Let's say I build a ship, get in it and take off into the dark. When I leave Earth, I measure my acceleration at 1g and my ship is capable of producing that level of power indefinitely. There will be a point when the amount of energy I am using will not be enough to continue accelerating me.
As I reach the point of diminishing returns, do I still feel 1g acceleration? At some point I will stop accelerating - how fast will I be going? What would be the time dilation? What would I, as a passenger on that ship, experience during my travel?
I'm just thinking if we could find a way to accelerate indefinitely (I'm looking, it's around here somewhere), we wouldn't actually have to achieve c in order to make the trip to wherever seem short to the people on the spacecraft.