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Two particles travelling with velocity .8c (observed from ground frame) each approach each other. What is their relative velocity wrt ground frame. According to me they should be added. I am very much aware that their relative velocity wrt each other is smaller than c i.e is velocity of one particle wrt other.

What is the relative speed of two near-light speed particles headed towards each other?

varang rai
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  • FWIW, their relative speed is 40c/41. – PM 2Ring Sep 19 '19 at 15:20
  • What's with the off-topic close votes? This seems to me to be a question stemming from legitimate confusion about what it means to add velocities in special relativity. – Ben51 Sep 19 '19 at 15:54
  • This is unclear. Is the $0.8 c$ their speed relative to the ground or relative to each other? You ask for “relative velocity wrt ground”, which is not what “relative velocity” usually means. – G. Smith Sep 19 '19 at 17:48
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    @G.Smith 0.8c is their velocity as observed from ground. – varang rai Sep 20 '19 at 16:48

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I agree with you: just add the velocities (or rather, subtract them: one has velocity $0.8c$, and the other $-0.8c$). In the ground frame, the distance between the particles decreases at a rate of $1.6c$. This does not violate any laws of physics.

Ben51
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