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Moving Faster Than The Speed Of Light? Special Relativity Velocity Addition Formula

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 Physics   |   Math   |   Science
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If train A is moving towards train B, and each train moves at 75% the speed of light (relative to the ground), will an observer on train A think that train B is moving at 150% the speed of light? But nothing moves faster than the speed of light, so what is going on? This video presents a formula to add velocities under special relativity. I then offer some justification of the formula by explaining time dilation and the formulas for change of coordinates under the Galilean and Lorentz transformation. From the assumed formulas, I show how to derive the velocity addition formula.

Velocity addition formula
https://einstein.stanford.edu/content/relativity/q1021.html

Time dilation
https://en.wikipedia.org/wiki/Time_dilation

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