Can two electron moving in opposite direction move faster than light?

Question

Suppose we are moving two electrons in opposite direction both having a speed of 1.6e8 meter per sec.When they will cross each other then their relative velocity will be 3.2e8 ms_1.Isn't it faster than speed of light?

Answer 1

The problem is that although your frame of reference(the electron) is moving at speeds close to light, you are using GALILEAN TRANSFORMATION. You should use LORENTZ TRANSFORMATION to get the right relative speed.

Below is the Relativistic Velocity Transformation : $$ u=\frac{\acute{u}+v}{1+\acute{u}v/c^2 }\ $$ Where,

u=velocity of particle as measured from frame S

$\acute{u} $=velocity of particle as measured from frame $\acute{S}$

v=velocity of frame $\acute{S}$

Answer 2

Just to add to the previous answer:

Lorentz transformations were constructed with the idea that no matter which frame you’re in, the speed of light is always mapped to the same number. This is relatively non trivial to imagine. So in all frames, the speed of light is preserved, whereas other speeds (less than the speed of light of course) get mapped to some other value. It turns out that this is a correct way to switch between frames as per STR, and using the velocity addition formula, derived from the Lorentz transformation, tells us that relative speed between two photons will always be the ‘speed of light’.