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forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete." The EPR paper ends by saying: "While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible." The 1935 EPR paper condensed the philosophical discussion into a physical argument. The authors claim that given a specific experiment, in which the outcome of a measurement is known before the measurement takes place, there must exist something in the real world, an "element of reality", that determines the measurement outcome. They postulate that these elements of reality are, in modern terminology,
958:. Einstein, Podolsky, and Rosen pointed out that, in this state, if the position of the first particle were measured, the result of measuring the position of the second particle could be predicted. If instead the momentum of the first particle were measured, then the result of measuring the momentum of the second particle could be predicted. They argued that no action taken on the first particle could instantaneously affect the other, since this would involve information being transmitted faster than light, which is impossible according to the
898:
1112:, meaning the choice to measure one excludes the possibility of measuring the other. Consequently, a fact deduced regarding one arrangement of laboratory apparatus could not be combined with a fact deduced by means of the other, and so, the inference of predetermined position and momentum values for the second particle was not valid. Bohr concluded that EPR's "arguments do not justify their conclusion that the quantum description turns out to be essentially incomplete."
1458:; however, it turns out that the usual rules for combining quantum mechanical and classical descriptions violate EPR's principle of locality without violating special relativity or causality. Causality is preserved because there is no way for Alice to transmit messages (i.e., information) to Bob by manipulating her measurement axis. Whichever axis she uses, she has a 50% probability of obtaining "+" and 50% probability of obtaining "−", completely at
1337:
hidden-variable theory, but it had a grossly nonlocal character. Bell set out to investigate whether it was indeed possible to solve the nonlocality problem with hidden variables, and found out that first, the correlations shown in both EPR's and Bohm's versions of the paradox could indeed be explained in a local way with hidden variables, and second, that the correlations shown in his own variant of the paradox couldn't be explained by
5612:
1219:
991:, it is impossible to measure both the momentum and the position of particle B exactly; however, it is possible to measure the exact position of particle A. By calculation, therefore, with the exact position of particle A known, the exact position of particle B can be known. Alternatively, the exact momentum of particle A can be measured, so the exact momentum of particle B can be worked out. As
1028:
1747:
1470:, which makes it impossible for him to make an arbitrary number of copies of the electron he receives, perform a spin measurement on each, and look at the statistical distribution of the results. Therefore, in the one measurement he is allowed to make, there is a 50% probability of getting "+" and 50% of getting "−", regardless of whether or not his axis is aligned with Alice's.
5151:
2044:
987:. The original paper purports to describe what must happen to "two systems I and II, which we permit to interact", and after some time "we suppose that there is no longer any interaction between the two parts." The EPR description involves "two particles, A and B, interact briefly and then move off in opposite directions." According to
1070:"Any information upon which the article 'Einstein Attacks Quantum Theory' in your issue of May 4 is based was given to you without authority. It is my invariable practice to discuss scientific matters only in the appropriate forum and I deprecate advance publication of any announcement in regard to such matters in the secular press."
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has several different meanings in physics. EPR describe the principle of locality as asserting that physical processes occurring at one place should have no immediate effect on the elements of reality at another location. At first sight, this appears to be a reasonable assumption to make, as it seems
1317:
the measurement. Therefore, Bob's positron will have a definite spin when measured along the same axis as Alice's electron, but when measured in the perpendicular axis its spin will be uniformly random. It seems as if information has propagated (faster than light) from Alice's apparatus to make Bob's
1132:
quantum states of particle B. He argued that, because of locality, the real state of particle B could not depend on which kind of measurement was done in A and that the quantum states therefore cannot be in one-to-one correspondence with the real states. Einstein struggled unsuccessfully for the rest
1336:
published a paper investigating the puzzling situation at that time: on one hand, the EPR paradox purportedly showed that quantum mechanics was nonlocal, and suggested that a hidden-variable theory could heal this nonlocality. On the other hand, David Bohm had recently developed the first successful
1085:
later noted, "t remains a historical fact that the earliest criticism of the EPR paper — moreover, a criticism which correctly saw in
Einstein's conception of physical reality the key problem of the whole issue — appeared in a daily newspaper prior to the publication of the criticized paper itself."
1388:
Bell showed, however, that such models can only reproduce the singlet correlations when Alice and Bob make measurements on the same axis or on perpendicular axes. As soon as other angles between their axes are allowed, local hidden-variable theories become unable to reproduce the quantum mechanical
1120:
In his own publications and correspondence, Einstein indicated that he was not satisfied with the EPR paper and that Rosen had authored most of it. He later used a different argument to insist that quantum mechanics is an incomplete theory. He explicitly de-emphasized EPR's attribution of "elements
1908:
1401:
in the 1980s; all experiments conducted to date have found behavior in line with the predictions of quantum mechanics. The present view of the situation is that quantum mechanics flatly contradicts
Einstein's philosophical postulate that any acceptable physical theory must fulfill "local realism".
1007:
EPR tried to set up a paradox to question the range of true application of quantum mechanics: Quantum theory predicts that both values cannot be known for a particle, and yet the EPR thought experiment purports to show that they must all have determinate values. The EPR paper says: "We are thus
966:
equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity." From this, they inferred that the second particle must have a definite value of both position and of momentum prior to either quantity being measured. But quantum mechanics
939:
is incomplete. In a 1935 paper titled "Can
Quantum-Mechanical Description of Physical Reality be Considered Complete?", they argued for the existence of "elements of reality" that were not part of quantum theory, and speculated that it should be possible to construct a theory containing these
2217:
2081:
1344:
To understand the first result, consider the following toy hidden-variable theory introduced later by J.J. Sakurai: in it, quantum spin-singlet states emitted by the source are actually approximate descriptions for "true" physical states possessing definite values for the
995:
writes, "EPR argued that they had proved that ... B can have simultaneously exact values of position and momentum. ... Particle B has a position that is real and a momentum that is real. EPR appeared to have contrived a means to establish the exact values of
1790:
2577:
2448:
1742:{\displaystyle S_{x}={\frac {\hbar }{2}}{\begin{bmatrix}0&1\\1&0\end{bmatrix}},\quad S_{y}={\frac {\hbar }{2}}{\begin{bmatrix}0&-i\\i&0\end{bmatrix}},\quad S_{z}={\frac {\hbar }{2}}{\begin{bmatrix}1&0\\0&-1\end{bmatrix}},}
1154:
proposed a variant of the EPR thought experiment in which the measurements have discrete ranges of possible outcomes, unlike the position and momentum measurements considered by EPR. The EPR–Bohm thought experiment can be explained using
1353:-spin. In these "true" states, the positron going to Bob always has spin values opposite to the electron going to Alice, but the values are otherwise completely random. For example, the first pair emitted by the source might be "(+
2942:>." Emphasis from the original. "Ist mir wurst" is a German expression that literally translates to "It is a sausage to me", but means "I couldn't care less". Letter from Einstein to Schrödinger, dated 19th June 1935.
117:
3638:
Reid, M. D.; Drummond, P. D.; Bowen, W. P.; Cavalcanti, E. G.; Lam, P. K.; Bachor, H. A.; Andersen, U. L.; Leuchs, G. (2009-12-10). "Colloquium: The
Einstein-Podolsky-Rosen paradox: From concepts to applications".
1222:
The EPR thought experiment, performed with electron–positron pairs. A source (center) sends particles toward two observers, electrons to Alice (left) and positrons to Bob (right), who can perform spin measurements.
2039:{\displaystyle \left|+x\right\rangle \leftrightarrow {\frac {1}{\sqrt {2}}}{\begin{bmatrix}1\\1\end{bmatrix}},\quad \left|-x\right\rangle \leftrightarrow {\frac {1}{\sqrt {2}}}{\begin{bmatrix}1\\-1\end{bmatrix}}.}
1402:
The fact that quantum mechanics violates Bell inequalities indicates that any hidden-variable theory underlying quantum mechanics must be non-local; whether this should be taken to imply that quantum mechanics
1477:
is possible; however, the principle of locality appeals powerfully to physical intuition, and
Einstein, Podolsky and Rosen were unwilling to abandon it. Einstein derided the quantum mechanical predictions as
1385:) to Bob", and so forth. Therefore, if Bob's measurement axis is aligned with Alice's, he will necessarily get the opposite of whatever Alice gets; otherwise, he will get "+" and "−" with equal probability.
1049:
that, "it did not come out as well as I had originally wanted; rather, the essential thing was, so to speak, smothered by the formalism." Einstein would later go on to present an individual account of his
1121:
of reality" to the position and momentum of particle B, saying that "I couldn't care less" whether the resulting states of particle B allowed one to predict the position and momentum with certainty.
