#### samalkhaiat

Science Advisor

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How about you give me a counter-example?However I reaffirm my only objection to your demonstration, i.e. that straight lines transforming into straight lines requires that the transformation be linear.(this is the only argument you should attack)

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Okay, I give you a transition functions [itex]F_{21}: x \to \bar{x}[/itex] between two Minkowski charts. It ia assumed that [itex]F_{21}[/itex] is a [itex]\mathscr{C}^{3}[/itex] homeomorphism, i.e., continuosly thirce differentiable (smooth and regular). Furthermore, we demand that [itex]F_{21}[/itex] (or its inverse) maps straight (world) lines onto straight lines. Now, you show me one such homeomorphism that does not correspond to linear tranformation?