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nomadreid

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- In the Minkowski metric, using the usual inner product relationship, finding the angle A between (1,0,0,0) and (2^0.5, 0, 0, (3^0.5)/c gives cos A = -2^0.5, which indicates that A is not real, but what is it? (source given)

On pages 42-43 of the book "Tensors: Mathematics of Differential Geometry and Relativity" by Zafar Ahsan (Delhi, 2018), the calculation for the angle between A

ds

is carried out with the calculation cos A = g

^{i}=(1,0,0,0) (the superscript being tensor, not exponent, notation) and B^{i}=(√2,0,0,(√3)/c), where c is the speed of light, in the Minkowski metric with the (- - - +) convention, i.e.,ds

^{2}=-dx^{2}-dy^{2}-dz^{2}+c^{2}⋅dt^{2},is carried out with the calculation cos A = g

_{ij}A^{i}B^{i}/√((A_{i}A^{i})(B_{j}B^{j})) (Einstein summation convention). The result, -√2, then tells us that |cos A| = √2, which the author uses to conclude: "the angle between A^{i}and B^{i}is not real." I do not understand this: does he mean that the concept of angle has no meaning here, or that the angle is complex (whatever that means), or what?