
1885:
1877:
1873:
1864:
1862:
1854:
1853:
1849:
1821:
1820:
1816:
1766:
1765:
1758:
1708:
1707:
1700:
1650:
1649:
1642:
1606:
1605:
1601:
1561:
1560:
1556:
1506:
1505:
1501:
1451:
1450:
1443:
1393:
1392:
1379:
1370:
1368:
1354:
1353:
1346:
1340:
1326:"Quantum Rebel"
1323:
1322:
1313:
1309:
1282:
1251:
1142:
1141:
1138:never really is
1136:
1099:
1094:
1058:
993:
950:
888:
859:
858:
857:
622:
614:
613:
559:
558:Advanced topics
551:
550:
549:
501:Hidden-variable
491:de Broglie–Bohm
470:
468:Interpretations
460:
459:
458:
428:
420:
419:
418:
376:
368:
367:
366:
333:
289:CHSH inequality
278:
270:
269:
268:
197:Complementarity
191:
183:
182:
181:
149:
120:
59:
43:
42:
23:
22:
18:Shahriar Afshar
15:
12:
11:
5:
3013:
3011:
3003:
3002:
2997:
2992:
2982:
2981:
2975:
2974:
2972:
2971:
2960:
2957:
2956:
2954:
2953:
2948:
2943:
2938:
2937:
2936:
2925:
2923:
2919:
2918:
2916:
2915:
2910:
2905:
2904:
2903:
2893:
2888:
2886:Casimir effect
2883:
2877:
2875:
2871:
2870:
2868:
2867:
2862:
2857:
2852:
2847:
2845:Quantum optics
2842:
2837:
2832:
2827:
2822:
2817:
2812:
2807:
2802:
2797:
2792:
2787:
2782:
2777:
2772:
2767:
2766:
2765:
2755:
2750:
2745:
2740:
2739:
2738:
2728:
2723:
2718:
2712:
2710:
2704:
2703:
2701:
2700:
2695:
2690:
2685:
2680:
2675:
2670:
2665:
2660:
2655:
2650:
2644:
2642:
2636:
2635:
2633:
2632:
2627:
2622:
2620:Quantum eraser
2617:
2612:
2607:
2602:
2597:
2592:
2587:
2582:
2576:
2574:
2570:
2569:
2567:
2566:
2561:
2556:
2551:
2546:
2541:
2536:
2535:
2534:
2533:
2532:
2517:
2512:
2507:
2502:
2497:
2491:
2489:
2483:
2482:
2480:
2479:
2474:
2469:
2464:
2459:
2453:
2451:
2447:
2446:
2444:
2443:
2438:
2433:
2428:
2423:
2418:
2413:
2407:
2405:
2401:
2400:
2398:
2397:
2396:
2395:
2390:
2380:
2375:
2370:
2365:
2360:
2355:
2350:
2345:
2340:
2335:
2330:
2325:
2320:
2319:
2318:
2313:
2308:
2303:
2293:
2291:Density matrix
2288:
2283:
2278:
2272:
2270:
2266:
2265:
2263:
2262:
2257:
2252:
2247:
2246:
2245:
2235:
2229:
2227:
2223:
2222:
2217:
2215:
2214:
2207:
2200:
2192:
2185:
2184:
2177:
2157:
2125:
2084:
2029:
2014:
1999:
1978:
1951:
1936:
1908:
1883:
1881:Science Friday
1871:
1847:
1814:
1777:(12): 123009.
1756:
1698:
1661:(4): 649–658.
1640:
1599:
1554:
1499:
1441:
1404:(2): 295–305.
1377:
1344:
1338:(2457): 30–35.
