# Instructor guide: Curved-spacetime QFT scale hierarchy audit

Course: Quantum fields in curved spacetime

Suggested time: 70–90 minutes

## Learning target

Learners distinguish basis-dependent particle number from detector observables and test the validity of fixed-background semiclassical reasoning.

## Prepare

- Review Bogoliubov normalization and detector response.
- Declare state, trajectory, and switching function.
- Define a backreaction smallness criterion.

## Facilitation moves

- Ask which observer and time evolution define particles.
- Keep occupation, response, and stress-energy in separate columns.
- Require hierarchy checks before interpreting thermal language.

## Misconception checks

- **Observer-dependent particle number makes every prediction subjective.** Detector response and renormalized correlations are operational once state, trajectory, and protocol are specified.
- **A thermal spectrum automatically supplies usable net work.** Temperature, detector coupling, preparation, switching, and complete-cycle thermodynamics remain distinct.

## Accessibility and participation

- Pair scale diagrams with numeric ratios.
- State every observer and state label in prose.
- Provide a hierarchy checklist before tensor calculations.

## Evidence of learning

- A declared state/observer protocol
- Three separated diagnostics
- A justified backreaction validity statement

## Extension

Compare two admissible vacuum choices and compute both Bogoliubov occupation and one detector-response difference.

## Evidence boundary

Assess the learner's reasoning only within the declared model and recorded observations. Do not upgrade a simulation result into a claim about an unmodeled physical system.