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I understand how a beam of light emitted from the middle of a moving space ship would fail to synchronize the clocks in the ship from the perspective of someone 'statinary', but if the clocks are synchronized at the start (before the ship moves ) how do they fall out of sync when moving? Does it have to do with acceleration? Why do the clocks at the front lag behind those at the back?

Cosmic Dust
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  • Lag according to who? – user253751 Aug 13 '21 at 14:08
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    If you search for "Minkowski spacetime line element," you'll probably find plenty of introductions. Look for one that explains how to quantify this: In spacetime, if two objects meet each other twice, taking different journeys in between, then their journeys generally have different durations. This is just (spacetime) geometry, very much analogous to the familiar fact that different paths in space from point A to point B generally have different lengths. – Chiral Anomaly Aug 13 '21 at 14:24

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No, it is nothing to do with acceleration- it is just that the plane of simultaneity in one reference frame is angled compared to that in another moving relative to it, the degree of tilt increasing with the relative speed of motion of the two frames.

If the two clocks in your spaceship are synchronised within the spaceship, they will remain so. However, they will appear to be out of synch compared with clocks that are moving relative to them.

Suppose your spaceship is stationary relative to an observer standing next to it. That observer will see that the clocks inside the ship are synchronised. Now suppose the spaceship is passed by ten other observers, each one moving faster than the next. The ten observers moving past at different speeds will each see the clocks out of synch by different amounts.

It is not that the clocks 'become' unsynchronised- it is just that they are synchronised in one frame and not in any others moving relative to it.

Marco Ocram
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