Can relative speed be faster than c

Question

If there are two spaceships moving away from each other(in opposite directions) at a speed 0.6c, then wouldnt that make the relative speed of one from the other's frame of reference 1.2c? Does this mean that the spacecrafts would disappear, since its light would never reach the other? Is there a contradiction here that I'm missing?

Answer 1

Relative speed can be greater than "c". This does not mean that in an inertial frame fixed on one ship the other ship looks like it is going faster than "c". In an inertial frame fixed on one ship the other ship looks like it is going slower than "c", so light from one could in principle reach the other. In an inertial frame fixed on one ship the other ship looks like it is going at speed (1.2/1.36)*c = 0.88c. You can get this result using the Lorentz velocity transformation: $$ u'=\frac{u-v}{1-\frac{uv}{c^2}}\;, $$ with u=0.6c and v=-0.6c giving u'=0.88c.