PhilGoetz comments on The Benefits of Rationality? - Less Wrong
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In a TV tube, an electron gun shoots electrons at a cathode ray tube. An electromagnet bends these rays in a precisely-timed manner to make them scan the screen. Since they're travelling at relativistic speeds, they are time-dilated from our point of view; and you need to use relativity to bend them the right amount.
And engineers wouldn't have discovered this fact without relativity theory?