Consider the 4-dimensional parallelepiped V whose legs are

where (t , x, y, z) = (x⁰, x¹, x², x³) are the coordinates of some inertial frame. The boundary ∂V of this V has eight 3-dimensional “faces.” Identify these faces, and write the integral ∫_∂V T^0βd∑_β as the sum of contributions from each of them. According to the law of energy conservation, this sum must vanish. Explain the physical interpretation of each of the eight contributions to this energy conservation law.

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