# Explain how the concept of simultaneity in special relativity leads to the conclusion that two observers in relative motion will each measure the other's clock to be running slower than their own.

> IB DP Physics Higher Level (2023 syllabus) — A.5 Galilean and special relativity (HL only) · Explain · 4 marks

> Two spaceships, A and B, pass each other in empty space at a constant relative velocity of 0.80c. Each ship carries an identical clock. An observer on ship A measures the time interval between two events that both occur at the same location on ship A.

## Mark scheme (4 marks)

1. The observer on A measures a proper time interval between the two events (since both events occur at the same location in A's frame), which is the shortest possible time interval for those events.
2. The observer on B measures a longer (dilated) time interval between the same two events because the events occur at different locations in B's frame, requiring synchronised clocks at different positions.
3. The situation is symmetric: by the same reasoning, an observer on A measures B's clock to be running slow, because events at a fixed location on B are spatially separated in A's frame.
4. This apparent paradox is consistent because simultaneity is relative: the two observers disagree on which events are simultaneous, so there is no single universal 'now' to compare the clocks at the same instant — the contradiction only arises if absolute simultaneity is assumed.

## Key terms

- [simultaneity](https://www.gradenine.co.uk/glossary/simultaneity)

## Related

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