971:
and thus does not associate simultaneous values for both to any system. Einstein, Podolsky, and Rosen therefore concluded that quantum theory does not provide a complete description of reality.
2343:{\displaystyle \left|\psi \right\rangle =-{\frac {1}{\sqrt {2}}}{\biggl (}\left|+x\right\rangle \otimes \left|-x\right\rangle -\left|-x\right\rangle \otimes \left|+x\right\rangle {\biggr )},}
2204:{\displaystyle \left|\psi \right\rangle ={\frac {1}{\sqrt {2}}}{\biggl (}\left|+z\right\rangle \otimes \left|-z\right\rangle -\left|-z\right\rangle \otimes \left|+z\right\rangle {\biggr )},}
5218:
1473:
As a summary, the results of the EPR thought experiment do not contradict the predictions of special relativity. Neither the EPR paradox nor any quantum experiment demonstrates that
2903:
4668:
Rowe, M. A.; Kielpinski, D.; Meyer, V.; Sackett, C. A.; Itano, W. M.; Monroe, C.; Wineland, D. J. (2001). "Experimental violation of a Bell's inequality with efficient detection".
5522:
2936:
962:. They invoked a principle, later known as the "EPR criterion of reality", positing that: "If, without in any way disturbing a system, we can predict with certainty (i.e., with
5547:
2432:
5133:
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1891:{\displaystyle \left|+z\right\rangle \leftrightarrow {\begin{bmatrix}1\\0\end{bmatrix}},\quad \left|-z\right\rangle \leftrightarrow {\begin{bmatrix}0\\1\end{bmatrix}}}
1246:
into state I. The quantum state determines the probable outcomes of any measurement performed on the system. In this case, if Bob subsequently measures spin along the
2690:{\displaystyle \left|-z\right\rangle \otimes \left|+z\right\rangle =\left|-z\right\rangle \otimes {\frac {\left|+x\right\rangle +\left|-x\right\rangle }{\sqrt {2}}}.}
2561:{\displaystyle \left|+z\right\rangle \otimes \left|-z\right\rangle =\left|+z\right\rangle \otimes {\frac {\left|+x\right\rangle -\left|-x\right\rangle }{\sqrt {2}}}.}
1424:
et al. formalised it in 2007 as the phenomenon of quantum steering. They defined steering as the situation where Alice's measurements on a part of an entangled state
1767:
1462:; according to quantum mechanics, it is fundamentally impossible for her to influence what result she gets. Furthermore, Bob is able to perform his measurement only
5158:
1081:, who said, "Of course, a great deal of the argument hinges on just what meaning is to be attached to the word 'reality' in physics." The physicist and historian
383:
1215:. Because it is in a superposition of states, it is impossible without measuring to know the definite state of spin of either particle in the spin singlet.
5078:
884:
5552:
1041:
Though the EPR paper has often been taken as an exact expression of
Einstein's views, it was primarily authored by Podolsky, based on discussions at the
1066:
ran a news story about it, under the headline "Einstein
Attacks Quantum Theory". The story, which quoted Podolsky, irritated Einstein, who wrote to the
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3311:
1285:
applies to alternating measurements of them: a quantum state cannot possess a definite value for both of these variables. Suppose Alice measures the
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135:
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1266:-axis: according to quantum mechanics the spin singlet state may equally well be expressed as a superposition of spin states pointing in the
988:
3024:
2752:
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about the nature of quantum reality.) He argued that EPR had reasoned fallaciously. Bohr said measurements of position and of momentum are
470:
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of its point in spacetime (i.e. in the past). These claims are founded on assumptions about nature that constitute what is now known as
945:
1004:
the position of B due to measurements made on particle A, without the slightest possibility of particle B being physically disturbed."
5542:
5365:
5207:
5048:
4921:
3908:
3176:
4180:
Wiseman, H. M.; Jones, S. J.; Doherty, A. C. (2007). "Steering, Entanglement, Nonlocality, and the
Einstein-Podolsky-Rosen Paradox".
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model, where Bob would have a fixed quantum state in his side, that is classically correlated but otherwise independent of Alice's.
130:
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1175:. According to quantum mechanics, we can arrange our source so that each emitted pair occupies a quantum state called a
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1501:, with each quantum state corresponding to a vector in that space. The operators corresponding to the spin along the
493:
5258:
3232:
Kaiser, David (1994). "Bringing the human actors back on stage: the personal context of the
Einstein-Bohr debate".
870:
522:
5113:
5093:
4551:
Hardy, Lucien (1993-09-13). "Nonlocality for two particles without inequalities for almost all entangled states".
3603:
D. Bohm; Y. Aharonov (1957). "Discussion of
Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky".
2742:
1105:
441:
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2777:
1109:
979:
The term "Einstein–Podolsky–Rosen paradox" or "EPR" arose from a paper written in 1934 after Einstein joined the
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339:
199:
1016:. Each element may, again in modern terminology, only be influenced by events which are located in the backward
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Whatever axis their spins are measured along, they are always found to be opposite. In quantum mechanics, the
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pairs. Suppose we have a source that emits electron–positron pairs, with the electron sent to destination
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331:
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264:
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3859:
Bohm, D. (1952). "A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II".
3524:
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
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254:
239:
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Bohm, D. (1952). "A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I".
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where the two terms on the right hand side are what we have referred to as state I and state II above.
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The thought experiment involves a pair of particles prepared in what would later become known as an
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Blaylock, Guy (January 2010). "The EPR paradox, Bell's inequality, and the question of locality".
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Schrödinger, E. (October 1935). "Discussion of Probability Relations between Separated Systems".
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1393:", is in principle experimentally testable. After the publication of Bell's paper, a variety of
1128:, that the choice of measurement done in particle A, either position or momentum, would lead to
3787:
3593:, Prentice-Hall, Englewood Cliffs, page 29, and Chapter 5 section 3, and Chapter 22 Section 19.
2849:
2350:
where the terms on the right hand side are what we have referred to as state Ia and state IIa.
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38:
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Stanford Encyclopedia of Philosophy: The Einstein–Podolsky–Rosen Argument in Quantum Theory;
4503:
Fine, Arthur (1982-02-01). "Hidden Variables, Joint Probability, and the Bell Inequalities".
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1494:. The spin degree of freedom for an electron is associated with a two-dimensional complex
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The Philosophy of Quantum Mechanics: The Interpretations of QM in Historical Perspective
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2214:
From the above equations, it can be shown that the spin singlet can also be written as
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P. Pluch, "Theory for Quantum Probability", PhD Thesis University of Klagenfurt (2006)
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in the second case. The right hand side of the equations show that the measurement of
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3073:
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4792:
4078:
Schrödinger, E. (October 1936). "Probability relations between separated systems".
1495:
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local hidden-variable theory. This second result became known as the Bell theorem.
1176:
992:
932:
840:
835:
770:
755:
720:
214:
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Einstein, Albert (1949). "Autobiographical Notes". In Schilpp, Paul Arthur (ed.).
1293:, so that the quantum state collapses into state I. Now, instead of measuring the
1104:), in the same year, using the same title. (This exchange was only one chapter in
1482:". The conclusion they drew was that quantum mechanics is not a complete theory.
5587:
5266:
5088:
4877:
4841:
4810:
4607:
4572:
4459:"Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"
3553:
3374:"Can Quantum-Mechanical Description of Physical Reality be Considered Complete?"
3115:"Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"
3020:
2976:"Can Quantum-Mechanical Description of Physical Reality be Considered Complete?"
1187:
of two states, which we call state I and state II. In state I, the electron has
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760:
695:
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5592:
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4916:
Does Bell's Inequality Principle rule out local theories of quantum mechanics?
4762:
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4150:
4099:
3458:
3425:(2010). "Einstein, incompleteness, and the epistemic view of quantum states".
3344:
3245:
3208:
2445:, this means that immediately after measurement the system state collapses to
1777:
1459:
1428:
Bob's part of the state. That is, Bob's observations cannot be explained by a
1151:
1095:
1082:
1031:
Article headline regarding the EPR paradox paper in the May 4, 1935, issue of
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To illustrate the paradox, we need to show that after Alice's measurement of
112:{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }
4856:
Quantum Mechanics Versus Local Realism: The Einstein–Podolsky–Rosen Paradox
4409:
2762:
1490:
Bohm's variant of the EPR paradox can be expressed mathematically using the
1394:
1301:-spin. According to quantum mechanics, when the system is in state I, Bob's
1013:
286:
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4588:
4545:
Philosophical Consequences of Quantum Theory: Reflections on Bell's Theorem
4486:
4227:
3880:
3845:
3403:
3139:
3114:
3005:
1313:. It is impossible to predict which outcome will appear until Bob actually
4547:, edited by Cushing & McMullin (University of Notre Dame Press, 1986).
