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## Homework Statement

Imagine there exists reference two frames, a frame O which is stationary and another, O' moving relative to O. If there is a four vector A--> (A

^{0},A

^{1},A

^{2},A

^{3}). Then why is A

^{a}e

^{->}

_{a}as measured by the observer O equal to A

^{a'}e

^{->}

_{a'}as measured by the observer O'?

The components are different, I know that the lengths of the vectors are the same, regardless of rotation or translation but assuming Galilean relativity, shouldn't velocity vectors not be equal in both frames? Does that mean velocity is not a four component vector? If not, why not? if so, why?

so if I applied the Lorentz transformation, A

^{a'}e

^{->}

_{a'}= Λ

_{b}

^{a'}A

^{b}e

_{a'}, why is that important?

Are the vectors equal if and only if I applied the Lorentz transformation? If so why? if not? why not?

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