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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@jgreen2015 maybe you should just do the Lorentz transformation. If something is simultaneous in the Earth's frame (say, reaching 0.9c), then it simply cannot be simultaneous in a moving frame, since the relativistic invariant is s^2 =(ct)^2 - x^2. In this case, if the string length L, the invariant is s^2 = -L^2. In the moving frame, the spatial separation is (gL)^2 where g>1 is the Lorentz factor. The time separation then must satisfy:
(cT)^2 - (gL)^2 = -L^2 so that:
|T| = gLv/c > 0.
If you need clarification, that's fine, but if you want to argue that I am wrong: please don't.
Anyone here who thinks I am wrong, is wrong. I studied this stuff under the greatest masters at the time, not from a rando youtuber.
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