{{short description|Thought experiment devised by the physicist Erwin Schrödinger}}<br>
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薛定谔的猫是一个'''思想实验 thought experiment''',有时被称为'''悖论 paradox''',由奥地利物理学家埃尔温·薛定谔于1935年提出,但该想法起源于阿尔伯特·爱因斯坦<ref name="Schrodinger1935">Fine, Arthur. "The Einstein-Podolsky-Rosen Argument in Quantum Theory". Stanford Encyclopedia of Philosophy. Retrieved 11 June 2020.</ref>。
[[File:Schrodingers cat.svg|thumb|upright=1.5|Schrödinger's cat: a cat, a flask of poison, and a [[radioactive]] source are placed in a sealed box. If an internal monitor (e.g. [[Geiger counter]]) detects radioactivity (i.e. a single atom decaying), the flask is shattered, releasing the poison, which kills the cat. The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is ''simultaneously'' alive ''and'' dead. Yet, when one looks in the box, one sees the cat ''either'' alive ''or'' dead, not both alive ''and'' dead. This poses the question of when exactly quantum superposition ends and reality collapses into one possibility or the other.|链接=Special:FilePath/Schrodingers_cat.svg]]
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Schrödinger's cat: a cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal monitor (e.g. Geiger counter) detects radioactivity (i.e. a single atom decaying), the flask is shattered, releasing the poison, which kills the cat. The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive and dead. Yet, when one looks in the box, one sees the cat either alive or dead, not both alive and dead. This poses the question of when exactly quantum superposition ends and reality collapses into one possibility or the other.
'''Schrödinger's cat''' is a [[thought experiment]], sometimes described as a [[paradox]], devised by Austrian physicist [[Erwin Schrödinger]] in 1935, though the idea originated from [[Albert Einstein]].<ref name="Schrodinger1935"><br>
It illustrates what he saw as the problem of the [[Copenhagen interpretation]] of [[quantum mechanics]] applied to everyday objects. The scenario presents a hypothetical [[cat]] that may be simultaneously both alive and dead,<ref name="Moring"><nowiki>{{cite book</nowiki><br>
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</ref>a state known as a [[quantum superposition]], as a result of being linked to a random [[Subatomic particle|subatomic]] event that may or may not occur.
The thought experiment is also often featured in theoretical discussions of the [[interpretations of quantum mechanics]], particularly in situations involving the [[measurement problem]]. Schrödinger coined the term ''Verschränkung'' ([[Quantum entanglement|entanglement]]) in the course of developing the thought experiment.{{Quantum mechanics|cTopic=Experiments}}
[[File:Schroedinger cat.jpg|thumb|left|A life-size—and moveable—cat figure in the garden of Huttenstrasse 9, Zurich, where Erwin Schrödinger lived 1921–1926. A visitor to the house cannot know in advance where the cat will be.<ref>{{cite web |last1=Suarez |first1=Antoine |title=The limits of quantum superposition: Should "Schrödinger's cat" and "Wigner's friend" be considered "miracle" narratives? |url=https://www.researchgate.net/publication/334031988 |website=ResearchGate |accessdate=27 February 2020 |page=3 |date=2019}}</ref>|链接=Special:FilePath/Schroedinger_cat.jpg]]
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A life-size—and moveable—cat figure in the garden of Huttenstrasse 9, Zurich, where Erwin Schrödinger lived 1921–1926. A visitor to the house cannot know in advance where the cat will be.
Schrödinger intended his thought experiment as a discussion of the [[EPR paradox|EPR article]]—named after its authors [[Albert Einstein|Einstein]], [[Boris Podolsky|Podolsky]], and [[Nathan Rosen|Rosen]]—in 1935.<ref name=":0">[http://prola.aps.org/abstract/PR/v47/i10/p777_1 Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?] {{webarchive|url=https://web.archive.org/web/20060208145129/http://prola.aps.org/abstract/PR/v47/i10/p777_1 |date=2006-02-08 }} A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935)</ref> The EPR article highlighted the counterintuitive nature of [[quantum superposition]]s, in which a quantum system such as an [[atom]] or [[photon]] can exist as a combination of multiple states corresponding to different possible outcomes.
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1935年,薛定谔本来想将该思想实验作为对'''EPR佯谬'''论文(以其作者爱因斯坦、波多尔斯基和罗森英文首字母命名)的讨论<ref name=":2">Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Archived 2006-02-08 at the Wayback Machine A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935)</ref><ref name=":3"> Fine, Arthur (2017). "The Einstein-Podolsky-Rosen Argument in Quantum Theory". Stanford Encyclopedia of Philosophy. Stanford University. Retrieved 11 April 2021.</ref> 。EPR论文强调了量子叠加的反直觉性,在量子叠加中,一个量子系统,比如原子或者光子,可以处于多个状态,对应不同的结果。
The prevailing theory, called the [[Copenhagen interpretation]], says that a quantum system remains in superposition until it interacts with, or is observed by the external world. When this happens, the superposition collapses into one or another of the possible definite states. The EPR experiment shows that a system with multiple particles separated by large distances can be in such a superposition. Schrödinger and [[Albert Einstein|Einstein]] exchanged letters about [[EPR paradox|Einstein's EPR article]], in the course of which Einstein pointed out that the state of an [[Instability|unstable]] keg of [[gunpowder]] will, after a while, contain a superposition of both exploded and unexploded states.
