system
Given the following post, respond as if you're commenting on Reddit:
human
Since there isn't any resistance in space, is reaching lightspeed possible?

Without any resistance deaccelerating the object, the acceleration never stops. So, is it possible for the object (say, an empty spaceship) to keep accelerating until it reaches light speed?   


If so, what would happen to it then? Would the acceleration stop, since light speed is the limit?
gpt
The most intrinsic problem is that Newton's second law (F=ma) is actually only a low speed approximation. If you are thrusting in the direction of your motion, the force is actually:

F = (1-v^(2)/c^(2))^(-3/2) ma

When v is much less than c, that first term is basically 1 and you get F=ma. But as v gets closer to c, the first term gets bigger and bigger, and starts to asymptote towards infinity.

This means that the faster you go, the more force you need to get the same amount of acceleration. And the force you need ends up increasing so rapidly as you approach the speed of light that you can never beat it, and never reach the speed of light.

(Side note: it used to be taught that your *mass* increases as you approach the speed of light, but we generally prefer to say that *force for a given acceleration* increases instead, because the required force actually depends on the direction of the force, and it's more weird and confusing if your mass depends on what direction you're being pushed from)

But as a secondary point, space isn't *entirely* empty. There is a thin medium of ionised gas throughout the Milky Way, containing clouds of denser "molecular" gas. Even though the density is extremely low, as you approach the speed of light, you are going so fast that you are smashing through a pretty large volume of space every second, and you do indeed feel a drag force from smashing into these interstellar plasma particles (mostly protons). And not only does this slow you down, over time these high energy protons are going to cause significant damage to your ship!