1047:
which conditions a definite outcome for the collision. Ought we to hope later to discover such properties ... and determine them in individual cases? Or ought we to believe that the agreement of theory and experimentâas to the impossibility of prescribing conditions for a causal evolutionâis a pre-established harmony founded on the nonexistence of such conditions? I myself am inclined to give up determinism in the world of atoms. But that is a philosophical question for which physical arguments alone are not decisive.
3432:
2336:"While the testable predictions of Bohmian mechanics are isomorphic to standard Copenhagen quantum mechanics, its underlying hidden variables have to be, in principle, unobservable. If one could observe them, one would be able to take advantage of that and signal faster than light, which â according to the special theory of relativity â leads to physical temporal paradoxes." J. Kofler and A. Zeilinger, "Quantum Information and Randomness",
1135:
macroscopic ball bouncing elastically between rigid barriers. He argues that such a quantum representation does not represent a specific ball, but "time ensemble of systems". As such the representation is correct, but incomplete because it does not represent the real individual macroscopic case. Einstein considered quantum mechanics incomplete "because the state function, in general, does not even describe the individual event/system".
2198:, p. 531: "Moreover, the complete definition of the phenomenon must essentially contain the indication of some permanent mark left upon a recording device which is part of the apparatus; only by thus envisaging the phenomenon as a closed event, terminated by a permanent record, can we do justice to the typical wholeness of the quantal processes."
1446:
excluded the possibility that any extension of quantum theory (not necessarily in the form of local hidden variables) can help predict the outcomes of any measurement on any quantum state. In this sense, we show the following: under the assumption that measurement settings can be chosen freely, quantum theory really is complete".
1261:
behavior of the system. Since these conditions constitute an inherent element of the description of any phenomenon to which the term "physical reality" can be properly attached, we see that the argumentation of the mentioned authors does not justify their conclusion that quantum-mechanical description is essentially incomplete."
1129:
hile we consider ... a quantum mechanical treatment of the electromagnetic field ... as not yet finished, we consider quantum mechanics to be a closed theory, whose fundamental physical and mathematical assumptions are no longer susceptible of any modification.... On the question of the 'validity of
1046:
Here the whole problem of determinism comes up. From the standpoint of our quantum mechanics there is no quantity which in any individual case causally fixes the consequence of the collision; but also experimentally we have so far no reason to believe that there are some inner properties of the atom
1587:
The debate whether
Quantum Mechanics is a complete theory and probabilities have a non-epistemic character (i.e. nature is intrinsically probabilistic) or whether it is a statistical approximation of a deterministic theory and probabilities are due to our ignorance of some parameters (i.e. they are
1260:
Einstein, Podolsky and Rosen contains an ambiguity as regards the meaning of the expression "without in any way disturbing a system." ... ven at this stage , there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future
1428:
A possible weakness of Bohm's theory is that some (including
Einstein, Pauli, and Heisenberg) feel that it looks contrived. (Indeed, Bohm thought this of his original formulation of the theory.) Bohm said he considered his theory to be unacceptable as a physical theory due to the guiding wave's
1134:
Although there is no record of
Einstein responding to Born and Heisenberg during the technical sessions of the Fifth Solvay Congress, he did challenge the completeness of quantum mechanics at various times. In his tribute article for Born's retirement he discussed the quantum representation of a
993:
Macroscopic physics requires classical mechanics which allows accurate predictions of mechanical motion with reproducible, high precision. Quantum phenomena require quantum mechanics, which allows accurate predictions of statistical averages only. If quantum states had hidden-variables awaiting
1827:, ed. Paul Arthur Shilpp, Harper, 1949, p. 211: "...in spite of all divergencies of approach and opinion, a most humorous spirit animated the discussions. On his side, Einstein mockingly asked us whether we could really believe that the providential authorities took recourse to dice-playing ("
1445:
published a proof that any extension of quantum mechanical theory, whether using hidden variables or otherwise, cannot provide a more accurate prediction of outcomes, assuming that observers can freely choose the measurement settings. Colbeck and Renner write: "In the present work, we have ...
1083:
in Berlin, on 5 May 1927, titled "Bestimmt Schrödinger's
Wellenmechanik die Bewegung eines Systems vollstÀndig oder nur im Sinne der Statistik?" ("Does Schrödinger's wave mechanics determine the motion of a system completely or only in the statistical sense?"). However, as the paper was being
1983:
Hermann, G.: Die naturphilosophischen
Grundlagen der Quantenmechanik (Auszug). Abhandlungen der Friesâschen Schule 6, 75â152 (1935). English translation: Chapter 15 of âGrete Hermann â Between physics and philosophyâ, Elise Crull and Guido Bacciagaluppi, eds., Springer, 2016, 239- 278.
1130:
the law of causality' we have this opinion: as long as one takes into account only experiments that lie in the domain of our currently acquired physical and quantum mechanical experience, the assumption of indeterminism in principle, here taken as fundamental, agrees with experience.
1084:
prepared for publication in the academy's journal, Einstein decided to withdraw it, possibly because he discovered that, contrary to his intention, his use of
Schrodinger's field to guide localized particles allowed just the kind of non-local influences he intended to avoid.
1001:. More fundamentally however, a successful model of quantum phenomena with hidden variables implies quantum entities with intrinsic values independent of measurements. Existing quantum mechanics asserts that state properties can only be known after a measurement. As
1835:, Princeton University Press, 1983, p. 117,: "But he still stood by his watchword, which he clothed in the words: 'God does not play at dice.' To which Bohr could only answer: 'But still, it cannot be for us to tell God, how he is to run the world.'"
