Authors: Germano Resconi, Koji Nagata
Feynman pointed out on a logic and mathematical paradox in particle physics. The paradox is that we get for the same entity only local dependence and global dependence at the time. This contradiction is coming from the dual nature of the particle viewed as a wave. In the first capacity it has only local dependence in the second (wave) capacity it has a global dependence. The classical logic has difficulties to resolve this paradox. Changing the classical logic to logic makes the paradox apparent. Particle has the local property or zero dependence with other particles, media has total dependence so is a global unique entity. Now, in set theory, any element is independent from the other so disjoint set has not element in common. With this condition we have that the true false logic can be applied and set theory is the principal foundation. Now with conditional probability and dependence by copula the long distance dependence has effect on any individual entity that now is not isolate but can have different type of dependence or synchronism ( constrain ) which effect is to change the probability of any particle. So particle with different degree of dependence can be represented by a new type of set as fuzzy set in which the boundary are not completely defined or where we cannot separate a set in its parts as in the evidence theory. In conclusion the Feynman paradox and Bell violation can be explained at a new level of complexity by many valued logic and new type of set theory.
Comments: Journal of Modern Physics, Volume 7, No.1 (2016), Page 65--73.
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