4320:
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of the electron's and positron's vector spaces. The spin singlet state is
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3163:
Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality
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For Einstein, the crucial part of the argument was the demonstration of
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of his life to find a theory that could better comply with his idea of
4846:
The God Particle: If the Universe Is the Answer, What Is the Question?
4283:
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2951:"Spukhaften Fernwirkung", in the German original. Used in a letter to
1389:
correlations. This difference, expressed using inequalities known as "
4689:
1420:
Inspired by Schrödinger's treatment of the EPR paradox back in 1935,
4308:(in German) (3 ed.). München: Langen Müller. 2005. p. 254.
3125:(10). Princeton, New Jersey: Institute for Advanced Study: 777–780.
1450:, which states that energy can never be transmitted faster than the
4353:
Eberhard, P. H. (1977). "Bell's theorem without hidden variables".
4039:
3722:
Laloe, Franck (2012). "Do We Really Understand Quantum Mechanics".
3293:
English translation by Jean Piccard, pp 349–382 in the same issue,
4946:
4937:
Spooky Actions At A Distance?: Oppenheimer Lecture by Prof. Mermin
4266:
3953:
3653:
3441:
2697:
The left hand side of both equations show that the measurement of
1217:
935:
which argues that the description of physical reality provided by
3113:
Einstein, Albert; Podolsky, Boris; Rosen, Nathan (May 15, 1935).
944:. Resolutions of the paradox have important implications for the
4731:
Smerlak, Matteo; Rovelli, Carlo (2007-02-03). "Relational EPR".
3520:"An Einstein manuscript on the EPR paradox for spin observables"
4950:
4131:
Mathematical Proceedings of the Cambridge Philosophical Society
4080:
Mathematical Proceedings of the Cambridge Philosophical Society
4889:
The Einstein-Podolsky-Rosen Argument and the Bell Inequalities
4888:
4931:
3483:
Howard, D. (1985). "Einstein on locality and separability".
1466:: there is a fundamental property of quantum mechanics, the
1305:-spin measurement will have a 50% probability of producing +
4023:(2014). "Quantum non-locality—it ain't necessarily so...".
2395:) is uniformly random. This follows from the principles of
3167:(Reprint ed.). W. W. Norton & Company. pp.
1318:
positron assume a definite spin in the appropriate axis.
4815:
The Shaky Game: Einstein, Realism and the Quantum Theory
1199:) and the positron has spin pointing downward along the
4410:"Bell's theorem and the different concepts of locality"
1242:. Informally speaking, the quantum state of the system
1012:, in the sense that each belongs to a certain point in
2009:
1948:
1867:
1818:
1702:
1636:
1573:
1250:-axis, there is 100% probability that he will obtain −
5219:
Die Grundlagen der Einsteinschen Relativitäts-Theorie
2911:
2879:
2852:
2580:
2451:
2412:
2220:
2084:
2054:
1911:
1793:
1755:
1544:
1230:-axis. She can obtain one of two possible outcomes: +
1045:
with Einstein and Rosen. Einstein later expressed to
50:
4457:
Einstein, A.; Podolsky, B.; Rosen, N. (1935-05-15).
3976:
Werner, R. F. (2014). "Comment on 'What Bell did'".
1094:
The publication of the paper prompted a response by
1054:
ideas. Shortly before the EPR paper appeared in the
5515:
5424:
5355:
5309:
5206:
5132:
4984:
3485:
Studies in History and Philosophy of Science Part A
4610:(2005). "Einstein, Podolsky, Rosen, and Shannon".
3160:
2930:
2897:
2865:
2689:
2560:
2426:
2342:
2203:
2066:
2048:The vector space of the electron-positron pair is
2038:
1890:
1761:
1741:
1281:-spin are "incompatible observables", meaning the
111:
5152:Investigations on the Theory of Brownian Movement
2704:on Bob's positron is now determined, it will be −
2332:
2252:
2193:
2113:
4306:Albert Einstein Max Born, Briefwechsel 1916-1955
3692:
3690:
3688:
3275:Einstein, Albert (1936). "Physik und Realität".
4911:EPR, Bell & Aspect: The Original References
4848:Houghton Mifflin Company, pp. 21, 187–189.
4597:A classical interpretation of Bell's inequality
2974:Einstein, A; B Podolsky; N Rosen (1935-05-15).
2719:on Bob's positron will return, in both cases, +
1406:is non-local is a matter of continuing debate.
5159:Relativity: The Special and the General Theory
4932:EPR experiment with single photons interactive
4797:Speakable and Unspeakable in Quantum Mechanics
3926:"Bell's inequality test: more ideal than ever"
1262:. There is nothing special about choosing the
4962:
4321:"Bertlmann's socks and the nature of reality"
3339:
3337:
3335:
2570:Similarly, if Alice's measurement result is −
1077:story also sought out comment from physicist
878:
8:
2421:
2381:) is uniquely determined and Bob's value of
1106:a prolonged debate between Bohr and Einstein
106:
80:
4599:. Annales de la Fondation Louis de Broglie
4247:
4245:
3154:
3152:
3150:
1534:respectively, can be represented using the
4969:
4955:
4947:
3892:
3890:
3234:British Journal for the History of Science
2743:Bohr-Einstein debates: The argument of EPR
1397:were carried out, notably by the group of
1098:, which he published in the same journal (
885:
871:
29:
4744:
4697:
4623:
4485:
4366:
4265:
4193:
4038:
3952:
3808:
3735:
3652:
3543:
3478:
3476:
3440:
3402:
3138:
3004:
2918:
2910:
2884:
2878:
2857:
2851:
2638:
2579:
2509:
2450:
2413:
2411:
2331:
2330:
2251:
2250:
2238:
2219:
2192:
2191:
2112:
2111:
2099:
2083:
2053:
2004:
1992:
1943:
1931:
1910:
1862:
1813:
1792:
1754:
1697:
1687:
1678:
1631:
1621:
1612:
1568:
1558:
1549:
1543:
98:
87:
86:
72:
57:
49:
5654:Thought experiments in quantum mechanics
5598:Emergency Committee of Atomic Scientists
3897:Sakurai, J. J.; Napolitano, Jim (2010).
3788:"On the Einstein Podolsky Rosen Paradox"
1773:(or the Planck constant divided by 2π).
1026:
896:
27:Historical critique of quantum mechanics
4922:Theoretical use of EPR in teleportation
2966:
2839:
1756:
1689:
1623:
1560:
1395:experiments to test Bell's inequalities
1207:). In state II, the electron has spin −
1167:, and the positron sent to destination
54:
37:
5337:Albert Einstein World Award of Science
3577:Albert Einstein: Philosopher-Scientist
2898:{\displaystyle \psi _{\underline {B}}}
1492:quantum mechanical formulation of spin
1226:Alice now measures the spin along the
4541:Do Correlations need to be explained?
3416:
3414:
7:
4927:Effective use of EPR in cryptography
3026:Quantum Theory: Concepts and Methods
2905:als Eigenfunktionen von Observabeln
2753:Correlation does not imply causation
1179:. The particles are thus said to be
4896:Stanford Encyclopedia of Philosophy
4884:Internet Encyclopedia of Philosophy
3810:10.1103/PhysicsPhysiqueFizika.1.195
1171:, where there is an observer named
1163:, where there is an observer named
946:interpretation of quantum mechanics
5366:Albert Einstein: Creator and Rebel
5079:Einstein–Infeld–Hoffmann equations
5049:Einstein relation (kinetic theory)
3203:. Springer Verlag. pp. 9–15.
2931:{\displaystyle B,{\underline {B}}}
989:Heisenberg's uncertainty principle
417:Sum-over-histories (path integral)
103:
77:
33:Part of a series of articles about
25:
5558:Einstein–Oppenheimer relationship
5227:The Einstein Theory of Relativity
4817:. 2nd ed. Univ. of Chicago Press.
3699:Introduction to Quantum Mechanics
3312:"Einstein Attacks Quantum Theory"
3277:Journal of the Franklin Institute
2938:aufgefasst werden können ist mir
2434:collapses into an eigenvector of
5611:
5610:
5342:Einstein Prize for Laser Science
3903:(2nd ed.). Addison-Wesley.
3579:. Open Court Publishing Company.
3087:Levenson, Thomas (9 June 1917).