1310:
1308:
1305:
1304:
1303:
1298:
1293:
1288:
1281:
1278:
1277:
1276:
1261:John G. Cramer
1257:
1256:
1250:
1247:
1246:
1245:
1244:
1243:
1236:
1235:
1234:
1219:
1218:
1217:
1203:
1202:
1201:
1188:
1187:
1186:
1167:
1166:
1165:
1151:
1134:
1098:
1095:
1093:
1090:
1057:
1054:
992:
989:
949:
946:
938:John G. Cramer
890:
889:
887:
886:
879:
872:
864:
861:
860:
856:
855:
850:
845:
840:
835:
830:
825:
820:
815:
810:
805:
800:
795:
790:
785:
780:
775:
770:
765:
760:
755:
750:
745:
740:
735:
730:
725:
720:
715:
710:
705:
700:
695:
690:
685:
680:
675:
670:
665:
660:
655:
650:
645:
640:
635:
630:
624:
623:
620:
619:
616:
615:
612:
611:
606:
601:
596:
594:Density matrix
591:
586:
581:
576:
571:
566:
560:
557:
556:
553:
552:
548:
547:
542:
537:
532:
527:
522:
517:
516:
515:
514:
513:
498:
493:
488:
483:
478:
472:
471:
466:
465:
462:
461:
457:
456:
451:
446:
441:
436:
430:
429:
426:
425:
422:
421:
417:
416:
411:
406:
401:
396:
391:
385:
384:
383:
377:
374:
373:
370:
369:
365:
364:
359:
354:
348:
347:
346:
345:
344:
342:Delayed-choice
337:Quantum eraser
332:
331:
326:
321:
316:
311:
306:
301:
296:
291:
286:
280:
279:
276:
275:
272:
271:
267:
266:
265:
264:
254:
249:
244:
239:
234:
229:
227:Quantum number
224:
219:
214:
209:
204:
199:
193:
192:
189:
188:
185:
184:
180:
179:
174:
168:
167:
166:
161:
156:
150:
147:
146:
143:
142:
141:
140:
135:
130:
122:
121:
116:
105:
102:
98:
91:
88:
82:
79:
76:
72:
65:
62:
58:
53:
50:
39:
38:
32:
31:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3012:
3001:
2998:
2996:
2993:
2991:
2988:
2987:
2985:
2970:
2962:
2961:
2958:
2952:
2949:
2947:
2944:
2942:
2939:
2935:
2932:
2931:
2930:
2927:
2926:
2924:
2920:
2914:
2911:
2909:
2906:
2902:
2899:
2898:
2897:
2894:
2892:
2889:
2887:
2884:
2882:
2879:
2878:
2876:
2872:
2866:
2863:
2861:
2858:
2856:
2853:
2851:
2848:
2846:
2843:
2841:
2838:
2836:
2833:
2831:
2828:
2826:
2823:
2821:
2818:
2816:
2813:
2811:
2808:
2806:
2805:Quantum logic
2803:
2801:
2798:
2796:
2793:
2791:
2788:
2786:
2783:
2781:
2778:
2776:
2773:
2771:
2768:
2764:
2761:
2760:
2759:
2756:
2754:
2751:
2749:
2746:
2744:
2741:
2737:
2734:
2733:
2732:
2729:
2727:
2724:
2722:
2719:
2717:
2714:
2713:
2711:
2709:
2705:
2699:
2696:
2694:
2691:
2689:
2686:
2684:
2681:
2679:
2676:
2674:
2671:
2669:
2666:
2664:
2661:
2659:
2658:Quantum chaos
2656:
2654:
2651:
2649:
2646:
2645:
2643:
2641:
2637:
2631:
2628:
2626:
2625:Stern–Gerlach
2623:
2621:
2618:
2616:
2613:
2611:
2608:
2606:
2603:
2601:
2598:
2596:
2593:
2591:
2588:
2586:
2583:
2581:
2578:
2577:
2575:
2571:
2565:
2562:
2560:
2559:Transactional
2557:
2555:
2552:
2550:
2549:Quantum logic
2547:
2545:
2542:
2540:
2537:
2531:
2528:
2527:
2526:
2523:
2522:
2521:
2518:
2516:
2513:
2511:
2508:
2506:
2503:
2501:
2498:
2496:
2493:
2492:
2490:
2488:
2484:
2478:
2475:
2473:
2470:
2468:
2465:
2463:
2460:
2458:
2455:
2454:
2452:
2448:
2442:
2439:
2437:
2434:
2432:
2429:
2427:
2424:
2422:
2419:
2417:
2414:
2412:
2409:
2408:
2406:
2402:
2394:
2391:
2389:
2386:
2385:
2384:
2383:Wave function
2381:
2379:
2376:
2374:
2371:
2369:
2366:
2364:
2361:
2359:
2358:Superposition
2356:
2354:
2353:Quantum state
2351:
2349:
2346:
2344:
2341:
2339:
2336:
2334:
2331:
2329:
2326:
2324:
2321:
2317:
2314:
2312:
2309:
2307:
2306:Excited state
2304:
2302:
2299:
2298:
2297:
2294:
2292:
2289:
2287:
2284:
2282:
2279:
2277:
2274:
2273:
2271:
2267:
2261:
2258:
2256:
2253:
2251:
2248:
2244:
2241:
2240:
2239:
2236:
2234:
2231:
2230:
2228:
2224:
2220:
2213:
2208:
2206:
2201:
2199:
2194:
2193:
2190:
2180:
2174:
2170:
2169:
2161:
2158:
2147:on 2004-12-08
2146:
2142:
2141:
2136:
2129:
2126:
2121:
2117:
2113:
2109:
2104:
2099:
2095:
2088:
2085:
2080:
2076:
2072:
2068:
2064:
2060:
2055:
2050:
2046:
2042:
2041:
2033:
2030:
2025:
2018:
2015:
2010:
2003:
2000:
1994:
1989:
1982:
1979:
1974:
1970:
1966:
1962:
1955:
1952:
1947:
1940:
1937:
1929:
1925:
1924:
1923:New Scientist
1919:
1912:
1909:
1904:
1900:
1899:
1898:New Scientist
1894:
1887:
1884:
1880:
1875:
1872:
1861:
1857:
1851:
1848:
1842:
1837:
1833:
1829:
1825:
1818:
1815:
1810:
1806:
1802:
1798:
1794:
1790:
1785:
1780:
1776:
1772:
1771:
1763:
1761:
1757:
1752:
1748:
1744:
1740:
1736:
1732:
1727:
1722:
1718:
1714:
1713:
1705:
1703:
1699:
1694:
1690:
1686:
1682:
1678:
1674:
1669:
1664:
1660:
1656:
1655:
1647:
1645:
1641:
1636:
1632:
1627:
1622:
1618:
1614:
1610:
1603:
1600:
1595:
1591:
1587:
1583:
1579:
1575:
1571:
1567:
1566:
1558:
1555:
1550:
1546:
1542:
1538:
1534:
1530:
1525:
1520:
1516:
1512:
1511:
1503:
1500:
1495:
1491:
1487:
1483:
1479:
1475:
1470:
1465:
1461:
1457:
1456:
1448:
1446:
1442:
1437:
1433:
1429:
1425:
1421:
1417:
1412:
1407:
1403:
1399:
1398:
1390:
1388:
1386:
1384:
1382:
1378:
1367:on 2012-03-05
1366:
1362:
1358:
1351:
1349:
1345:
1337:
1333:
1332:
1331:New Scientist
1327:
1320:
1318:
1316:
1312:
1306:
1302:
1299:
1297:
1294:
1292:
1289:
1287:
1284:
1283:
1279:
1274:
1270:
1266:
1262:
1259:
1258:
1253:
1252:
1248:
1240:
1239:
1237:
1232:
1227:
1226:
1224:
1220:
1214:
1213:
1211:
1207:
1204:
1198:
1197:
1196:
1192:
1189:
1183:
1182:
1180:
1176:
1172:
1168:
1139:
1133:
1129:
1124:
1120:
1119:
1117:
1113:
1112:
1111:
1108:
1105:
1096:
1091:
1089:
1088:is violated.