To further illustrate, Schrödinger described how one could, in principle, create a superposition in a large-scale system by making it dependent on a quantum particle that was in a superposition. He proposed a scenario with a cat in a locked steel chamber, wherein the cat's life or death depended on the state of a [[Radioactive decay|radioactive]] atom, whether it had decayed and emitted radiation or not. According to Schrödinger, the Copenhagen interpretation implies that ''the cat remains both alive and dead'' until the state has been observed. Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; on the contrary, he intended the example to illustrate the absurdity of the existing view of quantum mechanics.<ref name="Schrodinger1935"/>
However, since Schrödinger's time, other [[interpretations of quantum mechanics|interpretations of the mathematics of quantum mechanics]] have been advanced by physicists, some of which regard the "alive and dead" cat superposition as quite real.<ref name="Polkinghorne">{{cite book
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但是,自从薛定谔时代以来,物理学家提出了诸多其他量子力学的数学解释,其中一些解释认为 “既生又死”的猫叠加态非常真实<ref name="Polkinghorne">Polkinghorne, J. C. (1985). The Quantum World. Princeton University Press. p. 67. ISBN 0691023883. Archived from the original on 2015-05-19.</ref><ref name="Tetlow">Tetlow, Philip (2012). Understanding Information and Computation: From Einstein to Web Science. Gower Publishing, Ltd. p. 321. ISBN 978-1409440406. Archived from the original on 2015-05-19.</ref>。薛定谔的猫思想实验意在批判哥本哈根诠释(1935年的主流正统学说),至今仍是各种现代量子力学诠释的试金石,具有决定性意义。物理学家经常用各种诠释解释薛定谔的猫的方式来说明和比较各种诠释的特点、优点和缺点。
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}}</ref><ref name="Tetlow">{{cite book
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}}</ref> Intended as a critique of the Copenhagen interpretation (the prevailing orthodoxy in 1935), the Schrödinger's cat thought experiment remains a defining [[Touchstone (metaphor)|touchstone]] for modern interpretations of quantum mechanics. Physicists often use the way each interpretation deals with Schrödinger's cat as a way of illustrating and comparing the particular features, strengths, and weaknesses of each interpretation.
Schrödinger wrote:<ref name="Schrodinger1935" /><ref name=":1">{{cite journal|last1=Trimmer|first1=John D.|title=The Present Situation in Quantum Mechanics: A Translation of Schrödinger's "Cat Paradox" Paper|journal=Proceedings of the American Philosophical Society|date=1980|volume=124|issue=5|pages=323–338|jstor=986572}} Reproduced with some inaccuracies here:
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Schrödinger wrote:<nowiki><ref> Reproduced with some inaccuracies here:</nowiki>
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薛定谔写道: 引用这里的一些不准确之处:
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[https://archive.is/20121204184041/http://www.tuhh.de/rzt/rzt/it/QM/cat.html#sect5 Schroedinger: "The Present Situation in Quantum Mechanics." 5. Are the Variables Really Blurred?]</ref>
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One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
薛定谔写道:<ref name=":6">Schrödinger, Erwin (November 1935). "Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics)". Naturwissenschaften. 23 (48): 807–812. Bibcode:1935NW.....23..807S. doi:10.1007/BF01491891. S2CID 206795705.</ref><ref name=":7">Trimmer, John D. (1980). "The Present Situation in Quantum Mechanics: A Translation of Schrödinger's "Cat Paradox" Paper". Proceedings of the American Philosophical Society. 124 (5): 323–338. JSTOR 986572. Reproduced with some inaccuracies here: Schroedinger: "The Present Situation in Quantum Mechanics." 5. Are the Variables Really Blurred?</ref>
[https://archive.is/20121204184041/http://www.tuhh.de/rzt/rzt/it/QM/cat.html#sect5 Schroedinger: "The Present Situation in Quantum Mechanics." 5. Are the Variables Really Blurred?]</ref>
One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a [[Geiger counter]], there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of [[hydrocyanic acid]]. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has [[radioactive decay|decayed]]. The first atomic decay would have poisoned it. The [[wave function|psi-function]] of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
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'''<font color="#32CD32">One can even set up quite ridiculous cases.</font>''' A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. '''<font color="#32CD32">The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.</font>'''
It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naïvely accepting as valid a "blurred model" for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.}}
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It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naïvely accepting as valid a "blurred model" for representing reality. In itself, it would not embody anything unclear or contradictory. '''<font color="#32CD32">There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.}}</font>'''
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It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naïvely accepting as valid a "blurred model" for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.
Schrödinger's famous [[thought experiment]] poses the question, "''when'' does a quantum system stop existing as a superposition of states and become one or the other?" (More technically, when does the actual quantum state stop being a non-trivial [[linear combination]] of states, each of which resembles different classical states, and instead begin to have a unique classical description?) If the cat survives, it remembers only being alive. But explanations of the EPR experiments that are consistent with standard microscopic quantum mechanics require that macroscopic objects, such as cats and notebooks, do not always have unique classical descriptions. The thought experiment illustrates this apparent paradox. Our intuition says that no observer can be in a mixture of states—yet the cat, it seems from the thought experiment, can be such a mixture. Is the cat required to be an observer, or does its existence in a single well-defined classical state require another external observer? Each alternative seemed absurd to Einstein, who was impressed by the ability of the thought experiment to highlight these issues. In a letter to Schrödinger dated 1950, he wrote:
{{Quote|You are the only contemporary physicist, besides [[Max von Laue|Laue]], who sees that one cannot get around the assumption of reality, if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gun powder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation.<ref>{{cite journal|title=Induction and Scientific Realism: Einstein versus van Fraassen Part Three: Einstein, Aim-Oriented Empiricism and the Discovery of Special and General Relativity|first=Nicholas|last=Maxwell|date=1 January 1993|volume=44|issue=2|pages=275–305|doi=10.1093/bjps/44.2.275|jstor=687649|journal=The British Journal for the Philosophy of Science}}</ref>}}<br>
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You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality, if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gun powder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation.
Note that the charge of gunpowder is not mentioned in Schrödinger's setup, which uses a Geiger counter as an amplifier and hydrocyanic poison instead of gunpowder. The gunpowder had been mentioned in Einstein's original suggestion to Schrödinger 15 years before, and Einstein carried it forward to the present discussion.
