The text exploits the homogeneity of space to conclude that the Lorentz transformation must be linear. Some authors state that this conclusion also follows if we demand that uniform rectilinear motion in K corresponds to uniform rectilinear motion in K'. Show, to the contrary, that the same property is a consequence of the non-linear transformation law'

Examine the points which transform to infinity and, using this information, invent a physical argument which forces c_j = 0.

It is convenient to set x₄ = ct so ν₄ = dx₄/dt = c.

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xi = Aijxj + bi Cjx; + d i = 1, 2, 3, 4.