1265:
Bohr is here choosing to define a "physical reality" as limited to a phenomenon that is immediately observable by an arbitrarily chosen and explicitly specified technique, using his own special definition of the term 'phenomenon'. He wrote in 1948:
1922:
This paper, whose original title was "Elementare
Uberlegungen zur Interpretation š der Grundlagen der Quanten-Mechanik", has been translated from the German by Dileep Karanth, Department of Physics, University of Wisconsin-Parkside, Kenosha,
1009:"It is a fundamental quantum doctrine that a measurement does not, in general, reveal a pre-existing value of the measured property. On the contrary, the outcome of a measurement is brought into being by the act of measurement itself..."
1831:"), to which I replied by pointing at the great caution, already called for by ancient thinkers, in ascribing attributes to Providence in everyday language." Werner Heisenberg, who also attended the congress, recalled the exchange in
1059:
Quantum mechanics is very worthy of respect. But an inner voice tells me this is not the genuine article after all. The theory delivers much but it hardly brings us closer to the Old One's secret. In any event, I am convinced that
1283:
If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical
124:
1398:
is performed, the electron goes through either one of the slits. Also, the slit passed through is not random but is governed by the (hidden) pilot wave, resulting in the wave pattern that is observed.
1172:
The debates between Bohr and
Einstein essentially concluded in 1935, when Einstein finally expressed what is widely considered his best argument for the incompleteness of quantum mechanics. Einstein,
1339:
that have found violations of these inequalities up to 242 standard deviations. This rules out local hidden-variable theories, but does not rule out non-local ones. Theoretically, there could be
1375:
had proposed in 1927 (and abandoned) â hence this theory is commonly called "de
Broglie-Bohm theory". Assuming the validity of Bell's theorem, any deterministic hidden-variable theory that is
1079:
Shortly after making his famous "God does not play dice" comment, Einstein attempted to formulate a deterministic counter proposal to quantum mechanics, presenting a paper at a meeting of the
1457:
described a model which, "under a different free choice assumption violates for almost all states of a bipartite two-level system, in a possibly experimentally testable way".
981:
experiments have demonstrated broad violation of these constraints, ruling out such theories. Bell's theorem, however, does not rule out the possibility of nonlocal theories or
1184:
their definition of a "complete" description as one that uniquely determines the values of all its measurable properties. Einstein later summarized their argument as follows:
1013:
In other words, whereas a hidden-variable theory would imply intrinsic particle properties, in quantum mechanics an electron has no definite position and velocity to even
1845:
The
Collected Papers of Albert Einstein, Volume 15: The Berlin Years: Writings & Correspondence, June 1925-May 1927 (English Translation Supplement), p. 512
1795:
The Collected Papers of Albert Einstein, Volume 15: The Berlin Years: Writings & Correspondence, June 1925-May 1927 (English Translation Supplement), p. 403
1394:
the quantum particle, e.g. an electron, and a hidden 'guiding wave' that governs its motion. Thus, in this theory electrons are quite clearly particles. When a
994:
ingenious new measurement technologies, then the latter (statistical results) might be convertible to a form of the former (classical-mechanical motion).
1125:
made a presentation summarizing the recent tremendous theoretical development of quantum mechanics. At the conclusion of the presentation, they declared:
2661:
1454:
1051:
Born's interpretation of the wave function was criticized by Schrödinger, who had previously attempted to interpret it in real physical terms, but
54:
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1438:
1220:
function of the total system. This determination, however, gives a result which depends upon which of the physical quantities (observables) of
1601:
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1144:
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1405:
constitutes an implicate (hidden) order which organizes a particle, and which may itself be the result of yet a further implicate order: a
891:
1807:
The BornâEinstein letters: correspondence between Albert Einstein and Max and Hedwig Born from 1916â1955, with commentaries by Max Born
3400:
1936:
2711:
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1387:, maintaining the existence of instantaneous or faster-than-light relations (correlations) between physically separated entities.
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958:
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1099:, apparently unaware of Einstein's aborted attempt earlier in the year. In his theory, every particle had an associated, hidden
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after the interaction which cannot reasonably be considered to depend on the particular measurement we perform on the system
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1150:
had presented a proof that there could be no "hidden parameters", but the validity of von Neumann's proof was questioned by
2953:
1410:
1274:
to refer exclusively to observations obtained under specified circumstances, including an account of the whole experiment."
477:
1103:
which served to guide its trajectory through space. The theory was subject to criticism at the Congress, particularly by
934:. Most hidden-variable theories are attempts to avoid this indeterminacy, but possibly at the expense of requiring that
2374:
1071:
reportedly replied to Einstein's later expression of this sentiment by advising him to "stop telling God what to do."
2684:
2647:
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137:
1910:
Einstein, Albert (2011). "Elementary Considerations on the Interpretation of the Foundations of Quantum Mechanics".
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31:
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published a paper, in which he was the first to clearly enunciate the probabilistic interpretation of the quantum
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proposed a hidden variable theory. Bohm unknowingly rediscovered (and extended) the idea that Louis de Broglie's
884:
333:
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181:
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2514:
Giancarlo Ghirardi; Raffaele Romano (2013). "Onthological models predictively inequivalent to quantum theory".
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function after the interaction has taken place. Let us now determine the physical state of the partial system
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a hidden-variable theory, and necessarily so. The major reference for Bohm's theory today is his book with
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2621:
Symposium on the Foundations of Modern Physics: 50 years of the EinsteinâPodolskyâRosen Gedankenexperiment
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have been measured (for instance, coordinates or momenta). Since there can be only one physical state of
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328:
318:
1055:'s response became one of the earliest and most famous assertions that quantum mechanics is incomplete:
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Michael K.-H. Kiessling: "Misleading Signposts Along the de BroglieâBohm Road to Quantum Mechanics",
1429:
existence in an abstract multi-dimensional configuration space, rather than three-dimensional space.
