The free will theorem of
John H. Conway and
Simon B. Kochen states that if we have a
free will
Free will is the capacity of agents to choose between different possible courses of action unimpeded.
Free will is closely linked to the concepts of moral responsibility, praise, culpability, sin, and other judgements which apply only to ac ...
in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some
elementary particles
In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions (quarks, leptons, anti ...
. Conway and Kochen's paper was published in ''
Foundations of Physics
''Foundations of Physics'' is a monthly journal "devoted to the conceptual bases and fundamental theories of modern physics and cosmology, emphasizing the logical, methodological, and philosophical premises of modern physical theories and procedur ...
'' in 2006. In 2009, the authors published a stronger version of the theorem in the ''
Notices of the American Mathematical Society
''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine since ...
''.
Later, in 2017, Kochen elaborated some details.
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
In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude
Magnitude may refer to:
Mathematics
*Euclidean vector, a quantity defined by both its magnitude and its direction
*Magnitude (ma ...
for propagation of
information
Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...
(not necessarily the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
). This assumption rests upon
causality.
# 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).
# 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
Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of ...
, 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",
[ 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 ]space-like
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why diffe ...
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
In relativistic physics, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same ...
.
The theorem
The free will theorem states:
That is an "outcome open" theorem.
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 theories:
Reception
According to Cator and Landsman,[ 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. Some critics argue that the theorem applies only to deterministic models.][Sheldon Goldstein, Daniel V. Tausk, Roderich Tumulka, and Nino Zanghì (2010)]
What Does the Free Will Theorem Actually Prove?
''Notices of the AMS'', December, 1451–1453.
See also
* Bell's inequalities
*Compatibilism
Compatibilism is the belief that free will and determinism are mutually compatible and that it is possible to believe in both without being logically inconsistent.
Compatibilists believe that freedom can be present or absent in situations for re ...
*Contextualism
Contextualism, also known as epistemic contextualism, is a family of views in philosophy which emphasize the ''context'' in which an action, utterance, or expression occurs. Proponents of contextualism argue that, in some important respect, the a ...
*Counterfactual definiteness
In quantum mechanics, counterfactual definiteness (CFD) is the ability to speak "meaningfully" of the definiteness of the results of measurements that have not been performed (i.e., the ability to assume the existence of objects, and properties of ...
*Einstein–Podolsky–Rosen paradox
The Einstein–Podolsky–Rosen (EPR) paradox is a thought experiment proposed by physicists Albert Einstein, Boris Podolsky and Nathan Rosen, with which they argued that the description of physical reality provided by quantum mechanics was inco ...
* Libertarianism (metaphysics)
*No-communication theorem
In physics, the no-communication theorem or no-signaling principle is a no-go theorem from quantum information theory which states that, during measurement of an entangled quantum state, it is not possible for one observer, by making a measurem ...
*Principle of locality
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of ins ...
* Superdeterminism
* Quantum mind
* Orchestrated objective reduction
Notes
References
* Conway and Kochen
The Strong Free Will Theorem
published in Notices of the AMS. Volume 56, Number 2, February 2009.
*
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
Physics theorems
Free will
John Horton Conway