I might misunderstand the higgs mechanism. And I have a puzzle. Consider an electron in an accelerater. It is massive at low energy and its speed is something lower than the speed of light. However when it is accelerated to the electroweak scale, su(2) becomes unbroken and the electron turns to be massless and its speed turns into the speed of light at this point. It seems there is an infinite acceleration when the electron energy reaches electroweak scale. I just feel this is unnatural, or I missed something there.