Since Schrödinger's time, other interpretations of quantum mechanics have been proposed that give different answers to the questions posed by Schrödinger's cat of how long superpositions last and when (or ''whether'') they collapse.
量子力学的主流诠释之一是哥本哈根诠释<ref name="Wimmel1992">Wimmel, Hermann (1992). Quantum physics & observed reality: a critical interpretation of quantum mechanics. World Scientific. p. 2. ISBN 978-981-02-1010-6. Archived from the original on 20 May 2013. Retrieved 9 May 2011.</ref>。该诠释认为,一个系统在观察时将不再处于叠加态,而是坍缩为叠加态中的任意一种状态。薛定谔的思维实验清楚地表明,哥本哈根诠释没有明确定义测量和观察的本质。实验可以解释为,盒子关闭时,系统处于“衰变的原子核/死猫”和“未衰变的原子核/活猫”叠加态中,只有打开盒子进行观察时,波函数才会坍缩成这两种状态之一。
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但是,哥本哈根诠释的主要科学家尼尔斯·玻尔从未认为是观察者引起了波函数的坍缩,因为他并不认为波函数真实存在,它只是一个统计工具。因此薛定谔的猫对他来说不是什么谜题。早在意识的观察者<ref name="Faye2008"> Faye, J (2008-01-24). "Copenhagen Interpretation of Quantum Mechanics". Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab Center for the Study of Language and Information, Stanford University. Retrieved 2010-09-19.</ref>打开盒子前,猫就已经死去或者仍然活着。分析一个真实的实验会发现,尽管实验涉及的有效性尚有争议<ref name="Okon2006">Okón E, Sebastián MA (2016). "How to Back up or Refute Quantum Theories of Consciousness". Mind and Matter. 14 (1): 25–49.</ref>,在有意识的观察者对测量结果<ref name="Carpenter2006">Carpenter RHS, Anderson AJ (2006). "The death of Schroedinger's cat and of consciousness-based wave-function collapse" (PDF). Annales de la Fondation Louis de Broglie. 31 (1): 45–52. Archived from the original (PDF) on 2006-11-30. Retrieved 2010-09-10.</ref>进行观察前,测量本身(比如盖革计数器)就足以使量子波函数发生坍缩。(这种当原子核中的粒子撞击监测器时“观察”已经发生的观点可以发展为客观坍缩理论。在薛定谔的思维实验中,波函数要发生坍缩,监测器需要进行“无意识观察”。相比之下,“多世界理论”否认曾发生过坍缩。
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{{Main|Copenhagen interpretation}}
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A commonly held interpretation of quantum mechanics is the Copenhagen interpretation.<ref name="Wimmel1992">{{cite book|first=Hermann|last=Wimmel|title=Quantum physics & observed reality: a critical interpretation of quantum mechanics|url=https://books.google.com/?id=-4sJ_fgyZJEC&pg=PA2|accessdate=9 May 2011|year=1992|publisher=World Scientific|isbn=978-981-02-1010-6|page=2|url-status=live|archiveurl=https://web.archive.org/web/20130520185205/http://books.google.com/books?id=-4sJ_fgyZJEC&pg=PA2|archivedate=20 May 2013}}</ref> In the Copenhagen interpretation, a system stops being a superposition of states and becomes either one or the other when an observation takes place. This thought experiment makes apparent the fact that the nature of [[Measurement in quantum mechanics|measurement]], or observation, is not well-defined in this interpretation. The experiment can be interpreted to mean that while the box is closed, the system simultaneously exists in a superposition of the states "decayed nucleus/dead cat" and "undecayed nucleus/living cat", and that only when the box is opened and an observation performed does the [[wave function]] collapse into one of the two states.
However, one of the main scientists associated with the Copenhagen interpretation, [[Niels Bohr]], never had in mind the observer-induced collapse of the wave function, as he did not regard the wave function as physically real, but a statistical tool; thus, Schrödinger's cat did not pose any riddle to him. The cat would be either dead or alive long before the box is opened by a conscious [[Observer (quantum physics)|observer]].<ref name='Faye2008'>{{cite web | url = http://plato.stanford.edu/entries/qm-copenhagen/ | title = Copenhagen Interpretation of Quantum Mechanics | accessdate = 2010-09-19 | last = Faye | first = J | date = 2008-01-24 | encyclopedia = [[Stanford Encyclopedia of Philosophy]] | publisher = The Metaphysics Research Lab Center for the Study of Language and Information, [[Stanford University]]}}</ref> Analysis of an actual experiment found that measurement alone (for example by a Geiger counter) is sufficient to collapse a quantum wave function before there is any conscious observation of the measurement,<ref name='Carpenter2006'>{{cite journal | title = The death of Schroedinger's cat and of consciousness-based wave-function collapse | journal = [[Annales de la Fondation Louis de Broglie]] | year = 2006 | author = Carpenter RHS, Anderson AJ | volume = 31 | issue = 1 | pages = 45–52| id = | url = http://www.ensmp.fr/aflb/AFLB-311/aflb311m387.pdf | accessdate = 2010-09-10 |archiveurl = https://web.archive.org/web/20061130173850/http://www.ensmp.fr/aflb/AFLB-311/aflb311m387.pdf |archivedate = 2006-11-30}}</ref> although the validity of their design is disputed.<ref name='Okon2006'>{{cite journal | title = How to Back up or Refute Quantum Theories of Consciousness | journal = Mind and Matter | year = 2016 | author = Okón E, Sebastián MA | volume = 14 | issue = 1 | pages = 25–49}}</ref> (The view that the "observation" is taken when a particle from the nucleus hits the detector can be developed into [[objective collapse theories]]. The thought experiment requires an "unconscious observation" by the detector in order for waveform collapse to occur. In contrast, the [[many worlds]] approach denies that collapse ever occurs.)
