Comments by "Dr Gamma D" (@DrDeuteron) on "Kyle Hill"
channel.
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It specified in the set-up that they do not act as a single body. The only specification is that they have the same acceleration profiles, and hence the same velocity profiles, with respect to time as measured in the Earth's frame. If you boost those profiles into the average-ship-frame, you get two different time coordinates for each. Colloquially, the from ship's clock is running ahead of the rear ship's clock (it's a clock bias/offset, not time dilation), hence, the front ship is moving a little bit faster than the rear, and it tears the string.
Conversely, for one large ship accelerating uniformly in its own reference frame, Earth will see the nose cone's velocity profile lagging the tail's profile as the ship Lorentz contracts.
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