Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being relational, that is, the state is the relation between the observer and the system. This interpretation was first delineated by Carlo Rovelli in a 1994 preprint, and has since been expanded upon by a number of theorists. It is inspired by the key idea behind special relativity, that the details of an observation depend on the reference frame of the observer, and Wheeler's idea that information theory would make sense of quantum mechanics. The physical content of the theory has not to do with objects themselves, but the relations between them. As Rovelli puts it:
"Quantum mechanics is a theory about the physical description of physical systems relative to other systems, and this is a complete description of the world". The essential idea behind RQM is that different observers may give different accurate accounts of the same system. For example, to one observer, a system is in a single, "collapsed" eigenstate. To a second observer, the same system is in a superposition of two or more states and the first observer is in a correlated superposition of two or more states. RQM argues that this is a complete picture of the world because the notion of "state" is always relative to some observer. There is no privileged, "real" account. The state vector of conventional quantum mechanics becomes a description of the correlation of some degrees of freedom in the observer, with respect to the observed system. The terms "observer" and "observed" apply to any arbitrary system, microscopic or macroscopic. The classical limit is a consequence of aggregate systems of very highly correlated subsystems. A "measurement event" is thus described as an ordinary physical interaction where two systems become correlated to some degree with respect to each other. Rovelli criticizes describing this as a form of "observer-dependence" which suggests reality depends upon the presence of a conscious observer, when his point is instead that reality is relational and thus the state of a system can be described even in relation to any physical object and not necessarily a human observer. The proponents of the relational interpretation argue that this approach resolves some of the traditional interpretational difficulties with quantum mechanics. By giving up our preconception of a global privileged state, issues around the measurement problem and local realism are resolved.
History and development Relational quantum mechanics arose from a comparison of the quandaries posed by the interpretations of quantum mechanics with those resulting from Lorentz transformations prior to the development of special relativity. Rovelli suggested that just as pre-relativistic interpretations of Lorentz's equations were complicated by incorrectly assuming an observer-independent time exists, a similarly incorrect assumption frustrates attempts to make sense of the quantum formalism. The assumption rejected by relational quantum mechanics is the existence of an observer-independent state of a system. The idea has been expanded upon by Lee Smolin and Louis Crane, who have both applied the concept to quantum cosmology, and the interpretation has been applied to the EPR paradox, revealing not only a peaceful co-existence between quantum mechanics and special relativity, but a formal indication of a completely local character to reality. In 2020, Rovelli published an account of the main ideas of the relational interpretation in his pop-science book Helgoland. In 2023, Rovelli published a paper with Emily Adlam that presented a significant revision to relational quantum mechanics. Adlam and Rovelli introduced a new axiom, positing the existence of "cross-perspective links", which has been seen as a major move away from relationalism.
The problem of the observer and the observed This problem was initially discussed in detail in Everett's thesis, The Theory of the Universal Wavefunction. Consider observer O {\displaystyle O} , measuring the state of the quantum system S {\displaystyle S} . We assume that O {\displaystyle O} has complete information on the system, and that O {\displaystyle O} can write down the wavefunction | ψ ⟩ {\displaystyle |\psi \rangle } describing it. At the same time, there is another observer O ′ {\displaystyle O'} , who is interested in the state of the entire O {\displaystyle O} - S {\displaystyle S} system, and O ′ {\displaystyle O'} likewise has complete information. To analyse this system formally, we consider a system S {\displaystyle S} which may take one of two states, which we shall designate | ↑ ⟩ {\displaystyle |{\uparrow }\rangle } and | ↓ ⟩ {\displaystyle |{\downarrow }\rangle } , ket vectors in the Hilbert space H S {\displaystyle H_{S}} . Now, the observer O {\displaystyle O} wishes to make a measurement on the system. At time t 1 {\displaystyle t_{1}} , this observer may characterize the system as follows:
| ψ ⟩ = α | ↑ ⟩ + β | ↓ ⟩ , {\displaystyle |\psi \rangle =\alpha |{\uparrow }\rangle +\beta |{\downarrow }\rangle ,}
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