# Learner lab record: Semiclassical source and backreaction scale test

Course: Semiclassical and induced gravity

Name: ____________________  Date: ____________________  Group: ____________________

## Investigation question

When can a renormalized quantum stress tensor source a classical geometry without invalidating the approximation that produced it?

## Setup

Use the semiclassical-scale workspace. Declare field count, quantum state, curvature radius, and renormalization scale; compare quantum source magnitude with background curvature and fluctuation diagnostics.

## Variables

| Variable | Role | Unit |
| --- | --- | --- |
| Field count and mass scale | matter inputs | count and energy |
| Curvature radius | background input | length |
| Renormalized stress scale | dependent source | energy/volume |
| Backreaction and fluctuation ratios | validity diagnostics | dimensionless |

## Predict before changing controls

1. Predict how shorter curvature radius changes local curvature terms.

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2. Predict why small mean stress may be insufficient if stress fluctuations are large.

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## Observation table

| state | field count | mass | curvature radius | stress scale | backreaction ratio | fluctuation ratio |
| --- | --- | --- | --- | --- | --- | --- |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |

## Analyze

1. Which term renormalizes a gravitational coupling?

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2. Is the source small enough for perturbative backreaction?

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3. Are fluctuations compatible with a classical metric description?

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4. Does induced action prove microscopic emergence of all gravity?

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## Evidence-bounded conclusion

At curvature radius ___, the mean backreaction ratio was ___ and fluctuation diagnostic ___; the semiclassical approximation is ___ under assumptions ___.

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