Relational Quantum Mechanics - Derivation

Derivation

A promising feature of this interpretation is that RQM offers the possibility of being derived from a small number of axioms, or postulates based on experimental observations. Rovelli's derivation of RQM uses three fundamental postulates. However, it has been suggested that it may be possible to reformulate the third postulate into a weaker statement, or possibly even do away with it altogether. The derivation of RQM parallels, to a large extent, quantum logic. The first two postulates are motivated entirely by experimental results, while the third postulate, although it accords perfectly with what we have discovered experimentally, is introduced as a means of recovering the full Hilbert space formalism of quantum mechanics from the other two postulates. The 2 empirical postulates are:

• Postulate 1: there is a maximum amount of relevant information that may be obtained from a quantum system.
• Postulate 2: it is always possible to obtain new information from a system.

We let denote the set of all possible questions that may be "asked" of a quantum system, which we shall denote by, . We may experimentally find certain relations between these questions:, corresponding to {intersection, orthogonal sum, orthogonal complement, inclusion, and orthogonality} respectively, where .