# Learner lab record: Light-cone interval and causality atlas

Course: Special relativity without shortcuts

Name: ____________________  Date: ____________________  Group: ____________________

## Investigation question

Which event pairs can exchange a signal, and which descriptions remain invariant when coordinates change?

## Setup

Use the light-cone laboratory. Classify event pairs by comparing spatial separation with light-travel distance, then test boundary cases on the cone.

## Variables

| Variable | Role | Unit |
| --- | --- | --- |
| Time separation | independent | s |
| Spatial separation | independent | light-seconds |
| Interval | calculated | light-second² |
| Causal class | dependent | timelike, lightlike, or spacelike |

## Predict before changing controls

1. Predict the class when distance equals light-travel distance.

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2. Predict whether changing inertial coordinates can change the causal class.

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## Observation table

| Δt | Δx | cΔt | interval sign | class | signal possible? |
| --- | --- | --- | --- | --- | --- |
|   |   |   |   |   |   |
|   |   |   |   |   |   |
|   |   |   |   |   |   |
|   |   |   |   |   |   |
|   |   |   |   |   |   |
|   |   |   |   |   |   |

## Analyze

1. Which run lies exactly on the cone?

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2. What does each interval sign mean?

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3. Why may observers reorder spacelike events without creating a causal paradox?

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4. What remains locally true in proposed curved metrics?

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## Evidence-bounded conclusion

Events separated by ___ s and ___ light-seconds are ___ because ___; every inertial observer agrees on ___.

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