Free will theorem

Free will theorem

The free will theorem of John H. Conway and Simon B. Kochen states that, if we have a certain amount of "free will", then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in Foundations of Physics in 2006.[1]

Contents

Axioms

The proof of the theorem relies on three axioms, which Conway and Kochen call "fin", "spin", and "twin". The spin and twin axioms can be verified experimentally.

  1. Fin: There is a maximum speed for propagation of information (not necessarily the speed of light). This assumption rests upon causality.
  2. Spin: The squared spin component of certain elementary particles of spin one, taken in three orthogonal directions, will be a permutation of (1,1,0).
  3. 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 (but more limited than) quantum entanglement.

In their later paper, "The Strong Free Will Theorem," Conway and Kochen weaken the Fin axiom (thereby strengthening the theorem) to a new axiom called Min, which asserts only that two experimenters separated in a space-like way can make choices of measurements independently of each other. In particular, they are not asserting that all information must travel finitely fast; only the particular information about choices of measurements.

The Theorem

The theorem states that, 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. 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.

Limitations

Conway and Kochen do not prove that free will does exist. The definition of "free will" used in the proof of this theorem is simply that an outcome is "not determined" by prior conditions, and some philosophers strongly dispute the equivalence of "not determined" with free will. Some critics argue that the theorem only applies to deterministic models.[2]

See also

Notes

  1. ^ Conway, John; Simon Kochen (2006). "The Free Will Theorem". Foundations of Physics 36 (10): 1441. arXiv:quant-ph/0604079. Bibcode 2006FoPh...36.1441C. doi:10.1007/s10701-006-9068-6. 
  2. ^ What Does the Free Will Theorem Actually Prove? Sheldon Goldstein, Daniel V. Tausk, Roderich Tumulka, and Nino Zanghì, Notices of the AMS, Dec. 2010, http://www.ams.org/notices/201011/rtx101101451p.pdf

References


Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Free will — This article is about the philosophical questions of free will. For other uses, see Free will (disambiguation). A domino s movement is determined completely by laws of physics. Incompatibilists say that this is a threat to free will, but… …   Wikipedia

  • Will to power — For other uses, see Will to power (disambiguation). The will to power (German: der Wille zur Macht ) is widely seen as a prominent concept in the philosophy of Friedrich Nietzsche. The will to power describes what Nietzsche may have believed to… …   Wikipedia

  • Free-market environmentalism — is a position that argues that the free market, property rights, and tort law provide the best tools to preserve the health and sustainability of the environment. This is in contrast to the most common modern approach of proactive environmental… …   Wikipedia

  • Free trade debate — Free trade is one of the most debated topics in economics of the 20th and 21st century Fact|date=December 2007. Arguments over free trade can be divided into economic, moral, and socio political arguments. The academic debate among economists is… …   Wikipedia

  • Free product — In abstract algebra, the free product of groups constructs a group from two or more given ones. Given, for example, groups G and H , the free product G*H can be constructed as follows: given presentations of G and of H , take the generators of G… …   Wikipedia

  • Free electron model — In three dimensions, the density of states of a gas of fermions is proportional to the square root of the kinetic energy of the particles. In solid state physics, the free electron model is a simple model for the behaviour of valence electrons in …   Wikipedia

  • No free lunch in search and optimization — This article is about mathematical analysis of computing. For associated folklore, see No free lunch theorem. The problem is to rapidly find a solution among candidates a, b, and c that is as good as any other, where goodness is either 0 or 1.… …   Wikipedia

  • Ugly duckling theorem — The Ugly Duckling theorem is an argument asserting that classification is impossible without some sort of bias. It is named for Hans Christian Andersen s famous story of The Ugly Duckling. It gets its name because it shows that, all things being… …   Wikipedia

  • Original proof of Gödel's completeness theorem — The proof of Gödel s completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a rewritten version of the dissertation, published as an article in 1930) is not easy to read today; it uses concepts and formalism that are… …   Wikipedia

  • Coase theorem — In law and economics, the Coase theorem (pronounced /ˈkoʊs/), attributed to Ronald Coase, describes the economic efficiency of an economic allocation or outcome in the presence of externalities. The theorem states that if trade in an externality… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”