1087:
1083:
1079:
1075:
1071:
1066:
1064:
1053:
1050:
1046:
1042:
1037:
1034:
1030:
1026:
1022:
1013:
1005:
997:
990:
988:
986:
985:New Scientist
982:
978:
973:
972:New Scientist
969:
965:
964:
963:New Scientist
959:
955:
947:
945:
943:
939:
934:
932:
928:
924:
919:
917:
913:
909:
905:
901:
897:
885:
880:
878:
873:
871:
866:
865:
863:
862:
854:
851:
849:
846:
844:
841:
839:
836:
834:
831:
829:
826:
824:
821:
819:
816:
814:
811:
809:
806:
804:
801:
799:
796:
794:
791:
789:
786:
784:
781:
779:
776:
774:
771:
769:
766:
764:
761:
759:
756:
754:
751:
749:
746:
744:
741:
739:
736:
734:
731:
729:
726:
724:
721:
719:
716:
714:
711:
709:
706:
704:
701:
699:
696:
694:
691:
689:
686:
684:
681:
679:
676:
674:
671:
669:
666:
664:
661:
659:
656:
654:
651:
649:
646:
644:
641:
639:
636:
634:
631:
629:
626:
625:
618:
617:
610:
607:
605:
602:
600:
597:
595:
592:
590:
587:
585:
584:Quantum chaos
582:
580:
577:
575:
572:
570:
567:
565:
562:
561:
555:
554:
546:
543:
541:
540:Transactional
538:
536:
533:
531:
530:Quantum logic
528:
526:
523:
521:
518:
512:
509:
508:
507:
504:
503:
502:
499:
497:
494:
492:
489:
487:
484:
482:
479:
477:
474:
473:
469:
464:
463:
455:
452:
450:
447:
445:
442:
440:
437:
435:
432:
431:
424:
423:
415:
412:
410:
407:
405:
402:
400:
397:
395:
392:
390:
387:
386:
382:
379:
378:
372:
371:
363:
360:
358:
355:
353:
350:
349:
343:
340:
339:
338:
335:
334:
330:
327:
325:
322:
320:
317:
315:
312:
310:
307:
305:
302:
300:
297:
295:
292:
290:
287:
285:
282:
281:
274:
273:
263:
260:
259:
258:
257:Wave function
255:
253:
250:
248:
245:
243:
240:
238:
237:Superposition
235:
233:
230:
228:
225:
223:
220:
218:
215:
213:
210:
208:
205:
203:
200:
198:
195:
194:
187:
186:
178:
175:
173:
170:
169:
165:
162:
160:
157:
155:
152:
151:
145:
144:
139:
136:
134:
131:
129:
126:
125:
124:
123:
119:
86:
80:
63:
60:
56:
48:
41:
40:
37:
33:
29:
28:
19:
2688:Quantum mind
2600:Franck–Hertz
2462:Klein–Gordon
2411:Formulations
2404:Formulations
2333:Interference
2323:Entanglement
2301:Ground state
2296:Energy level
2269:Fundamentals
2233:Introduction
2167:
2160:
2149:. Retrieved
2145:the original
2138:
2128:
2093:
2087:
2044:
2038:
2032:
2017:
2002:
1981:
1964:
1954:
1945:
1939:
1927:
1921:
1911:
1902:
1896:
1886:
1874:
1863:. Retrieved
1859:
1850:
1831:
1827:
1817:
1774:
1768:
1716:
1710:
1658:
1652:
1616:
1612:
1602:
1569:
1563:
1557:
1514:
1508:
1502:
1459:
1453:
1401:
1395:
1369:. Retrieved
1365:the original
1360:
1335:
1329:
1230:
1137:
1131:
1127:
1109:
1100:
1081:
1077:
1073:
1069:
1067:
1059:
1045:dark fringes
1044:
1038:
1028:
1018:
984:
971:
961:
951:
935:
920:
895:
893:
439:Klein–Gordon
375:Formulations
212:Energy level
207:Entanglement
190:Fundamentals
177:Interference
128:Introduction
2946:EPR paradox
2726:Quantum bus
2595:Double-slit
2573:Experiments
2539:Many-worlds
2477:Schrödinger
2441:Phase space
2431:Schrödinger
2421:Interaction
2378:Uncertainty
2348:Nonlocality
2343:Measurement
2338:Decoherence
2328:Hamiltonian
1930:(2591): 13.
