The Principle of Relativity

by Albert Einstein; H. Minkowski

| X_z Y_z Z_z -iT_z |

| -iX_t -iY_t -iZ_t T_t |

Now X_x = ½[m_xM_x - m_yM_y - m_zM_z + e_xE_x - e_yE_y - e_zE_z]

so

(75) X_y = m_xM_y + e_yE_x, Y_x = m_yM_x + e_xE_y etc.

X_t = e_yM_z - e_zM_y, T_x = m_xE_y - m_yE_z, etc.

T_t = ½[m_xM_x + m_yM_y + m_zM_z + e_xE_x + e_yE_y + e_zE_z]

L_t = ½[m_xM_x + m_yM_y + m_zM_z - e_xE_x - e_yE_y - e_zE_z]

These quantities[^[27]] are all real. In the theory for bodies at rest, the combinations (X_x, X_y, X_z, Y_z, Y_y, Y_z, Z_x, Z_y, Z_z) are known as “Maxwell’s Stresses,” T_x, T_y, T_z are known as the Poynting’s Vector, T_t as the electromagnetic energy-density, and L as the Langrangian function.

On the other hand, by multiplying the alternating matrices of f* and F*, we obtain