# How does going faster than light cause going backward in time? [duplicate]

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I have read in many places that some virtual particles can "travel faster than light (1)" and thereby "go backwards in time (2)".

My question is about the connection between these two. I have always perceived this connection as follows:

If a thing can go faster than light, it leaves the image of now behind so can witness the past. Like a thing has traveled from a star to the Earth in 1 year, while the star is 2 light-years away. Therefore this thing can see its past.

However, this thing is not in its original location anymore. And if it tries to go there, even with infinite speed, can only land into the future of its star. So it cannot interfere the history.

Is this what is meant by backward time travel when going faster than light?

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Suppose an object moves right at speed $\beta c$. Its four-velocity is $\gamma c\left(\begin{array}{c} 1\\ \beta \end{array}\right)$ with $\gamma:=(1-\beta^2)^{-1/2}$. A Lorentz transformation $\gamma^{'}\left(\begin{array}{cc} 1 & -\beta^{'}\\ -\beta^{'} & 1 \end{array}\right)$ with $\gamma':=(1-\beta'^2)^{-1/2}$ changes this four-velocity to $\gamma\gamma' c\left(\begin{array}{c} 1-\beta\beta^{'}\\ \beta-\beta^{'} \end{array}\right)$. If $\beta\beta'>1$, the time change is negative. While the Lorentz transformation requires $\beta'<1$, we can choose $\beta'$ large enough to achieve this effect provided $\beta>1$.