Time will pass for you normally no matter what velocity you travel at, except the speed of light. This includes even impossible velocities faster than the speed of light. At the speed of light, either your travel velocity is undefined, or you spent 0 time travelling to your destination, so the rate of which time passed for you is a 0/0 problem.
What happens at the speed of light? Well the laws of physics requires the speed of light to be constant, even if you are are travelling at the speed of light. But special relativity also requires relative velocities to be opposite and equal. Which means if I observe two spaceships travelling at velocities through
→
v
1
v1→ and
→
v
2
v2→ .
The captain of spaceship 1 will measure spaceship 2 moving at:
→
v
2
'
=
c
2
(
→
v
2
−
→
v
1
)
c
2
−
→
v
1
⋅
→
v
2
v2′→=c2(v2→−v1→)c2−v1→⋅v2→
And the captain of spaceship 2 will measure spaceship 1 moving at:
→
v
1
'
=
c
2
(
→
v
1
−
→
v
2
)
c
2
−
→
v
1
⋅
→
v
2
v1′→=c2(v1→−v2→)c2−v1→⋅v2→
Both of these have the same speed:
v
=
c
√
1
−
(
c
2
−
v
2
1
)
(
c
2
−
v
2
2
)
(
c
2
−
→
v
1
⋅
→
v
2
)
2
v=c1−(c2−v12)(c2−v22)(c2−v1→⋅v2→)2
Now you might notice if I plug in the value
c
c for
v
2
v2 I get:
v
=
c
v=c
Likewise if I plug in
c
c for
v
1
v1 .
This is why we say the speed of light is absolute.
But if I plug in
c
c for both, and both are exactly in the same direction I get a 0/0 error. Which means the relative velocity for two beams of light heading in the same direction is undefined.
If I can’t define the relative velocity of light, I certainly can’t define how time flows at the speed of light. So that means at the speed of light, time is undefined.
If you think about it another way, as we travel closer to the speed of light relative to whatever we are travelling to, the distance to that destination approaches 0. Which means the time it takes to travel to the destination also approaches 0. So zero time passes on the journey. The only ways to have an a destination that takes a finite amount of time to reach is if your destination is infinitely far away, or your destination is moving away from you at the same speed you are are. In either case, you can reasonably say you do not have a destination. As such, your travel velocity is undefined not
c
c .
Now it gets more complicated if you consider general relativity. Because it is possible to travel to galaxies receding away faster than the speed of light, even for a particle with rest mass, like a neutrino. So if you were to consider recession velocity part of your travel velocity, then I would say time is passing for you normally.