Higgs Field and Einstein's Special Relativity

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John Murray
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At school I was taught that when any matter particle is accelerated until it almost reaches light speed, its mass increases exponentially. If this is not the case, how does an applied force continue to increase the kinetic energy of an accelerated particle without significantly increasing its velocity? If the mass of the particle does in fact increase, does this imply that objects traveling very close to light speed interract with the Higgs boson to a much greater extent than relatively stationary objects?
 
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the mass that is "generated" by the higgs mechanism is the rest mass.
kinetic energy would still be there even if there were no higgs field and the particles are massless.

massless means zero "rest" mass