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Question

Suppose that k and x are both known to be four-vectors and that in every inertial frame k is a multiple of x. That is, k = λx in frame S, and k' = λ'x' in frame S', and so on. Then the factor λ (the "quotient" of k and x) is in fact a four-scalar with the same value in all frames, λ = λ'. Prove this quotient rule.

Solution

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1 of 3 Let's say $k$ and $x$ are four-vectors and in every inertial frame $x$ is a multiple of $k$, so $x=\lambda k$ in frame $S$ and $x'=\lambda' k'$ in frame $S'$. We have to prove $\lambda=\lambda'$ in all frames, where $\lambda$ is a four-scalar discussed in this chapter.

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