Question

If you were to somehow be able to accelerate at a constant 10 m/s^2 indefinitely, aka had an infinite amount of energy, ive been told that from an outside reference frame you would assymptotically approach the speed of light... my question is what does the person in teh accelerating reference frame experience? what does their speed do? i think time dilation occurs and distance shrinks, but how would this affect it. (please do not say its not possible because of the energy required or any human limitations, im only looking for what would happen if it were possible as im sure the reason you cant reach the speed of light is deeper than needing an infinite amount of energy, because irs constant in all reference frames)

Answer 1

From the reference frame of the accelerating person, he is at rest and all other things are approaching the speed of light. From that reference frame if he measures the distance, due to time dilation the clock in his frame will be running slower. We know that distance is equal to the product of speed and time. Here speed will same irrespective of the frame, but the time will be dilated and the time will decrease. So the measured length will be lesser than the actual length. This is the phenomenon of length contraction. ie. we can say that Time dilation is the reason why length contraction happens or vice versa. Hence we can say that he will experiencing slower time, and will see all the distances as lesser than the actual one.