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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2$\begingroup$ If you ignore relativistic effects of acceleration/forces and energy, sure you can exceed $c$ easily enough. $\endgroup$– Kyle KanosCommented Dec 30, 2019 at 22:27
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4$\begingroup$ Just to be clear, you don’t need general relativity to treat accelerating motion in flat space. GR is needed only for gravitational systems. $\endgroup$– Bob KnightonCommented Dec 30, 2019 at 22:31
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$\begingroup$ Doesn't Einstein thought experiment with the elevator show that acceleration is equal to gravity? $\endgroup$– LarryCommented Dec 30, 2019 at 22:51
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2$\begingroup$ Larry, no, acceleration is not equal to gravity. Gravity is, according to GR, spacetime curvature. Acceleration doesn't require curved spacetime. But this isn't at the root of your question. $\endgroup$– Alfred CentauriCommented Dec 30, 2019 at 23:18
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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.
answered Dec 30, 2019 at 23:06