# Which Frame of Reference is Correct?

I am reading a lot about the theory of special relativity, but I have a very basic question about this theory I still don't understand. Consider a particle in two inertial reference frames $$\Sigma$$ and $$\Sigma'$$. The reference frame $$\Sigma'$$ is moving with uniform velocity $$v$$ relative to $$\Sigma$$. The particle is at rest in $$\Sigma'$$. Both reference frames have common axes $$x$$ and $$x'$$. When doing a certain calculation in both reference frames, which one of the obtained results is considered correct? Are they considered both correct or the one obtained by an observer in $$\Sigma'$$?