# Explain how the Lorentz transformation for time differs from the Galilean transformation for time, and describe the physical consequence this difference has for the synchronisation of clocks in two inertial frames moving relative to each other.

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

> In Galilean relativity, time is assumed to be absolute — the same for all observers regardless of their state of motion. Special relativity replaces this assumption with a transformation that couples time to spatial displacement.

## Mark scheme (4 marks)

1. In the Galilean transformation, time is absolute: t′ = t, meaning all observers agree on the time of any event regardless of their relative velocity.
2. The Lorentz transformation for time includes a spatial term: t′ = γ(t − vx/c²), so the time of an event depends on both its time coordinate and its spatial position x in the original frame.
3. Because the Lorentz time transformation depends on position, two spatially separated events that are simultaneous (t₁ = t₂) in one frame will in general have different time coordinates in the other frame, so clocks synchronised in one frame are not synchronised in the other.
4. The greater the spatial separation of the clocks, the larger the synchronisation discrepancy (proportional to vx/c²), showing that this is not a mechanical or practical limitation but a fundamental feature of spacetime.

## Key terms

- [Galilean transformation](https://www.gradenine.co.uk/glossary/galilean-transformation)
- [Lorentz transformation](https://www.gradenine.co.uk/glossary/lorentz-transformation)
- [synchronisation](https://www.gradenine.co.uk/glossary/synchronisation)

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- [Revision notes for IB DP Physics Higher Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
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