Quantum Mechanics without amplitudes

Amplitudes are the major logical object in Quantum Theory. Despite this fact they presents no physical reality and in consequence only observables can be experimetally checked. We discuss the possibility of a theory of Quantum Probabilities capable of give full account to quantum phenomena. Advanteges of this formulation are the evidence of physical processes not described by the orotodox formulation using amplitudes and the possibility of a full algoritimization of Quantum Mechanics. The difficulties in treating Quantum Mechanics as a closed theory comes from the fact that its main logical object the amplitudes has no reality content, cannot be measured. Because this an interpretation is needed, like Copenhagen School, in order to connect properly physics to formalism. Interpretations introduces additional logical elements, like wave packet reduction or Schrödinger’s cat, all also sharing the property of having no reality content. Recently Diósi et all [1] and Brun [2] showed that the measurement process, treated as a quantum open system, select paths in the evolution of the amplitudes that are relevant to another interpretation, the Consistent Histories, introduced by Griffits in the 80’s [3] and by Omnes [4] and Gell-Man and Hartle [5]. In some sense this interpretation closes the theory because amplitude histories are selected by chance and this process is algoritimizable. This means that a physical content may be given to the process of selecting histories. However amplitudes are still used by this interpretation so the reality of the evolution of a quantum system has meaning only at the measurement time. In this context we can ask about a theory minimally open, meaning a formulation of Quantum Theory with a minimum set of non-algoritimizable objects. It would be desirable that such a approach eliminate amplitudes from its formalism and treat quantum phenomena as a fully probabilistic process. A difficulty in this case is how to include phase effects. The possibility of such formulation is the focus of this work. We will show that Quantum Mechanics itself provide the elements needed for establishment of a theory of Quantum Probabilities and as consequence, new