2397:measurement in quantum mechanics
1297:-spin as well, Bob measures the
1283:Heisenberg uncertainty principle
967:considers these two observables
5387:Einstein: His Life and Universe
3701:(2nd ed.). Prentice Hall.
3089:"The Scientist and the Fascist"
3042:"Did Einstein really say that?"
3040:Robinson, Andrew (2018-04-30).
2441:. If the measurement result is
1972:
1842:
1673:
1607:
5009:Mass–energy equivalence (E=mc)
4825:In Search of Schrödinger's Cat
4799:. Cambridge University Press.
4057:10.1088/1751-8113/47/42/424009
3998:10.1088/1751-8113/47/42/424011
2427:{\displaystyle |\psi \rangle }
2414:
2406:is measured, the system state
1989:
1928:
1859:
1810:
567:Relativistic quantum mechanics
99:
92:
73:
1:
4212:10.1103/PhysRevLett.98.140402
3299:10.1016/S0016-0032(36)91047-5
3289:10.1016/S0016-0032(36)91045-1
3188:– via Internet Archive.
985:fled the rise of Nazi Germany
607:Quantum statistical mechanics
4878:1.2 The argument in the text
3697:Griffiths, David J. (2004).
3518:Sauer, Tilman (2007-12-01).
3505:10.1016/0039-3681(85)90001-9
2828:Ward's probability amplitude
1369:) to Bob", the next pair "(−
1254:. Similarly, if Alice gets −
1115:
1043:Institute for Advanced Study
981:Institute for Advanced Study
5332:Albert Einstein Peace Prize
5109:Unsuccessful investigations
4918:from the Usenet Physics FAQ
4573:10.1103/physrevlett.71.1665
4254:American Journal of Physics
3724:American Journal of Physics
3554:10.1016/j.shpsb.2007.03.002
2727:with probability 1/2 each.
1480:spooky action at a distance
1211:and the positron has spin +
577:Quantum information science
5670:
5259:Picasso at the Lapin Agile
5197:Russell–Einstein Manifesto
5069:Bose–Einstein correlations
4858:. New York: Plenum Press.
4525:10.1103/physrevlett.48.291
3671:10.1103/RevModPhys.81.1727
3066:10.1038/d41586-018-05004-4
2067:{\displaystyle V\otimes V}
1413:
1325:
1309:and a 50% probability of -
1191:pointing upward along the
1183:. This can be viewed as a
5606:
5167:The Meaning of Relativity
4763:10.1007/s10701-007-9105-0
4642:10.1007/s10701-004-1986-6
4151:10.1017/s0305004100013554
4100:10.1017/s0305004100019137
3641:Reviews of Modern Physics
3459:10.1007/s10701-009-9347-0
3246:10.1017/S0007087400031861
3209:10.1007/978-3-642-37629-0
2866:{\displaystyle \psi _{B}}
2778:Philosophy of information
2574:, the state collapses to
5563:Albert Einstein Archives
5488:Bernhard Caesar Einstein
5235:Relics: Einstein's Brain
5183:The Evolution of Physics
5064:Bose–Einstein statistics
5059:Bose–Einstein condensate
5039:Einstein field equations
4408:Eberhard, P. H. (1978).
3900:Modern Quantum Mechanics
3625:10.1103/PhysRev.108.1070
3320:. 4 May 1935. p. 11
2808:Quantum pseudo-telepathy
1486:Mathematical formulation
612:Quantum machine learning
365:Wheeler's delayed-choice
5573:Einstein Papers Project
5084:Einstein–de Haas effect
4553:Physical Review Letters
4505:Physical Review Letters
4182:Physical Review Letters
3924:Aspect A (1999-03-18).
3796:Physics Physique Физика
3372:Bohr, N. (1935-10-13).
3351:. John Wiley and Sons.
1898:and the eigenstates of
1771:reduced Planck constant
1446:to be a consequence of
1321:
1145:
1116:Einstein's own argument
923:proposed by physicists
909:Einstein–Podolsky–Rosen
322:Leggett–Garg inequality
5500:Thomas Martin Einstein
5408:Introducing Relativity
5380:Einstein for Beginners
5283:Einstein and Eddington
5074:Einstein–Cartan theory
4733:Foundations of Physics
4612:Foundations of Physics
4487:10.1103/physrev.47.777
3881:10.1103/PhysRev.85.180
3846:10.1103/PhysRev.85.166
3428:Foundations of Physics
3404:10.1103/PhysRev.48.696
3199:Jaeger, Gregg (2014).
3159:Kumar, Manjit (2011).
3140:10.1103/PhysRev.47.777
3029:. Kluwer. p. 149.
3006:10.1103/PhysRev.47.777
2932:
2899:
2867:
2708:in the first case or +
2691:
2562:
2428:
2344:
2205:
2068:
2040:
1892:
1763:
1762:{\displaystyle \hbar }
1743:
1475:superluminal signaling
1223:
1038:
904:
113:
5578:Einstein refrigerator
5568:Einstein's Blackboard
5442:(second wife; cousin)
5373:Einstein and Religion
5322:Albert Einstein Medal
5317:Albert Einstein Award
5175:The World as I See It
5114:Wave–particle duality
5094:Bohr–Einstein debates
5054:Cosmological constant
5034:Equivalence principle
5024:Einstein coefficients
4325:J. Physique Colloques
2933:
2900:
2868:
2813:Quantum teleportation
2783:Philosophy of physics
2692:
2563:
2429:
2345:
2206:
2069:
2041:
1893:
1764:
1744:
1221:
1185:quantum superposition
1089:
1030:
900:
307:Elitzur–Vaidman
297:Davisson–Germer
114:
5452:Hans Albert Einstein
5401:I Am Albert Einstein
5347:Einstein Prize (APS)
5019:Photoelectric effect
4992:Theory of relativity
4026:Journal of Physics A
3978:Journal of Physics A
3786:Bell, J. S. (1964).
3421:Harrigan, Nicholas;
2955:dated March 3, 1947.
2909:
2877:
2850:
2798:Quantum entanglement
2578:
2449:
2410:
2218:
2082:
2052:
1909:
1791:
1753:
1542:
1238:. Suppose she gets +
960:theory of relativity
572:Quantum field theory
484:Consistent histories
121:Schrödinger equation
48:
5649:Quantum measurement
5104:Thought experiments
4755:2007FoPh...37..427S
4682:2001Natur.409..791R
4634:2005FoPh...35..511P
4565:1993PhRvL..71.1665H
4517:1982PhRvL..48..291F
4478:1935PhRv...47..777E
4426:1978NCimB..46..392E
4377:1977NCimB..38...75E
4337:1988nbpw.conf..245B
4319:Bell, John (1981).
4276:2010AmJPh..78..111B
4204:2007PhRvL..98n0402W
4143:1935PCPS...31..555S
4092:1936PCPS...32..446S
4049:2014JPhA...47P4009Z
3990:2014JPhA...47P4011W
3945:1999Natur.398..189A
3873:1952PhRv...85..180B
3838:1952PhRv...85..166B
3746:2001AmJPh..69..655L
3663:2009RvMP...81.1727R
3617:1957PhRv..108.1070B
3536:2007SHPMP..38..879S
3497:1985SHPSA..16..171H
3451:2010FoPh...40..125H
3423:Spekkens, Robert W.
3395:1935PhRv...48..696B
3131:1935PhRv...47..777E
3058:2018Natur.557...30R
2997:1935PhRv...47..777E
2818:Quantum Zeno effect
2803:Quantum information
2788:Popper's experiment
2773:Measurement problem
2738:Aspect's experiment
1905:are represented as
1787:are represented as
1513:direction, denoted
1391:Bell's inequalities
975:The "Paradox" paper
360:Stern–Gerlach
157:Classical mechanics
5644:Physical paradoxes
5553:Things named after
5415:Subtle is the Lord
5238:(1994 documentary)
5230:(1923 documentary)
5222:(1922 documentary)
5119:Gravitational wave
5002:General relativity
4997:Special relativity
4434:10.1007/bf02728628
4414:Il Nuovo Cimento B
4385:10.1007/bf02726212
4355:Il Nuovo Cimento B
3317:The New York Times
2928:
2926:
2895:
2892:
2863:
2687:
2558:
2424:
2367:), Bob's value of
2340:
2201:
2064:
2036:
2027:
1963:
1888:
1882:
1833:
1759:
1739:
1730:
1664:
1598:
1468:no-cloning theorem
1454:without violating
1448:special relativity
1430:local hidden state
1289:-spin and obtains
1224:
1141:Later developments
1063:The New York Times
1039:
1034:The New York Times
921:thought experiment
905:
548:Von Neumann–Wigner
528:Objective-collapse
327:Mach–Zehnder
317:Leggett inequality
312:Franck–Hertz
162:Old quantum theory
109:
5626:
5625:
5523:Awards and honors
5506:Siegbert Einstein
5394:Einstein's Cosmos
4833:978-0-552-12555-0
4676:(6822): 791–794.
