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第1行： − The '''free will theorem''' of [[John Horton Conway|John H. Conway]] and [[Simon B. Kochen]] states that if we have a [[free will]] in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some [[elementary particles]]. Conway and Kochen's paper was published in ''[[Foundations of Physics]]'' in 2006.<ref>{{cite journal | last = Conway | first = John |author2=Simon Kochen | year = 2006 | title = The Free Will Theorem | journal = Foundations of Physics | volume = 36 | issue = 10 | pages = 1441 | doi = 10.1007/s10701-006-9068-6 |arxiv = quant-ph/0604079 |bibcode = 2006FoPh...36.1441C }}</ref> In 2009, the authors published a stronger version of the theorem in the [[Notices of the American Mathematical Society|Notices of the AMS]].<ref name=Later>{{cite journal |author1=Conway, John H. |author2=Simon Kochen |title=The strong free will theorem |journal= Notices of the AMS |volume=56 |issue=2 |year=2009 |pages=226–232 |url=http://www.ams.org/notices/200902/rtx090200226p.pdf?q=will&sa=U&ei=k71jU8X7DoypyASw9YGoCA&ved=0CCAQFjAB&usg=AFQjCNE7L-k87yWE32ru0rDjkLOdg12LRQ}}</ref> Later, in 2017, Kochen elaborated some details.<ref name=":0">Kochen S., (2017), [https://arxiv.org/abs/1710.00868 ''Born's Rule, EPR, and the Free Will Theorem''] [[arxiv]]</ref>+ + + + − ==Axioms== − The proof of the theorem as originally formulated relies on three axioms, which Conway and Kochen call "fin", "spin", and "twin". The spin and twin axioms can be verified experimentally. − # Fin: There is a maximal [[speed]] for propagation of [[information]] (not necessarily the [[speed of light]]). This assumption rests upon [[causality]]. − # Spin: The squared [[spin (physics)|spin]] component of certain elementary particles of spin one, taken in three orthogonal directions, will be a permutation of (1,1,0). − # Twin: It is possible to "entangle" two elementary particles and separate them by a significant distance, so that they have the same squared spin results if measured in parallel directions. This is a consequence of [[quantum entanglement]], but full entanglement is not necessary for the ''twin'' axiom to hold (entanglement is sufficient but not necessary). − In their later 2009 paper, "The Strong Free Will Theorem",<ref name=Later/> Conway and Kochen replace the Fin axiom by a weaker one called Min, thereby strengthening the theorem. Min asserts only that two experimenters separated in a [[Spacetime#Space-like interval|space-like]] way can make choices of measurements independently of each other. In particular it is not postulated that the speed of transfer of ''all'' information is subject to a maximum limit, but only of the particular information about choices of measurements. In 2017, Kochen argued that Min could be replaced by Lin - experimentally testable [[Lorentz covariance]].<ref name=":0" />+ − == The theorem == − The free will theorem states: − − {{quotation|Given the axioms, if the two experimenters in question are free to make choices about what measurements to take, then the results of the measurements cannot be determined by anything previous to the experiments.}} That is an "outcome open" theorem. − {{quotation|If the outcome of an experiment was open, then one or two of the experimenters might have acted under free will.