Im just skimming here, but isn't it a proven fact that if we could travel at the speed of light that time would actually speed up and you'd age faster?

i asked my teacher that same thing about light travel and what not and he said that you are going to fast that things seem normal for you once you get used to it and you dont age a day. but when you get back lets say twenty years after you left, you would look maybe a few months older or just the exact same, but EVERYTHING around you is 20 years older to you, and everything to them is normal because they have seen it change but when you get back they freak out because you look like you did twenty years ago