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The time rate of change of the position of an object

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Can speed be defined in the complex plane?

While by itself it looks okay, if you plug i into a Lorentz transformation everywhere there's a velocity you will also need to either have your time component complex or one of your spatial components … calculations in general relativity but this is done for both T and T' (I assumed that you were only defining it for one side of the equation); while this does result in what appears to be an imaginary velocity
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