Do Frames Affect Dimensional Units?

[BitWiz]

Say a ship is coasting in space at an arbitrary speed and velocity with respect to an observer. If a joule of energy (generated on the ship) is used to instantaneously accelerate the ship:

From an external observer, the acceleration and delta-v observed is dependent on the ship's initial speed (not velocity), correct? The higher the measured speed, the less acceleration and delta-v observed? If I apply a second joule in a separate event, both the acceleration and delta-v will appear to be less than the first time for that observer. Correct?

From within the ship, the perceived acceleration will be the same for both events? If I observe a destination star directly in front of me, the delta-v's will also appear to be the same with the relativistic inertia, time, and length effects canceling out?

Say the ship is already accelerating at a steady rate, and I again apply an extra joule in two events. From the ship's frame, will both events now be different, the second being of less magnitude than the first? What will the external observer see?

Finally, do frames affect or have dimensional units?

Say that two observers each have their own frame and a frame in common. If their individual motions have fixed vectors such that the two observers appear fixed in space with respect to each other, then their individual frames and the common frame are the same.(?) Newtonian mechanics apply. Is it fair to say that this state has a unit dimensional term of γ⁰?

If the vectors do not match, then motion will appear in the common frame, and relativistic effects will apply, but the individual frames are unaffected, and to the observers, interchangeable. Is this correct? Is it fair to say that the common frame has a unit dimension of γ¹ but the individual frames have a γ⁰ dimension?

If one of the vectors is changing over time, then each observer will appear to observe an identical force being applied to the other, but only one will be able to measure the force with an accelerometer. Correct? If so, should this accelerating frame be described with different dimensional units even though from the observers' points-of-view, all else is the same. (?) Would we now have a unit dimension of γ⁰ for one observer, γ¹ for the other, and γ² for the common frame?

Thank you kindly for your comments.

Chris

 

[mfb]

If a joule of energy (generated on the ship) is used to instantaneously accelerate the ship:

It matters how this energy is used.

From an external observer, the acceleration and delta-v observed is dependent on the ship's initial speed (not velocity), correct?

It depends on the acceleration method, the speed, the direction of the spaceship and the direction of the acceleration.

If I apply a second joule in a separate event, both the acceleration and delta-v will appear to be less than the first time for that observer. Correct?

From within the ship, the perceived acceleration will be the same for both events?

Again, depends on how you spend that 1J.

Finally, do frames affect or have dimensional units?

What does that mean?

Say that two observers each have their own frame and a frame in common.

Which frame, what do you mean with "in common"? Observers do not own frames.