What you seem to be describing is the proper velocity or celerity, this is the same as velocity in Newton's theory but is not the same as velocity in relativity.Wrt sb?
If the person inside the craft has a drive that can push 3333G per second (that is, 30km/s^2). That means that in 10 000 seconds of HIS TIME he will reach speed of light. Whatever THAT means. It says on the darn user manual :) And my problem is, I see nothing preventing him from doing that except flattening of space. In some explanations of "fast movement" it is noted that the observer inside the craft does not see much out of the ordinary it his reference frame.
Sorry can't read formulas. Maybe someone could explain what happens and why.
Perhaps a picture will help.
See below 'Einstein vs Newton'. While in Newton's theory a constant acceleration would pass the speed of light after 1 second (in this example) Einstein's theory changed all that. Think of it as some kind of law of 'diminished return" if your relative speed increases. The blue dotted line is the speed of light which I have set to 1. What you see here is a transformation from celerity to velocity.
Now can you see that the red line (Einstein) can never pass or even reach the one mark?
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