I read this question at another forum but the thread was already closed. Here's the description: Two observers A and B are both moving at a velocity of 0.9 times the speed of light with respect to a stationary object. So, won't A see B moving at a speed greater than light?
Two observers moving opposite to each other will see each other moving at speeds greater than light?
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No, A will not see B moving faster than the speed of light due to time dilation. What you are doing is a "Galilean Transformation" which is really just an approximation for objects moving with a velocity much less than the speed of light. The proper equation for velocity transformations in special relativity is:
$$ u'= \frac{u+v}{1+\frac{uv}{c^2}} $$
Where u is B's speed with respect to the stationary observer and v is the speed of A's reference frame which is moving with respect to the stationary observer. A is stationary within its own frame. Plugging in we see that A sees B moving away at $.9945c$ indeed less than the speed of light. Full derivations are available everywhere online like the one mentioned above. Hope this helps.
ClassicStyle
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No, you are imagining the Newtonian addition of velocities. For parallel velocities, the sum is $\frac {0.9+0.9}{1+0.9\cdot 0.9} \approx 0.9945 \lt 1$
Ross Millikan
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