# Tachyons and Lorentz velocity transformation

In general, is it possible to apply the Lorentz velocity transformation to a tachyon?

I have tried to do so but the results seemed very illogical. Here's my attempt: suppose an evil spaceship named XYZ is moving away from Earth at speed $0.6c$ in the +x direction. We send a futuristic tachyonic spaceship named TY to attack XYZ at speed $4.0c$, also in the +x direction.

Now consider a person on the tachyonic spaceship. He attempts to find the speed which the XYZ is approaching himself (therefore, the speed must be negative). Using the Lorentz velocity transformation: $$\begin{eqnarray*} v'&=&\frac{v-u}{1-uv/c^2}\\ &=&\frac{0.6c-4.0c}{1-(0.6)(4.0)}\\ &=&2.4c \end{eqnarray*}$$

This implies that the XYZ is moving forward, away from TY at a speed even faster! The tachyonic spaceship will not be able to catch up to XYZ. What is the problem here?

• Dec 1, 2015 at 16:51
• There is no transformation between frames with a relative velocity greater than $c$. They are causally disconnected. Applying any formula derived from the Lorentz transformation will just give meaningless results. Dec 1, 2015 at 16:53