Traces, Dispersions of States and Hidden Variables

Stanley Gudder

Pavel Pták

We investigate dispersion-free states which are additive only on the pairs containing a central element (central-absolutely compatible). We show that any logic possesses plenty of such states, in fact, as many as a certain Boolean algebra. The latter result matches the hidden variables conjecture.

Umberto Lombardo, G. Giuliani, Yifei Niu

Jiří Binder

We consider a cr-additive version of "centrally additive" hidden variables as intro duced in [9].As the main result we construct a logic without sufficiently many centrally additive dispersion free states.Consequently, this logic does not admit weak hidden variables.

Emilio d’Emilio, Luigi E. Picasso

Platon C. Deliyannis

Two versions of the hidden variables theorem are presented with minimum hypotheses. The second is intended to be an answer to a question raised by Jauch and Mackey regarding the existence of approximately dispersion-free states.