# Learner lab record: Curved-spacetime QFT scale hierarchy audit

Course: Quantum fields in curved spacetime

Name: ____________________  Date: ____________________  Group: ____________________

## Investigation question

When is particle language, detector response, and semiclassical backreaction self-consistent in a curved or time-dependent background?

## Setup

Use the QFT scale workspace. Declare curvature, field mass, detector gap, switching duration, and state choice; vary one hierarchy at a time and record which approximation remains controlled.

## Variables

| Variable | Role | Unit |
| --- | --- | --- |
| Curvature or horizon scale | background input | 1/length² or temperature |
| Field mass and detector gap | quantum inputs | energy |
| Switching/observation duration | protocol input | time |
| Occupation, detector response, backreaction ratio | dependent diagnostics | dimensionless/rate |

## Predict before changing controls

1. Predict the response when the detector gap greatly exceeds the curvature temperature scale.

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2. Predict what fails when renormalized stress-energy is no longer small compared with background curvature.

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## Observation table

| state | curvature scale | mass/gap | duration | occupation | detector response | backreaction ratio |
| --- | --- | --- | --- | --- | --- | --- |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |

## Analyze

1. Which result depends on the mode basis?

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2. Which quantity is directly operational for a specified trajectory?

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3. Does the switching protocol create transient response?

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4. Where does the fixed-background approximation fail?

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## Evidence-bounded conclusion

For state ___ and hierarchy ___, detector response was ___ while backreaction ratio was ___; the controlled interpretation is ___.

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