4559:(11): 1665–1668.
4284:10.1119/1.3243279
3773:10.1119/1.1466818
3754:10.1119/1.1356698
3708:978-0-13-111892-8
3589:Bohm, D. (1951).
3218:978-3-642-37628-3
2919:
2885:
2682:
2681:
2553:
2552:
2248:
2247:
2109:
2108:
2002:
2001:
1941:
1940:
1695:
1629:
1566:
1422:Howard M. Wiseman
1377:) to Alice and (+
1361:) to Alice and (−
1334:John Stewart Bell
1047:Erwin Schrödinger
937:quantum mechanics
895:
894:
602:Scattering theory
582:Quantum computing
355:Schrödinger's cat
287:Bell's inequality
95:
70:
39:Quantum mechanics
16:(Redirected from
5661:
5614:
5613:
5508:(distant cousin)
5502:(great-grandson)
5464:Hermann Einstein
5446:Lieserl Einstein
5124:Tea leaf paradox
4971:
4964:
4957:
4948:
4782:
4748:
4746:quant-ph/0604064
4727:
4701:
4690:10.1038/35057215
4661:
4627:
4625:quant-ph/0310010
4592:
4536:
4499:
4489:
4463:
4453:
4404:
4370:
4368:quant-ph/0010047
4341:
4340:
4316:
4310:
4309:
4302:
4296:
4295:
4269:
4249:
4240:
4239:
4197:
4195:quant-ph/0612147
4177:
4171:
4170:
4126:
4120:
4119:
4075:
4069:
4068:
4042:
4016:
4010:
4009:
3973:
3967:
3966:
3956:
3939:(6724): 189–90.
3930:
3921:
3915:
3914:
3894:
3885:
3884:
3856:
3850:
3849:
3821:
3815:
3814:
3812:
3792:
3783:
3777:
3776:
3765:
3739:
3737:quant-ph/0209123
3719:
3713:
3712:
3694:
3683:
3682:
3656:
3647:(4): 1727–1751.
3635:
3629:
3628:
3600:
3594:
3587:
3581:
3580:
3572:
3566:
3565:
3547:
3515:
3509:
3508:
3480:
3471:
3470:
3444:
3418:
3409:
3408:
3406:
3378:
3369:
3363:
3362:
3341:
3330:
3329:
3327:
3325:
3308:
3302:
3292:
3272:
3266:
3265:
3229:
3223:
3222:
3196:
3190:
3189:
3187:
3185:
3166:
3156:
3145:
3144:
3142:
3110:
3104:
3103:
3101:
3099:
3084:
3078:
3077:
3037:
3031:
3030:
3017:
3011:
3010:
3008:
2980:
2971:
2956:
2949:
2943:
2937:
2935:
2934:
2929:
2927:
2904:
2902:
2901:
2896:
2894:
2893:
2872:
2870:
2869:
2864:
2862:
2861:
2844:
2793:Superdeterminism
2696:
2694:
2693:
2688:
2683:
2677:
2676:
2675:
2671:
2656:
2652:
2639:
2634:
2630:
2615:
2611:
2596:
2592:
2567:
2565:
2564:
2559:
2554:
2548:
2547:
2546:
2542:
2527:
2523:
2510:
2505:
2501:
2486:
2482:
2467:
2463:
2433:
2431:
2430:
2425:
2417:
2349:
2347:
2346:
2341:
2336:
2335:
2329:
2325:
2310:
2306:
2291:
2287:
2272:
2268:
2256:
2255:
2249:
2243:
2239:
2231:
2210:
2208:
2207:
2202:
2197:
2196:
2190:
2186:
2171:
2167:
2152:
2148:
2133:
2129:
2117:
2116:
2110:
2104:
2100:
2095:
2073:
2071:
2070:
2065:
2045:
2043:
2042:
2037:
2032:
2031:
2003:
1997:
1993:
1988:
1984:
1968:
1967:
1942:
1936:
1932:
1927:
1923:
1897:
1895:
1894:
1889:
1887:
1886:
1858:
1854:
1838:
1837:
1809:
1805:
1768:
1766:
1765:
1760:
1748:
1746:
1745:
1740:
1735:
1734:
1696:
1688:
1683:
1682:
1669:
1668:
1630:
1622:
1617:
1616:
1603:
1602:
1567:
1559:
1554:
1553:
1416:Quantum steering
1258:, Bob will get +
942:hidden variables
887:
880:
873:
514:Superdeterminism
167:Bra–ket notation
118:
116:
115:
110:
102:
97:
96:
88:
76:
71:
69:
58:
30:
21:
5669:
5668:
5664:
5663:
5662:
5660:
5659:
5658:
5639:Albert Einstein
5629:
5628:
5627:
5622:
5602:
5548:Religious views
5543:Political views
5511:
5496:(granddaughter)
5494:Evelyn Einstein
5482:Robert Einstein
5476:Eduard Einstein
5420:
5357:
5351:
5305:
5275:Einstein's Gift
5209:
5202:
5143:Annus mirabilis
5128:
5099:Teleparallelism
5044:Einstein radius
5014:Brownian motion
4980:
4978:Albert Einstein
4975:
4873:
4852:Selleri, Franco
4838:Leaderman, Leon
4789:
4730:
4667:
4606:
4550:
4502:
4472:(10): 777–780.
4466:Physical Review
4461:
4456:
4407:
4352:
4349:
4347:Selected papers
4344:
4318:
4317:
4313:
4304:
4303:
4299:
4251:
4250:
4243:
4179:
4178:
4174:
4128:
4127:
4123:
4077:
4076:
4072:
4018:
4017:
4013:
3975:
3974:
3970:
3928:
3923:
3922:
3918:
3911:
3896:
3895:
3888:
3861:Physical Review
3858:
3857:
3853:
3826:Physical Review
3823:
3822:
3818:
3790:
3785:
3784:
3780:
3767:(Erratum:
3766:
3721:
3720:
3716:
3709:
3696:
3695:
3686:
3637:
3636:
3632:
3605:Physical Review
3602:
3601:
3597:
3588:
3584:
3574:
3573:
3569:
3545:10.1.1.571.6089
3517:
3516:
3512:
3482:
3481:
3474:
3420:
3419:
3412:
3382:Physical Review
3376:
3371:
3370:
3366:
3359:
3343:
3342:
3333:
3323:
3321:
3310:
3309:
3305:
3274:
3273:
3269:
3231:
3230:
3226:
3219:
3201:Quantum Objects
3198:
3197:
3193:
3183:
3181:
3179:
3158:
3157:
3148:
3119:Physical Review
3112:
3111:
3107:
3097:
3095:
3086:
3085:
3081:
3039:
3038:
3034:
3019:
3018:
3014:
2991:(10): 777–780.
