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RobinZ comments on Harry Potter and the Methods of Rationality discussion thread - Less Wrong
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You're right - and the speed-of-light delay in a straight line even through the diameter of the earth is only 42.55 milliseconds. That might be small enough not to be noticed.
Though through the diameter of the earth is not an easy way to transmit messages.
Neutrinos! However by the time you're postulating teleportation and time travel and so forth, I don't think it's necessary to insist on (obvious) conservation of energy in the first place.
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...