===Many-worlds interpretation and consistent histories===<br>
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多世界诠释和历史一致论
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[[File:Schroedingers cat film.svg|thumb|right|350px|The quantum-mechanical "Schrödinger's cat" paradox according to the many-worlds interpretation. In this interpretation, every event is a branch point. The cat is both alive and dead—regardless of whether the box is opened—but the "alive" and "dead" cats are in different branches of the universe that are equally real but cannot interact with each other.|链接=Special:FilePath/Schroedingers_cat_film.svg]]
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The quantum-mechanical "Schrödinger's cat" paradox according to the many-worlds interpretation. In this interpretation, every event is a branch point. The cat is both alive and dead—regardless of whether the box is opened—but the "alive" and "dead" cats are in different branches of the universe that are equally real but cannot interact with each other.
In 1957, [[Hugh Everett]] formulated the many-worlds interpretation of quantum mechanics, which does not single out observation as a special process. In the many-worlds interpretation, both alive and dead states of the cat persist after the box is opened, but are [[quantum decoherence|decoherent]] from each other. In other words, when the box is opened, the observer and the possibly-dead cat split into an observer looking at a box with a dead cat, and an observer looking at a box with a live cat. But since the dead and alive states are decoherent, there is no effective communication or interaction between them.
打开盒子时,观察者与猫纠缠在一起,因此形成了对应猫生与死的“观察者状态”;每个观察者状态都与猫纠缠或联系在一起,因此“猫状态的观察”与“猫的状态”相对应。量子退相干确保不同的结果不会相互影响,对多世界诠释的历史一致论也很重要。在多世界诠释中,只有“死猫”或“活猫”才能称为一致历史的一部分。通常认为退相干是为了避免同时对多个叠加态<ref name="zurek03">Zurek, Wojciech H. (2003). "Decoherence, einselection, and the quantum origins of the classical". Reviews of Modern Physics. 75 (3): 715. arXiv:quant-ph/0105127. Bibcode:2003RvMP...75..715Z. doi:10.1103/revmodphys.75.715. S2CID 14759237.</ref><ref name="zurek91">Wojciech H. Zurek, "Decoherence and the transition from quantum to classical", Physics Today, 44, pp. 36–44 (1991)</ref>进行观察。
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When opening the box, the observer becomes entangled with the cat, so "observer states" corresponding to the cat's being alive and dead are formed; each observer state is [[quantum entanglement|entangled or linked]] with the cat so that the "observation of the cat's state" and the "cat's state" correspond with each other. Quantum decoherence ensures that the different outcomes have no interaction with each other. The same mechanism of quantum decoherence is also important for the interpretation in terms of [[consistent histories]]. Only the "dead cat" or the "alive cat" can be a part of a consistent history in this interpretation. Decoherence is generally considered to prevent simultaneous observation of multiple states.<ref name="zurek03">{{cite journal | last1 = Zurek | first1 = Wojciech H. | authorlink = Wojciech H. Zurek | year = 2003 | title = Decoherence, einselection, and the quantum origins of the classical | arxiv = quant-ph/0105127 | journal = Reviews of Modern Physics | volume = 75 | issue = 3| page = 715 | doi=10.1103/revmodphys.75.715| bibcode = 2003RvMP...75..715Z }}</ref><ref name="zurek91">[[Wojciech H. Zurek]], "Decoherence and the transition from quantum to classical", ''Physics Today'', 44, pp. 36–44 (1991)</ref>
A variant of the Schrödinger's cat experiment, known as the [[Quantum suicide and immortality|quantum suicide]] machine, has been proposed by cosmologist [[Max Tegmark]]. It examines the Schrödinger's cat experiment from the point of view of the cat, and argues that by using this approach, one may be able to distinguish between the Copenhagen interpretation and many-worlds.
这一诠释抛弃了单一量子力学系统有一个始终对应的数学描述这一观点<ref name=":14">Smolin, Lee (October 2012). "A real ensemble interpretation of quantum mechanics". Foundations of Physics. 42 (10): 1239–1261. arXiv:1104.2822. Bibcode:2012FoPh...42.1239S. doi:10.1007/s10701-012-9666-4. ISSN 0015-9018.</ref>。
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===Ensemble interpretation===<br>
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===关系诠释===
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系综诠释
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'''关系诠释 relational interpretation'''认为人类实验者、猫或装置之间,或者生命体与非生命体之间没有本质区别;所有这些遵循相同波函数演化规则的量子系统都可以被认为是“观察者”。但是关系诠释允许不同的观察者根据掌握的不同盒内系统信息<ref name=":15">Rovelli, Carlo (1996). "Relational Quantum Mechanics". International Journal of Theoretical Physics. 35 (8): 1637–1678. arXiv:quant-ph/9609002. Bibcode:1996IJTP...35.1637R. doi:10.1007/BF02302261. S2CID 16325959.</ref>,对同一系列事件给出不同的解释。猫可以被认为是装置的观察者;同时,实验者可以被认为是盒内系统(猫和装置)的另一个观察者。在盒子被打开之前,根据自身的死活,猫拥有关于设备状态的信息(原子要么已经衰变要么没有衰变);但是实验者并不掌握这些信息。这样,在同一时刻两个观察者对于盒子的状态有不同的描述:对猫来说,装置的波函数“坍缩”了,对实验者来说,盒内系统处于叠加态。直到盒子被打开,两个观察者对所发生的事情都掌握了同样的信息,两个系统才“坍缩”为同样一个确定结果,既猫不是活着就是死了。
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The [[Ensemble Interpretation|ensemble interpretation]] states that superpositions are nothing but subensembles of a larger statistical ensemble. The state vector would not apply to individual cat experiments, but only to the statistics of many similarly prepared cat experiments. Proponents of this interpretation state that this makes the Schrödinger's cat paradox a trivial matter, or a non-issue.