1270:
As a more appropriate way of expression, one may strongly advocate limitation of the use of the word
1116:
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1091:, held in Belgium in October 1927 and attended by all the major theoretical physicists of the era,
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function cannot be interpreted as a (complete) description of a physical state of a single system.
1110:
1107:, which de Broglie did not adequately answer; de Broglie abandoned the theory shortly thereafter.
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could not be explained by local hidden variables, the Bell inequality would be violated. Another
997:
Such a classical mechanics would eliminate unsettling characteristics of quantum theory like the
787:
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413:
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2943:
2619:(1985). "The EPR Problem in Its Historical Development". In Lahti, P.; Mittelstaedt, P. (eds.).
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Max Born and Werner Heisenberg, "Quantum mechanics", proceedings of the Fifth Solvay Congress.
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function is not unambiguously coordinated to the physical state. This coordination of several
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as completely as possible by measurements. Then quantum mechanics allows us to determine the
998:
923:
261:
246:
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1543:
Genovese, M. (2005). "Research on hidden variable theories: A review of recent progresses".
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function before their interaction be given. Then the Schrödinger equation will furnish the
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in his essay "Discussion with Einstein on Epistemological Problems in Atomic Physics", in
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Kwiat P. G.; et al. (1999). "Ultrabright source of polarization-entangled photons".
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This was, of course, in conflict with the definition used by the EPR paper, as follows:
3407:
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2007:
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that if local hidden variables exist, certain experiments could be performed involving
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1966:
1881:
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186:
45:
2401:
2282:
Gerard 't Hooft (2009). "Entangled quantum states in a local deterministic theory".
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1582:
930:; moreover, bounds for indeterminacy can be expressed in a quantitative form by the
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1956:
1819:
This is a common paraphrasing. Bohr recollected his reply to Einstein at the 1927
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298:
2115:"Can Quantum-Mechanical Description of Physical Reality be Considered Complete?"
2055:"Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"
1502:"Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"
1409:
which organizes a field. Nowadays Bohm's theory is considered to be one of many
926:
of the state of a system previous to measurement is assumed to be a part of the
3352:
3321:
3311:
2933:
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2742:
2582:
1606:
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1111:
Declaration of completeness of quantum mechanics, and the BohrâEinstein debates
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119:{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }
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loophole and proposed some ideas to construct local deterministic models.
965:
might indicate quantum mechanics is an incomplete description of reality.
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2222:
1422:
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1167:
913:
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30:
This article is about a class of mechanics theories. For other uses, see
2261:
Gerard 't Hooft (2007). "The Free-Will Postulate in Quantum Mechanics".
2616:
2482:
2154:
1765:
1414:
1368:
1068:
802:
772:
692:
667:
662:
647:
1961:
3046:
2727:
2186:(). 'Niels Bohr's contribution to epistemology', pp. 522â535 in
978:
293:
2639:
2608:
2449:"No extension of quantum theory can have improved predictive power"
2012:
1693:
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which interact with each other only during a limited time. Let the
1031:
672:
2528:
2465:
2288:
1916:
916:
physical model which seeks to explain the probabilistic nature of
2513:
1602:"Sorry, Einstein. Quantum Study Suggests 'Spooky Action' Is Real"
1316:. If, on the other hand, statistical correlations resulting from
905:
1349:
has disputed the validity of Bell's theorem on the basis of the
2426:. Routledge & Kegan Paul and D. Van Nostrand. p. 110.
1188:
Consider a mechanical system consisting of two partial systems
2190:, Cohen, R.S., Stachel, J.J. (editors), D. Riedel, Dordrecht,
1074:
920:
by introducing additional (possibly inaccessible) variables.
2157:(1948). "On the notions of causality and complementarity".
2446:
1788:
1042:
earlier in the year. Born concluded the paper as follows:
1630:"On the Problem of Hidden Variables in Quantum Mechanics"
1097:
his own version of a deterministic hidden-variable theory
1158:; the critical issue concerned averages over ensembles.
2633:
The Shaky Game: Einstein Realism and the Quantum Theory
1343:
that affect the validity of the experimental findings.
1588:
epistemic) dates to the beginning of the theory itself
1417:
theory to explain quantum phenomena. Nevertheless, it
938:
be allowed. One notable hidden-variable theory is the
2052:
1499:
1025:
985:; these therefore cannot be falsified by Bell tests.
973:
proved that correlations between particles under any
57:
2310:, February/March 1993, Theosophical University Press
1994:
Mermin, N. David; Schack, RĂŒdiger (September 2018).
1677:"Hidden variables and the two theorems of John Bell"
2281:
2260:
2507:
2440:
2382:International Studies in the Philosophy of Science
1996:"Homer Nodded: Von Neumann's Surprising Oversight"
118:
3448:
2623:. Singapore: World Scientific. pp. 129â149.
2585:(1982). "Is quantum theory universally valid?".
2372:
1937:"Einstein's Interpretation of Quantum Mechanics"
1356:
1121:Also at the Fifth Solvay Congress, Max Born and
1256:Bohr answered Einstein's challenge as follows:
1244:functions to the same physical state of system
2053:Einstein, A.; Podolsky, B.; Rosen, N. (1935).
1876:. New York: Oxford University Press. pp.
1500:Einstein, A.; Podolsky, B.; Rosen, N. (1935).
2655:
977:must obey certain constraints. Subsequently,
928:mathematical formulation of quantum mechanics
885:
1993:
113:
87:
2417:
2415:
2375:"On some early objections to Bohm's theory"
2207:
1324:concerning hidden-variable theories is the
2662:
2648:
2577:
2421:
2323:, volume 40, number 4, 2010, pp. 418â429 (
2094:Einstein A (1936). "Physics and Reality".
