Relational Quantum Mechanics

Relational quantum mechanics treats values of physical quantities and quantum states as relative to systems that interact. An observer need not be conscious: another physical system can establish a correlation. The central move is to reject an absolute state assignment that simultaneously describes every perspective.

Required background. Born rule: Translate a specified state and measurement into outcome probabilities.

Relations established in an interaction

Let system $S$ interact with a record $F$:

$$(\alpha|0\rangle+\beta|1\rangle)|R\rangle \longrightarrow \alpha|0,R_0\rangle+\beta|1,R_1\rangle.$$

Relative to $F$, an outcome can be definite. A third system $W$ that has not interacted with the composite may assign the entangled state. The two descriptions have different relational reference systems.

This is not the ordinary statement that inertial coordinates differ. It concerns the status of events and state assignments. Nor is it merely ignorance about a single hidden absolute value: the interpretation changes which value claims are meaningful.

Comparing records is a physical event

If $W$ later measures the record in its stable basis, ideal correlations imply agreement with the corresponding record of $F$. In the unitary description, an additional record produces

$$\alpha|0,R_0,W_0\rangle+\beta|1,R_1,W_1\rangle.$$

There are no terms with mismatched record labels in this ideal model. Agreement is therefore encoded in correlations when the comparison interaction is specified.

One should not combine arbitrary claims made relative to different systems as if all belonged to one absolute Boolean catalogue. Whether relational accounts provide sufficient rules for all such cross-perspective inferences is an important subject of debate, especially in Wigner’s friend scenarios.

Probability and collapse

The interpretation normally retains the Born rule. State updating is relative to the system for which an event has occurred, while another system may retain a unitary description. This differs both from a universal objective collapse and from Everettian descriptions of all branches as parts of one absolute universal account.

Decoherence helps explain why stable records support nearly classical agreement among many systems. It does not, on its own, define the relational meaning of a fact or eliminate every question about comparisons.

Locality and empirical claims

Quantum correlations and Bell violations remain. A relational account may question absolute assumptions used in a particular conceptual argument, but it must identify those assumptions explicitly. No-signaling, local interactions, and Bell-local hidden-variable factorization are different properties.

The basic interpretive proposal does not automatically furnish a new deviation from standard quantum mechanics. Claims about tests of “observer-independent facts” require the exact premises of a specified theorem and experiment; such tests do not by themselves uniquely confirm relational quantum mechanics.

Strengths and unresolved questions

The proposal treats observers as ordinary physical systems and gives a uniform role to interactions. Questions remain about the ontology of relations, the scope of inter-observer consistency rules, and the relationship between stable relative facts and a shared classical world. Different developments of the interpretation need not answer these identically.

Exercises

Why does the perfectly correlated state above not authorize assigning a single system-independent outcome to every observer before comparison?

Solution

The state gives probabilities and correlations for a specified comparison interaction. It contains multiple terms in $W$‘s description before that interaction. Interpreting one term as an already selected absolute fact adds a premise that the relational proposal does not assume. Correlation and absolute value assignment are distinct claims.

References

• C. Rovelli, “Relational quantum mechanics,” International Journal of Theoretical Physics 35, 1637–1678 (1996), author manuscript.
• A. Di Biagio and C. Rovelli, “Stable facts, relative facts,” Foundations of Physics 51, 30 (2021), doi:10.1007/s10701-021-00429-w.