I would like to know if "imaginary velocity" has serious problem

I am writing a SF story, in this story, a life-form(You can just call them alien) from another universe comes to earth. They used "imaginary velocity" to make their time elapse faster than all beings on the earth. When the alien is using "imaginary velocity", they eat humans.

From SR, the formula for time dilation is: $$t^{{}^{\prime }}=\frac{t}{\sqrt{1-\frac{v^2}{c^2}}}=\gamma t$$

if I plug in a imaginary number for $v$, for example $2ic$($i$ is the imaginary unit), then I get: $$t^{{}^{\prime }}=\frac{t}{\sqrt{5}}$$ $\gamma$ is less than 1.

this means the time for the objects with imaginary velocity elapse faster than the objects in inertial frame.

In the story i will make it ${10}^{16}$ faster than inertial frame.(human's ${10}^{-16}s$ = alien's $1s$, when the alien spent one day in their reference frame, only $86400\ast {10}^{-16}=8.64\ast {10}^{-12}s$ passed from human's reference frame) So no people can see what's happening, also no machine can detect the actions of aliens.(in the latter part of the story, the situation will change)

Is their any contradiction with the theory of relativity or other physics?

ps. There is a known problem that all observable must be real numbers. However, I decided to ignore it. Since tachyons have imaginary mass and some SF story also used this in their story.

--recently added

$v=2ic$ means the object move $2ic$ m in 1 s, the distance is also imaginary. So, it is not moving in the real spacetime. You will see that object as "not moving" even if it has $2ic$ speed.

posted almost 10 years ago

fairytale‭

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