Use the Lorentz transformations (4.26) expressed in the differential form to obtain the velocity Use transformation rules consistent with Lorentz invariance. Show that for the special case of two inertial frames moving along the x-axis with relative velocity u, the velocity transformation law is и — v u' = 1– uv/c²' and that this embodies the constancy of the speed of light in all inertial frames, but reduces to the result expected from Galilean invariance for small U.

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Use the Lorentz transformations (4.26) expressed in the differential form to obtain
the velocity Use transformation rules consistent with Lorentz invariance. Show
that for the special case of two inertial frames moving along the x-axis with
relative velocity u, the velocity transformation law is
и — v
-
u' =
1– uv/c²'
and that this embodies the constancy of the speed of light in all inertial frames,
but reduces to the result expected from Galilean invariance for small U.
Transcribed Image Text:Use the Lorentz transformations (4.26) expressed in the differential form to obtain the velocity Use transformation rules consistent with Lorentz invariance. Show that for the special case of two inertial frames moving along the x-axis with relative velocity u, the velocity transformation law is и — v - u' = 1– uv/c²' and that this embodies the constancy of the speed of light in all inertial frames, but reduces to the result expected from Galilean invariance for small U.
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