Free will theorem
Encyclopedia
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.
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.
, which shows that the result of any individual measurement of spin was not fixed independently of the choice of measurements.
" 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.
John Horton Conway
John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
and Simon B. Kochen
Simon B. Kochen
Simon Bernhard Kochen is an American mathematician, working in the fields of model theory, number theory and quantum mechanics....
states that, if we have a certain amount of "free will
Free will
"To make my own decisions whether I am successful or not due to uncontrollable forces" -Troy MorrisonA pragmatic definition of free willFree will is the ability of agents to make choices free from certain kinds of constraints. The existence of free will and its exact nature and definition have long...
", then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in Foundations of Physics
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 procedures"...
in 2006.
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.- Fin: There is a maximum speedSpeedIn kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...
for propagation of informationInformationInformation in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
(not necessarily the speed of lightSpeed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
). This assumption rests upon causalityCausalityCausality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....
. - Spin: The squared spinSpin (physics)In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
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 (but more limited than) quantum entanglementQuantum entanglementQuantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...
.
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 theoremKochen-Specker theorem
In quantum mechanics, the Kochen–Specker theorem is a "no go" theorem proved by Simon B. Kochen and Ernst Specker in 1967. It places certain constraints on the permissible types of hidden variable theories which try to explain the apparent randomness of quantum mechanics as a deterministic model...
, 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 willFree will
"To make my own decisions whether I am successful or not due to uncontrollable forces" -Troy MorrisonA pragmatic definition of free willFree will is the ability of agents to make choices free from certain kinds of constraints. The existence of free will and its exact nature and definition have long...
" 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.
See also
- Einstein-Podolsky-Rosen paradox
- Bell's inequalities
- CompatibilismCompatibilismCompatibilism is the belief that free will and determinism are compatible ideas, and that it is possible to believe both without being logically inconsistent. It may, however, be more accurate to say that compatibilists define 'free will' in a way that allows it to co-exist with determinism...
- ContextualismContextualismContextualism describes a collection of views in philosophy which emphasize the context in which an action, utterance, or expression occurs, and argues that, in some important respect, the action, utterance, or expression can only be understood relative to that context...
- Principle of localityPrinciple of localityIn physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. Experiments have shown that quantum mechanically entangled particles must violate either the principle of locality or the form of philosophical realism known as counterfactual...
- No-communication theoremNo-communication theoremIn quantum information theory, a no-communication theorem is a result which gives conditions under which instantaneous transfer of information between two observers is impossible. These results can be applied to understand the so-called paradoxes in quantum mechanics such as the EPR paradox or...
- Libertarianism (metaphysics)Libertarianism (metaphysics)Libertarianism is one of the main philosophical positions related to the problems of free will and determinism, which are part of the larger domain of metaphysics. In particular, libertarianism, which is an incompatibilist position, argues that free will is logically incompatible with a...