This interpretation serves to ''discard'' the idea that a single physical system in quantum mechanics has a mathematical description that corresponds to it in any way.<ref name=":2">{{Cite journal|last=Smolin|first=Lee|date=October 2012|title=A real ensemble interpretation of quantum mechanics|journal=Foundations of Physics|volume=42|issue=10|pages=1239–1261|doi=10.1007/s10701-012-9666-4|issn=0015-9018|arxiv=1104.2822|bibcode=2012FoPh...42.1239S}}</ref>
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这一诠释抛弃了单一量子力学系统有一个始终对应的数学描述这一观点<ref name=":2" />。
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===Relational interpretation===<br>
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关系诠释
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The [[Relational quantum mechanics|relational interpretation]] makes no fundamental distinction between the human experimenter, the cat, or the apparatus, or between animate and inanimate systems; all are quantum systems governed by the same rules of wavefunction [[Time evolution|evolution]], and all may be considered "observers". But the relational interpretation allows that different observers can give different accounts of the same series of events, depending on the information they have about the system.<ref name=":3">{{Cite journal|last = Rovelli|first = Carlo|authorlink = Carlo Rovelli|title = Relational Quantum Mechanics|journal = International Journal of Theoretical Physics|volume = 35|pages = 1637–1678|year = 1996|arxiv = quant-ph/9609002 |doi = 10.1007/BF02302261|bibcode = 1996IJTP...35.1637R|issue = 8 }}</ref> The cat can be considered an observer of the apparatus; meanwhile, the experimenter can be considered another observer of the system in the box (the cat plus the apparatus). Before the box is opened, the cat, by nature of its being alive or dead, has information about the state of the apparatus (the atom has either decayed or not decayed); but the experimenter does not have information about the state of the box contents. In this way, the two observers simultaneously have different accounts of the situation: To the cat, the wavefunction of the apparatus has appeared to "collapse"; to the experimenter, the contents of the box appear to be in superposition. Not until the box is opened, and both observers have the same information about what happened, do both system states appear to "collapse" into the same definite result, a cat that is either alive or dead.
In the [[transactional interpretation]] the apparatus emits an advanced wave backward in time, which combined with the wave that the source emits forward in time, forms a standing wave. The waves are seen as physically real, and the apparatus is considered an "observer". In the transactional interpretation, the collapse of the wavefunction is "atemporal" and occurs along the whole transaction between the source and the apparatus. The cat is never in superposition. Rather the cat is only in one state at any particular time, regardless of when the human experimenter looks in the box. The transactional interpretation resolves this quantum paradox.<ref name=":4">{{Cite book|last=Cramer|first=John G.|url=https://www.researchgate.net/publication/280926546|title=The transactional interpretation of quantum mechanics|publisher=Reviews of Modern Physics|date=July 1986|isbn=|volume=58|location=|pages=647–685}}</ref>
在'''交易诠释 transactional interpretation'''中,实验装置发射一个逆着时间行进的超前波,超前波与粒子源发射的顺着时间行进的波相互作用,形成驻波。这些波被认为是真实存在的,装置被视为“观察者”。在交易诠释中,波函数的坍缩是“非时间性的”,并且发生在粒子源与实验装置相互作用的整个阶段。猫从未处于叠加态,相反,不管人类实验者什么时候看盒子,猫在任何特定时间都只处于一种状态。这样交易诠释就解决了这一量子悖论<ref name=":16">Cramer, John G. (July 1986). The transactional interpretation of quantum mechanics. 58. Reviews of Modern Physics. pp. 647–685.</ref>。
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===量子芝诺效应===
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'''量子芝诺效应 zeno effect'''指延缓量子从对初始状态到其他状态的演化。
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另一方面,存在加速量子系统演化的反芝诺效应。例如,如果你频繁地窥视放置猫的盒子,你可能会延迟或加速决定性选择。芝诺效应和反芝诺效应都是真实存在的,并且已知会发生在真实的原子上。被测量的量子系统必须与周围环境(在这个例子中是实验装置、实验室等)强耦合,以获得更准确的信息。但是,在薛定的猫实验中,没有信息传递到盒子外部,这种与环境的耦合被认为是一种准测量,但是一旦猫的生死(通过窥视盒子)传递到了盒子外部,准测量就变成了测量。准测量和测量一样都会引起芝诺效应<ref name=":17">"How the quantum Zeno effect impacts Schrodinger's cat". phys.org. Archived from the original on 17 June 2017. Retrieved 18 June 2017.</ref>。芝诺效应告诉我们,即使不窥视盒子,猫的死亡也会因为环境而被延迟或加速。
On the other hand, the anti-Zeno effect accelerates the changes. For example, if you peek a look into the cat box frequently you may either cause delays to the fateful choice or, conversely, accelerate it. Both the Zeno effect and the anti-Zeno effect are real and known to happen to real atoms. The quantum system being measured must be strongly coupled to the surrounding environment (in this case to the apparatus, the experiment room ... etc.) in order to obtain more accurate information. But while there is no information passed to the outside world, it is considered to be a ''quasi-measurement'', but as soon as the information about the cat's well-being is passed on to the outside world (by peeking into the box) quasi-measurement turns into measurement. Quasi-measurements, like measurements, cause the Zeno effects.<ref name=":5">{{cite web|title=How the quantum Zeno effect impacts Schrodinger's cat|url=https://phys.org/news/2017-06-quantum-zeno-effect-impacts-schroedinger.html|website=phys.org|accessdate=18 June 2017|url-status=live|archiveurl=https://web.archive.org/web/20170617153012/https://phys.org/news/2017-06-quantum-zeno-effect-impacts-schroedinger.html|archivedate=17 June 2017}}</ref> Zeno effects teach us that even without peeking into the box, the death of the cat would have been delayed or accelerated anyway due to its environment.
According to [[objective collapse theories]], superpositions are destroyed spontaneously (irrespective of external observation), when some objective physical threshold (of time, mass, temperature, [[irreversibility]], etc.) is reached. Thus, the cat would be expected to have settled into a definite state long before the box is opened. This could loosely be phrased as "the cat observes itself", or "the environment observes the cat".
