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The free will theorem states: Given the axioms, if the choice about what measurement to take is not a function of the information accessible to the experimenters (free will assumption), then the results of the measurements cannot be determined by anything previous to the experiments. That is an "outcome open" theorem:
[35]: 247-248 The free will theorem of John H. Conway and Simon B. Kochen further establishes that if we have free will, then quantum particles also possess free will. [ 36 ] [ 37 ] This means that starting from the assumption that humans have free will, it is possible to pinpoint the origin of their free will in the quantum particles that ...
The free will theorem says that if we have free will, then particles must have free will. This presumably is counterintuitive. It makes no claim about a world in which we don't have free will (a deterministic world). There's no way to argue for free will on the basis of this theorem - and yet, this is what the section claims, without any ...
A linear group is not amenable if and only if it contains a non-abelian free group (thus the von Neumann conjecture, while not true in general, holds for linear groups). The Tits alternative is an important ingredient [2] in the proof of Gromov's theorem on groups of polynomial growth. In fact the alternative essentially establishes the result ...
By postulating that all systems being measured are correlated with the choices of which measurements to make on them, the assumptions of the theorem are no longer fulfilled. A hidden variables theory which is superdeterministic can thus fulfill Bell's notion of local causality and still violate the inequalities derived from Bell's theorem. [1]
A renewal process has asymptotic properties analogous to the strong law of large numbers and central limit theorem. The renewal function () (expected number of arrivals) and reward function () (expected reward value) are of key importance in renewal theory. The renewal function satisfies a recursive integral equation, the renewal equation.
Every adapted right continuous Feller process on a filtered probability space (,, ()) satisfies the strong Markov property with respect to the filtration (+), i.e., for each (+)-stopping time, conditioned on the event {<}, we have that for each , + is independent of + given .
Given a discrete-time stationary ergodic stochastic process on the probability space (,,), the asymptotic equipartition property is an assertion that, almost surely, (,, …,) where () or simply denotes the entropy rate of , which must exist for all discrete-time stationary processes including the ergodic ones.