}}+ + + + + − Since the theorem applies to any arbitrary physical theory consistent with the axioms, it would not even be possible to place the information into the universe's past in an ad hoc way. The argument proceeds from the [[Kochen–Specker theorem]], which shows that the result of any individual measurement of spin was not fixed independently of the choice of measurements. As stated by Cator and Landsman regarding [[Hidden-variable theory|hidden-variable theories]]:<ref name=Cator>{{cite journal |author1=Cator, Eric |author2=Klaas Landsman |title=Constraints on determinism: Bell versus Conway–Kochen |journal=Foundations of Physics |volume=44 |issue=7 |year=2014 |pages=781–791 |doi=10.1007/s10701-014-9815-z|arxiv = 1402.1972 |bibcode = 2014FoPh...44..781C }}</ref> "There has been a similar tension between the idea that the hidden variables (in the pertinent causal past) should on the one hand include all ontological information relevant to the experiment, but on the other hand should leave the experimenters free to choose any settings they like."+ − ==Reception== − According to Cator and Landsman<ref name=Cator/>, Conway and Kochen prove that "determinism is incompatible with a number of ''a priori'' desirable assumptions". Cator and Landsman compare the Min assumption to the locality assumption in [[Bell's theorem]] and conclude in the strong free will theorem's favor that it "uses fewer assumptions than Bell’s 1964 theorem, as no appeal to probability theory is made". The philosopher David Hodgson supports this theorem as showing quite conclusively that "science does not support determinism": that quantum mechanics proves that particles do indeed behave in a way that is not a function of the past.<ref>{{cite book |author=David Hodgson |title=Rationality + Consciousness = Free Will |chapter=Chapter 7: Science and determinism |isbn=9780199845309 |year=2012 |publisher=Oxford University Press |chapter-url=https://books.google.com/books?id=4SGsmowYARsC&pg=PA121&dq=%22Conway+and+Kochen+call+the+free+will+theorem%22&hl=en&sa=X&ei=UiMYVeTBII3woATFkoKAAQ&ved=0CB4Q6AEwAA#v=onepage&q=%22Conway%20and%20Kochen%20call%20the%20free%20will%20theorem%22&f=false}}</ref> Some critics argue that the theorem applies only to deterministic models.<ref>Sheldon Goldstein, Daniel V. Tausk, Roderich Tumulka, and Nino Zanghì (2010). [http://www.ams.org/notices/201011/rtx101101451p.pdf What Does the Free Will Theorem Actually Prove?] ''Notices of the AMS'', December, 1451–1453.</ref>+ + + + − ==See also==+ − *[[Bell's inequalities]] − *[[Compatibilism]] − *[[Contextualism]] − *[[Counterfactual definiteness]] − *[[Einstein–Podolsky–Rosen paradox]] − *[[Libertarianism (metaphysics)]] − *[[No-communication theorem]] − *[[Principle of locality]] − + + + + + + + + + − + 第70行：
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{{#seo:
* |keywords=自由意志,the free will theorem,John Horton Conway
* |description=自由意志,the free will theorem,John Horton Conway
* }}
[[约翰·何顿·康威 John Horton Conway]]和Simon B. Kochen的自由意志定理指出，如果我们拥有自由意志，即我们的选择不是过去的功能，那么在一定假设的前提下，一些基本粒子也必须如此。 Conway和Kochen的论文发表在2006年的《物理学基础 Foundations of Physics》上。ref>{{cite journal | last = Conway | first = John |author2=Simon Kochen | year = 2006 | title = The Free Will Theorem | journal = Foundations of Physics | volume = 36 | issue = 10 | pages = 1441 | doi = 10.1007/s10701-006-9068-6 |arxiv = quant-ph/0604079 |bibcode = 2006FoPh...36.1441C }}</ref> 2009年，Conway在AMS中发布了该定理的一个加强版本。<ref name=Later>{{cite journal |author1=Conway, John H. |author2=Simon Kochen |title=The strong free will theorem |journal= Notices of the AMS |volume=56 |issue=2 |year=2009 |pages=226–232 |url=http://www.ams.org/notices/200902/rtx090200226p.pdf?q=will&sa=U&ei=k71jU8X7DoypyASw9YGoCA&ved=0CCAQFjAB&usg=AFQjCNE7L-k87yWE32ru0rDjkLOdg12LRQ}}</ref>后来，在2017年，Kochen对其中一些细节进行深一步的阐释论证。<ref name=":0">Kochen S., (2017), [https://arxiv.org/abs/1710.00868 ''Born's Rule, EPR, and the Free Will Theorem''] </ref>
