Superlucenic Motion: Motion of Particles with Velocity Greater than that of Light.
Let me neologize the word Lucenic (lux is Latin for light) to refer to motion of particles whose velocity compares with that of light, c.
Sublucenic motion will refer to the motion of particles with velocity less than that of light, while superlucenic motion will refer to that whose theoretical velocity will be greater than that of light.
The Lorentz () factor:
The Lorentz factor is determined as:
For v > c, becomes , a modified Lorentz factor to take into account the presence of the imaginary number, i.
For addition of velocities:
Let u > c, v < c, then , same for u < c, v > c.
But if both u > c and v > c, then surprisingly, w < c.
For Time Dilatation, if T is the time interval in the S frame and T’ the equivalent in the S’ frame, then .
Also notice that the Lorentz-Fitgerald contraction will give , where L, L’ are the lengths in S and S’ respectively.
Recall that .
Because of the presence of , if we are to achieve Superlucenic motion, then we have to go out of the three-dimensional space and venture into the fourth-space dimension (different from Minkowski’s fourth space-time dimension). The particle in question will “disappear” into the fourth dimension since it will be faster that the observing (or observation) medium (light in this case).
The particles in question need be massless, otherwise the mass will be infinite as the velocity of the said particles approaches c, the asymptotic limit for sublucenic velocity.