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A, you'll have one part that looks like time,
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and one part that looks like an ordinary vector.
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And B, is another four-vector.
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It's got a part that looks time
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and another part that looks like an ordinary vector.
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It's a union up of former vector with a former scalar.
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And they will transform under Lorentz transformation
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just like x0 and t.
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But the following quantity A dot B,
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which is A0·B0 minus the usual dot product of the spatial components,
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is invariant.
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That means all people will agree on this quantity.