Objective collapse theories require a modification of standard quantum mechanics to allow superpositions to be destroyed by the process of time evolution.<ref name=":6">{{Cite journal|last=Okon|first=Elias|last2=Sudarsky|first2=Daniel|date=2014-02-01|title=Benefits of Objective Collapse Models for Cosmology and Quantum Gravity|journal=Foundations of Physics|language=en|volume=44|issue=2|pages=114–143|doi=10.1007/s10701-014-9772-6|issn=1572-9516|arxiv=1309.1730|bibcode=2014FoPh...44..114O}}</ref>
[[File:Quantum superposition of states and decoherence.ogv|thumb|upright=1.5|Schrödinger's cat quantum superposition of states and effect of the environment through decoherence|链接=Special:FilePath/Quantum_superposition_of_states_and_decoherence.ogv]]
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Schrödinger's cat quantum superposition of states and effect of the environment through decoherence
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==应用和测试==
薛定谔的猫量子叠加态和退相干环境效应
薛定谔的猫量子叠加态和退相干环境效应
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薛定谔的猫实验是纯理论性的,所涉及的实验装置并被制造出来。但是,很多涉及类似原理的实验已经取得成功,例如一些(在量子力学标准中)相对较大系统的叠加态已经实现<ref name=":19">"What is the world's biggest Schrodinger cat?". stackexchange.com. Archived from the original on 2012-01-08.</ref>。这些实验并没有表明与猫大小一样的物体可以处于叠加态,但是这些实验提升了存在“猫态”的系统的大小上线。在很多实验中,即使冷却到接近绝对零度,猫态也只能短暂存在。
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* 多光子的“猫态”已经实现<ref name=":20">"Schrödinger's Cat Now Made Of Light". www.science20.com. 27 August 2014. Archived from the original on 18 March 2012.</ref>。
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The experiment as described is a purely theoretical one, and the machine proposed is not known to have been constructed. However, successful experiments involving similar principles, e.g. superpositions of [[mesoscopic|relatively large]] (by the standards of quantum physics) objects have been performed.<ref name=":7">{{cite web|url=http://physics.stackexchange.com/questions/3309/what-is-the-worlds-biggest-schrodinger-cat|title=What is the world's biggest Schrodinger cat?|website=stackexchange.com|url-status=live|archiveurl=https://web.archive.org/web/20120108000629/http://physics.stackexchange.com/questions/3309/what-is-the-worlds-biggest-schrodinger-cat|archivedate=2012-01-08}}</ref> These experiments do not show that a cat-sized object can be superposed, but the known upper limit on "[[cat state]]s" has been pushed upwards by them. In many cases the state is short-lived, even when cooled to near [[absolute zero]].
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* 观测到处于叠加态的被捕获的铍离子<ref name=":21">C. Monroe, et al. A "Schrödinger Cat" Superposition State of an Atom Archived 2012-01-07 at the Wayback Machine</ref>。
* A "cat state" has been achieved with photons.<ref name=":8">{{cite web|url=http://www.science20.com/news_articles/schr%C3%B6dingers_cat_now_made_light|title=Schrödinger's Cat Now Made Of Light|date=27 August 2014|website=www.science20.com|url-status=live|archiveurl=https://web.archive.org/web/20120318091956/http://www.science20.com/news_articles/schr%C3%B6dingers_cat_now_made_light|archivedate=18 March 2012}}</ref><br>多光子的“猫态”已经实现<ref name=":8" />。
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* A beryllium ion has been trapped in a superposed state.<ref name=":9">[http://www.quantumsciencephilippines.com/seminar/seminar-topics/SchrodingerCatAtom.pdf C. Monroe, et al. ''A "Schrödinger Cat" Superposition State of an Atom''] {{webarchive|url=https://web.archive.org/web/20120107013418/http://www.quantumsciencephilippines.com/seminar/seminar-topics/SchrodingerCatAtom.pdf |date=2012-01-07 }}</ref><br>观测到处于叠加态的被捕获的铍离子<ref name=":9" />。
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* An experiment involving a [[superconducting quantum interference device]] ("SQUID") has been linked to the theme of the thought experiment: "The superposition state does not correspond to a billion electrons flowing one way and a billion others flowing the other way. Superconducting electrons move en masse. All the superconducting electrons in the SQUID flow both ways around the loop at once when they are in the Schrödinger's cat state."<ref name=":10">[https://physicsworld.com/a/schrodingers-cat-comes-into-view/ Physics World: ''Schrödinger's cat comes into view'']</ref><br>一项涉及超导量子干涉仪( SQUID)的实验与薛定谔思想实验的主题联系在一起:“叠加态并不是说十亿个电子正向流动,十亿个电子反向流动。超导电子总是沿同一方向移动,当超导量子干涉仪中的所有超导电子都处于薛定谔的猫态<ref name=":10" />时,它们会同时在回路中双向流动。“
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* A [[piezoelectric]] "tuning fork" has been constructed, which can be placed into a superposition of vibrating and non vibrating states. The resonator comprises about 10 trillion atoms.<ref name=":11">[http://www.scientificamerican.com/article.cfm?id=quantum-microphone Scientific American :'' Macro-Weirdness: "Quantum Microphone" Puts Naked-Eye Object in 2 Places at Once: A new device tests the limits of Schrödinger's cat''] {{webarchive|url=https://web.archive.org/web/20120319021316/http://www.scientificamerican.com/article.cfm?id=quantum-microphone |date=2012-03-19 }}</ref><br>一种压电“音叉”已经被制造出来,可被置于振动和非振动状态的叠加态。谐振器包含约10万亿个原子<ref name=":11" />。
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* An experiment involving a flu virus has been proposed.<ref name=":12">{{cite web|url=http://www.technologyreview.com/blog/arxiv/24101/|title=How to Create Quantum Superpositions of Living Things|first=Emerging Technology from the|last=arXiv|publisher=}}</ref><br>一项涉及流感病毒的实验已被提出<ref name=":12" />。
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* An experiment involving a bacterium and an electromechanical oscillator has been proposed.<ref name=":13">{{cite web|url=http://physicsworld.com/cws/article/news/2015/sep/21/could-schrodingers-bacterium-be-placed-in-a-quantum-superposition|title=Could 'Schrödinger's bacterium' be placed in a quantum superposition?|website=physicsworld.com|url-status=live|archiveurl=https://web.archive.org/web/20160730174613/http://physicsworld.com/cws/article/news/2015/sep/21/could-schrodingers-bacterium-be-placed-in-a-quantum-superposition|archivedate=2016-07-30}}</ref><br>一项利用机电振荡器和细菌的实验已被提出<ref name=":13" />。
