Explain why two observers in different inertial frames of reference will disagree on whether two spatially separated events are simultaneous, even if both observers correctly apply the laws of physics.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A rocket travels at a speed of 0.8c relative to a space station. A light signal is emitted from the midpoint between two detectors that are at rest relative to the rocket. The signal reaches both detectors at the same time according to an observer on the rocket.
Model answer (4 marks)
The postulate of special relativity states that the speed of light is the same (c) in all inertial frames of reference.
In the space‑station frame the two detectors are moving relative to the light source. The light therefore has to travel a longer distance to reach the detector that is moving away from the source and a shorter distance to reach the detector that is moving toward the source.
Because light still travels at c in the station frame but covers unequal distances, it arrives at the two detectors at different times according to the station observer.
Thus the two observers disagree on the simultaneity of the two events. Neither observer is wrong; simultaneity is relative and depends on the inertial frame, a direct consequence of the invariance of c.
In the space‑station frame the two detectors are moving relative to the light source. The light therefore has to travel a longer distance to reach the detector that is moving away from the source and a shorter distance to reach the detector that is moving toward the source.
Because light still travels at c in the station frame but covers unequal distances, it arrives at the two detectors at different times according to the station observer.
Thus the two observers disagree on the simultaneity of the two events. Neither observer is wrong; simultaneity is relative and depends on the inertial frame, a direct consequence of the invariance of c.
Examiner tips
- Use the key phrase "simultaneity is relative" to show understanding of the concept.
- Show the light‑travel argument clearly – mention unequal distances in the station frame.
- Mention the postulate that c is invariant – this is the core reason for the disagreement.
- Keep the answer concise and to the point – 4 marks only.
Common mistakes
- Assuming the detectors are at rest in both frames – they are only at rest in the rocket frame.
- Forgetting to state that light still travels at c in the station frame.
- Claiming that one observer is wrong – the disagreement is physical, not an error.
Mark scheme (4 marks)
- The postulate of special relativity states that the speed of light is the same (c) in all inertial frames of reference.
- From the space station frame, the two detectors are moving (toward or away from the oncoming light), so light must travel different distances to reach each detector.
- Since light still travels at c in the station frame but covers unequal distances to each detector, it arrives at the two detectors at different times according to the station observer.
- This is a genuine (physical) disagreement: neither observer is wrong; simultaneity is relative and depends on the inertial frame, a direct consequence of the invariance of c.
Related
- All IB DP Physics Higher Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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