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创建页面，内容为“The '''free will theorem''' of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are…”
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]]
==Notes==
<references />
==References==
* 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.
*{{Cite journal
| last =Rehmeyer
| first =Julie
| title = Do Subatomic Particles Have Free Will?
| journal = Science News
| volume =
| issue =
| pages =
| date = August 15, 2008
| url = http://www.sciencenews.org/view/generic/id/35391/title/Math_Trek__Do_subatomic_particles_have_free_will%3F
| doi =
| postscript =<!--None--> }}
*[https://mediacentral.princeton.edu/tag/tagid/free%20will Introduction to the Free Will Theorem], videos of six lectures given by J. H. Conway, Mar. 2009.
* {{cite encyclopedia
|last= Wüthrich
|first= Christian
|editor1-first= Claus
|editor1-last= Beisbart
|editor2-first= Stephan
|editor2-last= Hartmann
|encyclopedia= Probabilities in Physics
|title= Can the world be shown to be indeterministic after all?
|trans-title=
|date= September 2011
|publisher= Oxford University Press
|isbn= 978-0199577439
|doi= 10.1093/acprof:oso/9780199577439.003.0014
|pages= 365–389
|chapter-url= http://philsci-archive.pitt.edu/8437/
|chapter= Can the World Beshown to be Indeterministic after all?
|url= http://philsci-archive.pitt.edu/8437/1/WuthrichChristian2010PhilSci_IndeterministicWorld.pdf
}}
[[Category:Physics theorems]]
[[Category:Free will]]
==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]]
==Notes==
<references />
==References==
* 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.
*{{Cite journal
| last =Rehmeyer
| first =Julie
| title = Do Subatomic Particles Have Free Will?
| journal = Science News
| volume =
| issue =
| pages =
| date = August 15, 2008
| url = http://www.sciencenews.org/view/generic/id/35391/title/Math_Trek__Do_subatomic_particles_have_free_will%3F
| doi =
| postscript =<!--None--> }}
*[https://mediacentral.princeton.edu/tag/tagid/free%20will Introduction to the Free Will Theorem], videos of six lectures given by J. H. Conway, Mar. 2009.
* {{cite encyclopedia
|last= Wüthrich
|first= Christian
|editor1-first= Claus
|editor1-last= Beisbart
|editor2-first= Stephan
|editor2-last= Hartmann
|encyclopedia= Probabilities in Physics
|title= Can the world be shown to be indeterministic after all?
|trans-title=
|date= September 2011
|publisher= Oxford University Press
|isbn= 978-0199577439
|doi= 10.1093/acprof:oso/9780199577439.003.0014
|pages= 365–389
|chapter-url= http://philsci-archive.pitt.edu/8437/
|chapter= Can the World Beshown to be Indeterministic after all?
|url= http://philsci-archive.pitt.edu/8437/1/WuthrichChristian2010PhilSci_IndeterministicWorld.pdf
}}
[[Category:Physics theorems]]
[[Category:Free will]]