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DanArmak comments on Harry Potter and the Methods of Rationality discussion thread - Less Wrong
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Taking a great circle route increases lightspeed time to approximately 66.8 milliseconds. That might still be small enough to miss if you're teleoperating from Britain a body in New Zealand, but it's pushing the boundary. Wikipedia suggests 50 milliseconds.
Getting light to follow the curvature of the Earth without a fiber-optic cable or some other specialized medium seems difficult. Probably better to go straight through and just use a wavelength to which the Earth is transparent.
Of course the Muggle solution is a network of satellites...