1905:(2461): 26.
1719:(9): 1370.
1517:: 294–299.
1462:: 229–244.
1191:W. G. Unruh
1049:diffraction
828:von Neumann
813:Schrödinger
589:EPR paradox
520:Many-worlds
454:Schrödinger
409:Schrödinger
404:Phase-space
394:Interaction
299:Double-slit
277:Experiments
252:Uncertainty
222:Nonlocality
217:Measurement
202:Decoherence
172:Hamiltonian
2984:Categories
2874:Extensions
2708:Technology
2554:Relational
2505:Copenhagen
2416:Heisenberg
2363:Tunnelling
2226:Background
2151:2004-12-21
2054:2006.05315
1865:2023-09-21
1834:: 327278.
1572:(5): 484.
1371:2013-12-01
1307:References
1206:Luboš Motl
1175:Bratislava
823:Sommerfeld
738:Heisenberg
733:Gutzwiller
673:de Broglie
621:Scientists
535:Relational
486:Copenhagen
389:Heisenberg
247:Tunnelling
148:Background
2580:Bell test
2450:Equations
2276:Born rule
2120:119028739
2079:219559143
1967:: 40011.
1860:irims.org
1784:0807.5079
1693:119438183
1635:2090-4681
1594:121934786
1549:117905639
1494:119375418
1231:inference
1102:that the
1092:Reception
853:Zeilinger
698:Ehrenfest
427:Equations
104:⟩
101:Ψ
90:^
78:⟩
75:Ψ
52:ℏ
2969:Category
2763:Timeline
2515:Ensemble
2495:Bayesian
2388:Collapse
2260:Glossary
2243:Timeline
1751:53056142
1619:: 1–37.
1280:See also
1271:and the
1179:Slovakia
1029:circular
778:Millikan
703:Einstein
688:Davisson
643:Blackett
628:Aharonov
496:Ensemble
476:Bayesian
381:Overview
262:Collapse
242:Symmetry
133:Glossary
2922:Related
2901:History
2640:Science
2472:Rydberg
2238:History
2059:Bibcode
1969:Bibcode
1809:2627030
1789:Bibcode
1731:Bibcode
1673:Bibcode
1574:Bibcode
1529:Bibcode
1474:Bibcode
1436:2161197
1416:Bibcode
948:History
818:Simmons
808:Rydberg
773:Moseley
753:Kramers
743:Hilbert
728:Glauber
723:Feynman
708:Everett
678:Compton
449:Rydberg
138:History
2615:Popper
2175:
2118:
2077:
1807:
1749:
1691:
1633:
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1434:
1225:, UK.
970:. The
923:photon
848:Zeeman
843:Wigner
793:Planck
763:Landau
748:Jordan
399:Matrix
329:Popper
2525:Local
2467:Pauli
2457:Dirac
2116:S2CID
2098:arXiv
2075:S2CID
2049:arXiv
1988:arXiv
1805:S2CID
1779:arXiv
1747:S2CID
1721:arXiv
1689:S2CID
1663:arXiv
1590:S2CID
1545:S2CID
1519:arXiv
1490:S2CID
1464:arXiv
1432:S2CID
1406:arXiv
1025:laser
904:laser
803:Raman
788:Pauli
783:Onnes
718:Fermi
693:Debye
683:Dirac
648:Bloch
638:Bethe
506:Local
444:Pauli
434:Dirac
232:State
2173:ISBN
1832:2012
1631:ISSN
1617:2012
1460:5866
1033:lens
977:SPIE
933:.
908:lens
894:The
838:Wien
833:Weyl
798:Rabi
768:Laue
758:Lamb
713:Fock
668:Bose
663:Born
658:Bohr
653:Bohm
633:Bell
2108:doi
2067:doi
1928:197
1903:183
1836:doi
1797:doi
1739:doi
1681:doi
1621:doi
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