Not a physicist, but I think it might not be that simple. From our
point of view, a ship with constant 1g acceleration increases its
speed by 9.8 m/s every second, but people on a ship moving at a
significant fraction of c take more than one of our seconds to
experience one of their seconds. During the time they experience one of
their seconds, the speed increases more than 9.8 m/s, so they must
experience greater than 1g acceleration. I haven't done the math but it
would be interesting to work out how the acceleration in our reference
frame needs to reduce to ensure constant acceleration in the ship's
reference frame, and how long it would really take to reach .99c
without squashing the passengers.
Err, that isn't a correct understanding of physics, I believe. The ship wouldn't need to reduce its output as it gets faster relative to some other object in the universe. It can happily keep accelerating at 9.8 m/s for as long as it likes (or has fuel). No passengers would get squashed.
If the ship's means of propulsion is set to impart a constant force,
then I understand that the passengers could experience a constant
acceleration indefinitely, but that constant acceleration would be
with respect to the ship's reference frame, not ours. A constant
acceleration of 1g in our reference frame would mean by definition
that the speed reaches 2c in two years, which can't be right. Subject
again to the disclaimer that I'm not a physicist and haven't done the
math, the only outcome I can picture is that in our reference frame
the speed asymptotically approaches c in some interesting way.
Oh I see! 1G from our reference frame! Fascinating! That’s a perspective I haven’t seen before, I didn’t realize that that’s what you meant. Indeed, it isn’t possible. We’d see the ship slowly approach but never reach the speed of light, no matter how hard or long they step on the accelerator.
Isn't a second now officially defined as a single period of atomic decay of a certain atom (I think Cessium?)? So this theoretical near-lightspeed craft could adjust it's accelerators based on an onboard atomic clock that would not be based on seconds as we tend to perceive them, but on SI seconds. I assume these would be getting longer as velocity approached 1c.
Unless radioactive decay is also affected by relativity (obviously I am not a scientist), in which case of course that wouldn't work.
One of the consequences of the theory of relativity is that there is no "absolute time". The atomic clock will perceive time just as you will–that is, slower than an inertial reference frame.