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* 一项涉及超导量子干涉仪( SQUID)的实验与薛定谔思想实验的主题联系在一起:“叠加态并不是说十亿个电子正向流动,十亿个电子反向流动。超导电子总是沿同一方向移动,当超导量子干涉仪中的所有超导电子都处于薛定谔的猫态<ref name=":22">Physics World: Schrödinger's cat comes into view</ref>时,它们会同时在回路中双向流动。”
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* 一种压电“音叉”已经被制造出来,可被置于振动和非振动状态的叠加态。谐振器包含约10万亿个原子<ref name=":23">Scientific American : Macro-Weirdness: "Quantum Microphone" Puts Naked-Eye Object in 2 Places at Once: A new device tests the limits of Schrödinger's cat Archived 2012-03-19 at the Wayback Machine</ref>。
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* 一项涉及流感病毒的实验已被提出<ref name=":24">arXiv, Emerging Technology from the. "How to Create Quantum Superpositions of Living Things".</ref>。
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In [[quantum computing]] the phrase "cat state" sometimes refers to the [[Greenberger–Horne–Zeilinger state|GHZ state]], wherein several qubits are in an equal superposition of all being 0 and all being 1; e.g.,
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* 一项利用机电振荡器和细菌的实验已被提出<ref name=":25">"Could 'Schrödinger's bacterium' be placed in a quantum superposition?". physicsworld.com. Archived from the original on 2016-07-30.</ref>。
至少有一种观点认为,有可能在观察猫之前就确定它的状态<ref name="LS-20191107">{{cite news |last=Najjar |first=Dana |title=Physicists Can Finally Peek at Schrödinger's Cat Without Killing It Forever |url=https://www.livescience.com/schrodingers-cat-can-be-peeked-at.html |date=7 November 2019 |work=Live Science |accessdate=7 November 2019 }}</ref><ref name="NJP-20191001">{{cite journal |last1=Patekar |first1=Kartik |last2=Hofmann |first2=Holger F. |title=The role of system–meter entanglement in controlling the resolution and decoherence of quantum measurements |journal=New Journal of Physics |volume=21 |issue=10 |pages=103006 |doi=10.1088/1367-2630/ab4451 |year=2019 |doi-access=free }}</ref>。
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According to at least one proposal, it may be possible to determine the state of the cat ''before'' observing it.<ref name="LS-20191107">{{cite news |last=Najjar |first=Dana |title=Physicists Can Finally Peek at Schrödinger's Cat Without Killing It Forever |url=https://www.livescience.com/schrodingers-cat-can-be-peeked-at.html |date=7 November 2019 |work=[[Live Science]] |accessdate=7 November 2019 }}</ref><ref name="NJP-20191001">{{cite journal |last1=Patekar |first1=Kartik |last2=Hofmann |first2=Holger F. |title=The role of system–meter entanglement in controlling the resolution and decoherence of quantum measurements |journal=[[New Journal of Physics]] |volume=21 |issue=10 |pages=103006 |doi=10.1088/1367-2630/ab4451 |year=2019 |doi-access=free }}</ref>
[[Wigner's friend]] is a variant on the experiment with two human observers: the first makes an observation on whether a flash of light is seen and then communicates his observation to a second observer. The issue here is, does the wave function "collapse" when the first observer looks at the experiment, or only when the second observer is informed of the first observer's observations?
另一方面,一些著名物理学家甚至认为,1998年观测到宇宙暗能量的天文学家可能通过一个伪薛定谔猫的假设“缩短了它的寿命”,尽管这是一个有争议的观点。<ref name=":28">Chown, Marcus (2007-11-22). "Has observing the universe hastened its end?". New Scientist. Archived from the original on 2016-03-10. Retrieved 2007-11-25.</ref><ref name=":29">Krauss, Lawrence M.; James Dent (April 30, 2008). "Late Time Behavior of False Vacuum Decay: Possible Implications for Cosmology and Metastable Inflating States". Phys. Rev. Lett. US. 100 (17): 171301. arXiv:0711.1821.</ref>
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==另请参阅==
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* 基本功能
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In another extension, prominent physicists have gone so far as to suggest that astronomers observing [[dark energy]] in the universe in 1998 may have "reduced its life expectancy" through a pseudo-Schrödinger's cat scenario, although this is a controversial viewpoint.<ref name=":14">{{cite web
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* 互补性(物理)
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In another extension, prominent physicists have gone so far as to suggest that astronomers observing dark energy in the universe in 1998 may have "reduced its life expectancy" through a pseudo-Schrödinger's cat scenario, although this is a controversial viewpoint.<nowiki><ref>{{cite web
*流行文化中的薛定谔的猫 [[Schrödinger's cat in popular culture]]
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==References==
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==参考文献==
{{Reflist|30em}}
{{Reflist|30em}}
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==延申阅读==
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* The EPR paper: {{cite journal|last1=Einstein |first1=Albert |last2=Podolsky|first2=Boris |last3=Rosen|first3=Nathan |title=Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?|journal=Physical Review|date=15 May 1935|volume=47|issue=10|pages=777–780|doi=10.1103/PhysRev.47.777 |bibcode=1935PhRv...47..777E|doi-access=free}}
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==Further reading==
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* The EPR paper: {{cite journal|last1=Einstein |first1=Albert |last2=Podolsky|first2=Boris |last3=Rosen|first3=Nathan|author-link1=Albert Einstein |author-link2=Boris Podolsky |author-link3=Nathan Rosen |title=Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?|journal=Physical Review|date=15 May 1935|volume=47|issue=10|pages=777–780|doi=10.1103/PhysRev.47.777 |bibcode=1935PhRv...47..777E|doi-access=free}}
* {{cite web |last1=Leggett |first1=Tony |title=New Life for Schrödinger's Cat |url=https://jrfriedman.people.amherst.edu/Leggett%20Physics%20World%20article/PW%20article.pdf |pages=23–24 |date= August 2000 |publisher=Physics World |accessdate=28 February 2020}} An article on experiments with "cat state" superpositions in superconducting rings, in which the electrons go around the ring in two directions simultaneously.
