Take an acceleration equal to g for 1 year. Isn't the speed of light reached? And exceeded after this time? In the Indian journal Pramana Soviet's scientists made this argument. They explained we leave the realm of special relativity and it's light speed restriction and enter the realm of general relativity where acceleration is treated.
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Take an acceleration equal to g for 1 year. Isn't the speed of light reached?
Note that for the 1-D acceleration case, the proper acceleration $\alpha$ (the acceleration measured by an ideal accelerometer attached to the object) is related to the coordinate acceleration $a$ as follows:
$$\alpha = \gamma^3a$$
where $\gamma$ is the Lorentz factor.
As the speed of the accelerated object approaches $c$ in some inertial coordinate system, the coordinate acceleration must approach zero for any finite proper acceleration. Thus, assuming constant proper acceleration equal to $g$, the speed of the object asymptotically approaches $c$.
I feel certain I've answered one or more similar questions like this but I'm having trouble finding them now. When I do, I'll update with links to these answers.
Alfred Centauri
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