Space Travel Theory

so i was playing mass effect where the idea behind FTL travel (faster then light) is magic 'element 0' that can be used to reduce mass thus taking less energy to bla bla bla.

the immediate problem i spotted is the the reason you cant go faster then the speed of light is that even a pea starts to weigh millions of tonnes once you really get going. thus just reducing mass won't do shit. in my thinking i accidentally came up with this.

a method of acceleration that would cause no increase of mass. as going faster and faster causes an exponential increase of required energy to go faster. finally hitting infinity somewhere at or past the speed of light. if you could have a linear acceleration then the problem is solved. for remarkably little energy you could break the speed of light and go several times faster again with no issues cept maybe hitting something in deep space.

I'm not pretending it's possible or that the technology to do it exists but it dose solve the most basic problems of space travel.


any thoughts?

I recall reading something that was trying to explain an FTL problem using communication across massive distances with near-instantaneous travel.  Something about subjective, I thjink; what event happened first?  For the life of me, I can't remember what was so paradoxical.