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I heard it explained that Special Relativity does not actually forbid faster-than-light travel. Instead – it was argued – it is impossible to transcend the speed of light by any massive object, because, according to Special Relativity, mass increases with speed and becomes infinite at $c$, which means a body would take an infinite amount of energy to accelerate further. However, relativistic effects only apply to external observers moving relative to the observed object.

Being in a spaceship, stationary with respect to that ship, but observing its motion relative to a star, I perceive the mass of my ship as being constant (right?). How then can I explain the fact that it's increasingly difficult to accelerate the ship further as it travels faster and faster relative to the star? Can I use Special Relativity to predict increase in energy cost of further acceleration over increase of my speed relative to the star?

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    $\begingroup$ Relativistic mass is an outdated and confusing concept. It is the energy that depends on the referential, not the mass. $\endgroup$
    – Jeanbaptiste Roux
    Commented Nov 28, 2020 at 9:15

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Sure you can from the equation $E=\gamma mc^2$. You will find : \begin{equation} \frac{v^2}{c^2}=1-\frac{m^2 c^4}{E^2} \end{equation} Thus for the first term to be 1 you have to have an infinite amount of energy.

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  • $\begingroup$ Thanks a lot, I think that's what I was looking for. So if I understand correctly, I have to compute $E$ for my current and desired speed, and the difference of these is the energy I need to put into the spaceship in order to accelerate it to the desired speed, right? $\endgroup$
    – Sventimir
    Commented Nov 28, 2020 at 9:29
  • $\begingroup$ I think this is correct. $\endgroup$
    – Jeanbaptiste Roux
    Commented Nov 28, 2020 at 9:59

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