THE ULTRAMETRIC HILBERT-SPACE DESCRIPTION OF QUANTUM MEASUREMENTS WITH A FINITE EXACTNESS

We provide a mathematical description of quantum measurements with a f inite exactness. The exactness of a quantum measurement is used as a n ew metric on the space of quantum states. This metric differs very muc h from the standard Euclidean metric. This is the so-called ultrametri c. We show that a finite exactness of a quantum measurement cannot be described by real numbers. Therefore, we must change the basic number field. There exist nonequivalent ultrametric Hilbert space representat ions already in the finite-dimensional case (compare with the ideas of L. de Brogliea). Different preparation procedures could generate none quivalent representations. The Heisenberg uncertainty principle is a c onsequence of properties of a preparation procedure. The uncertainty p rinciple ''time-energy'' is a consequence of the Schrodinger dynamics.