2984:Physical Review
2978:
2973:
2972:
2968:
2964:
2959:
2950:
2946:
2907:
2906:
2880:
2875:
2874:
2853:
2848:
2847:
2845:
2841:
2837:
2832:
2758:CHSH inequality
2733:
2718:
2703:
2664:
2660:
2645:
2641:
2640:
2623:
2619:
2604:
2600:
2585:
2581:
2576:
2575:
2535:
2531:
2516:
2512:
2511:
2494:
2490:
2475:
2471:
2456:
2452:
2447:
2446:
2440:
2408:
2407:
2405:
2393:
2386:
2379:
2372:
2365:
2358:
2318:
2314:
2299:
2295:
2280:
2276:
2261:
2257:
2221:
2216:
2215:
2179:
2175:
2160:
2156:
2141:
2137:
2122:
2118:
2085:
2080:
2079:
2050:
2049:
2026:
2025:
2016:
2015:
2005:
1977:
1973:
1962:
1961:
1955:
1954:
1944:
1916:
1912:
1907:
1906:
1903:
1881:
1880:
1874:
1873:
1863:
1847:
1843:
1832:
1831:
1825:
1824:
1814:
1798:
1794:
1789:
1788:
1785:
1751:
1750:
1729:
1728:
1720:
1714:
1713:
1708:
1698:
1674:
1663:
1662:
1657:
1651:
1650:
1642:
1632:
1608:
1597:
1596:
1591:
1585:
1584:
1579:
1569:
1545:
1540:
1539:
1532:
1525:
1518:
1488:
1438:
1418:
1412:
1330:
1324:
1148:
1143:
1118:
1101:Physical Review
1092:
1057:Physical Review
977:
925:Albert Einstein
902:Albert Einstein
891:
862:
861:
860:
625:
617:
616:
562:
561:Advanced topics
554:
553:
552:
504:Hidden-variable
494:de Broglie–Bohm
473:
471:Interpretations
463:
462:
461:
431:
423:
422:
421:
379:
371:
370:
369:
336:
292:CHSH inequality
281:
273:
272:
271:
200:Complementarity
194:
186:
185:
184:
152:
123:
62:
46:
45:
28:
23:
22:
15:
12:
11:
5:
5667:
5665:
5657:
5656:
5651:
5646:
5641:
5631:
5630:
5624:
5623:
5621:
5620:
5607:
5604:
5603:
5601:
5600:
5595:
5590:
5585:
5580:
5575:
5570:
5565:
5560:
5555:
5550:
5545:
5540:
5535:
5530:
5525:
5519:
5517:
5513:
5512:
5510:
5509:
5503:
5497:
5491:
5485:
5479:
5473:
5467:
5461:
5455:
5449:
5443:
5437:
5430:
5428:
5422:
5421:
5419:
5418:
5411:
5404:
5397:
5390:
5383:
5376:
5369:
5361:
5359:
5353:
5352:
5350:
5349:
5344:
5339:
5334:
5329:
5324:
5319:
5313:
5311:
5307:
5306:
5304:
5303:
5295:
5287:
5286:(2008 TV film)
5279:
5271:
5263:
5255:
5251:Young Einstein
5247:
5243:Insignificance
5239:
5231:
5223:
5214:
5212:
5204:
5203:
5201:
5200:
5194:
5191:Why Socialism?
5187:
5179:
5171:
5163:
5155:
5148:
5138:
5136:
5130:
5129:
5127:
5126:
5121:
5116:
5111:
5106:
5101:
5096:
5091:
5086:
5081:
5076:
5071:
5066:
5061:
5056:
5051:
5046:
5041:
5036:
5031:
5029:Einstein solid
5026:
5021:
5016:
5011:
5006:
5005:
5004:
4999:
4988:
4986:
4982:
4981:
4976:
4974:
4973:
4966:
4959:
4951:
4945:
4944:
4942:Original paper
4939:
4934:
4929:
4924:
4919:
4913:
4908:
4905:Bell's Theorem
4892:
4880:
4872:
4871:External links
4869:
4868:
4867:
4849:
4835:
4827:. Black Swan.
4818:
4808:
4788:
4785:
4784:
4783:
4739:(3): 427–445.
4728:
4665:
4662:
4618:(3): 511–514.
4604:
4593:
4548:
4537:
4511:(5): 291–295.
4500:
4454:
4420:(2): 392–419.
4405:
4348:
4345:
4343:
4342:
4311:
4297:
4260:(1): 111–120.
4241:
4188:(14): 140402.
4172:
4137:(4): 555–563.
4121:
4086:(3): 446–452.
4070:
4033:(42): 424009.
4019:Żukowski, M.;
4011:
3984:(42): 424011.
3968:
3916:
3910:978-0805382914
3909:
3886:
3851:
3816:
3803:(3): 195–200.
3778:
3730:(6): 655–701.
3714:
3707:
3684:
3630:
3595:
3591:Quantum Theory
3582:
3567:
3530:(4): 879–887.
3510:
3491:(3): 171–201.
3472:
3410:
3389:(8): 696–702.
3364:
3357:
3331:
3303:
3283:(3): 313–347.
3267:
3240:(2): 129–152.
3224:
3217:
3191:
3178:978-0393339888
3177:
3146:
3105:
3079:
3032:
3012:
2965:
2963:
2960:
2958:
2957:
2944:
2925:
2922:
2917:
2914:
2891:
2888:
2883:
2860:
2856:
2838:
2836:
2833:
2831:
2830:
2825:
2820:
2815:
2810:
2805:
2800:
2795:
2790:
2785:
2780:
2775:
2770:
2768:GHZ experiment
2765:
2760:
2755:
2750:
2745:
2740:
2734:
2732:
2729:
2716:
2701:
2686:
2680:
2674:
2670:
2667:
2663:
2659:
2655:
2651:
2648:
2644:
2637:
2633:
2629:
2626:
2622:
2618:
2614:
2610:
2607:
2603:
2599:
2595:
2591:
2588:
2584:
2557:
2551:
2545:
2541:
2538:
2534:
2530:
2526:
2522:
2519:
2515:
2508:
2504:
2500:
2497:
2493:
2489:
2485:
2481:
2478:
2474:
2470:
2466:
2462:
2459:
2455:
2438:
2423:
2420:
2416:
2403:
2391:
2384:
2377:
2370:
2363:
2356:
2339:
2334:
2328:
2324:
2321:
2317:
2313:
2309:
2305:
2302:
2298:
2294:
2290:
2286:
2283:
2279:
2275:
2271:
2267:
2264:
2260:
2254:
2246:
2242:
2237:
2234:
2230:
2227:
2224:
2200:
2195:
2189:
2185:
2182:
2178:
2174:
2170:
2166:
2163:
2159:
2155:
2151:
2147:
2144:
2140:
2136:
2132:
2128:
2125:
2121:
2115:
2107:
2103:
2098:
2094:
2091:
2088:
2076:tensor product
2063:
2060:
2057:
2035:
2030:
2024:
2021:
2018:
2017:
2014:
2011:
2010:
2008:
2000:
1996:
1991:
1987:
1983:
1980:
1976:
1971:
1966:
1960:
1957:
1956:
1953:
1950:
1949:
1947:
1939:
1935:
1930:
1926:
1922:
1919:
1915:
1901:
1885:
1879:
1876:
1875:
1872:
1869:
1868:
1866:
1861:
1857:
1853:
1850:
1846:
1841:
1836:
1830:
1827:
1826:
1823:
1820:
1819:
1817:
1812:
1808:
1804:
1801:
1797:
1783:
1758:
1738:
1733:
1727:
1724:
1721:
1719:
1716:
1715:
1712:
1709:
1707:
1704:
1703:
1701:
1694:
1691:
1686:
1681:
1677:
1672:
1667:
1661:
1658:
1656:
1653:
1652:
1649:
1646:
1643:
1641:
1638:
1637:
1635:
1628:
1625:
1620:
1615:
1611:
1606:
1601:
1595:
1592:
1590:
1587:
1586:
1583:
1580:
1578:
1575:
1574:
1572:
1565:
1562:
1557:
1552:
1548:
1536:Pauli matrices
1530:
1523:
1516:
1487:
1484:
1452:speed of light
1437:
1434:
1414:Main article:
1411:
1408:
1328:Bell's theorem
1326:Main article:
1323:
1322:Bell's theorem
1320:
1147:
1146:Bohm's variant
1144:
1142:
1139:
1117:
1114:
1091:
1088:
976:
973:
929:Boris Podolsky
893:
892:
890:
889:
882:
875:
867:
864:
863:
859:
858:
853:
848:
843:
838:
833:
828:
823:
818:
813:
808:
803:
798:
793:
788:
783:
778:
773:
768:
763:
758:
753:
748:
743:
738:
733:
728:
723:
718:
713:
708:
703:
698:
693:
688:
683:
678:
673:
668:
663:
658:
653:
648:
643:
638:
633:
627:
626:
623:
622:
619:
618:
615:
614:
609:
604:
599:
597:Density matrix
594:
589:
584:
579:
574:
569:
563:
560:
559:
556:
555:
551:
550:
545:
540:
535:
530:
525:
520:
519:
518:
517:
516:
501:
496:
491:
486:
481:
475:
474:
469:
468:
465:
464:
460:
459:
454:
449:
444:
439:
433:
432:
429:
428:
425:
424:
420:
419:
414:
409:
404:
399:
394:
388:
387:
386:
380:
377:
376:
373:
372:
368:
367:
362:
357:
351:
350:
349:
348:
347:
345:Delayed-choice
340:Quantum eraser
335:
334:
329:
324:
319:
314:
309:
304:
299:
294:
289:
283:
282:
279:
278:
275:
274:
270:
269:
268:
267:
257:
252:
247:
242:
237:
232:
230:Quantum number
