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Einstein's (small) mistake

Breakthrough Starshot plans to accelerate a gram-mass spacecraft up to one-fifth the speed of light to reach nearby stars in our lifetimes. In a recent video (https://youtu.be/Ksb6Vh0BT_E), I discussed some work I'd taken on calculating how the speed of the spacecraft (a light sail) changes as one shines an intense laser beam on it. It turns out my equations differ with the predictions of the Breakthrough team, and indeed just about everyone whose worked on this problem all the way to Einstein himself, who treated it as an example calculation for relativity. Remarkably, there does appear to…

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