  For effect algebras, the so-called tense operators were already introduced by
Chajda and Paseka. They presented also a canonical construction of them using
the notion of a time frame.
  Tense operators express the quantifiers "it is always going to be the case
that" and "it has always been the case that" and hence enable us to express the
dimension of time both in the logic of quantum mechanics and in the many-valued
logic.
  A crucial problem concerning tense operators is their representation. Having
an effect algebra with tense operators, we can ask if there exists a time frame
such that each of these operators can be obtained by the canonical
construction. To approximate physical real systems as best as possible, we
introduce the notion of a q-effect algebra and we solve this problem for
q-tense operators on q-representable q-Jauch-Piron q-effect algebras.