2093:
1934:
1872:The Quantum Story: A History in 40 Moments
1401:In Bohm's interpretation, the (non-local)
1075:Early attempts at hidden-variable theories
892:
878:
2527:
2490:
2464:
2287:
2266:
2221:
2138:
2078:
2029:
2011:
1960:
1915:
1692:
1556:
1527:
1216:from the measurements made, and from the
2412:
1909:
1542:
2635:. Chicago: University of Chicago Press.
2153:
1867:
1599:
14:
3449:
2615:
2424:Causality and Chance in Modern Physics
2112:
1825:Albert Einstein, PhilosopherâScientist
1742:"Zur Quantenmechanik der StoĂvorgĂ€nge"
1674:
1432:
1138:
2669:
2643:
2447:Roger Colbeck; Renato Renner (2011).
1495:
1493:
2627:
2304:"David Bohm and the Implicate Order"
1739:
1627:
1411:interpretations of quantum mechanics
24:
2171:10.1111/j.1746-8361.1948.tb00703.x
1490:
424:Sum-over-histories (path integral)
110:
84:
40:Part of a series of articles about
25:
3473:
2188:Selected Papers of LĂ©on Rosenfeld
2096:Journal of the Franklin Institute
1600:Markoff, Jack (21 October 2015).
1593:
1312:where the result would satisfy a
1289:
61:
3431:
3430:
2340:(2010), Vol. 18, No. 4, 469â480.
1935:Ballentine, L. E. (1972-12-01).
932:Heisenberg uncertainty principle
27:Type of quantum mechanics theory
2571:
2366:
2343:
2330:
2313:
2296:
2275:
2254:
2201:
2177:
2147:
2106:
2087:
2046:
1987:
1977:
1928:
1903:
1894:
1861:
1849:
1838:
1675:Mermin, N. David (1993-07-01).
1212:function of the partial system
1038:, which had been introduced by
3380:Relativistic quantum mechanics
2546:10.1103/PhysRevLett.110.170404
1813:
1809:. Macmillan. 1971. p. 91.
1799:
1733:
1668:
1621:
1536:
1468:Einstein's thought experiments
1335:and Paul Kwiat have performed
1161:
574:Relativistic quantum mechanics
106:
99:
80:
13:
1:
3358:Quantum statistical mechanics
3135:Quantum differential calculus
3057:Delayed-choice quantum eraser
2825:Symmetry in quantum mechanics
1575:10.1016/j.physrep.2005.03.003
1484:
1473:PuseyâBarrettâRudolph theorem
1357:Bohm's hidden-variable theory
1236:it may be concluded that the
988:
614:Quantum statistical mechanics
1628:Bell, John S. (1966-07-01).
975:local hidden variable theory
7:
3160:Quantum stochastic calculus
3150:Quantum measurement problem
3072:MachâZehnder interferometer
2588:American Journal of Physics
1941:American Journal of Physics
1460:
584:Quantum information science
10:
3478:
1425:, published posthumously.
1360:
1293:
1165:
1114:
1020:
29:
3426:
3388:
3340:
3220:Quantum complexity theory
3198:Quantum cellular automata
3173:
3105:
3039:
2952:
2901:
2888:Path integral formulation
2855:
2720:
2677:
2373:Wayne C. Myrvold (2003).
2349:D. Bohm and B. J. Hiley,
2031:10.1007/s10701-018-0197-5
1829:ob der liebe Gott wĂŒrfelt
1711:10.1103/RevModPhys.65.803
1681:Reviews of Modern Physics
1654:10.1103/RevModPhys.38.447
1634:Reviews of Modern Physics
3287:Quantum machine learning
3267:Quantum key distribution
3257:Quantum image processing
3247:Quantum error correction
3097:Wheeler's delayed choice
2240:10.1103/physreva.60.r773
1856:Albert Einstein Archives
1833:Encounters with Einstein
1026:"God does not play dice"
619:Quantum machine learning
372:Wheeler's delayed-choice
3203:Quantum finite automata
2516:Physical Review Letters
1413:. Some consider it the
329:LeggettâGarg inequality
3462:Hidden variable theory
3307:Quantum neural network
2394:10.1080/02698590305233
2352:The Undivided Universe
2321:Foundations of Physics
2140:10.1103/physrev.48.696
2080:10.1103/physrev.47.777
2000:Foundations of Physics
1746:Zeitschrift fĂŒr Physik
1529:10.1103/PhysRev.47.777
1396:double-slit experiment
1363:de BroglieâBohm theory
1326:KochenâSpecker theorem
1287:
1276:
1263:
1254:
1132:
1066:
1049:
1011:
940:de BroglieâBohm theory
910:hidden-variable theory
120:
18:Hidden variable theory
3332:Quantum teleportation
2845:Waveâparticle duality
2453:Nature Communications
1868:Baggott, Jim (2011).
1341:experimental problems
1280:
1268:
1258:
1248:shows again that the
1186:
1127:
1117:BohrâEinstein debates
1089:Fifth Solvay Congress
1057:
1044:
1007:
999:uncertainty principle
936:nonlocal interactions
314:Elitzur–Vaidman
304:Davisson–Germer
121:
3363:Quantum field theory
3292:Quantum metamaterial
3237:Quantum cryptography
2967:Consistent histories
1407:superimplicate order
1318:quantum entanglement
1310:quantum entanglement
1064:is not playing dice.
963:quantum entanglement
579:Quantum field theory
491:Consistent histories
128:Schrödinger equation
55:
3457:Quantum measurement
3348:Quantum fluctuation
3317:Quantum programming
3277:Quantum logic gates
3262:Quantum information
3242:Quantum electronics
2702:Classical mechanics
2601:1982AmJPh..50..807P
2538:2013PhRvL.110q0404G
2475:2011NatCo...2..411C
2422:David Bohm (1957).