227:
222:
217:
212:
207:
202:
196:
195:
192:
191:
188:
187:
183:
182:
177:
171:
170:
169:
164:
159:
153:
150:
149:
146:
145:
144:
143:
138:
133:
125:
124:
119:
108:
105:
101:
94:
91:
85:
82:
79:
75:
68:
65:
61:
56:
53:
42:
41:
35:
34:
26:
24:
18:EPR experiment
14:
13:
10:
9:
6:
4:
3:
2:
5666:
5655:
5652:
5650:
5647:
5645:
5642:
5640:
5637:
5636:
5634:
5619:
5618:
5609:
5608:
5605:
5599:
5596:
5594:
5591:
5589:
5586:
5584:
5581:
5579:
5576:
5574:
5571:
5569:
5566:
5564:
5561:
5559:
5556:
5554:
5551:
5549:
5546:
5544:
5541:
5539:
5536:
5534:
5531:
5529:
5526:
5524:
5521:
5520:
5518:
5514:
5507:
5504:
5501:
5498:
5495:
5492:
5489:
5486:
5483:
5480:
5477:
5474:
5471:
5470:Maja Einstein
5468:
5465:
5462:
5459:
5456:
5453:
5450:
5447:
5444:
5441:
5440:Elsa Einstein
5438:
5435:
5432:
5431:
5429:
5427:
5423:
5417:
5416:
5412:
5410:
5409:
5405:
5403:
5402:
5398:
5396:
5395:
5391:
5389:
5388:
5384:
5382:
5381:
5377:
5375:
5374:
5370:
5368:
5367:
5363:
5362:
5360:
5354:
5348:
5345:
5343:
5340:
5338:
5335:
5333:
5330:
5328:
5327:Kalinga Prize
5325:
5323:
5320:
5318:
5315:
5314:
5312:
5308:
5301:
5300:
5296:
5294:(2017 series)
5293:
5292:
5288:
5285:
5284:
5280:
5277:
5276:
5272:
5269:
5268:
5264:
5261:
5260:
5256:
5253:
5252:
5248:
5245:
5244:
5240:
5237:
5236:
5232:
5229:
5228:
5224:
5221:
5220:
5216:
5215:
5213:
5211:
5205:
5198:
5195:
5192:
5188:
5185:
5184:
5180:
5177:
5176:
5172:
5169:
5168:
5164:
5161:
5160:
5156:
5153:
5149:
5146:
5144:
5140:
5139:
5137:
5135:
5131:
5125:
5122:
5120:
5117:
5115:
5112:
5110:
5107:
5105:
5102:
5100:
5097:
5095:
5092:
5090:
5087:
5085:
5082:
5080:
5077:
5075:
5072:
5070:
5067:
5065:
5062:
5060:
5057:
5055:
5052:
5050:
5047:
5045:
5042:
5040:
5037:
5035:
5032:
5030:
5027:
5025:
5022:
5020:
5017:
5015:
5012:
5010:
5007:
5003:
5000:
4998:
4995:
4994:
4993:
4990:
4989:
4987:
4983:
4979:
4972:
4967:
4965:
4960:
4958:
4953:
4952:
4949:
4943:
4940:
4938:
4935:
4933:
4930:
4928:
4925:
4923:
4920:
4917:
4914:
4912:
4909:
4906:
4902:
4901:Abner Shimony
4898:
4897:
4893:
4890:
4886:
4885:
4881:
4879:
4875:
4874:
4870:
4865:
4864:0-306-42739-7
4861:
4857:
4853:
4850:
4847:
4843:
4839:
4836:
4834:
4830:
4826:
4822:
4821:Gribbin, John
4819:
4816:
4812:
4809:
4806:
4805:0-521-36869-3
4802:
4798:
4794:
4793:Bell, John S.
4791:
4790:
4786:
4780:
4776:
4772:
4768:
4764:
4760:
4756:
4752:
4747:
4742:
4738:
4734:
4729:
4725:
4721:
4717:
4713:
4709:
4705:
4700:
4699:2027.42/62731
4695:
4691:
4687:
4683:
4679:
4675:
4671:
4666:
4663:
4659:
4655:
4651:
4647:
4643:
4639:
4635:
4631:
4626:
4621:
4617:
4613:
4609:
4605:
4602:
4598:
4594:
4590:
4586:
4582:
4578:
4574:
4570:
4566:
4562:
4558:
4554:
4549:
4546:
4542:
4538:
4534:
4530:
4526:
4522:
4518:
4514:
4510:
4506:
4501:
4497:
4493:
4488:
4483:
4479:
4475:
4471:
4467:
4460:
4455:
4451:
4447:
4443:
4439:
4435:
4431:
4427:
4423:
4419:
4416:. Series 11.
4415:
4411:
4406:
4402:
4398:
4394:
4390:
4386:
4382:
4378:
4374:
4369:
4364:
4360:
4357:. Series 11.
4356:
4351:
4350:
4346:
4338:
4334:
4330:
4326:
4322:
4315:
4312:
4307:
4301:
4298:
4293:
4289:
4285:
4281:
4277:
4273:
4268:
4263:
4259:
4255:
4248:
4246:
4242:
4237:
4233:
4229:
4225:
4221:
4217:
4213:
4209:
4205:
4201:
4196:
4191:
4187:
4183:
4176:
4173:
4168:
4164:
4160:
4156:
4152:
4148:
4144:
4140:
4136:
4132:
4125:
4122:
4117:
4113:
4109:
4105:
4101:
4097:
4093:
4089:
4085:
4081:
4074:
4071:
4066:
4062:
4058:
4054:
4050:
4046:
4041:
4036:
4032:
4028:
4027:
4022:
4015:
4012:
4007:
4003:
3999:
3995:
3991:
3987:
3983:
3979:
3972:
3969:
3964:
3960:
3955:
3954:10.1038/18296
3950:
3946:
3942:
3938:
3934:
3927:
3920:
3917:
3912:
3906:
3902:
3901:
3893:
3891:
3887:
3882:
3878:
3874:
3870:
3866:
3862:
3855:
3852:
3847:
3843:
3839:
3835:
3831:
3827:
3820:
3817:
3811:
3806:
3802:
3798:
3797:
3789:
3782:
3779:
3774:
3770:
3763:
3759:
3755:
3751:
3747:
3743:
3738:
3733:
3729:
3725:
3718:
3715:
3710:
3704:
3700:
3693:
3691:
3689:
3685:
3680:
3676:
3672:
3668:
3664:
3660:
3655:
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3358:0-471-43958-4
3354:
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3307:
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3184:September 12,
3180:
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3141:
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2889:
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2823:Synchronicity
2821:
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2061:
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2046:
2033:
2028:
2022:
2019:
2012:
2006:
1998:
1994:
1985:
1981:
1978:
1974:
1969:
1964:
1958:
1951:
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1140:
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1131:
1130:two different
1127:
1122:
1113:
1111:
1110:complementary
1107:
1103:
1102:
1097:
1087:
1084:
1080:
1079:Edward Condon
1076:
1071:
1069:
1065:
1064:
1060:
1058:
1053:
1052:local realist
1048:
1044:
1036:
1035:
1029:
1025:
1023:
1022:local realism
1019:
1015:
1011:
1005:
1003:
1000:the momentum
999:
994:
990:
986:
982:
974:
972:
970:
965:
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629:
628:
621:
620:
613:
610:
608:
605:
603:
600:
598:
595:
593:
590:
588:
587:Quantum chaos
585:
583:
580:
578:
575:
573:
570:
568:
565:
564:
558:
557:
549:
546:
544:
543:Transactional
541:
539:
536:
534:
533:Quantum logic
531:
529:
526:
524:
521:
515:
512:
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510:
507:
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288:
285:
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277:
276:
266:
263:
262:
261:
260:Wave function
258:
256:
253:
251:
248:
246:
243:
241:
240:Superposition
238:
236:
233:
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228:
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89:
83:
66:
63:
59:
51:
44:
43:
40:
36:
32:
31:
19:
5615:
5583:Einsteinhaus
5458:Pauline Koch
5436:(first wife)
5434:Mileva Marić
5413:
5406:
5399:
5392:
5385:
5378:
5371:
5364:
5297:
5289:
5281:
5273:
5265:
5257:
5249:
5241:
5233:
5225:
5217:
5181:
5173:
5165:
5157:
5142:
4894:
4882:
4855:
4845:
4842:Teresi, Dick
4824:
4814:
4811:Fine, Arthur
4796:
4736:
4732:
4673:
4669:
4615:
4611:
4608:Peres, Asher
4600:
4596:
4556:
4552:
4544:
4540:
4508:
4504:
4469:
4465:
4417:
4413:
4361:(1): 75–80.
