I am a visual person, so it's hard to imagine the information I keep getting, but shouldn't time be a constant?
If you were traveling at the speed of light and your able to cover $299{,}792{,}458$ meters in one second, aren't you just going faster than anything else? Why does time slow down as you approach high speeds?
Think about it on a $x-y$ 2D grid. I start off from point $(0,0)$. Then I travel at $299{,}792{,}458\ \mathrm{m/s}$ horizontally, so my $x$ after traveling one second should be at $299{,}792{,}458$. If each $x$ point is one meter apart, wouldn't this mean you are just traveling so fast that your eyes are all blurred up until the point where you slow down to a speed where your eyes could distinctly see what's going on around you, yet nothing is slowed down, it's just you were able to physically reach that speed within a second. So time doesn't stop it's always constant in the sense that it never stops or increases in speed, it's just ticks a constant pace.
If I throw a ball at a speed and it will travel at that same speed, but if I threw the ball at the speed of light, I can pretty much make the ball reach the location faster than the time it should of reached mathematical wise, which that doesn't even make any sense.
Best Answer
Probably, you misunderstood the non-absolute Time interval concept. At near $c$, your eyes can't perceive that your time is dilated (and, length is contracted). You and your measurement tools won't feel any difference at near $c$. Your clocks would tick at the same rate for you like that of rest observer.
The only glitch: A rest observer won't be agree with your measured values (of time interval and length) and you won't be agree with theirs. There's nothing to understand here. It's similar to how two different observers don't agree with measured speed.