2355:, Routledge, 1993,
2232:1999PhRvA..60..773K
2131:1935PhRv...48..696B
2071:1935PhRv...47..777E
2022:2018FoPh...48.1007M
1953:1972AmJPh..40.1763B
1758:1926ZPhy...37..863B
1703:1993RvMP...65..803M
1646:1966RvMP...38..447B
1567:2005PhR...413..319G
1520:1935PhRv...47..777E
1433:Recent developments
1331:Physicists such as
1139:von Neumann's proof
1081:Academy of Sciences
367:Stern–Gerlach
164:Classical mechanics
3401:in popular culture
3183:Quantum algorithms
3031:Von NeumannâWigner
3011:Objective collapse
2707:Old quantum theory
2483:10.1038/ncomms1416
1766:10.1007/BF01397477
1740:Born, Max (1926).
1558:quant-ph/0701071v1
1478:Spekkens toy model
1451:Giancarlo Ghirardi
1306:his famous theorem
1180:had proposed in a
555:Von NeumannâWigner
535:Objective-collapse
334:Mach–Zehnder
324:Leggett inequality
319:Franck–Hertz
169:Old quantum theory
116:
3444:
3443:
3418:Quantum mysticism
3396:Schrödinger's cat
3327:Quantum simulator
3297:Quantum metrology
3225:Quantum computing
3188:Quantum amplifier
3165:Quantum spacetime
3130:Quantum cosmology
3120:Quantum chemistry
2820:Scattering theory
2768:Zero-point energy
2763:Degenerate levels
2671:Quantum mechanics
2210:Physical Review A
2196:978-90-277-0652-2
2165:(3â4): 312â319 .
1962:10.1119/1.1987060
1947:(12): 1763â1771.
1887:978-0-19-956684-6
1449:In January 2013,
1403:quantum potential
1383:would have to be
1381:quantum mechanics
1373:pilot wave theory
1302:John Stewart Bell
1156:John Stewart Bell
1123:Werner Heisenberg
1040:Erwin Schrödinger
971:eponymous theorem
967:John Stewart Bell
918:quantum mechanics
902:
901:
609:Scattering theory
589:Quantum computing
362:Schrödinger's cat
294:Bell's inequality
102:
77:
46:Quantum mechanics
16:(Redirected from
3469:
3434:
3433:
3145:Quantum geometry
3140:Quantum dynamics
2997:Superdeterminism
2929:RaritaâSchwinger
2878:Matrix mechanics
2733:Braâket notation
2664:
2657:
2650:
2641:
2640:
2636:
2624:
2612:
2566:
2565:
2531:
2511:
2505:
2504:
2494:
2468:
2444:
2438:
2437:
2419:
2410:
2409:
2404:. Archived from
2379:
2370:
2364:
2347:
2341:
2334:
2328:
2317:
2311:
2308:Sunrise magazine
2300:
2294:
2293:
2291:
2279:
2273:
2272:
2270:
2268:quant-ph/0701097
2258:
2252:
2251:
2225:
2223:quant-ph/9810003
2216:(2): R773âR776.
2205:
2199:
2181:
2175:
2174:
2151:
2145:
2144:
2142:
2110:
2104:
2103:
2091:
2085:
2084:
2082:
2050:
2044:
2043:
2033:
2015:
2006:(9): 1007â1020.
1991:
1985:
1981:
1975:
1974:
1964:
1932:
1926:
1925:
1919:
1907:
1901:
1898:
1892:
1891:
1875:
1865:
1859:
1858:reel 2, item 100
1853:
1847:
1842:
1836:
1817:
1811:
1810:
1803:
1797:
1792:
1786:
1785:
1737:
1731:
1730:
1696:
1672:
1666:
1665:
1625:
1619:
1618:
1616:
1614:
1597:
1591:
1590:
1560:
1540:
1534:
1533:
1531:
1497:
1437:In August 2011,
1351:superdeterminism
1148:John von Neumann
1093:Louis de Broglie
983:superdeterminism
969:in 1964, in his
894:
887:
880:
521:Superdeterminism
174:Braâket notation
125:
123:
122:
117:
109:
104:
103:
95:
83:
78:
76:
65:
37:
36:
21:
3477:
3476:
3472:
3471:
3470:
3468:
3467:
3466:
3447:
3446:
3445:
3440:
3422:
3408:Wigner's friend
3384:
3375:Quantum gravity
3336:
3322:Quantum sensing
3302:Quantum network
3282:Quantum machine
3252:Quantum imaging
3215:Quantum circuit
3210:Quantum channel
3169:
3115:Quantum biology
3101:
3077:ElitzurâVaidman
3052:DavissonâGermer
3035:
2987:Hidden-variable
2977:de BroglieâBohm
2954:Interpretations
2948:
2897:
2851:
2738:Complementarity
2716:
2673:
2668:
2609:10.1119/1.13086
2583:Zurek, Wojciech
2574:
2569:
2512:
2508:
2445:
2441:
2434:
2420:
2413:
2377:
2371:
2367:
2348:
2344:
2338:European Review
2335:
2331:
2318:
2314:
2301:
2297:
2280:
2276:
2259:
2255:
2206:
2202:
2182:
2178:
2152:
2148:
2119:Physical Review
2113:Bohr N (1935).
2111:
2107:
2092:
2088:
2065:(10): 777â780.
2059:Physical Review
2051:
2047:
1992:
1988:
1982:
1978:
1933:
1929:
1908:
1904:
1899:
1895:
1888:
1866:
1862:
1854:
1850:
1843:
1839:
1821:Solvay Congress
1818:
1814:
1805:
1804:
1800:
1793:
1789:
1752:(12): 863â867.
