We have particle accelerators on Earth that can speed up particles to near the speed of light. Earth itself is hurtling through space, as is the solar system and galaxy that its a part of. If an observer were to float outside of our galaxy and observe those speeding particles in the accelerator on Earth, how would the cumulative movement of the particles, Earth, the solar system, and the galaxy not add up to more than the speed of light (Aside from the fact that the velocities might not add up)? Time dilation? I know that FTL travel is impossible, so I'm not trying disprove it or anything futile like that. I just can't wrap my head around how this works, and I couldn't find a thread that addressed this question. Is this question basically the same thing as, "If I walk forward on a train moving at the speed of light, how do I not travel faster than light?" Would that answer to THAT question change from the perspective of an observer watching that person walk to the front of the light speed train from the ground as the train passes?" Phewph! Thanks for your help.