# Instructor guide: Semiclassical source and backreaction scale test

Course: Semiclassical and induced gravity

Suggested time: 70–90 minutes

## Learning target

Learners test mean-source, fluctuation, scale-separation, and renormalization conditions before interpreting semiclassical or induced-gravity results.

## Prepare

- Review effective-action curvature terms.
- Declare renormalization conditions.
- Define mean-field and fluctuation validity thresholds.

## Facilitation moves

- Separate coupling renormalization from microscopic derivation.
- Require both mean and variance diagnostics.
- Ask where higher-curvature terms become important.

## Misconception checks

- **Any one-loop R term proves gravity is entirely induced.** It shows an effective gravitational contribution; universality, dynamics, state dependence, and UV completion require further argument.
- **Small average stress guarantees a classical source.** Large stress fluctuations or entanglement structure can undermine a mean-field metric treatment.

## Accessibility and participation

- Use a validity decision tree.
- Pair effective-action notation with term-by-term physical roles.
- Provide dimensionless ratios before full tensors.

## Evidence of learning

- A complete validity hierarchy
- Mean and fluctuation diagnostics
- An induced-term-versus-emergence distinction

## Extension

Add a higher-curvature term and identify the radius at which it competes with Einstein curvature.

## 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.