1738:
1734:
1673:
1669:
1626:
1622:
1612:
1610:
1598:
1594:
1545:Physics Reports
1541:
1537:
1514:(10): 777â780.
1507:Physical Review
1498:
1491:
1487:
1482:
1463:
1455:Raffaele Romano
1435:
1365:
1359:
1347:Gerard 't Hooft
1314:Bell inequality
1304:showed through
1298:
1292:
1232:separated from
1170:
1164:
1141:
1119:
1113:
1077:
1053:Albert Einstein
1028:
1023:
1003:N. David Mermin
991:
947:Albert Einstein
898:
869:
868:
867:
632:
624:
623:
569:
568:Advanced topics
561:
560:
559:
511:Hidden-variable
501:de BroglieâBohm
480:
478:Interpretations
470:
469:
468:
438:
430:
429:
428:
386:
378:
377:
376:
343:
299:CHSH inequality
288:
280:
279:
278:
207:Complementarity
201:
193:
192:
191:
159:
130:
105:
94:
93:
79:
69:
64:
56:
53:
52:
35:
32:Hidden variable
28:
23:
22:
15:
12:
11:
5:
3475:
3465:
3464:
3459:
3442:
3441:
3439:
3438:
3427:
3424:
3423:
3421:
3420:
3415:
3410:
3405:
3404:
3403:
3392:
3390:
3386:
3385:
3383:
3382:
3377:
3372:
3371:
3370:
3360:
3355:
3353:Casimir effect
3350:
3344:
3342:
3338:
3337:
3335:
3334:
3329:
3324:
3319:
3314:
3312:Quantum optics
3309:
3304:
3299:
3294:
3289:
3284:
3279:
3274:
3269:
3264:
3259:
3254:
3249:
3244:
3239:
3234:
3233:
3232:
3222:
3217:
3212:
3207:
3206:
3205:
3195:
3190:
3185:
3179:
3177:
3171:
3170:
3168:
3167:
3162:
3157:
3152:
3147:
3142:
3137:
3132:
3127:
3122:
3117:
3111:
3109:
3103:
3102:
3100:
3099:
3094:
3089:
3087:Quantum eraser
3084:
3079:
3074:
3069:
3064:
3059:
3054:
3049:
3043:
3041:
3037:
3036:
3034:
3033:
3028:
3023:
3018:
3013:
3008:
3003:
3002:
3001:
3000:
2999:
2984:
2979:
2974:
2969:
2964:
2958:
2956:
2950:
2949:
2947:
2946:
2941:
2936:
2931:
2926:
2921:
2916:
2911:
2905:
2903:
2899:
2898:
2896:
2895:
2890:
2885:
2880:
2875:
2870:
2865:
2859:
2857:
2853:
2852:
2850:
2849:
2848:
2847:
2842:
2832:
2827:
2822:
2817:
2812:
2807:
2802:
2797:
2792:
2787:
2782:
2777:
2772:
2771:
2770:
2765:
2760:
2755:
2745:
2743:Density matrix
2740:
2735:
2730:
2724:
2722:
2718:
2717:
2715:
2714:
2709:
2704:
2699:
2698:
2697:
2687:
2681:
2679:
2675:
2674:
2667:
2666:
2659:
2652:
2644:
2638:
2637:
2625:
2613:
2595:(9): 807â810.
2573:
2570:
2568:
2567:
2522:(17): 170404.
2506:
2439:
2432:
2411:
2408:on 2014-07-02.
2365:
2342:
2329:
2312:
2306:. Appeared in
2295:
2274:
2253:
2200:
2176:
2146:
2105:
2086:
2045:
1986:
1976:
1927:
1902:
1893:
1886:
1860:
1848:
1837:
1812:
1798:
1787:
1732:
1687:(3): 803â815.
1667:
1640:(3): 447â452.
1620:
1607:New York Times
1592:
1551:(6): 319â396.
