The speed of light is constant [186000 mls/sec.] in a VACUUM.
Light speed [and time] are affected by gravitational force[an acceleration]. Time is constant only in a specific reference frame; a clock runs faster on an accelerating space vehicle than it appears to run as seen by an observer at relative rest. It therefor follows that it is possible to travel into SOME-ONE ELSE'S future---but never your own. Time SEEMS to speed up as you get older. A year, for instance, as far as this old codger is concerned seems to be as long as a month 'way back in the teenage days.