Specify the Hamiltonian (dynamics) governing the universal quantum state

Develop an explicit Hamiltonian (or equivalent dynamical law) encoding the forces that operate in the universal quantum state, suitable for a full account of cosmic evolution in foundational interpretations and quantum cosmology.

Background

The proposal to identify possible worlds with Everettian branches presupposes a well-defined cosmic dynamics. The author notes that the Hamiltonian governing the universal state—the operator encoding the forces—has not been explicitly formulated.

This gap hinders precise statements about branching structure, decoherence, and the modal significance of branches.

References

Similarly, the proposal implies that the forces operating within the quantum cosmos (encoded in the Hamiltonian that, as I stressed in Chapters 4 and 5, nobody knows how to write down!) could not have been other than they are.

— The Multiverse: a Philosophical Introduction  (2505.23639 - Butterfield, 29 May 2025) in Chapter 6, Section 3

An important open question is whether superposed dynamics can arise intrinsically, rather than through engineered control or post-selection. Any setting in which no unique Hamiltonian can be identified upon quantization is a potential candidate.

— Superposition of dynamics, indefinite causal order, and quantum histories  (2608.16694 - Anastopoulos et al., 17 Aug 2026) in Section Discussion and outlook

The central open problem is whether these boundary and gravitational data suffice to reconstruct a universal third-quantized Hamiltonian.

— A Third-Quantized Description of Spacetime Wormholes in AdS/CFT  (2608.23111 - Hirano, 24 Aug 2026) in Section 6, “Discussion and Outlook,” final paragraph