1535:
1488:
1486:
1483:
1481:
1480:
1475:
1470:
1464:
1462:
1459:
1434:
1431:
1361:Main article:
1358:
1355:
1296:Bell's theorem
1294:Main article:
1291:
1290:Bell's theorem
1288:
1174:Boris Podolsky
1166:Main article:
1163:
1160:
1140:
1137:
1115:Main article:
1112:
1109:
1105:Wolfgang Pauli
1076:
1073:
1030:In June 1926,
1027:
1024:
1022:
1019:
990:
987:
951:Boris Podolsky
900:
899:
897:
896:
889:
882:
874:
871:
870:
866:
865:
860:
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:
634:
633:
630:
629:
626:
625:
622:
621:
616:
611:
606:
604:Density matrix
601:
596:
591:
586:
581:
576:
570:
567:
566:
563:
562:
558:
557:
552:
547:
542:
537:
532:
527:
526:
525:
524:
523:
508:
503:
498:
493:
488:
482:
481:
476:
475:
472:
471:
467:
466:
461:
456:
451:
446:
440:
439:
436:
435:
432:
431:
427:
426:
421:
416:
411:
406:
401:
395:
394:
393:
387:
384:
383:
380:
379:
375:
374:
369:
364:
358:
357:
356:
355:
354:
352:Delayed-choice
347:Quantum eraser
342:
341:
336:
331:
326:
321:
316:
311:
306:
301:
296:
290:
289:
286:
285:
282:
281:
277:
276:
275:
274:
264:
259:
254:
249:
244:
239:
237:Quantum number
234:
229:
224:
219:
214:
209:
203:
202:
199:
198:
195:
194:
190:
189:
184:
178:
177:
176:
171:
166:
160:
157:
156:
153:
152:
151:
150:
145:
140:
132:
131:
126:
115:
112:
108:
101:
98:
92:
89:
86:
82:
75:
72:
68:
63:
60:
49:
48:
42:
41:
26:
9:
6:
4:
3:
2:
3474:
3463:
3460:
3458:
3455:
3454:
3452:
3437:
3429:
3428:
3425:
3419:
3416:
3414:
3411:
3409:
3406:
3402:
3399:
3398:
3397:
3394:
3393:
3391:
3387:
3381:
3378:
3376:
3373:
3369:
3366:
3365:
3364:
3361:
3359:
3356:
3354:
3351:
3349:
3346:
3345:
3343:
3339:
3333:
3330:
3328:
3325:
3323:
3320:
3318:
3315:
3313:
3310:
3308:
3305:
3303:
3300:
3298:
3295:
3293:
3290:
3288:
3285:
3283:
3280:
3278:
3275:
3273:
3272:Quantum logic
3270:
3268:
3265:
3263:
3260:
3258:
3255:
3253:
3250:
3248:
3245:
3243:
3240:
3238:
3235:
3231:
3228:
3227:
3226:
3223:
3221:
3218:
3216:
3213:
3211:
3208:
3204:
3201:
3200:
3199:
3196:
3194:
3191:
3189:
3186:
3184:
3181:
3180:
3178:
3176:
3172:
3166:
3163:
3161:
3158:
3156:
3153:
3151:
3148:
3146:
3143:
3141:
3138:
3136:
3133:
3131:
3128:
3126:
3125:Quantum chaos
3123:
3121:
3118:
3116:
3113:
3112:
3110:
3108:
3104:
3098:
3095:
3093:
3092:SternâGerlach
3090:
3088:
3085:
3083:
3080:
3078:
3075:
3073:
3070:
3068:
3065:
3063:
3060:
3058:
3055:
3053:
3050:
3048:
3045:
3044:
3042:
3038:
3032:
3029:
3027:
3026:Transactional
3024:
3022:
3019:
3017:
3016:Quantum logic
3014:
3012:
3009:
3007:
3004:
2998:
2995:
2994:
2993:
2990:
2989:
2988:
2985:
2983:
2980:
2978:
2975:
2973:
2970:
2968:
2965:
2963:
2960:
2959:
2957:
2955:
2951:
2945:
2942:
2940:
2937:
2935:
2932:
2930:
2927:
2925:
2922:
2920:
2917:
2915:
2912:
2910:
2907:
2906:
2904:
2900:
2894:
2891:
2889:
2886:
2884:
2881:
2879:
2876:
2874:
2871:
2869:
2866:
2864:
2861:
2860:
2858:
2854:
2846:
2843:
2841:
2838:
2837:
2836:
2835:Wave function
2833:
2831:
2828:
2826:
2823:
2821:
2818:
2816:
2813:
2811:
2810:Superposition
2808:
2806:
2805:Quantum state
2803:
2801:
2798:
2796:
2793:
2791:
2788:
2786:
2783:
2781:
2778:
2776:
2773:
2769:
2766:
2764:
2761:
2759:
2758:Excited state
2756:
2754:
2751:
2750:
2749:
2746:
2744:
2741:
2739:
2736:
2734:
2731:
2729:
2726:
2725:
2723:
2719:
2713:
2710:
2708:
2705:
2703:
2700:
2696:
2693:
2692:
2691:
2688:
2686:
2683:
2682:
2680:
2676:
2672:
2665:
2660:
2658:
2653:
2651:
2646:
2645:
2642:
2634:
2630:
2626:
2622:
2618:
2614:
2610:
2606:
2602:
2598:
2594:
2590:
2589:
2584:
2580:
2576:
2575:
2563:
2559:
2555:
2551:
2547:
2543:
2539:
2535:
2530:
2525:
2521:
2517:
2510:
2502:
2498:
2493:
2488:
2484:
2480:
2476:
2472:
2467:
2462:
2458:
2454:
2450:
2443:
2435:
2433:0-8122-1002-6
2429:
2425:
2418:
2416:
2407:
2403:
2399:
2395:
2391:
2387:
2383:
2376:
2369:
2362:
2361:0-415-06588-7
2358:
2354:
2353:
2346:
2339:
2333:
2326:
2322:
2316:
2309:
2305:
2302:David Pratt:
2299:
2290:
2285:
2278:
2269:
2264:
2257:
2249:
2245:
2241:
2237:
2233:
2229:
2224:
2219:
2215:
2211:
2204:
2197:
2193:
2189:
2185:
2184:Rosenfeld, L.