==公理==
定理的初始证明依赖于三个公理，Conway和Kochen将其称为“ 鳍式 fin”，“自旋 spin”和“孪生 twin”。自旋和孪生公理可以通过实验验证。
＃鳍式：信息的传播有一个最大的速度（不一定是光速）。这个假设基于因果关系。
＃自旋：在三个正交方向上获得的自旋一的某些基本粒子的平方[[spin（physics）| spin]]分量，将是（1,1,0）的排列。
＃孪生：可以“缠结”两个基本粒子，并将它们隔开很大的距离，因此，如果在平行方向上进行测量，它们具有相同的平方自旋结果。这是'''量子纠缠'''的结果，但是对于“孪生”公理来说，完全纠缠不是必需的（纠缠是充分不必要条件）。
在他们后来的2009年论文中，“强自由意志定理”（<ref name = Later />）Conway和Kochen用一个更弱的定理“Min”代替了鳍公理，从而加强了该定理。 Min断言：只有两个以时空性 spacetime 方式分开的实验者可以相互独立地进行测量选择。特别地，假定中“所有”信息的传输速度没有受到最大限制，而仅受有关测量选择的特定信息的限制。在2017年，Kochen辩称Min可以由Lin代替实验可验证（Lorentz covariance）。<ref name =“：0” />
== 定理概念 ==
自由意志定理指出：
{{quotation|根据公理，如果所讨论的两个实验对象可以自由选择要进行的测量，那么测量结果就不能由实验之前的任何事情来确定。}}这是“结果开放 outcome open”定理。
{{quotation |如果实验的结果是公开的，那么一个或两个实验对象可能会自由地选择所要采取的行动。}}
==Notes==
由于该定理适用于与公理一致的任何物理理论，因此它甚至不能以特殊的方式将信息放入宇宙的过去进行研究。该论点源自'''Kochen–Specker定理'''，该结果表明，对自旋的任何单独测量的结果都不是独立于测量选择而固定的。正如Cator和Landsman关于'''隐藏变量理论 hidden-variable theories'''所述<ref name=Cator>{{cite journal |author1=Cator, Eric |author2=Klaas Landsman |title=Constraints on determinism: Bell versus Conway–Kochen |journal=Foundations of Physics |volume=44 |issue=7 |year=2014 |pages=781–791 |doi=10.1007/s10701-014-9815-z|arxiv = 1402.1972 |bibcode = 2014FoPh...44..781C }}</ref>：“想法之间存在着类似的张力，即隐藏变量（在相关的因果关系上）一方面应包括与实验有关的所有本体信息，但另一方面应该让实验对象自由选择他们倾向的任何设置。”
==影响==
根据Cator和Landsman <ref name = Cator />的说法，Conway和Kochen证明“确定性与许多'先验'理想假设不相容”。 Cator和Landsman将'''Min'''假设与'''Bell定理'''中的局部性假设进行了比较，并得出加强版自由意志定理的结论，即“它使用的假设比Bell 1964年的定理更少，因为它没有用到概率论的相关内容”。
哲学家戴维·霍奇森（David Hodgson）支持该定理，因为该结论非常明确地表明“科学不支持决定论”：量子力学证，明粒子的确以与过去不同的方式运动。<ref>{{cite book |author=David Hodgson |title=Rationality + Consciousness = Free Will |chapter=Chapter 7: Science and determinism |isbn=9780199845309 |year=2012 |publisher=Oxford University Press |chapter-url=https://books.google.com/books?id=4SGsmowYARsC&pg=PA121&dq=%22Conway+and+Kochen+call+the+free+will+theorem%22&hl=en&sa=X&ei=UiMYVeTBII3woATFkoKAAQ&ved=0CB4Q6AEwAA#v=onepage&q=%22Conway%20and%20Kochen%20call%20the%20free%20will%20theorem%22&f=false}}</ref> Some critics argue that the theorem applies only to deterministic models.<ref>Sheldon Goldstein, Daniel V. Tausk, Roderich Tumulka, and Nino Zanghì (2010). [http://www.ams.org/notices/201011/rtx101101451p.pdf What Does the Free Will Theorem Actually Prove?] ''Notices of the AMS'', December, 1451–1453.</ref>
==文献引用==
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==References==
==其他参考文献==
* Conway and Kochen, [http://www.ams.org/notices/200902/rtx090200226p.pdf The Strong Free Will Theorem], published in Notices of the AMS. Volume 56, Number 2, February 2009.
* Conway and Kochen, [http://www.ams.org/notices/200902/rtx090200226p.pdf The Strong Free Will Theorem], published in Notices of the AMS. Volume 56, Number 2, February 2009.
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[[Category:Physics theorems]]
[[Category:Physics theorems]]
[[Category:Free will]]
[[Category:Free will]]