4358:
4354:
4328:
4324:
4314:
4305:
4300:
4257:
4253:
4185:
4181:
4175:
4134:
4130:
4124:
4083:
4079:
4073:
4030:
4024:
4014:
3981:
3977:
3971:
3936:
3932:
3919:
3898:
3864:
3860:
3854:
3829:
3825:
3819:
3800:
3794:
3781:
3727:
3723:
3717:
3698:
3644:
3640:
3633:
3608:
3604:
3598:
3590:
3585:
3576:
3570:
3527:
3523:
3513:
3488:
3484:
3432:
3426:
3386:
3380:
3367:
3348:
3322:. Retrieved
3315:
3306:
3280:
3276:
3270:
3237:
3233:
3227:
3200:
3194:
3182:. Retrieved
3162:
3122:
3118:
3108:
3096:. Retrieved
3093:The Atlantic
3092:
3082:
3052:(7703): 30.
3049:
3045:
3035:
3025:
3021:Peres, Asher
3015:
2988:
2982:
2969:
2947:
2939:
2842:
2724:
2720:
2713:
2709:
2705:
2698:
2571:
2569:
2442:
2435:
2400:
2389:
2382:
2375:
2368:
2361:
2354:
2352:
2213:
2047:
1899:
1781:
1775:
1528:
1521:
1514:
1510:
1506:
1502:
1498:
1496:vector space
1489:
1472:
1463:
1440:
1439:
1429:
1425:
1419:
1403:
1399:Alain Aspect
1387:
1382:
1378:
1374:
1370:
1366:
1362:
1358:
1354:
1350:
1346:
1343:
1338:
1331:
1314:
1310:
1306:
1302:
1298:
1294:
1290:
1286:
1278:
1274:
1272:
1267:
1263:
1259:
1255:
1251:
1247:
1239:
1235:
1231:
1227:
1225:
1212:
1208:
1204:
1200:
1196:
1192:
1177:spin singlet
1168:
1160:
1149:
1129:
1123:
1119:
1099:
1093:
1090:Bohr's reply
1074:
1072:
1067:
1061:
1055:
1040:
1032:
1021:
1006:
1001:
997:
993:Manjit Kumar
978:
969:incompatible
950:
933:Nathan Rosen
916:
912:
908:
906:
591:
442:Klein–Gordon
378:Formulations
215:Energy level
210:Entanglement
193:Fundamentals
180:Interference
131:Introduction
5588:Einsteinium
5356:Books about
5302:(2023 film)
5299:Oppenheimer
5278:(2003 play)
5270:(1994 film)
5262:(1993 play)
5254:(1988 film)
5246:(1985 film)
5089:EPR paradox
4595:M. Mizuki,
4021:Brukner, Č.
3611:(4): 1070.
3345:Jammer, Max
1778:eigenstates
1270:direction.
1126:nonlocality
964:probability
831:von Neumann
816:Schrödinger
592:EPR paradox
523:Many-worlds
457:Schrödinger
412:Schrödinger
407:Phase-space
397:Interaction
302:Double-slit
280:Experiments
255:Uncertainty
225:Nonlocality
220:Measurement
205:Decoherence
175:Hamiltonian
5633:Categories
5593:Max Talmey
5490:(grandson)
5448:(daughter)
5208:In popular
4603:683 (2001)
4040:1501.04618
3867:(2): 180.
3832:(2): 166.
3435:(2): 125.
3324:10 January
2962:References
1349:-spin and
1277:-spin and
1152:David Bohm
1096:Niels Bohr
1083:Max Jammer
1018:light cone
826:Sommerfeld
741:Heisenberg
736:Gutzwiller
676:de Broglie
624:Scientists
538:Relational
489:Copenhagen
392:Heisenberg
250:Tunnelling
151:Background
4771:0015-9018
4724:205014115
4708:0028-0836
4658:119556878
4650:0015-9018
4581:0031-9007
4539:A. Fine,
4533:0031-9007
4496:0031-899X
4450:118836806
4442:1826-9877
4393:1826-9877
4331:: 41–62.
4292:118520639
4267:0902.3827
4220:0031-9007
4167:121278681
4159:0305-0041
4116:122822435
4108:0305-0041
4065:119220867
4006:122180759
3762:123349369
3654:0806.0270
3562:1355-2198
3540:CiteSeerX
3442:0706.2661
3262:145143635
2924:_
2890:_
2882:ψ
2855:ψ
2748:Coherence
2666:−
2636:⊗
2625:−
2598:⊗
2587:−
2537:−
2529:−
2507:⊗
2477:−
2469:⊗
2422:⟩
2419:ψ
2312:⊗
2301:−
2293:−
2282:−
2274:⊗
2236:−
2226:ψ
2173:⊗
2162:−
2154:−
2143:−
2135:⊗
2090:ψ
2059:⊗
2020:−
1990:↔
1979:−
1929:↔
1860:↔
1849:−
1811:↔
1757:ℏ
1723:−
1690:ℏ
1645:−
1624:ℏ
1561:ℏ
1456:causality
1332:In 1964,
1244:collapses
1181:entangled
1155:electron–
1150:In 1951,
1014:spacetime
983:, having
953:entangled
856:Zeilinger
701:Ehrenfest
430:Equations
107:⟩
104:Ψ
93:^
81:⟩
78:Ψ
55:ℏ
5617:Category
5538:Memorial
5484:(cousin)
5472:(sister)
5466:(father)
5460:(mother)
5358:Einstein
5193:" (1949)
5154:" (1905)
4903:(2019) "
4854:(1988).
4844:(1993).
4823:(1984).
4813:(1996).
4795:(1987).
4779:11816650
4716:11236986
4589:10054467
4401:51759163
4236:30078867
4228:17501251
3963:44925917
3679:53407634
3467:32755624
3347:(1974).
3074:14013938
3023:(2002).
2953:Max Born
2846:"Ob die
2763:ER = EPR
2731:See also
2673:⟩
2654:⟩
2632:⟩
2613:⟩
2594:⟩
2544:⟩
2525:⟩
2503:⟩
2484:⟩
2465:⟩
2327:⟩
2308:⟩
2289:⟩
2270:⟩
2229:⟩
2188:⟩
2169:⟩
2150:⟩
2131:⟩
2093:⟩
1986:⟩
1925:⟩
1856:⟩
1807:⟩
1442:Locality
1436:Locality
1410:Steering
1315:performs
1203:-axis (−
1157:positron
1135:locality
781:Millikan
706:Einstein
691:Davisson
646:Blackett
631:Aharonov
499:Ensemble
479:Bayesian
384:Overview
265:Collapse
245:Symmetry
136:Glossary
5516:Related
5210:culture
4985:Physics
4751:Bibcode
4678:Bibcode
4630:Bibcode
4561:Bibcode
4513:Bibcode
4474:Bibcode
4422:Bibcode
4373:Bibcode
4333:Bibcode
4272:Bibcode
4200:Bibcode
4139:Bibcode
4088:Bibcode
4045:Bibcode
3986:Bibcode
3941:Bibcode
3869:Bibcode
3834:Bibcode
3742:Bibcode
3659:Bibcode
3613:Bibcode
3532:Bibcode
3493:Bibcode
3447:Bibcode
3391:Bibcode
3254:4027432
3169:305–306
3127:Bibcode
3098:28 June
3054:Bibcode
2993:Bibcode
2399:. When
1769:is the
1195:-axis (
917:paradox
821:Simmons
811:Rydberg
776:Moseley
756:Kramers
746:Hilbert
731:Glauber
726:Feynman
711:Everett
681:Compton
452:Rydberg
141:History
5426:Family
5310:Prizes
5291:Genius
5199:(1955)
5186:(1938)
5178:(1934)
5170:(1922)
5162:(1916)
5147:(1905)
5145:papers
4862:
4831:
4803:
4777:
4769:
4722:
4714:
4706:
4670:Nature
4656:
4648:
4587:
4579:
4531:
4494:
4448:
4440:
4399:
4391:
4290:
4234:
4226:
4218:
4165:
4157:
4114:
4106:
4063:
4004:
3961:
3933:Nature
3907:
3760:
3705:
3677:
3560:
3542:
3465:
3355:
3260:
3252:
3215:
3175:
3072:
3046:Nature
2074:, the
1749:where
1527:, and
1509:, and
1460:random
1404:itself
1068:Times,
998:either
851:Zeeman
846:Wigner
796:Planck
766:Landau
751:Jordan
402:Matrix
332:Popper
5533:House
5528:Brain
5478:(son)
5454:(son)
5134:Works
4787:Books
4775:S2CID
4741:arXiv
4720:S2CID
4654:S2CID
4620:arXiv
4543:, in
4462:(PDF)
4446:S2CID
4397:S2CID
4363:arXiv
4288:S2CID
4262:arXiv
4232:S2CID
4190:arXiv
4163:S2CID
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