It has always been assumed that whenever we accelerate an electron, it produces electromagnetic radiation, such as light or radio waves. This effect lies behind much of modern technology, such as wifi, microwaves, and x-rays. On the contrary, Yakir Aharonov, Sandu Popescu and I have discovered that it is possible to accelerate an electron without creating radiation. This is quite surprising, particularly since the production of radiation has been studied for over 150 years without this being noticed. Our method uses the dynamic non-locality of the Aharonov-Bohm effect, a fundamental effect in quantum electrodynamics, and may lead to useful applications.