I would add that in jazz we are usually working with a triplet continuum "feel" underlying per each quarter note (
bababa,
bababa,
bababa,
bababa). Making everything a coloration of those triplets yields some semblance of swing (hopefully

).
In double-time, this triplet continuum, obviously, now goes by twice as fast. Don't just play faster quarter notes...play/feel the faster triplet continuum, regardless of how you color it.