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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?

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  • $\begingroup$ Related: physics.stackexchange.com/q/39467/2451 $\endgroup$
    – Qmechanic ♦
    Dec 1, 2015 at 16:51
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    $\begingroup$ 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. $\endgroup$
    – John Rennie
    Dec 1, 2015 at 16:53

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Actually, you can consider a transformation to a tachyonic frame where the relative velocity is greater than c.

Then the solution becomes simple, and is no longer meaningless.

In the Earth's frame, XYZ was launched before TY.

In TY's frame, his spaceship was launched before XYZ.

Hence, it is XYZ that needs to catch up to TY! Not the other way round. Therefore we get +2.4c.

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