* {{cite web |last1=Leggett |first1=Tony |title=New Life for Schrödinger's Cat |url=https://jrfriedman.people.amherst.edu/Leggett%20Physics%20World%20article/PW%20article.pdf |pages=23–24 |date= August 2000 |publisher=Physics World |accessdate=28 February 2020}} An article on experiments with "cat state" superpositions in superconducting rings, in which the electrons go around the ring in two directions simultaneously.
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* {{cite journal | first=John D.| last=Trimmer | title=The Present Situation in Quantum Mechanics: A Translation of Schrödinger's "Cat Paradox" Paper | journal=[[Proceedings of the American Philosophical Society]] | volume =124| issue= 5 | pages=323–338 | date=1980 | jstor=986572 }}{{registration required}}
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* {{cite journal | first=John D.| last=Trimmer | title=The Present Situation in Quantum Mechanics: A Translation of Schrödinger's "Cat Paradox" Paper | journal=Proceedings of the American Philosophical Society | volume =124| issue= 5 | pages=323–338 | date=1980 }}
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* {{cite journal |last1=Yam |first1=Phillip |title=Bringing Schrödinger's Cat to Life |journal=Scientific American |date=October 9, 2012 |url=https://www.scientificamerican.com/article/bringing-schrodingers-quantum-cat-to-life/ |accessdate=28 February 2020}} A description of investigations of quantum "cat states" and wave function collapse by [[Serge Haroche]] and [[David J. Wineland]], for which they won the 2012 [[List of Nobel laureates in Physics|Nobel Prize in Physics]].
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* {{cite journal |last1=Yam |first1=Phillip |title=Bringing Schrödinger's Cat to Life |journal=Scientific American |date=October 9, 2012 |url=https://www.scientificamerican.com/article/bringing-schrodingers-quantum-cat-to-life/ |accessdate=28 February 2020}} A description of investigations of quantum "cat states" and wave function collapse by Serge Haroche and David J. Wineland, for which they won the 2012 List of Nobel laureates in Physics.
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==外部链接==
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* A spoken word version of this article (created from a revision of the article dated 2013-08-12).
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* [http://www.informationphilosopher.com/solutions/experiments/schrodingerscat/ Schrödinger's Cat]'' from the Information Philosopher.
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==External links==
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* [http://www.sixtysymbols.com/videos/schrodinger.htm Schrödinger's Cat - Sixty Symbols] - a video published by the University of Nottingham.
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{{Commons category|Schrödinger's Cat}}
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* [[:File:Schrodingers-cat.ogg|A spoken word version]] of this article (created from a revision of the article dated 2013-08-12).
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* ''[http://www.informationphilosopher.com/solutions/experiments/schrodingerscat/ Schrödinger's Cat]'' from the Information Philosopher.
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* [http://www.sixtysymbols.com/videos/schrodinger.htm Schrödinger's Cat - Sixty Symbols] - a video published by the [[University of Nottingham]].
* [http://soundcloud.com/siftpodcast/schr-dingers-cat Schrödinger's Cat] - a podcast produced by Sift.
* [http://soundcloud.com/siftpodcast/schr-dingers-cat Schrödinger's Cat] - a podcast produced by Sift.
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==编者推荐==
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===集智文章推荐===
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===课程推荐===
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{{Quantum mechanics topics}}
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[[Category:Thought experiments in quantum mechanics]]
↑ 1.01.1Fine, Arthur. "The Einstein-Podolsky-Rosen Argument in Quantum Theory". Stanford Encyclopedia of Philosophy. Retrieved 11 June 2020.
↑Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Archived 2006-02-08 at the Wayback Machine A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935)
↑ 3.03.1 Fine, Arthur (2017). "The Einstein-Podolsky-Rosen Argument in Quantum Theory". Stanford Encyclopedia of Philosophy. Stanford University. Retrieved 11 April 2021.
↑Polkinghorne, J. C. (1985). The Quantum World. Princeton University Press. p. 67. ISBN 0691023883. Archived from the original on 2015-05-19.
↑Tetlow, Philip (2012). Understanding Information and Computation: From Einstein to Web Science. Gower Publishing, Ltd. p. 321. ISBN 978-1409440406. Archived from the original on 2015-05-19.
↑Schrödinger, Erwin (November 1935). "Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics)". Naturwissenschaften. 23 (48): 807–812. Bibcode:1935NW.....23..807S. doi:10.1007/BF01491891. S2CID 206795705.
↑Trimmer, John D. (1980). "The Present Situation in Quantum Mechanics: A Translation of Schrödinger's "Cat Paradox" Paper". Proceedings of the American Philosophical Society. 124 (5): 323–338. JSTOR 986572. Reproduced with some inaccuracies here: Schroedinger: "The Present Situation in Quantum Mechanics." 5. Are the Variables Really Blurred?
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