2180:
2172:
2168:
2164:
2160:
2156:
2150:
2141:
2136:
2132:
2128:
2124:
2120:
2116:
2109:
2101:
2097:
2090:
2081:
2076:
2072:
2068:
2064:
2060:
2056:
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1443:Renato Renner
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1439:Roger Colbeck
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1390:Bohm posited
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1322:no-go theorem
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1152:Grete Hermann
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924:Indeterminacy
921:
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914:deterministic
911:
907:
895:
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888:
883:
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594:Quantum chaos
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550:Transactional
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540:Quantum logic
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19:
3155:Quantum mind
3067:FranckâHertz
2986:
2909:KleinâGordon
2863:Formulations
2856:Formulations
2785:Interference
2775:Entanglement
2753:Ground state
2748:Energy level
2721:Fundamentals
2685:Introduction
2632:
2629:Fine, Arthur
2620:
2592:
2586:
2579:Peres, Asher
2572:Bibliography
2519:
2515:
2509:
2456:
2452:
2442:
2423:
2406:the original
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2256:
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2003:
1999:
1989:
1979:
1944:
1940:
1930:
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1801:
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1623:
1611:. Retrieved
1605:
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1511:
1505:
1448:
1436:
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1366:
1345:
1333:Alain Aspect
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1209:
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1201:
1197:
1193:
1189:
1187:
1178:Nathan Rosen
1171:
1142:
1133:
1128:
1120:
1101:"pilot wave"
1086:
1078:
1067:
1061:
1058:
1050:
1045:
1029:
1014:
1012:
1008:
996:
992:
961:argued that
955:Nathan Rosen
944:
922:
909:
903:
510:
449:KleinâGordon
385:Formulations
222:Energy level
217:Entanglement
200:Fundamentals
187:Interference
138:Introduction
3413:EPR paradox
3193:Quantum bus
3062:Double-slit
3040:Experiments
3006:Many-worlds
2944:Schrödinger
2893:Phase space
2883:Schrödinger
2873:Interaction
2830:Uncertainty
2800:Nonlocality
2795:Measurement
2790:Decoherence
2780:Hamiltonian
2617:Jammer, Max
2388:(1): 8â24.
1423:Basil Hiley
1337:experiments
1168:EPR paradox
1162:EPR paradox
838:von Neumann
823:Schrödinger
599:EPR paradox
530:Many-worlds
464:Schrödinger
419:Schrödinger
414:Phase-space
404:Interaction
309:Double-slit
287:Experiments
262:Uncertainty
232:Nonlocality
227:Measurement
212:Decoherence
182:Hamiltonian
3451:Categories
3341:Extensions
3175:Technology
3021:Relational
2972:Copenhagen
2868:Heisenberg
2815:Tunnelling
2678:Background
2459:(8): 411.
2159:Dialectica
2125:(8): 700.
2013:1805.10311
1694:1802.10119
1613:21 October
1485:References
1377:consistent
1369:David Bohm
1272:phenomenon
1095:presented
1069:Niels Bohr
1017:revealed.
989:Motivation
833:Sommerfeld
748:Heisenberg
743:Gutzwiller
683:de Broglie
631:Scientists
545:Relational
496:Copenhagen
399:Heisenberg
257:Tunnelling
158:Background
3047:Bell test
2902:Equations
2728:Born rule
2529:1301.2695
2466:1005.5173
2289:0908.3408
2040:0015-9018
1971:0002-9505
1917:1107.3701
1782:119896026
1774:1434-6001
1727:119546199
1719:0034-6861
1662:0034-6861
1385:non-local
1367:In 1952,
1300:In 1964,
1284:quantity.
1005:puts it:
979:Bell test
959:EPR paper
957:in their
945:In 1935,
863:Zeilinger
708:Ehrenfest
437:Equations
114:⟩
111:Ψ
100:^
88:⟩
85:Ψ
62:ℏ
3436:Category
3230:Timeline
2982:Ensemble
2962:Bayesian
2924:Majorana
2840:Collapse
2712:Glossary
2695:Timeline
2631:(1986).
2554:23679689
2501:21811240
2402:10965929
2325:abstract
2248:16417960
1583:14833712
1461:See also
1415:simplest
1032:Max Born
788:Millikan
713:Einstein
698:Davisson
653:Blackett
638:Aharonov
506:Ensemble
486:Bayesian
391:Overview
272:Collapse
252:Symmetry
143:Glossary
3389:Related
3368:History
3107:Science
2939:Rydberg
2690:History
2597:Bibcode
2534:Bibcode
2492:3265370
2471:Bibcode
2228:Bibcode
2155:Bohr N.
2127:Bibcode
2067:Bibcode
2018:Bibcode
1949:Bibcode
1754:Bibcode
1699:Bibcode
1642:Bibcode
1563:Bibcode
1516:Bibcode
1087:At the
1021:History
906:physics
828:Simmons
818:Rydberg
783:Moseley
763:Kramers
753:Hilbert
738:Glauber
733:Feynman
718:Everett
688:Compton
459:Rydberg
148:History
3082:Popper
2562:197479
2560:
2552:
2499:
2489:
2430:
2400:
2359:
2246:
2194:
2038:
1969:
1884:
1880:â117.
1780:
1772:
1725:
1717:
1660:
1581:
1176:, and
953:, and
858:Zeeman
853:Wigner
803:Planck
773:Landau
758:Jordan
409:Matrix
339:Popper
2992:Local
2934:Pauli
2914:Dirac
2558:S2CID
2524:arXiv
2461:arXiv
2398:S2CID
2378:(PDF)
2284:arXiv
2263:arXiv
2244:S2CID
2218:arXiv
2008:arXiv
1912:arXiv
1778:S2CID
1723:S2CID
1689:arXiv
1579:S2CID
1553:arXiv
1379:with
1182:paper
1143:In a
912:is a
813:Raman
798:Pauli
793:Onnes
728:Fermi
703:Debye
693:Dirac
658:Bloch
648:Bethe
516:Local
454:Pauli
444:Dirac
242:State
2919:Weyl
2550:PMID
2497:PMID
2428:ISBN
2357:ISBN
2192:ISBN
2036:ISSN
1967:ISSN
1882:ISBN
1770:ISSN
1715:ISSN
1658:ISSN
1615:2015
1453:and
1441:and
1392:both
1192:and
908:, a
848:Wien
843:Weyl
808:Rabi
778:Laue
768:Lamb
723:Fock
678:Bose
673:Born
668:Bohr
663:Bohm
643:Bell
2605:doi
2542:doi
2520:110
2487:PMC
2479:doi
2390:doi
2236:doi
2167:doi
2135:doi
2100:221
2075:doi
2026:doi
1957:doi
1923:USA
1878:116
1762:doi
1707:doi
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