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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?

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marked as duplicate by rob Nov 21 '18 at 6:03

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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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 $\acute{S}$

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    $\begingroup$ With common questions like this, it's better to search for an existing duplicate than to write a fresh answer. $\endgroup$ – PM 2Ring Nov 21 '18 at 5:38
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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’.

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