In mid-2004, John Conway and Simon Kochen of Princeton University proved the Free-will Theorem. This theorem states “If there exist experimenters with (some) free will, then elementary particles also have (some) free will.” In other words, if some experimenters are able to behave in a way that is not completely predetermined, then the behavior of elementary particles is also not a function of their prior history. This is a very strong “no hidden variable” theorem.

This result has not currently been published, however, on January 27, 2005, Dr Conway gave a public lecture at the University of Auckland on the proof of this theorem. The following is my account of his talk. As a disclaimer, please note I am not a physicist and do not understand some of the subtler nuances of quantum mechanics. I have tried to faithfully reproduce Conway’s explanation and argument, however, there may still be some errors in this document. If you find such an error, do let me know so I can correct it.

In my (very weak) defense, I quote Dr Conway’s retelling of Feynman’s quip: If you meet someone who claims to understand quantum mechanics, the only thing you can be sure of is that you have met a liar.

Conway’s talk was informative, entertaining and very accessible. The audience consisted not only of mathematicians and physicists — I recognized many computer scientists, philosophers and at least one theologian.

In other words, the spin of a particle is dependent solely on the direction from which it was measured and not on its history. But we have already seen from the Kochen-Specker paradox, there is no way for a particle to predetermine its spin in every direction in a way consistent with SPIN.

Conway thus concluded that if the experimented had sufficient freewill to decide the directions in which he would measure the particle then the particle too must have the freewill to decide on the value of its spin in those directions such that it can be consistent with the 101-property. In concluding Dr Conway said that he believed he did have freewill. Holding up a piece of chalk, he said he felt he could choose whether or not he would drop it or continue to hold it. His theorem he said leads him to accept that the universe is teeming with freewill. He also said that while he did not have any proof for it, he believed that the cumulative freewill of particles is the source of his freewill as a person.

When the floor was opened for questions, one member of the audience questioned Dr Conway’s use of the term “Free Will”. She asked whether Dr Conway was “confusing randomness and free will”.

In a passionate reply, Dr Conway said that what he had shown, with mathematical precision, that if a given property was exhibited by an experimenter than that same property was exhibited by particles. He had been careful when constructing his theorem to use the same term “free will” in the antecedent and consequent of his theorem. He said he did not really care what people chose to call it. Some people choose to call it “free will” only when there is some judgment involved. He said he felt that “free will” was freer if it was unhampered by judgment – that it was almost a whim. “If you don’t like the term Free Will, call it Free Whim – this is the Free Whim Theorem”.

Para pensar:

– e se houver simetria bidireccional e uma propriedade das partículas, definida por cúmulo ou superioridade modal, for extensível ao compósito dessas partículas (eu)?

– Conway assume um conceito discutível ao postular que a informação viaja, que é transmitida; Bohm e Pribram e outros adeptos da não-localidade poderiam provar o que neste artigo se prova, sem recorrer a uma mecânica tão discorrente.

Mas ainda assim…


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