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I've been watching Leonard Susskind's lectures on special relativity here. At time 0:59:40 he says, "If the vectors are Lorentz invariant, then if the first 3 components of a 4vectors are equal to the first 3 components of another vector (equation), then the 4th components will be equal as well". He uses this to justify using the same equations that work for the space components to write the same equations with 4-vector notation. That's a neat trick. I think I've heard this other places. But I wonder if anyone could actually prove this to me. I'd like to see the proof worked out somewhere. Thanks.

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# If it works in 3D, then it works in 4D

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