Lorentz velocity transformation (25-17)
Question
\(x\) component of velocity of an object moving along the \(x\) axis as measured in frame \(S′\)
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Review
This is called the Lorentz velocity transformation. Notice that if the speed \(V\) of one frame relative to the other is small compared to \(c\), the ratio \(V/c\) is much less than 1 and the denominator is essentially equal to 1. Then Equation 25-17 becomes \(v_x' = v_x- V\), which is just the Galilean velocity transformation (the first of Equations 25-5). The same thing happens if the velocity \(v_x\) of the object relative to frame \(S\) is small compared to \(c\). So if either of the speeds involved is a small fraction of the speed of light, the Lorentz velocity transformation reduces to the Galilean velocity transformation. This justifies our use of the Galilean velocity transformation for slow-moving objects.
