Generalized Symmetries and Time

A model unifying general relativity and quantum mechanics is proposed the fundamental symmetry of which is not that of a group but rather that of a groupoid. With this groupoid there is associated a noncommutative C*-algebra {A}. It defines a certain noncommutative space. It is shown that both general relativity and quantum mechanics can be recovered from {A}. Noncommutative space defined by {A} is nonlocal. The usual concepts of space and time, as composed of points and instants, are meaningless in it. In spite of this, a generalized dynamics can be defined, but it is intrinsically probabilistic. It is demonstrated how, in the process of transition from the noncommutative regime to the commutative regime, the usual dynamics and time emerge.