I was going to post on another thread that a spaceship could theoretically accelerate forever without reaching the speed of light (let's say this is relative to the spaceport where it began its journey).(adsbygoogle = window.adsbygoogle || []).push({});

If I am at the spaceport, I can certainly agree. I see the spaceship getting closer and closer to the speed of light, but never reaching it. But I would be seeing the acceleration slowing down.

If I am in the spaceship, what happens? It the spaceship is accelerating, I will be able tell that, from the way things move if I let go of them. I know I am not in an inertial frame.

If I read what time has elapsed on my clock, then multiply that by the acceration that I can calculate by putting a known mass on a set of scales, then I should be able to calculate my change in velocity.

If I accelerate forever, I would have on my clock ([tex]\Delta t[/tex]=infinity), multiplied by the non-zero acceleration (a) and have a velocity of infinity.

This can't work.

What I think the resolution might be, is this:

According to the spaceport, the spaceship may accelerate forever, but at a hyperbolically reducing rate. I could calculate that the acceleration would seem constant according to the spaceship.

According someone on the spaceship, there would not be enough time to accelerate to the speed of light. For example, if the spaceship accelerated at a constant 10m/s^{2}to make a nice simulation of Earth gravity, then it would reach the final moment of the universe after 22 years (plus a bit).

I'm not totally happy with it.

Please note, I know there are issues with accelerating something forever, we have to apply some "mind experiment magic" to give us the ability to do so. Once the engineering issues are out of the way though, is my resolution correct, or does something else happen?

cheers,

neopolitan

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# Endless acceleration

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