Another thing is, if the person was able to achieve faster than light-speeds, time would dialate. Now I don't mean they would get tall or fat, but according to Einstein's theory of relativity, that person's mass would be come Infinite, along with the amount of energy needed to travel that far. But would that have a physical effect on the characters? First off, they would get large, very large. They could simply be moving so fast that they can not be seen. First off, where do they go in instant transmission? They simply disappear in one place and reappear in another. But, would that have an effect on the characters. That means characters would have to move 2.7 billion miles in a second. So let's say Earth and Neptune are currently on opposite sides of the Sun. When on the opposite side of the Sun from each other, they get to be around 2.7 billion miles away. When Earth and Neptune are on the same side of the Sun, the closest they get is 2.5 billion miles from each other. But how fast would these characters have to be moving in instant transmission to reach a destination instantly? Let's use a location that is fairly close to Earth and we can correctly use the distance between Earth and the planet in question. The character puts their index and middle finger to their forehead and thinks of a location and they are instantly transported there. If you aren't familiar with DBZ, I'll give you a quick rundown of instant transmission. Anyone who is fan of anime, or more specifically, Dragon Ball Z, knows about an ability many characters posses, instant transmission.

Instant transmission gif