Statement
Problem 3.1 of Goto et al.: in non-gravitational QFT, observables are specified intrinsically (local operators and correlators). In gravity, diffeomorphism invariance blurs this: defining an observable seems to require extra reference structure — a reference frame, an observer algebra, a reference state, or a code subspace. Which is required, and when?
Why It Matters
“Observer algebra” and “reference state” are the crossed-product language the group’s AQFT course develops (Witten/CPW/CLPW). The relational-observable/reference-frame framing is exactly what turns the bare type III₁ algebra into a traceable type II one, so this problem is the conceptual root of dynamical-observer-backreaction-and-algebra and observer-algebra-bell-chsh.
What We Know
- Crossed-product/CLPW: adjoining an observer (a clock/frame with a Hamiltonian) yields a well-defined dressed algebra and a gauge-invariant notion of observable.
- Quantum reference frames formalize relational observables.
- Different reference choices (frame vs. code subspace) may be inequivalent; a systematic map is missing.
Possible Approaches
- Classify reference structures by the algebra type they produce (III₁ vs II vs II₁).
- Use the free-field crossed-product analog (course Sem II) as a controlled testbed.