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Relational quantum mechanics is an interpretation of quantum mechanics which is distinguished by its construal of the state of a quantum system as being the correlation between this system and an observer. The interpretation was first put forward by Carlo Rovelli in 1994.

Fundamental propositions

The Third Man problem

This problem was initially discussed in detail in Everett's thesis, The Theory of the Universal Wavefunction. Consider a system ${\displaystyle S}$ which may take one of two states, which we shall designate ${\displaystyle |A\rangle }$ and ${\displaystyle |B\rangle }$, vectors in the Hilbert space ${\displaystyle H_{S}}$. Now, there is an observer ${\displaystyle O_{1}}$ who wishes to make a measurement on the system. At time ${\displaystyle t_{1}}$, the system may be characterised as follows:

${\displaystyle |\psi \rangle =\alpha |A\rangle +\beta |B\rangle }$

where ${\displaystyle |\alpha |^{2}}$ and ${\displaystyle |\beta |^{2}}$ are probabilities of finding the system in the respective states, and obviously add up to 1. For our purposes here, we can assume that in a single experiment, the outcome is the eigenstate ${\displaystyle |A\rangle }$ (but this can be substituted throughout, mutatis mutandis, by ${\displaystyle |B\rangle }$). So, we may represent the sequence of event in this experiment, with observer ${\displaystyle O_{1}}$ doing the observing, as follows:

${\displaystyle t_{1}\rightarrow t_{2}}$

${\displaystyle \alpha |A\rangle +\beta |B\rangle \rightarrow |A\rangle }$

This is observer ${\displaystyle O_{1}}$'s description of the measurement event. Now, any measurement is also a physical interaction between two or more systems. Accordingly, we can consider the tensor product Hilbert space ${\displaystyle H_{S}\otimes H_{O_{1}}}$, where ${\displaystyle H_{O_{1}}}$ is the Hilbert space inhabited by state vectors describing ${\displaystyle O_{1}}$. If the initial state of ${\displaystyle O_{1}}$ is ${\displaystyle |init\rangle }$. After the measurement, some degrees of freedom in ${\displaystyle O_{1}}$ become correlated with the state of ${\displaystyle S}$, and this correlation can take one of two values: ${\displaystyle |O_{1}A\rangle }$ or ${\displaystyle |O_{1}B\rangle }$, with obvious meanings. If we now consider the description of the measurement event by another observer, ${\displaystyle O_{2}}$,

Structure of questions

Relationship with other interpretations

References

Get Everett, Rovelli (Int Jour Theor phys), von Neumann.