As long as symmetry between the two is maintained (i.e. there exists an inertial frame where the two are symmetrical) it doesn’t matter, but equally because the observers are symmetrical they don’t find it any more difficult to accelerate.
I think I see it now (bear with me while I think out loud):
From Earth watching the rocket at some point going “1 mile per hour faster” is simply not possible. It would put the rocket ship over the speed of light and would need infinite fuel to try and still couldn’t do it.
However, for the people on the rocket ship they could drop a buoy overboard which would seem to be motionless with respect to the ship. If they want to accelerate to 1 mph to move away from the buoy they could do it and it’d still take them a liter of fuel (or whatever) from their perspective to do it.
From Earth’s perspective they did not increase velocity by 1 mph but something less.
Where I get confused again is how it works from the spaceship perspective. They throw the first buoy out and move away at 1 mph. They then throw a second buoy out and move 1 mph away from that one (so now 2 mph from the first buoy). They continue this for a long time. Sooner or later, while they can keep accelerating at 1 mph from the most recently dropped buoy, they will notice that they did not increase speed by one more mile per hour with respect to the first buoy dropped.
My brain hurts…
Acceleration in special relatvity s not necessarily that difficult to understand, but there’s plenty of places to trip up, especially to the inexperinced.
The best answer is ‘no’ to thsi question as the ship and it’s engines are in the ICIF (instantaneously co-moving inertial frame, see previous post) so the acceleration that affects them will be the instrinsic acceleration.
Conversley the answer is ‘yes’ to this question, but the point I’m making here is that it’s a ‘mile-per-hour faste’ in another frame. In order to maintain constant extrinsic acceleration (which is impossible to do indefinitely mind) in some inertial frame the intrinsic acceleration must be changing.
Well I replied to your post before you edited it, but again I draw your attention to the difference between intrinsic and extrinsic accleration. You can accelerate with constant intrinsic acceleration indefintely, but an object cannot have constant extrinsic acceleration in some frame indefintely.
In your buoy example, the can keep on doing that indefintely, but from lets say what we will call the earthbound frame for convience the spaceship’s acceleration will appear to drop off. The reason being the Earthbound observer is measuring extrinsic acceleration, but the spaceship (in a fashion) is measuring intrinsic acceleration.
You should probably say “level off” rather than “drop off”, there. At no point will Earth say that the ship’s speed is decreasing.
Pants said the acceleration will drop off, though, not the velocity. And indeed the acceleration will start at 1 g and decrease to “epsilon” over time.
Ah, right, I read that too hastily.
Puzzled again…
Consider the buoy example I gave above.
If the ship is using acceleration to simulate gravity then, from earth, we’d say that eventually the ship cannot maintain that acceleration indefinitely. As it approached the speed of light the ship cannot continue to go faster and faster. Presumably then the people on board will be getting lighter and lighter as “gravity” due to acceleration will decrease.
Yet with the buoy example the people on board the ship should always be able to say they can accelerate at 1g away from any buoy they drop overboard.
So what really happens to the people on the ship? Do they start floating or can they always maintain a 1g acceleration from their perspective and not start floating around the ship?
I’m so off of this thread, but intuevityly (if that is any word), I do hope tjat whack-whatever, is right. Because he is trying to challenge THE PHYSICS, psycos or whatever. Com’on… folks give a ship a Newton then give another one - it equls two…
The acceleration we measure from Earth is not the acceleration that’s relevant for artificial gravity on the ship. They can maintain artificial gravity on the ship for as long as their fuel lasts.